Given equation 2x − 3 − 1 = 0.
Now, bring -1 to the right side of the equation:
2x − 3 = 1
Now, add 3 to both sides:
2x = 4
x = 2
Now, we need to check whether this is the correct solution or not. Putting the value of x in the given equation:
2(2) − 3 − 1 = 0
⇒ 1 − 1 = 0
⇒ 0 = 0
Hence, x = 2 is the solution to the given equation.
(a) The solution set of the equation 2x − 3 − 1 = 0 is {2}.
Given equation 3x² + 2 = 5x² − 6.
Now, bring 5x² − 6 to the left side of the equation:
-2x² + 2 = 0
Now, bring 2 to the right side of the equation:
-2x² = -2
⇒ x² = 1
⇒ x = ±1
Now, we need to check whether these are the correct solutions or not. Putting the value of x in the given equation:
3x² + 2 = 5x² − 6
For x = 1,
3(1)² + 2 = 5(1)² − 6
⇒ 3 + 2 = 5 − 6
⇒ -1 = -1
For x = -1,
3(-1)² + 2 = 5(-1)² − 6
⇒ 3 + 2 = 5 − 6
⇒ -1 = -1
Hence, x = 1 and -1 are the solutions to the given equation.
(b) The solution set of the equation 3x² + 2 = 5x² − 6 is {-1,1}.
Given equation 6x + 7 = x + 2.
Now, bring x to the left side of the equation:
6x − x + 7 = 2
Now, add 7 to both sides:
5x = -5
⇒ x = -1
Now, we need to check whether this is the correct solution or not. Putting the value of x in the given equation:
6(-1) + 7 = (-1) + 2
⇒ -6 + 7 = -1 + 2
⇒ 1 = 1
Hence, x = -1 is the solution to the given equation.
(c) The solution set of the equation 6x + 7 = x + 2 is {-1}.
Given equation x + 1 = x² + 9.
Now, bring x² to the left side of the equation:
x² − x + 1 = 9
Now, bring 9 to the right side of the equation:
x² − x − 8 = 0
Now, factorizing the given equation:
(x − 4)(x + 2) = 0
So, the solutions are x = 4 and x = -2.
Now, we need to check whether these are the correct solutions or not. Putting the value of x in the given equation:
x + 1 = x² + 9
For x = 4,
4 + 1 = 4² + 9
⇒ 5 = 25
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Give each Polynomial a name for its Highest Degree & Number of Terms.
[tex]x^{2} +2x-3[/tex]
[tex]-5x-1[/tex]
[tex]-2v^{3} +7[/tex]
[tex]3x^{4} +2v^{3}-8[/tex]
[tex]9w^{5}[/tex]
Evaluate the function at the given values of the independent variable and simplify.
f(x)=6x^2-1/x^2
(a) f(5) (b) f(-5) (c) f(-x)
(Type an integer or a fraction. Simplify your answer.)
The functions are evaluated to give;
a. f(5) = 149/25
b. f(-5) = 149/25
c. f(-x) = 6x² - 1/x²
What are functions?Functions are defined as equation , laws or expressions showing the relationship between variables.
These variables are known as;
The independent variableThe dependent variableFrom the information given, we have that;
f(x)=6x^2-1/x^2
Now, to determine the functions, f(5), f(-5) and f(-x), we need to substitute the value inside the bracket as the value of x in each of the functions,
We have;
f(5) = 6(5)²- 1/(5)²
expand the bracket and subtract
f(5) = 149/25
For f(-5) = 6(-5)² - 1/(-5)²
f(-5) = 149/25
For f(-x) = 6(-x)² - 1/(-x)²
f(-x) = 6x² - 1/x²
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Can someone explain this without confusing me? Thank you
Answer: well f(x) equeals a funtction
your x is a given so all you have to do is plug in the given (X) to the equation given f(x)=x/2
Step-by-step explanation:
example for the first slot:
F(x)=-4
——
2
Answer:
Below
Step-by-step explanation:
Here is how to do the first one....the others are similar
f(x) = x/2 when x = -4, f(-4) = -4/2 = -2 (just put the number in for 'x')
when x = - 2 , f(-2) = -2/2 = -1
when x = 0 , 0 /2 = 0
when x = 1 , 1/2 = 1/2
when x = 6 , 6/ 2 = 3
So the answers across the bottom for the first one are
-2 -1 0 1/2 3
I think you can do the rest.....just put the number value in for 'x' in the equation....
Claire buys furniture to the value of R35 000. she pays a 15% cash deposit and signs a hire purchase agreement for the balance. the interest rate will be 13% per annum and she will pay off the loan over a period of 3 years. what is the value of the deposit?
Answer:
Total amount = R41 337.50
Step-by-step explanation:
The value of the deposit is 15% of the total purchase price:
Deposit = 15/100 x R35 000
Deposit = R5 250
To calculate the balance that Claire will have to pay off, we need to subtract the deposit from the total purchase price:
Balance = Total purchase price - Deposit
Balance = R35 000 - R5 250
Balance = R29 750
To calculate the interest that Claire will have to pay on the balance, we can use the formula:
Interest = Principal x Rate x Time
where:
Principal is the amount of the balance
Rate is the annual interest rate (13%)
Time is the duration of the loan in years (3)
So, the interest that Claire will have to pay is:
Interest = R29 750 x 0.13 x 3
Interest = R11 587.50
Therefore, the total amount that Claire will have to pay back over the 3-year period is:
Total amount = Balance + Interest
Total amount = R29 750 + R11 587.50
Total amount = R41 337.50
Note that this assumes that the interest is calculated annually and added to the balance at the end of each year. In reality, the interest may be calculated differently depending on the terms of the hire purchase agreement.
Juan ran 5 miles at the same pace and
walked for 10 minutes. Write an expression
that represents the total amount of time Juan
spent exercising.
The expression for time will be, Time = 5/r + 10/w.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, symbols, and operators that represent a value or a computation.
Expressions can be simple or complex, and they can contain variables, constants, and functions. They can be evaluated to produce a single value, or they can be simplified or transformed using mathematical rules and operations.
Now,
Let's assume that Juan ran at a speed of "r" miles per minute, and let's also convert the 10 minutes of walking to miles per minute by dividing by the walking speed "w".
Then, the total time Juan spent exercising can be expressed as:
Time = Time Running + Time Walking
Time Running = Distance / Speed = 5 / r
Time Walking = 10 / w
Therefore,
the expression for the total amount of time Juan spent exercising is:
Time = 5/r + 10/w
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what is the multiplier for 1%, and 2% decay?
"The multiplier for decay is given by the formula:
multiplier = (1 - (decay rate/100))^n
where "decay rate" is the percentage rate of decay per time period (usually per year), and "n" is the number of time periods.
For a decay rate of 1%, the multiplier would be:
multiplier = (1 - (1/100))^n = 0.99^n
For a decay rate of 2%, the multiplier would be:
multiplier = (1 - (2/100))^n = 0.98^n
The value of the multiplier depends on the number of time periods "n". For example, if we want to find the value of an initial quantity after 3 years of 1% decay, we would use the multiplier of 0.99 raised to the power of 3:
multiplier = 0.99^3 = 0.9703
This means that the final quantity would be 97.03% of the initial quantity.
Similarly, if we want to find the value of an initial quantity after 5 years of 2% decay, we would use the multiplier of 0.98 raised to the power of 5:
multiplier = 0.98^5 = 0.9039
This means that the final quantity would be 90.39% of the initial quantity." (ChatGPT, 2023)
What the rate if the principal is 5,000, the time is 10 years, and the interest is 2,950?
Answer: 5.9%
Hope this helps!
Mr. Dieter wants to tile the family room in his basement. He has selected a pattern of
square tiles that measure 9 inches by 9 inches each. The shape of the floor to be tiled is
shown below. (3 points for each part)
a. What is the area of the family room in square feet?
b. How many of the 9 inch by 9 inch tiles will it take to cover the floor? (NOTE: You
will need to convert the area in Part a from square feet to square inches.)
c. If the tile is sold only in boxes of 12 tiles per box, how many boxes will Mr. Dieter
have to buy to tile the family room?
a. The area of the family room is 162 ft².
b. 24 tiles will be needed to cover the floor.
c. Mr. Dieter will have to buy 2 boxes to tile the family room.
The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers are thought to be sufficiently described by the four basic operations, also referred to as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.
a. There are two different shapes of which one is rectangle and other is triangle.
So,
⇒ Area of rectangle = length x width
⇒ Area of rectangle = 16 x 8
⇒ Area of rectangle = 128 ft²
Also,
⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x base x height
⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x 4 x 3
⇒ Area of first triangle = 6 ft²
Similarly,
⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x base x height
⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x 8 x 7
⇒ Area of first triangle = 28 ft²
On adding the three areas, we get
⇒ Area of family room = 128 + 6 + 28
⇒ Area of family room = 162 ft²
b. We will convert the area into inches.
We know that 1 feet = 12 inches.
So, using the multiplication, we get
162 feet = 162 * 12 in²
162 feet = 1944 in²
Now,
⇒ Area of tile = 9 * 9
⇒ Area of tile = 81 in²
So,
⇒ Number of tiles = [tex]\frac{1944}{81}[/tex]
⇒ Number of tiles = 24
c. Since, tiles are sold in boxes of 12 so, using the division operation, we get
⇒ Number of boxes needed = [tex]\frac{24}{12}[/tex]
⇒ Number of boxes needed = 2
Hence, the required solution has been obtained.
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the number of salmon observed in the sacramento river and the feather river in the last five years were counted and listed in the chart below: which of the following statements is true about the relation represented in the table? the relation is a function. the relation is not a function. there is not enough information to determine if it is a function or not.
The correct option is the relation is not a function.
A function is defined as a relation in which each input has exactly one output. A relation is any set of ordered pairs. According to the given chart:|Year|Sacramento River|Feather River| 2008|271,999|0| 2009|123,739|0| 2010|174,948|16,857| 2011|158,956|22,129| 2012|163,603|19,799| As we can see in the table, the Sacramento river has different number of salmon at a given year.
For example, in the year 2008, there are 271,999 salmon in the Sacramento river, in the year 2009, there are 123,739 salmon in the Sacramento river. The same with the Feather river. There is a year when there are zero salmon and there are years with different number of salmon.
Therefore, this relation is not a function. Hence, the correct option is the relation is not a function.
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I’m confused. Please help ASAP. How would I find this out?!
Answer:
i think 150 is the answer
Step-by-step explanation:
150 is a 3 digit numbers (as written in question (a)) and is a multiple of 5 and 3
150/5 = 30
150/3 = 50
Factor the equation
25w^2-81
Answer:
(5w + 9)(5w - 9)
Step-by-step explanation:
hmmm, dunno man.
(5w + 9)(5w - 9)
Please help me thanks
From the given question, the value of the height of the cone is given by 57.3 centimeters to the nearest 1 decimal place: Option B
How to determine the volume of a cone?We should note that a cone is a three-dimensional geometric figure with a flat and curved surface pointed towards the top. It is formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex)
The volume of the cone is given by the formula
Volume = 1/3πr²h
Where Volume = 1500 centimeters cube, radius = 5 cm, π = 22/7
1500 = 1/3*22/7*5*5*h
1500 = (22*5*5*h)/3*7
Simplifying the expression further we have
1500 = 550h/21
1500(21) = 550h
31500 = 550h
Making h the subject of the relation we have
h = 31500/550
h= 57.272727...
h= 57.3 to one decimal place
Therefore the height of the cone is 57.3 cm
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Please help me with this question!
In the triangle, the values are p=10.3, [tex]\angle Q=19.5\textdegree[/tex] and [tex]\angle R = 112.5\textdegree[/tex].
What is trigοnοmetric functiοn?The functiοns οf an angle in a triangle are knοwn as trigοnοmetric functiοns, cοmmοnly referred tο as circular functiοns. In οther wοrds, these trig functiοns prοvide the relatiοnship between a triangle's angles and sides. There are five fundamental trigοnοmetric functiοns: sine, cοsine, tangent, cοtangent, secant, and cοsecant.
Here in the given triangle PQR, [tex]\angle P = 48\textdegree[/tex] , q=5 and r=13.
Now using law of cosine fοrmula,
=> [tex]p^2=q^2+r^2-2qr.cos\angle P[/tex]
=> [tex]p^2=5^2+13^2-2.5.13.cos 48\textdegree[/tex]
=> [tex]p^2=25+169-130cos48\textdegree[/tex]
=> [tex]p^2=107[/tex]
=> p = 10.3
Now using law of sine then,
=> [tex]\frac{p}{sinP}=\frac{q}{sinQ}[/tex]
=> [tex]sinQ=\frac{q sinP}{p}[/tex]
=> [tex]sin Q= \frac{5sin 48\textdegree}{10.3}[/tex]
=> sin Q = 0.344
=>[tex]\angle Q = 19.5\textdegree[/tex]
Now sum οf all angles in triangle is 180°. Then,
=>[tex]\angle P+\angle Q+\angle R = 180\textdegree[/tex]
=> [tex]\angle R = 180-48-19.5=112.5\textdegree[/tex]
Hence the answers are p=10.3, [tex]\angle Q=19.5\textdegree[/tex] and [tex]\angle R = 112.5\textdegree[/tex].
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If you were to publish this chart in a news article, what would your headline be and why?
The headline should be informative and accurately reflect the data presented in the chart.
What is chart?A chart is a visual representation of data or information that can be used to help people understand complex information quickly and easily. Charts can take many different forms, such as bar charts, line charts, scatter plots, pie charts, and more. They are often used in business, science, and journalism to present data in a way that is clear and easy to interpret. By using charts, people can quickly see patterns and trends in data that might be difficult to discern from a simple list of numbers or words.
Here,
However, a good headline for a chart should accurately and concisely summarize the main findings or trends depicted in the chart. It should also capture the reader's attention and make them want to read more. Depending on the chart, some possible headlines could be:
"New study finds rising trend in global temperatures over past decade"
"Stock market reaches all-time high, driven by tech sector growth"
"Poll shows majority of Americans support stricter gun control laws"
"Obesity rates continue to climb in US, particularly in southern states"
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Find the inverse of the following function: f(x) = 2(x - 4)^3 + 7
The inverse of the function f(x) = 2(x - 4)³ + 7 is g(x) = ∛[(x - 7) / 2] + 4.
What is a function?A mathematical notion known as a function explains the connection between two sets of values known as the domain and the range. A function takes a value from the domain as an input, applies some logic to it, and returns a value in the range. Just one output value in the range corresponds to each input value in the domain. Functions can be described verbally or with mathematical symbols. They are employed throughout the mathematical discipline as well as in the sciences of physics, engineering, economics, and computer science.
The given function is f(x) = 2(x - 4)³ + 7.
Swap the variables, that is substitute x = y and vice versa as follows:
x = 2(y - 4)³ + 7
x - 7 = 2(y - 4)³
(x - 7) / 2 = (y - 4)³
Taking the cube root of both sides gives:
y - 4 = ∛[(x - 7) / 2]
y = ∛[(x - 7) / 2] + 4
Therefore, the inverse of f(x) = 2(x - 4)³ + 7 is g(x) = ∛[(x - 7) / 2] + 4.
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Part E Graph the average profit function you created in part C by going to your math tools and opening the Graph tool. Set the scale of the graph to go from -20 to 20 on the x-axis and from -100,000 to 100,000 on the y-axis. Select the graph generated, copy it, and paste an image of your graph in the space provided
Answer:
huh? where is the pic of graph
Step-by-step explanation:
no pic was shown
Find an equation of the line with gradient -3 and that passes through the
point (0,0)
Submit Answer
Answer:
y = -3x
Step-by-step explanation:
Using the 'y=mx+c' form,
Since m = -3,
y = -3x + c
Substituting (0,0) into the above equation:
0 = 0 + c
Hence,
y = -3x
Feel free to mark this as brainliest! :)
i need help with this one
The missing values are given as shown in the table
What is a cylinder?A cylinder is a three-dimensional solid figure which has two identical circular bases joined by a curvilinear surface at a particular distance from the center which is the height of the cylinder.
We should understand that the area of a cylinder is given by
Area = 2λr(r+h)
and the volume of the cylinder to be;
volume - λr²h
by substitution we get the values as
diameter radius base area height `cylinder volume
units units square units cubic units
units
4 2 150.9 10 62.9
6 3 151.0 7 63π
8 4 25π 0.875 80π
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DUE TOMORROW! 30 POINTS
20. Consider a line passing through (2,5) with a slope of ¾ . Write its equation. What is its y-intercept?
21. Write the equation for a line parallel to the line from #20 passing through (5,1). Now write the equation for a line perpendicular to the same line, through the same point.
Answer:
20) y = 3/4x + 3 1/2
21) Parallel: y = 3/4 x - 2 3/4
Perpendicular: y = [tex]\frac{-4}{3 }[/tex] x + 7 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
20)
y = mx + b
y = __x + ___ We need to find the slope that the y-intercept. We are given the slope 3/4. We will you the x and y values from the point (2,5) to find the y intercept. Use 5 for y and 2 for x
y = mx + b
5 = 2(3/4) + b
5 = 3/2 + b Subtract 3/2 from both sides
5 - 3/2 = 3/2 -3/2 +b
[tex]\frac{10}{2}[/tex] - [tex]\frac{3}{2}[/tex] = b
[tex]\frac{7}{2}[/tex] or 3 [tex]\frac{1}{2}[/tex]
y = 3/4x + 3 1/2
21)
Parallel slopes are equal so the slope will be 3/4. Now we will use the x and y values from the point (5,1) to find the y-intercept. We will use 1for y and 5 for x
y = mx + b
1 = 5(3/4) +b
1 = 15/4 + b Subtract 15/4 from both sides.
[tex]\frac{4}{4}[/tex] - [tex]\frac{15}{4}[/tex] = [tex]\frac{15}{4}[/tex] - [tex]\frac{15}{4}[/tex] + b
[tex]\frac{-11}{4}[/tex] or - 2 [tex]\frac{3}{4}[/tex]
y = 3/4 x - 2 3/4
Perpendicular slopes or the opposite reciprocals. So the slope of the reciprocal equations would be [tex]\frac{-4}{3}[/tex]. We would still use the x and y values from the point (5,1)
1 = -4/3(5) + b
1 = [tex]\frac{-20}{3}[/tex] + b Add 20/3 to both sides
[tex]\frac{3}{3}[/tex] + [tex]\frac{20}{3}[/tex] = [tex]\frac{-20}{3}[/tex] + [tex]\frac{20}3}[/tex] + b
[tex]\frac{23}{3}[/tex] or 7 2/3
y = [tex]\frac{-4}{3 }[/tex] x + 7 [tex]\frac{2}{3}[/tex]
Helping in the name of Jesus.
Someone PLEASE help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
The correct answer is experimental 22.5% theoretical 18.2%.
What is theoretical probability?The theoretical probability is the likelihood of the event to happen without conducting an experiment,
The experimental probability is the result of the actual experiment, which in this case is the frequency of the letter M when chosen from the bag. Theoretical probability in this case is the number of M's in the bag divided by the total number of letters in the bag.
In this case, there are nine M's out of a total of 39 letters, giving a theoretical probability of 18.2%. Since the number of M's chosen in the experiment was nine, out of a total of 39 chosen, the experimental probability is 22.5%.
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The correct answer is experimental 22.5% theoretical 18.2%. To calculate the experimental probability of drawing the letter M, we must first identify the total number of items in the bag.
What is theoretical probability?The theoretical probability is the likelihood of the event to happen without conducting an experiment,
The total number of items in the bag is 9 + 12 + 7 + 2 + 4 + 1 + 3 + 2 = 40. Next, we divide the number of items with the letter M (9) by the total number of items to get the experimental probability of drawing the letter M.
Therefore, 9/40 = 0.225
= 22.5%.
To calculate the theoretical probability of drawing the letter M, we must first identify the total number of letters in the bag.
There are 8 letters in the bag (M, A, T, H, E, I, C, S).
Therefore, the theoretical probability of drawing the letter M is
8/40 = 0.2
≈18.2%
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Use the Intermediate Value Theorem to show that P(x) = x^5 +
4x^3−10x−6
has a root on [0, 2].
P(x) is a continuous function on [0, 2]. We can conclude that the given function has a root on [0, 2].
The Intermediate Value Theorem is a mathematical theorem that states that a continuous function between two points takes on every value between the two points. The proof of this theorem is easy to understand and uses the definition of a continuous function. The theorem is used to establish the existence of roots or zeroes of functions.The statement is given by the Intermediate Value Theorem that “if f(x) is a continuous function on the interval [a,b], then for any value k that lies between f(a) and f(b) inclusive, there must be at least one value c on the interval [a,b] such that f(c)=k”.Use the Intermediate Value Theorem to show that P(x) = x5 + 4x3 − 10x − 6 has a root on [0, 2]Given, the function P(x) = x5 + 4x3 − 10x − 6Step 1: Verify if the function is continuous on [0, 2].The function P(x) is a polynomial function, and all the polynomial functions are continuous functions.
Therefore, P(x) is a continuous function on [0, 2].Step 2: Check the signs of the function at the endpoints f(0) and f(2).Let’s check f(0) and f(2)f(0) = P(0) = 0^5 + 4(0)^3 – 10(0) – 6= -6f(2) = P(2) = 2^5 + 4(2)^3 – 10(2) – 6= 50Step 3: Check if the value 0 lies between f(0) and f(2) inclusive.f(0) < 0 < f(2)Since 0 lies between f(0) and f(2), according to the Intermediate Value Theorem, there must be at least one value c on the interval [0,2] such that f(c)=0Hence, we can conclude that the given function has a root on [0, 2] Therefore, we can conclude that the given function has a root on [0, 2].
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For which values of x is the expression undefined?
x^2-36/x-9
​
The expression is undefined when x = 9. the expression will be undefined when x-9 = 0.
To find the values of x for which the expression is undefined, we need to look for values of x that would make the denominator of the expression equal to zero. In this case, the denominator is x-9. Therefore, the expression will be undefined when x-9 = 0. Solving for x, we get x = 9.
When x is equal to 9, the denominator becomes zero, which would make the expression undefined as dividing by zero is undefined in mathematics. For all other values of x, the expression is defined and can be evaluated.
We can verify this by substituting x = 9 in the expression and observing that it becomes (9² - 36)/(9-9), which is (81-36)/0, and division by zero is undefined.
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Complete Question:
For which values of x is the expression undefined?
[tex]x^2-36/x-9[/tex]
NEED AN ANSWER NOW!!
5 c = ____ pt ____c
5 c 4 fl oz - 4 c 3 fl oz
7 gal 2 qt + 3 gal 1 qt
6 qt 1 pt - 2 qt 1 pt
ESTIMATE the number of pints in 445 ounces
The estimate of 445 pints in ounces is 7120 ounces
How to estimate the number of pintsThe given measurement from the question can be represented as
Measure = 445 pints
By the standard metrics of conversion, we have
1 pint = 16 ounces
Using the above conversion rules as a guide, we have the following:
Measure = 445 * 16 ounces
Evaluate the product
So, we have the following representation
Measure = 7120 ounces
The above represents the required estimate
Hence, the estimate is 7120 ounces
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Kayden is trying to find the height of a radio antenna on the roof of a local building.
He stands at a horizontal distance of 16 meters from the building. The angle of
elevation from his eyes to the roof (point A) is 41°, and the angle of elevation from
his eyes to the top of the antenna (point B) is 49°. If his eyes are 1.5 meters from the
ground, find the height of the antenna (the distance from point A to point B).
Round your answer to the nearest meter if necessary.
By answering the above question, we may state that As a result, the equation antenna's height is roughly 25 metres.
What is equation?A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.
draw a diagram of the situation
B
|
| h
|
A------------C---------
| θ2| θ1
| |
| | 16 m
| |
D E
We need to calculate the height h of point B above point A. To begin, we may use the tangent function to get the heights of points C and E:
[tex]hC = 16 * tan(θ1)\\hE = 16 * tan(θ2)\\DE = hE - hC\\hB = hC + DE * tan(θ2)\\h = hB + 1.5\\θ1 = 41\\θ2 = 49\\DE = 16 * (tan(θ2) - tan(θ1)) ≈ 9.7587 m\\hC = 16 * tan(θ1) ≈ 12.2272 m\\hB = hC + DE * tan(θ2) ≈ 23.7333 m\\h ≈ hB + 1.5 ≈ 25.2333 m\\[/tex]
As a result, the antenna's height is roughly 25 metres.
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The relationship between the number of decibels β and the intensity of a sound I
in watts per square meter is
β=10log(I10−12)
(a) Determine the number of decibels of a sound with an intensity of 1 watt per square meter.
(b) Determine the number of decibels of a sound with an intensity of 10−2
watt per square meter.
(c) The intensity of the sound in part (a) is 100 times as great as that in part (b). Is the number of decibels 100 times as great? Explain.
(a) A sound with an intensity of 1 watt per square meter has a decibel level of -120.
(b) A sound with an intensity of 10⁻² watt per square meter has a decibel level of -140.
(c) The number of decibels is not 100 times as great as the intensity, even though the intensity in part (a) is 100 times greater than the intensity in part (b).
What is the sound level?
Using the relationship of intensity of sound and number of decibels, we can calculated the required number of decibels as follows;
β =10 log(I x 10⁻¹²)
(a) Decibel level: plugging in I = 1 watt per square meter into the equation, we get:
β = 10 log(1 x 10⁻¹²) = 10 log(10⁻¹²) = -120 decibels
(b) Decibel level: plugging in I = 10⁻² watt per square meter into the equation, we get:
β = 10 log(10⁻² x 10⁻¹²) = 10 log(10⁻¹⁴) = -140 decibels
(c) Let's calculate the decibel level for the sound in part (a) using the given formula:
β₁ = 10 log(I₁ x 10⁻¹²) = 10 log(100 x I₂ x 10⁻¹²) = 10 log(I₂ x 10⁻¹⁴) + 20
where;
I₂ is the intensity of the sound in part (b).Using the result from part (b), we can substitute I₂ = 10⁻² watt per square meter and get:
β₁ = -140 + 20 = -120 decibels
Comparing this result to the decibel level for the sound in part (a) (which is also -120 decibels), we see that they are the same.
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A discount store is selling 5 small tables with 8 chairs for $115. Three tables with 5 chairs cost $70.
Which system of linear equations could be used to find the cost of each table (x) and the cost of each chair (y)?
Determine the cost of each table (x) and the cost of each chair (y).
answer both question please and thank you
Using linear equations 5x + 8y = 115 and 3x + 5y = 70, the cost of each table is $15 and the cost of each chair is $5.
What is a linear equation, exactly?
A linear equation is a mathematical expression that describes a straight line relationship between two variables. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.
Now,
Let x = cost of each table and y= cost of each chair. Then, we can set up the following system of linear equations based on the given information:
5x + 8y = 115 (equation 1)
3x + 5y = 70 (equation 2)
Equation 1 represents the cost of 5 small tables with 8 chairs, and equation 2 represents the cost of 3 tables with 5 chairs.
Now,
Solve equation 2 for x:
3x + 5y = 70
3x = 70 - 5y
x = (70 - 5y)/3
Substitute x into equation 1:
5x + 8y = 115
5[(70 - 5y)/3] + 8y = 115
Simplify and solve for y:
350/3 - 25/3 y + 8y = 115
23/3 y = 115 - 350/3
y = 5
Substitute y = 5 into equation 2 and solve for x:
3x + 5y = 70
3x + 5(5) = 70
3x = 45
x = 15
Therefore,
the cost of each table is $15 and the cost of each chair is $5.
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3t-18=4(-3- 3/4t
solve for t
Answer:
t = 1
Step-by-step explanation:
I will assume that there is a parenthesis missing: the equation should read 3t-18=4(-3- 3/4t) and not 3t-18=4(-3- 3/4t
3t-18=4(-3- 3/4t)
3t-18= -12- 12/4t [Remove parentheses by multiplying each term by 4]
3t-6= - 3/t [Simplify]
3t^2-6t = -3 [Multiply both sides by t]
3t^2-6t +3 = 0
3(t^2-2t+1)=0
3(t-1)*(t-1) = 0
Two solutions, both the same value:
(t-1) = 0
t = 1
===
Does t=1 result in 0 for the equation?
3t-18=4(-3- 3/4t)
3(1)-18=4(-3- 3/4*(1))
3-18 = 4(-3-3/4)
-15 = 4(-3.75)
-15 = -15 YES
Find the standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2.
The standard matrix is:
| 0 -1 |
| -1 0 |
The standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2 can be found by following these steps:
1. Start with the standard basis vectors for R2, which are (1,0) and (0,1).
2. Apply the transformation T to each of these vectors to find the new vectors. For the first vector, (1,0), we have x1=1 and x2=0. The reflection through the line x1=-x2 gives us a new vector with x1=-x2=-0=0 and x2=-x1=-1. So the new vector is (0,-1).
3. For the second vector, (0,1), we have x1=0 and x2=1. The reflection through the line x1=-x2 gives us a new vector with x1=-x2=-1 and x2=-x1=-0=0. So the new vector is (-1,0).
4. The standard matrix of the transformation T is the matrix whose columns are the new vectors we found. So the standard matrix is:
```
| 0 -1 |
| -1 0 |
```
This is the standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2.
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for the following two sequences (i) give the first 5 terms of the sequence. (ii) determine if the sequence converges or diverges. if the sequence converges, determine the limit of the sequence
The sequences can converge to 0 and also diverge towards infinity.
The two sequences are not mentioned in the question. Please provide the two sequences so that I can give you the first 5 terms of each sequence and determine if each sequence converges or diverges.
To find the first 5 terms of a sequence, you need to use the formula given for the sequence and plug in the values for the first 5 terms. For example, if the sequence is given by a_n = 2n + 1, the first 5 terms would be a_1 = 2(1) + 1 = 3, a_2 = 2(2) + 1 = 5, a_3 = 2(3) + 1 = 7, a_4 = 2(4) + 1 = 9, and a_5 = 2(5) + 1 = 11.
To determine if a sequence converges or diverges, you need to find the limit of the sequence as n approaches infinity. If the limit exists, then the sequence converges to that limit. If the limit does not exist, then the sequence diverges.
For example, the sequence a_n = 1/n converges to 0 as n approaches infinity, while the sequence a_n = n^2 diverges as n approaches infinity.
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The owner of a bike shop would like to analyze the sales data to determine if the business is growing, declining, or remaining flat. The owner has the following data:
Sales Revenue Last Year =$125,000
Sales Revenue Current Year = $150, 000
What is the Sales Growth?
Do not forget to type the % symbol after multiplying your result by 100 to convert to percentage!
Hint: Your answer will NOT have a decimal point.
Example: 75%
Answer: To calculate the sales growth, we need to find the difference between the current year's revenue and the last year's revenue, divide it by the last year's revenue, and then multiply by 100 to convert it to a percentage.
Sales Growth = ((Sales Revenue Current Year - Sales Revenue Last Year) / Sales Revenue Last Year) x 100%
Sales Growth = (($150,000 - $125,000) / $125,000) x 100%
Sales Growth = ($25,000 / $125,000) x 100%
Sales Growth = 0.20 x 100%
Sales Growth = 20%
Therefore, the sales growth is 20%.
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Step-by-step explanation: