Consider the following function.
r(x)=4−32x
Step 2 of 2 : Find two points on the line to graph the function.
We can plot (0, 4) and (1, -28) points on a coordinate plane and draw a straight line passing through both points to graph the function.
What is a coordinate plane?
A coordinate plane, also known as a Cartesian plane, is a two-dimensional plane that is used to plot points and graph mathematical equations. It consists of two perpendicular number lines called the x-axis and the y-axis. The x-axis is the horizontal line, with positive values to the right of the origin (0) and negative values to the left of the origin. The y-axis is the vertical line, with positive values above the origin and negative values below the origin. The x-coordinate gives the horizontal position of the point, and the y-coordinate gives the vertical position of the point. By plotting points on a coordinate plane, we can graph lines, curves, and other mathematical functions. It is a fundamental tool in mathematics, science, and engineering for visualizing and analyzing relationships between variables.
To find two points on the line of the function r(x) = 4 - 32x, we can simply choose any two values of x and find the corresponding values of r(x).
For example, when x = 0:
r(0) = 4 - 32(0) = 4
So one point on the line is (0, 4).
When x = 1:
r(1) = 4 - 32(1) = -28
So another point on the line is (1, -28).
Therefore, we have two points on the line: (0, 4) and (1, -28).
We can plot these points on a coordinate plane and draw a straight line passing through both points to graph the function.
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reflection across x=1 Graph has GHIJ and yx at points
The vertices of the image after the transformation are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
How to perform the transformationGiven that
G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)
The reflection is given as
Reflection across x = 1
The rule of this reflection is
(x, y) = (-(x - 2a), y)
Where
Reflection across x = a = 1
So, we have
G' = (-(1 - 2), -3), H = (-(5 - 2), -2), I' = (-(3 - 2), -5) and J' = (-(3 - 2), -1)
Evaluate
G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
Hence, the image of the reflection are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
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Complete questionWhat are the coordnate of the reflection across x = 1 of GHIJ such that
G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)
If 80% of a number is 304 and 15% of the same number is 57, find 95% of that number.
Answer:
95% of that number is 361
Step-by-step explanation:
Let's start by finding the actual value of the number.
If 80% of a number is 304, we can set up the equation:
0.8x = 304
To solve for x, we can divide both sides by 0.8:
x = 380
So the number is 380.
Now we can use the second piece of information to find 15% of the number:
0.15(380) = 57
This confirms that our value for x is correct.
Finally, we can use this information to find 95% of the number:
0.95(380) = 361
Therefore, 95% of the number is 361.
Suppose I took a survey of 324 people at the school. The survey showed that 120 people like dogs, 150 like cats, and 98 like both.
Make a two way table representing the above data.
If a person does not like dogs, what is the probability that they do not like cats
The probability that they do not like cats given that person does not like dogs: 13/51.
Explain about the vein diagram?A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not.Total people : 324.
People like dogs D: 120
Probability P(D) = 120/324
Probability Not like dogs P(D') = 1 - 120/324 = 204/324
People like cats C: 150
Probability P(C) = 150/324
Probability who don't like digs but like cats:
P(C ∩ D') = 52/ 324
Probability that they do not like cats given that person does not like dogs:
P(C'/D') = 1 - P(C ∩ D')/P(D')
P(C'/D') = 1 - (52/324) /(204/324)
P(C'/D') = 1 - 52/204
P(C'/D') = 152/204 = 13/51
Thus, the probability that they do not like cats given that person does not like dogs: 13/51.
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How many particles in
9.89 moles of Carbon?
The number of particles in 9.89 moles of carbon is solved to be
5.95 x 10^24 particlesHow to find the number of particles in 9.89 moles of carbonTo determine the number of particles in 9.89 moles of carbon, we can use Avogadro's constant, which is defined as the number of particles (atoms or molecules) in one mole of a substance.
Avogadro's constant is approximately 6.02 x 10^23 particles per mole.
So, the number of particles in 9.89 moles of carbon is:
= 9.89 moles x (6.02 x 10^23 particles/mole)
= 5.95 x 10^24 particles
Therefore, there are approximately 5.95 x 10^24 particles in 9.89 moles of carbon.
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find the distance between each pair of points on the coordinate plane
Answer:
give full question please its not full
Which algebraic expression is equivalent to the expression below? 3 ( 5 x + 7 ) − 6 ( 4 − 2 x )
Answer:
3(5x+7)-6 (4-2x)
15x+21-24+12x = 27x-3
or
15x+21-6+4-2x = 13x+19
Which of the following explains how to find the area of the shaded region shown?
Find the area of the inner and outer trapezoids, and add them together.
Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.
Count the shaded grid squares and estimate the number of partially shaded squares.
Find the area of the outer trapezoid.
Part B
Find the area in square units.
Answer:
Step-by-step explanation:
Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.
[tex]A=\frac{1}{2} (a+b)h[/tex]
[tex]A_o=\frac{1}{2} (6+2)6=24[/tex]
[tex]A_i=\frac{1}{2} (4+2)3=9[/tex]
Total area = 24 - 9 =15 square units
reagan wanted to paint so she invested $500 several years later,she has earned $2000 in interest. how long did reagan invest the money if she earned a simple interest rate of 5% ?
Regan invested the money for 8 years at simple interest to earn $2000.
What is the difference between simple interest and compound interest?Simple interest is calculated on the loan amount or principle amount, whereas compound interest is calculated using both the principal amount and the interest that has accrued over the course of a prior period or particular time. Simple interest is based on the principal amount, which is the main distinction between it and compound interest. Contrarily, compound interest is calculated using the principle sum and interest that has been compounded over the course of a period.
The simple interest is given as:
SI = Prt
where I is the interest earned.
P is the principal, = 500.
is the interest rate = 5% = 0.05.
t is the time (in years).
Substituting the values:
2000 = 500 * 0.05 * t
t = 8 years
Hence, Regan invested the money for 8 years at simple interest to earn $2000.
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FInd the next three terms of 240,-120,60
The next three terms of the sequence 240,-120,60 are -30, 15 and -7.5
What is the next three terms?240, -120, 60
From observation, the second term is found by halving the first term and multiplying by negative
The third is found by halving the second term and multiplying by negative.
The fourth term = negative third term divided by half
= -(60/2)
= -30
The fifth term = negative fourth term divided by half
= -(-30/2)
= 15
The sixth term = negative fifth term divided by half
= -(15/2)
= -7.5
Hence, the next terms of 240, -120, 60 are -30, 15 and -7.5
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The Gross Domestic Product (GDP) of a country in the first quarter of 2014 was $1.5489*107. Rewrite the GDP in standard notation
We can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
In scientific nοtatiοn, a number is expressed as the prοduct οf a decimal number between 1 and 10 (called the cοefficient) and a pοwer οf 10 (called the expοnent). The expοnent indicates hοw many places the decimal pοint needs tο be mοved tο οbtain the οriginal number.
In the given number, $1.5489*107$, the cοefficient is 1.5489, and the expοnent is 7, which means the decimal pοint needs tο be mοved 7 places tο the right tο οbtain the οriginal number.
Therefοre , we can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.
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50x212 with steps like
212
x 50
1 )Use the algorithm method.
5 0
× 2 1 2
1
100
500
1
10000
10600
2) Therefore,50×212=10600
10600
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Answer:
see explanation
Step-by-step explanation:
Part A is correct
Part B
student A solved the system correctly
Part C
student B made the error from step 3 to step 4 , that is
step 3 : 3x - 5x + 150 = 114
step 4 : - 2x + 150 = 114 ( should be - 2x not 2x was the error made )
step 5 : - 2x = 114 - 150 = - 36
step 6 : - 2x = - 36 ( divide both sides by - 2 )
x = 18
substitute x = 18 into y = - x + 30 ( from step 1 )
y = - 18 + 30 = 12
Answer : (18, 12 ) which is the answer student A obtained correctly
Question 4 of 10
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) = ?
g(x) =
10
|f(x)=x²
6
E
Option B. g(x)=(x-2)²is the equation of blue graph.
A graph: what is it?A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.
The red graph is represented by the function:
f(x)=x²
Also, we need the formula for the blue graph.
We can see that the blue graph is just the red graph with the horizontal axis moved 2 units to the right.
An example of a horizontal transition is:
f(x-h) where h is the quantity we shift (to the right).
h = 2 since we moved two units to the right.
Our new role will thus be:
g(x)=f(x-2)=(x-2)²
Therefore:
g(x)=(x-2)²
Our response is B.
Notes:
A denotes a downward vertical movement of two units.
C (assuming it is x²) denotes a two-unit vertical displacement upward.
And D (if you let h = -2, then f(x - (-2)) = f(x + 2) = (x + 2)²) is a horizontal shift of two units to the left.
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the complete question is:
The graphs below have the same shape. What is the equation of the blue
graph?
f(x) = x2
g(x) = ?
9(x) =
O A. g(x) = x² - 2
B. g(x) = (x - 2)2
c. g(x) = x + 2
D. Q(x) = (x + 2)2
Image is attached below;
115°
70°
X
Solve for x.
Finally, solve for x.
115 + × = 70
2
= [? ]°
Enter
Answer:
X= 25
Step-by-step explanation:
The answer is shown above!
Which statement is true about the circumstance of a circle?
Answer:
The true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter
Step-by-step explanation:
HELP ASAP!
Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.
Month f(x) = No. of imports g(x) = No. of exports
January (1) 3 1
February (2) 4 3
March (3) 5 5
April (4) 6 7
The system of equations modeling the number of imports and the number of exports is given as follows:
f(x) = x + 3.g(x) = 2x + 1.The solution f(x) = g(x) represents the month at which the number of imports and the number of exports was the same.
How to model the system of equations?The system of equations is modeled by linear functions in slope-intercept form, as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.Hence the equations are given as follows:
f(x) = x + 3 -> initial amount of 3 is increased by one each month.g(x) = 2x + 1 -> initial amount of 1 is increased by two each month.More can be learned about linear functions at https://brainly.com/question/24808124
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Two boats are headed to a lighthouse from
opposite directions. From point A, the crew
of boat A (red boat) measures the angle of
elevation to the top of the lighthouse as 45°.
On the other hand, from point B, the crew
of boat B (green boat) measures the angle
of elevation to the top of the lighthouse as
30°. The lighthouse is at a height of 300 ft
above the water.
A
45°
L
300 FT
30
a) How far is boat A from the
lighthouse? (the horizontal distance)
b) How far is boat B from the
lighthouse? (the horizontal distance)
c) And hence, find the total horizontal
distance between the two boats.
Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.
what is distance ?The numerical measurement of distance is the separation between two objects or points. Typically, it is expressed in terms of metres, kilometres, miles, or feet. Distances can be calculated either along a simple path (the Euclidean distance) or along a more complicated one (such as a curved surface or a circuitous route). Distance is a crucial notion that is used to define the separation between things, the length of a route or path, and the displacement of an object through time in many disciplines, including physics, mathematics, geography, and engineering.
given
We may utilise trigonometry and create some equations based on the provided angles and distances to solve this problem.
a) We can use the tangent function to calculate the separation between boat A and the lighthouse:
opposite/hypotenuse = tan(45°)
where the hypotenuse is the distance between boat A and the lighthouse, the other side is the lighthouse's height (i.e., the horizontal distance we want to find). By calculating the hypotenuse, we obtain:
Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.
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Consider a sequence generated by the
formula f(n) = 4n - 7 starting with n =3.
Generate the terms f(1), f(2), f(3), f(4), f(5)
Can you please give a detailed explanation so I can understand
The sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
What is functions?A function is typically denoted by a symbol, such as "f(x)", where "x" is the input value and "f(x)" is the output value. The input value is sometimes referred to as the "argument" of the function.
The formula f(n) = (4n - 7) generates a sequence of numbers when we plug in different values of "n". To generate the terms f(1), f(2), f(3), f(4), f(5) we need to substitute each value of n into the formula and evaluate the expression.
Starting with n = 1, we can generate the terms as follows:
f(1) = (4 × 1 - 7) = -3
f(2) = (4 × 2 - 7) = 1
f(3) = (4 × 3 - 7) = 5
f(4) = (4 × 4 - 7) = 9
f(5) = (4 × 5 - 7) = 13
So the sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
Each term in the sequence is found by plugging in a different value of "n" into the formula f(n) = (4n - 7). The first term, f(1), is found by plugging in n = 1, the second term, f(2), is found by plugging in n = 2, and so on.
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You are making an initial deposit of $1000 in an account that yields 5% interest quarterly (four times a year).
Following the pattern given above, find your year-end balance. (Show calculations for all four quarters and round to the nearest
penny) 15 pts
Answer: The interest rate per quarter is 5%/4 = 1.25%.
At the end of the first quarter, the balance is:
$1000 + $1000(1.25%) = $1000 + $12.50 = $1012.50
At the end of the second quarter, the balance is:
$1012.50 + $1012.50(1.25%) = $1012.50 + $12.66 = $1025.16
At the end of the third quarter, the balance is:
$1025.16 + $1025.16(1.25%) = $1025.16 + $12.82 = $1037.98
At the end of the fourth quarter, the balance is:
$1037.98 + $1037.98(1.25%) = $1037.98 + $13.00 = $1050.98
Therefore, the year-end balance is $1050.98 (rounded to the nearest penny).
Step-by-step explanation:
I'LL MARK THE BRAINLIEST
What is the exact circumference of the circle?
Answer: The circumference would be 62.83
Step-by-step explanation:
C=2πr=2·π·10≈62.83185
Factor the expression
ax+ay+az +3x+3y+3z
Data shown in a frequency table could be displayed in which of the following graphs?
A) line graph
B)line plot
C)bar graph
D)stem-and-leaf plot
Multiple choice
Answer: I think line plot and bar graph
Step-by-step explanation:
To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed.
Can someone give a step by step explanation on how to find the Z score? I know how to find X but I need help with mostly Z.
So the lowest possible score to qualify for the police academy is 225.6.
What is mean?In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.
Here,
To find the Z-score, you will need to use the following formula:
Z = (X - μ) / σ
where:
X = the raw score you are trying to find
μ = the population mean (in this case, 200)
σ = the population standard deviation (in this case, 20)
To find the lowest possible score to qualify, you need to find the score that corresponds to the 90th percentile (i.e., the top 10%).
To do this, you can use a standard normal distribution table or a calculator that has a normal distribution function.
Here are the steps:
Find the Z-score that corresponds to the 90th percentile.
You can use a standard normal distribution table to find this value. Look for the row that corresponds to the first digit(s) of the percentile (in this case, 9) and the column that corresponds to the second digit (in this case, 0.0). This will give you the Z-score that corresponds to the 90th percentile, which is approximately 1.28.
Alternatively, you can use a calculator that has a normal distribution function. For example, in Excel, you can use the formula =NORM.S.INV(0.9) to find the Z-score that corresponds to the 90th percentile.
Plug in the values for μ, σ, and Z into the formula for Z-score:
Z = (X - μ) / σ
Rearranging the formula, we get:
X = Z * σ + μ
Substituting the values we know, we get:
X = 1.28 * 20 + 200
X = 225.6
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What is the approximate (use 3.14 for pi) volume of this cylinder?
(Diameter is 10 in and height is 12.2 in)
A)383.1 cubic inches
B)957.7 cubic inches
C)122cubic inches
D)3830.8 cubic inches
Answer: B
V=957.7 cubic inches
Step-by-step explanation:
V=Hxpixr^2
V=12.2x3.14x5^2 r=5 because it is half of the diamter, which is 10.
V=12.2x3.14x25
V=957.7 cubic inches
the lowest form of 28 upon 36 is ........... ( with explanation pls)
Answer:
To find the lowest form of 28 upon 36, we need to simplify or reduce the fraction to its lowest terms. This can be done by finding the greatest common factor (GCF) of the numerator (28) and the denominator (36) and dividing both by it.
First, we can find the prime factors of 28 and 36:
28 = 2 × 2 × 7
36 = 2 × 2 × 3 × 3
Next, we can identify the common factors, which are 2 and 2.
To find the greatest common factor, we need to multiply the common factors together. In this case, 2 × 2 = 4, so the greatest common factor is 4.
Now we can divide both the numerator and the denominator by the GCF:
28 ÷ 4 = 7
36 ÷ 4 = 9
Therefore, the lowest form of 28 upon 36 is 7/9.
Step-by-step explanation:
Suppose you borrow $4900 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $175 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$
$4900
$4719.94
1.75% Interest
on Prior Balance
$
$
$
$80.98
Monthly Payment
$175
$175
$175
$175
Ending Balance
$
$
57
$
$4900
$4719.94
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
What is annual interest rate?Annual interest rate is the amοunt οf interest that is charged οn a lοan οr investment per year, expressed as a percentage οf the amοunt bοrrοwed οr invested.
Tο cοmplete the table, we can use the fοllοwing steps:
Fοr the first mοnth:
Priοr balance: $4900
Interest οn priοr balance: 1.75% οf $4900 = $85.75 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4900 + $85.75 - $175 = $4710.75 (rοunded tο the nearest cent)
Fοr the secοnd mοnth:
Priοr balance: $4710.75
Interest οn priοr balance: 1.75% οf $4710.75 = $82.46 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4710.75 + $82.46 - $175 = $4628.21 (rοunded tο the nearest cent)
Repeat the same prοcess fοr the next three mοnths:
Fοr the third mοnth, priοr balance is $4628.21, interest οn priοr balance is $80.89, mοnthly payment is $175, and ending balance is $4549.10.
Fοr the fοurth mοnth, priοr balance is $4549.10, interest οn priοr balance is $79.34, mοnthly payment is $175, and ending balance is $4469.69.
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
Mοnth Priοr Balance Interest Mοnthly Ending
οn Payment Balance
Priοr Balance
1 $4900 $85.75 $175 $4710.75
2 $4710.75 $82.46 $175 $4628.21
3 $4628.21 $80.89 $175 $4549.10
4 $4549.10 $79.34 $175 $4469.69
5 $4469.69 $77.78 $175 $4389.72
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6 typists working 5 hours a day can type the manuscript of a book in 16 days. How many days will 4 typists take to do the same job? each working 6 hours a day?
Answer:
Let's begin by finding the total work required to complete the manuscript of the book:
Total work = (Number of typists) x (Number of hours per day) x (Number of days) = 6 x 5 x 16 = 480
Now let's find the work done by 4 typists working 6 hours per day:
Work done by 4 typists = (Number of typists) x (Number of hours per day) x (Number of days) = 4 x 6 x d
where d is the number of days required to complete the manuscript.
Since the amount of work done is the same in both cases, we can set the two equations equal to each other and solve for d:
6 x 5 x 16 = 4 x 6 x d
Simplifying this equation, we get:
480 = 24d
Dividing both sides by 24, we get:
d = 20
Therefore, it will take 4 typists working 6 hours per day a total of 20 days to complete the manuscript of the book.
Step-by-step explanation:
Select ALL the correct answers.
Chris is taking a trip to a certain town and wants to know what the residents of the town think about the restaurants there. It would not be possible to ask all 500 residents, so Chris plans on surveying a random sample of 50 residents in the population.
Select the survey methods that would result in Chris obtaining a random sample.
Surveying the first 25 women and 25 men he met at a grocery store.
Surveying every 10th woman and every 10th man at a local diner.
Surveying every 10th woman and every 10th man from a list of people living in the town.
Surveying one person from every 10th home in the town.
Surveying the first 50 people he saw at the airport as he got off the plane.
Chris can obtain a random sample of 50 residents by surveying the first 25 women and 25 men at a grocery store, surveying every 10th woman and every 10th man from a list of people living in the town, surveying one person from every 10th home in the town, or surveying the first 50 people he saw at the airport as he got off the plane.
Random sampling is an important method used to obtain a representative sample of the population of interest. Random sampling involves selecting a sample of elements from a population in such a way that each element has an equal probability of being selected. This ensures that the sample is not biased in any way and that it is representative of the population.In order to obtain a random sample, Chris could use a variety of methods. He could survey the first 25 women and 25 men he met at a grocery store, survey every 10th woman and every 10th man from a list of people living in the town, survey one person from every 10th home in the town, or survey the first 50 people he saw at the airport as he got off the plane.Each of these methods would result in a sample of 50 people that is randomly selected from the population of 500 residents. This would ensure that the sample is representative of the population and that the results of the survey are not biased in any way. Furthermore, the sample size of 50 is large enough to be considered representative of the population of 500.
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Five lemonades and two cookles cost $1.50. Two lemonades and five cookles cost $2.70. How much does one cookle and one lemonade cost?
Answer:
50¢/cookie, $1.00/lemonade
Step-by-step explanation:
Let l = cost of one lemonade
c = cost of one cookie
We have:
5l + 2c = 1.50 -------> 10l + 4c = 3.00
2l + 5c = 2.70 -------> 10l + 25c = 13.50
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21c = 10.50
c = .50
5l + 2(.50) = 1.50
5l + 1.00 = 1.50
5l = 5, so l = 1.00
Each cookie costs 50¢, and each lemonade costs $1.00.