Name the line of reflection used to map the preimage to its image.

Answer:

4:3

Step-by-step explanation:

it will be 16:12 and when you divide both by 3 it will be 4:3

The mismatch in the number of variables in the ratio, implies that the ratio is undefined

The ratio expression is given as:

2 : 5 : 4 = n : 8

In the above ratio expression, we have the following observations:

If the ratio expression is to represent an equivalent expression, then the number of variables on both sides of the expression must be the same

This in other words implies that

When the number of variables on either sides of the ratio expression, then the ratio is either incorrect or undefined

In this case, we can conclude that the ratio is undefined

Hence, the value of n in the ratio given as 2 : 5 : 4 = n : 8 is undefined

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Answer:

5 miles in 50 minutes

If x represents the age of the youngest child, then the equation that models this scenario is x+3(x+4) = 5(x+2)-5 and the ages of the three sisters are 7, 9 and 11 years respectively.

According to the question,

We have the following information:

There sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister's age.

Age of youngest sister = x years

Middle sister = (x+2) years

Oldest sister = (x+4) years

Now, the equation according to the given situation is:

(a) x+3(x+4) = 5(x+2)-5

(b) Now, we can solve this equation:

x+3x+12 = 5x+10-5

4x+12 = 5x+5

12-5 = 5x-4x

x = 7

Middle sister = 7+2 = 9 years

Oldest sister = 7+4 = 11 years

Hence, the equation is x+3(x+4) = 5(x+2)-5 and their ages from the youngest to the oldest are 7, 9 and 11 years respectively.

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With the full question now given (see attached image), I would allocate equal resources to Whole Milk and 0-1% fat milk. This exercise is about the Allocation of Resources in a free economy with the help of market trends. See further explanation below.

The allocation of available resources to diverse purposes is referred to as resource allocation in economics. In the framework of a whole economy, resources can be distributed through a variety of mechanisms, including markets and planning.

Note that in the attached graph, the demand for Whole Milk has been falling while the demand for 0-1% fat is dropping. While the reasons for this trend is beyond the scope of this exercise, suffice it to say that it is reasonably expected that the consumption data in 2001 will most likely be equal to each other.

1980 to 1985 the movement in 0-1% fat milk was negligible but it shot up the next 5 year period.

It is logical to expect that this pattern will reoccur since the demeand has been stable for the last 10 years (hence a reoccurring pattern).

On the other hand, every 5 years, the demand (consumption) for Whole Milk has consistently dropped. Hence the reason for the decision.

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The equation of line in slope-intercept form is found as y = -3x + 7.

For the given question;

The two passing point of the line are;

(x1, y1) = (2,1)

(x2, y2) = (1,4)

Slope = m = (y2 - y1)/(x2 - x1)

Put the values.

m = (4 - 1)/(1 - 2)

m = -3

Then, the equation of the line in slope intercept form is found using two point equation.

y - y1 = m(x - x1)

y - 1 = -3(x - 2)

Simplifying,

y = -3x + 7

-3 is the slope and 7 is the y intercept.

Thus, the equation of line in slope-intercept form is found as y = -3x + 7.

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The product of 83 and 4.5 \times 10^64.5×106 is expressed in scientific notation is 830*10^-12.

Scientific notation can be described as the representation of the large numbers or very small numbers in the standard form which can be seen in the final answer of this question , it do make the handling of numbers to be easier when making a calculation.

From the question, we are asked for the product of 83 and 4.5 \times 10^64.5×10^6,

Then we can multiply 10^6 * 4.5×10^6 which is (4.5*10^11)

Then 4.5/(4.5*10^11) = 10 *10^-12

Then we can found the product  expression as (83* 10 *10^-12) = 830*10^-12.

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Substitute [tex]x=\sin(t)[/tex] and [tex]dx=\cos(t)\,dt[/tex], and recall the definition of the elliptic integral of the second kind,

[tex]\displaystyle E(k) = \int_0^{\pi/2} \sqrt{1 - k^2 \sin^2(\theta)} \, d\theta[/tex]

Then the integral has a value of

[tex]\displaystyle \int_0^1 \sqrt{\frac{2-x^2}{1-x^2}} \, dx = \int_0^{\pi/2} \sqrt{2-\sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \sqrt2 \int_0^{\pi/2} \sqrt{1 - \frac12 \sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~= \boxed{\sqrt2 E\left(\frac1{\sqrt2}\right)}[/tex]

SOLUTION:

The equation is;

Writing in matrix form, we have;

The augmented matrix is thus;

Answer:

2

Step-by-step explanation:

One yard = 3 feet

4+6 =10

4 times 3 is 12

12 - 10 = 2

Answer:

v = 4

Step-by-step explanation:

4(2v - 1) = 28

4(2v - 1)/4 = 28/4

2v - 1 = 7

2v - 1 + 1 = 7 + 1

2v = 8

2v/2 = 8/2

v = 4

Answer:

48

Step-by-step explanation:

Given:

[tex]\textsf{Maximize}: \quad z=6x+12y[/tex]

[tex]\begin{aligned}&\textsf{Subject to}: \quad &4x+5y & \leq 20\\&&8x+y &\leq 20\\&&x\geq 0, y&\geq 0\end{aligned}[/tex]

Graph the lines:

[tex]\textsf{Draw the line } \;\;4x+5y=20 \;\;\textsf{and shade under the line}.[/tex]

[tex]\textsf{Draw the line } \;\;8x+y=20 \;\;\textsf{and shade under the line}.[/tex]

[tex]\textsf{Draw the line } \;\;x=0\;\;\textsf{and shade above the line}.[/tex]

[tex]\textsf{Draw the line } \;\;y=0\;\;\textsf{and shade above (to the right of) the line}.[/tex]

Therefore, the feasible region is bounded by the corner points:

Determine the value of z at the corner points by substituting the x and y values of the points into the equation for z:

[tex]\textsf{Value of $z$ at $A(0,0)$}: \quad 6(0)+12(0)=0[/tex]

[tex]\textsf{Value of $z$ at $B(0,4)$}: \quad 6(0)+12(4)=48[/tex]

[tex]\textsf{Value of $z$ at $C\left(\dfrac{5}{2},0\right)$}: \quad 6\left(\dfrac{5}{2}\right)+12(0)=15[/tex]

[tex]\textsf{Value of $z$ at $D\left(\dfrac{20}{9},\dfrac{20}{9}\right)$}: \quad 6\left(\dfrac{20}{9}\right)+12\left(\dfrac{20}{9}\right)=40[/tex]

Hence, the maximum value of z is 48 at B(0, 4).

Answer: Yes  

Step-by-step explanation: The real number, which most exceeds its cube, is A 21

Answer: Option A. 18.2

Explanation:

Step 1. The two polygons are similar. To find the length of BC, we will first identify the corresponding sides of the polygon, which are shown here in the same color:

Step 2. There must be a proportion between corresponding sides:

In this case, using only the first and second part of the proportion:

Step 3. From the last equation, we can solve to find BC. Move 28 to multiply on the left-hand side of the equation:

Solving the operations:

The length of BC is 18.2. This result is shown in option A.

Answer: Option A. 18.2

Basketball should have 20.64 ft/s initial velocity.

When an object is moving, its velocity is the direction at which it is moving as a measure of how quickly its location is changing as seen from a certain point of view and as measured by a specific unit of time. velocity. It is the quickness, swiftness, or speed of movement, action, or operation. A measurement of a body's rate of motion in physics is the rate at which its location changes over time in a certain direction.

Given Data

The parabola y=(-16x2/0.434v2)+1.15x+8 can be used to represent the ath of a basketball through a hoop, where v is the ball's speed in feet per second, y is the hoop's height, and x is the distance from the hoop. When the basketball hoop is 10 feet high and 17 feet away, the following is true:

y = (-16x⁰.434v²)+1.15x+8

10 = [-16(17)⁰.434v²] + 1.15(17) + 8

v = 24.64 ft/s

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The option (A) the graphs are reflections of each other across the line y=x, and option (D) f(f⁻¹(x)) = x are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the b is related to exactly one value in the range.

The functions f(x) and f⁻¹(x) are inverses of each other.

As we know, the graph of the function and inverse function are reflections of each other about y = x.

From the property of the inverse of function:

f(f⁻¹(x)) = x

Thus, the option (A) the graphs are reflections of each other across the line y=x, and option (D) f(f⁻¹(x)) = x are correct.

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Answer:

The sand is 2/5 and the cement is 5/7

Step-by-step explanation:

You need to get the total parts of both by adding the numerator and the denominator, and then divide the amount of parts by the total amount of parts.

ANSWER:

STEP-BY-STEP EXPLANATION:

Let p be the figure of the pentagon.

We can establish the following equation:

Therefore, the correct answer is the 4th option a) 2p + 5 = 21

The given parallel lines have a transversal which passes through them.

Hence from the property of parallel lines we found the values of x and y as 16 and 10 respectively.

Given that two parallel lines are intersected by a transversal, pair of angles are created, such as:

angles that are vertically opposing and equal.

the related angle pairs that are equivalent.

the equal pairs of opposite exterior angles.

the opposite interior angle pairs that are equal.

From the diagram we have the alternate exterior angles which are equal.

Therefore, alternate angle 1 = (8x-14)°

and alternate exterior angle 2 = (5x+34)°

now equate them,

(8x-14)° =  (5x+34)°

8x-14=5x+34

8x-5x=34+14

3x=48

x=48/3

x=16

now substitute x value in angle 1:

8(16)-14

= 114°

therefore angle 1 = 180°-114°

= 66°

Hence (5y+16)° = 66

5y = 66-16

5y = 50

y = 50/5

y = 10

Therefore we get the values of x and y as 16 and 10 respectively.

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Yes, because 6 c+5=2(3 c+2)+1 and 3 c+2 is an integer. Option A

This is further explained below.

Generally, A natural number that is either positive or negative expressed as an integer, or the number zero itself are all examples of integers.

The additive inverses of the positive numbers that they relate to are represented by the negative numbers.

In conclusion, Because 6c+5=2(3c+2)+1 and 3c+2 is an integer, the answer to this question is yes.

is correct, Integer

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CQ

[tex](b) Is\ $6 c+5$ \an \odd \integer?\\\\Yes, because $6 c+5=2(3 c+2)+1$ and $3 c+2$ is \ an \ integer.\\\\Yes, because $6 c+5=2(3 c+2)$ and $3 c+2$ is \ an integer.\\\\No, because $6 c+5=2(3 c+2)+1$ and $3 c+2$ is an integer.\\\\No, because $6 c+5=2(3 c+2)$ and $3 c+2$ is an integer.[/tex]

The given equation is 1-degree linear equation in one variable.

What is linear equation?

A linear equation is one that may be written as a1x1+a2x2+......+anxn in mathematics, where a1, a2,...., an are the coefficients, which are frequently real integers. The coefficients, which may be any expressions as long as they don't contain any of the variables, can be thought of as the equation's parameters. The coefficients a1 to a must not all be 0 in order for the equation to have any sense. An alternative method for creating a linear equation is to equalize a linear polynomial over a field, from which the coefficients are drawn, to zero. The numbers that, when used to replace the unknowns in such an equation, result in the equality, are the solutions.

x+1 = x+1 is a 1-degree linear equation in one variable (x).

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depreciated value of truck after 1year is $16863.2  

% is a relative number that is used to represent hundredths of any quantity. Since one percent (1%) equals one tenth of something, 100 percent denotes the entire amount, and 200 percent denotes twice the amount mentioned.

new truck valued depreciates 14.4% then

if old truck value be 100 % , depreciated value will  be 85.6 %

so depreciated value will be = 19700* 85.6 /100

                                                 = $16863.2

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Answer:

The correct answer is c, 24.2°.

Step-by-step explanation:

[tex] { \tan}^{ - 1} ( \frac{7.2}{16}) = 24.2 [/tex]

The data points from the set of collected that are outside the [-2, 2] range means that the data is an outlier or unusual data

The z–score also known as standard score is the number of standard deviation a score is differs from the mean or average score

The z–score is given by the formula;

[tex]Z = \frac{x - \mu}{ \sigma} [/tex]

The Z–Score is therefore, the number of standard deviations, a data point, x is far from the mean, [tex] \mu [/tex]

The standard deviation, [tex] \sigma [/tex], is given by the formula;

[tex] \sigma = \sqrt{ \frac{ \sum {( x_{i} - \mu)}^{2} }{N} } [/tex]

As the value of [tex] \sigma [/tex] increases, the variability increases, and the Z–Score decreases, such that a Z–Score of less than -2 or greater than 2 are unusual.

From the z–score calculator, the probability that a data point has a z–score of less than -2 or more than 2 is 0.02275

Such a data point can be taken as an outlier

Therefore, data that is outside the [-2, 2] range is an unusual (outlier) data

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The new cost of the shirt is $135

Macy's offer a shirt at the cost of $300

One week later, they offer 25% off

25/100 × 300

0.25 × 300

= 75

300-75

= 225

The next week it was reduced by an additional 40% off

40/100 × 225

= 0.4 × 225

= 90

225-90

= 135

Hence Macy's new shirt costs $135

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106 would be student's score on ACT metric.

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range. It demonstrates how different things are from the standard.

Given Data

Mean = 500

Standard deviation = 100

ACT metric

Mean = 20

Standard deviation = 5

Score = [tex]\frac{550-20}{5}[/tex]

Score = [tex]\frac{530}{5}[/tex]

Score = 106

106 would be student's score on ACT metric.

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Answer:

c.

Step-by-step explanation:

13+6.2+5.8

= 13+(6.2+5.8)

- the sum in the parentheses is easy to calculate (it = 12).

Answer:

a = 22, b = 6, c = 14, d = 8

Step-by-step explanation:

sum the elements in the leading diagonal , that is

7 + 15 + 23 = 45

then all other rows and columns and the other diagonal total 45

top row

7 + a + 16 = 45

23 + a = 45 ( subtract 23 from both sides )

a = 22

middle row

24 + 15 + b = 45

39 + b = 45 ( subtract 39 from both sides )

b = 6

left column

7 + 24 + c = 45

31 + c = 45 ( subtract 31 from both sides )

c = 14

bottom row

c + d + 23 = 45 , that is

14 + d + 23 = 45

37 + d = 45 ( subtract 37 from both sides )

d = 8