Answer:
2
Step-by-step explanation:
First you do the 2² which is 4 then 5-4 is 1-3 is -2³ is -8/-4 is 2
find an equation for the plane consisting of all points that are equidistant from the points (−7, 1, 1) and (3, 3, 5).
The equation for the plane consisting of all points that are equidistant from the points (−7, 1, 1) and (3, 3, 5) is 20x + 4y + 8z = -9.
How to determine the equation for this plane?In order to determine the distance of this plane (x, y, z) with the given points, we would use the distance formula.
Mathematically, the distance between three (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
For these points (x, y, z) and (−7, 1, 1), the distance is given by:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Distance = √[(x₂ - (-7))² + (y₂ - 1)² + (z₂ - 1)²]
Distance = √[(x₂ + 7)² + (y₂ - 1)² + (z₂ - 1)²]
By using the algebraic formulas, the expanded expression is given by:
(a - b)² = a² - b² - 2ab
(a + b)² = a² + b² + 2ab
Distance = √[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)] .......equation 1.
For these points (x, y, z) and (3, 3, 5), the distance is given by:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Distance = √[(x - 3)² + (y - 3)² + (z - 5)²]
Distance = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)] .....equation2.
Since both distances are equidistant, we would equate eqn. 1 and eqn. 2 and then simplify:
√[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)] = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]
(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1) = (x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)
x² + 14x + 49 + y² - 2y + 1 + z² - 2z + 1 = x² - 6x + 9 + y² - 6y + 9 + z² - 10z + 25
14x + 6x - 2y + 6y - 2z + 10z + 52 - 43 = 0
20x + 4y + 8z + 9 = 0
20x + 4y + 8z = -9.
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Which situation can be represented by the expression 3 + (−7)?
A. A football team lost 3 yards on one play. The team gained 7 yards on the next play.
B. A football team gained 3 yards on one play. The team lost 7 yards on the next play.
C. A football team gained 3 yards on one play. The team gained 7 yards on the next play.
We get that statement (B) is the situation that is represented by the expression 3 + (−7).
We are given an expression:
3 + ( - 7 )
We need to identify the statement that represents the same expression:
For the statement, "A football team lost 3 yards on one play. The team gained 7 yards on the next play.", we get the expression as:
- 3 + 7
For the statement, "A football team gained 3 yards on one play. The team lost 7 yards on the next play.", we get the expression as:
3 + ( - 7 )
For the statement, "A football team gained 3 yards on one play. The team gained 7 yards on the next play.", we get the expression as:
3 + 7
Therefore, we get that statement (B) is the situation that is represented by the expression 3 + (−7).
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Find a polynomial f(x) of degree 5 that has the following zeros. 9,8,0,4,-3 leave your answer in factored form
Step-by-step explanation:
x(x-4)(x+1) is a 3 degree polynomial in factored form with zeros 0,4 and -1
Just take each zero and change its sign, then stick an x in front of it to get the 3 factors
(x-0)(x-4)(x- -1) = x(x-4)(x+1)
= x(x^2-3x-4)
= f(x) = x^3 -3x^2 -4x
f(0) = 0
f(4) = 64-3(16)-4(4) = 0
f(-1) = -1 -3(-1)^2 -4(-1) = 0
graph the polynomial and it intersects the x axis in 3 places, the origin (0,0), (4,0) and (-1,0)
What type of transformation is this? Be specific.
Answer:
Rotation because you can see that the shape is rotated on the other half of the graph.
Step-by-step explanation:
Pleaseee help! I WILL MARK BRAINLIEST.
The approximate weights of two animals are 4.23 x 103 lbs. and 8.7 x 103 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits. 1.29 x 104 lbs. 1.3 x 104 lbs. 5.1 x 103 lbs. 12 x 103 lbs.
The total weight of the two animals is 1.3 x 10^4 lbs.
How to determine the total weight of the two animals?The given parameters are
Animal 1 = 4.23 x 103 lbs.
Animal 2 = 8.7 x 103 lbs.
Rewrite the parameters properly
Animal 1 = 4.23 x 10^3 lbs.
Animal 2 = 8.7 x 10^3 lbs.
The total weight of the two animals is calculated as
Total weight = Animal 1 + Animal 2
This gives
Total weight = 4.23 x 10^3 lbs + 8.7 x 10^3 lbs.
Factor out 10^3 lbs
Total weight = (4.23 + 8.7) x 10^3 lbs.
Evaluate the sum
Total weight = 12.93 x 10^3 lbs.
Rewrite as
Total weight = 1.293 x 10^4 lbs.
Approximate
Total weight = 1.3 x 10^4 lbs.
Hence, the total weight of the two animals is 1.3 x 10^4 lbs.
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What two numbers add up to -5 and multiply to 4
A firm in perfectly competitive market has a cost function of the form C = 5000 10Q + Q2 . Find the profit maximizing quantity for the firm if the market price P is N100. Calculate the profit as a function Q
The profit as a function Q is Q² + 90Q + 5000.
How to calculate the profit?It should be noted total revenue = Price × Quantity = 100Q
Total cost = 5000 + 10Q + Q²
Therefore, profit will be:
= Revenue - Cost
= 100Q - (5000 + 10Q + Q²)
= -5000 -90Q - Q².
= Q² + 90Q + 5000
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Two thirds of twenty-two
Answer:
44/3 or 14 2/3
Step-by-step explanation:
22 * 2/3
= 44/3
In order to add
3/4 and 7/10
you need to find equivalent fractions that have the same denominators. What is a common denominator?
Answer:
a shared multiple of the denominators of several fractions
Explanation : The denominator is the number at the bottom of the fraction and when two fractions have the same number at the bottom(denominator) then they have a common denominator.
What is the five-number summary for the data 2, 2, 4, 4, 5, 5, 6, 7, 9?
The five-number summary for the data is: 2, 3, 5, 6.5, and 9.
How to Determine the Five-number Summary of a Data Set?Given the data, 2, 2, 4, 4, 5, 5, 6, 7, 9, the five-number summary can be determined as follows:
Minimum value: this is the lowest data value, which is, 2.
First Quartile (Q1); which is the middle of the first half of the data which is, 3.
Median: center of the data set, which is, 5.
Third Quartile (Q3): which is the center of the second half of the data set, which is, 6.5.
Maximum Value: which is the highest data value of the data set, which is, 9.
Therefore, the five-number summary for the data is: 2, 3, 5, 6.5, and 9.
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A secant is a line that intersects a circle in exactly one point.
Answer:Tangent
A chord is a segment whose endpoints are points on a circle. A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point. The point is called a point of tangency.
Step-by-step explanation:
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
Suppose two lines intersect in a plane to form four angles.
What do you know about the pairs of adjacent angles formed? Explain.
44339339393888383848448484848484848
Find the measure of the indicated angle.
Answer:
33°
Step-by-step explanation:
the whole angle of DAB is 57° and a line is drawn to split it into 2 parts and one part is given.
X+24°=57°
X=57-24
X=33°{angle CAD=33°}
Solve for X anything can help
Answer:
x = 35
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
x + 52 + x + 2x - 12 = 180
4x + 40 = 180 ( subtract 40 from both sides )
4x = 140 ( divide both sides by 4 )
x = 35
You want an average of at least 30 active minutes each day during the week. How many active minutes do you need on Sunday to achieve your goal? Make an argument for your answer using a bar graph.
Using the mean concept, it is found that you need at least 40 active minutes on Sunday to achieve your goal.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In a week, there will be 7 observations, and a bar graph can represent each observation(time in minutes). They are given as follows:
15, 45, 20, 0, 60, 30 and x.
We want the mean to be of 30, hence:
30 = (15 + 45 + 20 + 0 + 60 + 30 + x)/7
170 + x = 210
x = 210 - 170
x = 40.
You need at least 40 active minutes on Sunday to achieve your goal.
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use the fundamental identities to simplify the expression. there is more than one correct form of the answer. 9 sec2(x) 1 − sin2(x)
According to the given information the expression solution are:
Pythagorean identity = 9 sec2 x(cos2 x) Reciprocal identity = = 9 sec2 x(1/sec2 x)What are fundamental identities?An equation is referred to as an identity if it has one or more variables and is true for all alternate values of the variables for which both sides of the equation are defined.
For instance,
the equation x 2 + 2 x = x(x + 2) is an identity since it holds true for all possible replacement values for x.
A conditional equation is one that holds true only for specific replacement values of the variable.
For instance, the equation 3 x + 4 = 25 is a conditional equation because it isn't true for all possible replacement values for x.
Without specifying any limitations, an equation is claimed to be an identity, but in reality, it is only an identity for replacement values for which both sides of the identity are defined.
According to the given data:The trigonometric expression is 9 sec2 x (1 - sin2x)
Apply Pythagorean identity
1 - sin2 x = cos2 x9 sec2 x (1 - sin2x)
= 9 sec2 x(cos2 x)
Apply reciprocal identity cosx = 1/ secx
= 9 sec2 x(1/sec2 x)
= 9
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on an average, the number of students that choose to study arts subjects at greyin tide university is 17 each year. (hint: use poisson distribution formula. what is the probability that exactly 13 students will take up arts in the coming year?
The likelihood that exactly 13 students will pursue arts in the coming year is 76.47%.
What do we mean by probability?Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how probable they are. Statistics is the study of events governed by probability.So, to find the probability:
Given:
Each year, there are 17 students who study art.We now want to calculate the likelihood that 13 students will pursue arts in the following year.
That is,
P(13 will take art the next year) = 13/17 × 100%P(13 will take art the next year) = 76.47%Therefore, the likelihood that exactly 13 students will pursue arts in the coming year is 76.47%.
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At 6am, the temperature started
at -2°F. At 10am the temperature
increased by 8°. The last recorded
temperature of the day at 4pm
was 11°F. What was the recorded
temperature at 10am?
1.5, 21.5, 21.6 d: 20.0, 20.0, 20.0, 20.1, 20.2, 20.5, 20.5, 20.6, 20.7, 20.7, 21.0, 21.2, 21.5, 21.6, 22.1, 22.3 compute the standard deviation of the measurements for each method
The standard deviation of the method is 0.7193.
Standard Deviation:
Standard deviation of a data set is the square root of the calculated variance of a set of data.
The formula for standard deviation is,
[tex]\sigma^2 = \dfrac{\Sigma (x_{i} - \mu)^2}{n}[/tex]
Where
xi is an individual value
μ is the mean/expected value
N is the total number of values
Given,
Data set:
20.0, 20.0, 20.0, 20.1, 20.2, 20.5, 20.5, 20.6, 20.7, 20.7, 21.0, 21.2, 21.5, 21.6, 22.1, 22.3
Here we need to find the standard deviation.
To find the standard deviation we have to identify the following from the given set,
They are,
Count, N: 16
Sum, Σx: 333
Mean, μ: 20.8125
Now we have to apply the values on the formula,
In order to solve it,
[tex]\sigma^2=\frac{[(20-20.8125)^2+....+(22.3-20.8125)^2]}{16}[/tex]
When we simplify it then we get,
[tex]\sigma^2=\frac{8.2775}{16}[/tex]
So,
σ = √0.51734375
σ = 0.7193
Therefore, the standard deviation is 0.7193.
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Determine the image of A(1,-3) after the following composition of transformations:
Rotation 90 degrees about the origin
Translation: f(x,y)=(x+2,y)f(x,y)=(x+2,y)
The image of the point A after the given compositions of transformation will be (5, 1).
We are given the coordinate of the point A as:
A = (1, - 3)
Now, we have to rotate it 90° about the origin.
The rule for a rotation by 90° about the origin is given by (x, y) will become (− y, x)
So, we get for point A as:
A' = (3, 1)
Now, we have:
Translation: f(x,y)=(x+2,y)
So, for point A' we get the translation as:
A" = ( 3 + 2, 1)
A" = (5, 1)
Therefore, the image of the point A after the given compositions of transformation will be (5, 1).
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Write an equation in standard form for the line that passes through the given points.
(5,-2) and (5,3)
The equation of the line in standard form is
(Type your answer in standard form.)
x=5 is the required equation of straight line
What is slope of line ?The steepness of a line is determined by its slope. The slope is m in the equation for a line that is typically used, y = mx + b. The term "rise over run" is also frequently used to describe it and describes how much the y-value changes as the x-value does.
According to the given value;
slope of line is Y₂-Y₁/X₂-X₁
hence slope for given line will be
3-(-2)/5-5 =5/0 = ∞
slope is infinity means straight line is vertical in nature and vertical lines are of the form x=a where a is some constant
now we can observe that 5 is constant in both the given points so x=5 is the required line which passes through (-2,-6),(-2,5)
Hence,x=5 is the required equation of straight line .
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Nicholas drinks 8 ounces of milk for every 5 cookies, he eats. If he eats 20 cookies, how many ounces of milk does he drink?
Plss show work and explain or I won’t get credit.
Student is asked
to evaluate the expression 2 to the power of 4/ 2 to the power of 7 =8
What error did the student make? Explain. Then
evaluate the expression.
The value of the expression 2⁴/2⁷ = 1/8.
A student is asked to evaluate the expression 2⁴/2⁷.
And the student wrote the answer for this expression as 8.
The student made the mistake of subtracting 7 from 4.
4 - 7 = -3, but the student might have done 7 - 4 = 3 and arrived at the answer as 2³ = 8.
Let us evaluate the given expression.
2⁴/2⁷
Apply exponent rule aⁿ/aˣ = aⁿ⁻ˣ
2⁴/2⁷ = 2⁴ ⁻ ⁷
⇒ 2⁴/2⁷ = 2⁻³ (subtract the numbers: 4 - 7 = -3)
⇒ 2⁴/2⁷ = 1/2³ (apply the exponent rule: a⁻ⁿ = 1/aⁿ)
⇒ 2⁴/2⁷ = 1/8 (2³ = 2 × 2 × 2 = 8)
⇒ 2⁴/2⁷ = 1/8
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convert 4724.80345 base ten to a binary number via octal.
After the conversion of the given decimal number, the binary number is (1001001110100.11001101)₂.
What are binary numbers?A binary number is a number expressed in the base-2 numeral system, also known as the binary numeral system, which is a method of mathematical expression that uses only two symbols, typically "0" and "1." The base-2 numeral system has a radix of 2 and is a positional notation. Each digit is known as a bit or binary digit.For the decimal number 4724.80345, the binary number is (1001001110100.11001101)₂.
(Refer to the table given below for working)
Therefore, after the conversion of the given decimal number, the binary number is (1001001110100.11001101)₂.
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The correct question is given below:
Convert 4724.80345 base ten to a binary number.
in the proportion a/b=c/d and bc are the
Answer:
The numbers a,b,c and d in a : b = c : d are called the ratio of the proportion. The terms a and d are called the extremes. The terms b and c are called the means
Answer:
gsjscsiscjscsksvshsvshzhsvshshsgsvhshshshsgsgsg
Step-by-step explanation:
gCHGhshgg1gsjdfzjfzhzfshsgsjcdhs
The bar graph shows the estimated number of
K
3200 Females
Group 4
Males
Group 3
2407
2210
calories per day needed to maintain energy balance Calories Needed to Maintain Energy Balance for Sedentary Lifestyles
for various gender and age groups for sedentary
lifestyles. (Sedentary means a lifestyle that includes
only the light physical activity associated with typical
day-to-day life.) The mathematical model
F=-81x² +655x+617 describes the number of
calories needed per day, F, by females in age group
x with sedentary lifestyles. According to the model,
how many calories per day are needed by females
between the ages of 9 and 13, inclusive, with this
lifestyle? Does this underestimate or overestimate
the number shown by the graph? By how much?
Calories per Day
2400
Group 2
Group 116751795 1931
1600- 1407
1121
800-
***
0-
4-8
9-13
Group 5
2193
1861 1797
14-18 19-30 31-50
Age Range
Group 6
1996
1553
51+
According to the model, how many calories per day are needed by females between the ages of 9 and 13,
inclusive, with this lifestyle?
Type a whole number.)
Using the given bar graph, it is found that 1675 calories per day are needed by females between 9 and 13 years old, with this lifestyle.
What does a bar graph show?A bar graph shows the number of times that each observation appears in the data-set.
From the bar graph in this problem, the number of calories needed for females given the age is as follows:
4-8: 1407.9-13: 1675.14-18: 2210.19-30: 2407.31-50: 2193.51+: 1996.Hence, 1675 calories per day are needed by females between 9 and 13 years old, with this lifestyle.
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to do this, the researchers select a random sample of of 100 gas stations, and record the pump prices for both regular unleaded and premium unleaded. the average price for the 100 stations is calculated, and used as an estimate for the average price of gasoline for the entire city.
The correct option is A. Quantitative.
In the study Quantitative data is collected as the calculation of quantity is being done.
What is defined as the Quantitative data?Quantitative data is any collection of information that may be recognized and analyzed numerically.
Some key points related to Quantitative data are-
Quantitative data data is the most important type of data for use in mathematics and statistics because it is the only form of information that can be counted objectively. Quantitative data answers questions like "How many? ", "How frequently? ", "How much is it?" ”. Using mathematical techniques, this data can be easily verified and evaluated.There are, for example, quantities that correspond to various parameters. "How much just do that laptop cost?" for example. " is a quantitative data collection question. Most measuring parameters have values associated with them, such as lbs or kilograms for mass, dollars for cost, and so on.Because of the convenience of mathematical derivation that quantitative data provides, it makes assessing various parameters controllable.To know more about Quantitative data, here
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The complete question is-
Determine whether the data collected in the study is qualitative or quantitative:
A study is conducted to estimate the average price of gasoline in a large city. To do this, the researchers select a random sample of of 100 gas stations, and record the pump prices for both regular unleaded and premium unleaded. The average price for the 100 stations is calculated, and used as an estimate for the average price of gasoline for the entire city.
A. Quantitative
B. Qualitative
Evaluate -2x(to the second power) for x= -3
The value of the expression when x = -3 is - 18
What is index form?Index form is defined as the power or exponent that is raised to a number or a variable.
From the information given, we have;
-2x(to the second power)
This is expressed as;
-2x²
Now, let's substitute the value of x as -3, we get;
-2(-3)²
Take the square
-2(9)
-18
Thus, the value of the expression when x = -3 is - 18
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yall I really need help. Ill give brainliest^^
What are the domain and range of the function the quantity of x squared minus 4 x minus 12, all over x plus 2? domain is x is all real numbers where x does not equal negative 2 comma range is y is all real numbers where y does not equal negative 8 domain is x is all real numbers where x does not equal 4 comma range is y is all real numbers where y does not equal negative 2 domain is x is all real numbers where x does not equal 2 comma range is y is all real numbers where y does not equal 8 domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal 2
Using it's concept and the graph of the function, the domain and the range are given as follows:
Domain: All real values of x.Range: All real values of y.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input of the function.The range of a function is the set that contains all the values of the output of the function.In a graph, the domain and the range are found as follows:
The domain is given by the values of x, present in the horizontal axis of the graph.The range is given by the values of y, present in the vertical axis of the graph.For this problem, the function is given by the following rule stated in the problem:
f(x) = (x² - 4x - 12)/(x + 2).
The graph of the function is given at the end of the answer. From it, we can see that the function unexpectedly devolves into a linear function. This is because -2 is a factor of x² - 4x - 12, hence (x² - 4x - 12) = (x + a)(x + 2), and x + 2 is simplified with the denominator.
The function is defined for all real values, and also assume all real values, hence:.
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7/6m=1/6 please help I suck at fractions
Answer: m=1/7
Step-by-step explanation:
7/6m=1/6
7/6 * m=1/6
7*6/6 * m = 1*6/6==> Multiply by 6 on both sides to get rid of denominators
42/6 * m=6/6
7m=1
m=1/7
Answer:
m = 1/7
Step-by-step explanation:
hope i helped out :)