In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of [? ], reflectedacross the [ ], and movedthrough the translation [ ].

a) From the graph,

shortest side length of original figure = 1/2 units

By dilating the original figure by 4, we would multiply each length by 4

Thus,

shortest side length of final figure = 1/2 x 4 = 2 units

b) shortest side length of the final figure = 4 x shortest side length of the original figure

c) A dilation with a positive scale factor greater than 1 gives an enlarged figure.Thus, the answer is False

d) After dilation, the original and final figures are similar. Thus, the answer is False

Answer:

A

Step-by-step explanation:

Answer:

h = 2

k = 5

Step-by-step explanation:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies (6, 0)=\left(\dfrac{k-3+3h+4}{2},\dfrac{k-2+1-2h}{2}\right)[/tex]

[tex]\implies (6, 0)=\left(\dfrac{k+3h+1}{2},\dfrac{k-2h-1}{2}\right)[/tex]

Equating the x-values to create an expression for k:

[tex]\implies \dfrac{k+3h+1}{2}=6[/tex]

[tex]\implies k+3h+1=12[/tex]

[tex]\implies k+3h=11[/tex]

[tex]\implies k=11-3h[/tex]

Equating the y-values to create an expression for k:

[tex]\implies \dfrac{k-2h-1}{2}=0[/tex]

[tex]\implies k-2h-1=0[/tex]

[tex]\implies k-2h=1[/tex]

[tex]\implies k=2h+1[/tex]

Equate the expressions for k and solve for h:

[tex]\implies 2h+1=11-3h[/tex]

[tex]\implies 5h=10[/tex]

[tex]\implies h=2[/tex]

Substitute the found value of h into one of the equations for k and solve for k:

[tex]\implies k=2(2)+1[/tex]

[tex]\implies k=4+1[/tex]

[tex]\implies k=5[/tex]

n = number of nickles

p = number of pennies

Therefore,

p = 12 + n

1 nickel = 0.05 dollars

1 penny = 0.01 dollars

Therefore,

Therefore,

p = 12 + 99 = 111

n = 99

One linear equation for the sytem is p + 5n = 606 is true

The system has one solution is true.

Answer:

42/11 or 4.454545..

Step-by-step explanation:

square both sides
(SQRT(9x+7) + SQRT(2x))^2 = 7^2

9x+7 + 2x = 49

11x = 42

x = 42/11 or 4.4545...

Given:

Let's evaluate the integral:

Thus, we have:

Expand using distributive property:

ANSWER:

The correct option is A. i.e., [tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]°

Given,

From the figure:

The triangle which of the following equations correctly represents the relationship between a ,b, c

Now, According to the question:

The relationship between the three sides of a triangle ABC is:

[tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]°

From the diagram,

The angle opposite to c is 90°

Thus, [tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]

Hence, The correct option is A. i.e., [tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]°

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Answer:

f(10) = -300

Step-by-step explanation:

f(x) = -3x^2

f(10) = -3(10)^2

f(10) = -3(100)

f(10) = -300

On a number line, the coordinate of point A is negative and the coordinate of point B is positive.

The mid point is defined as:

a. When will the midpoint of line AB be positive?

When B>A

b. when will the midpoint of line AB be negative?

When A>B

c. when will the midpoint of line AB be zero?

When:

d. when will the distance from A to B be negative?

Never the distance is not defined as negative by definition of distance.

The distance is a magnitude and for this reason not makes sense say negative distance because is always 0 or positive, if for example we find the distance from A to A is 0 since we are in the same point, but we never say we travel -200 m to reach a city for example.

Okay, here we have this:

Considering the provided quadratic function, we are going to rewrite in standard form, so we obtain the following:

So to rewrite the function in standard form we will complete the square:

And from this equation we get that the vertex is (4, -16)

Therefore the correct graph is the one in the upper right corner.

The dimensions of the enlargement will be: 32 inches by 28.8 inches.

The new dimensions can be gotten with the formula below:

Scale factor = Dimensions of new image / Dimensions of the original image.

Dimensions of new image = Scale factor × Dimensions of the original image

8 × 4 = 32 inches

8 × 3.6 = 28.8 inches.

Therefore, the new dimensions of the enlargement will be:

3 inches by 28.3 inches.

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Answer:

No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.

Step-by-step explanation:

The correct relationship between the hikers distance and time is;

No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A group of hikers tracked how long it took to hike a 20-mile trail.

And, They hiked 3.75 miles in 3 hours, 7.5 miles in 6 hours, and 12 miles in 8 hours.

Now,

Find the proportional as;

For hiked 3.75 miles in 3 hours,

Proportional = 3.75 / 3

                   = 1.25

For hiked 7.5 miles in 6 hours,

Proportional = 7.5 / 6

                   = 1.25

For hiked 12 miles in 8 hours,

Proportional = 12 / 8

                   = 1.5

Thus, The correct relationship between the hikers distance and time is;

No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.

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Answer:

im pretty sure its 90000

Step-by-step explanation:

As given by the question

There are given that 4<6, so 204<216.

Now,

On the number line, 4 is less tha6 and 204 is also less than 216

Hence, the given reasoning is correct.

In order to find the length of the side CD in the pentagon ABCDE we would need to find the distance between the two points (4,-2) and (8, 2)

We would use the following formula:

plug in x1= 4, x2= 8, y1=-2, y2=2

So,

d=5,65

The length of the side CD in the pentagon ABCDE would be 5,62

We are given the following expression:

We are asked to find the value of the expression when x = 6. To do that, we replace the value of "x" in the expression:

Solving the operations we get:

We are given the population and the area of the city and asked to calculate the population density.

Recall that the population density is the calculation that consists of dividing the population by the area. Then, in this case it would be

Then, the population density is 8750 habitants per square mile

The evaluated version of   ((x²-xy)-5x)-(4(2xy+2x²) is:

-x • (7x + 9y + 5)

Given, the expression is  ((x²-xy)-5x)-(4(2xy+2x²)

open the brackets.

x²-xy-5x-8xy-8x²

pull out the like terms.

-7x²-9xy-5x

= -x • (7x + 9y + 5)

Hence after evaluating ((x²-xy)-5x)-(4(2xy+2x²), we get -x • (7x + 9y + 5)

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The cost function is given by

C(t)=250t+750

Where

C(t) is the cost to rent a crane in t hours of use in a day.

t is the number of hours of use

And the derivatitve of the cost function with respect to t is given by

dC/dt=250

Hence, the rate of change of cost with respect to hours rented 250 dollars per hour

The mixed fraction form

is equivalent to

since 5/6 is equal to 0.8333, then

Therefore, since 5.83333 is greater than 5.6, then 5 5/6 is greater than 5.6

Answer:

inverse is

- if two angles are not supplementary than the angles are not a linear pair. True because if they dont equal 180 they arent a linear pair

Converse is

- If two angles are a linear pair theyre supplementary

True because if theyre a linear pair they will always equal 180

Contrapositive is

- if two angles are not supplementary, they are not a linear pair

True because linear pairs always equal 180

Answer:

f(x) = |x-2| + 10

Step-by-step explanation:

The value of x is 71 degree .

Triangles that have two sides at least equally spaced apart are said to be isosceles. As three-sided enclosed polygons with three sides, triangles are known to exist. Depending on the length of their sides, triangles can be categorized as equilateral, isosceles, or scalene.

The three interior angles of a triangle will always have a sum of 180°. A triangle cannot have an individual angle measure of 180°, because then the other two angles would not exist (180°+0°+0°).

So ,

x +x+38 = 180

2x = 180 -38

2x = 142

x = 71

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To first start our problem, we will draw some coordinate axis at point E, since we are rotating the figure around this vertex. We get something like this

We are going to fix the point E. But we are going to rotate the figure in the direction in which the arrow shows. Since it is a 90° rotation, our goal is to align the blue vertical line, with the red horizontal line, following the direction of the black arrow. The picture would look like this

Note that the lengths of the new figure should remaing the same. That is, the side H' E should have a length of 3 squares and the length of H' G' should be 2 squares.

Quantity 1

30

Unit 1

miles

Quantity 2

2.5

Unit 2

hours

= ?

Answer:

= 12 miles per hour

Showing Work

This is a fraction equal to

30 miles ÷ 2.5 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 2.5

30 miles ÷ 2.5

2.5 hours ÷ 2.5

=

12 miles

1 hour

=

12 miles

hour

= 12 miles per hour

Given:

A hemisphere has a radius of 8 cm.

Required:

To find the volume of the hemisphere.

Explanation:

The formula for volume of the hemisphere is,

Final Answer:

Both Anya  and Todd  are correct that  with 24 counters both 6 arrays and 8 arrays are possible.

Whats is an array?

An array is a set of items, images, or numbers arranged in rows and columns. Arrays are practical illustrations of multiplication theories (among other ideas in mathematics).

Here 24 can also be expressed as 6x4 and 8x3 therefore both ways are possible.

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Given:

The inequalities are,

To find:

The correct graphs.

Explanation:

Let us find the intercepts.

For the first inequality,

When x = 0, we get,

When y = 0, we get

So, the intercepts are

For the second inequality,

When x = 0, we get,

When y = 0, we get

So, the intercepts are

So, the graph becomes,

Answer:

  7.5 parts yellow

Step-by-step explanation:

The color moss green has violet and yellow paint mixed in the proportion 2 to 3. You want to know the number of parts of yellow paint that should be mixed with 5 parts of violet paint.

The proportion can be written different ways. We like to put the unknown value in the numerator. (x is the number of parts of yellow paint)

  yellow : violet = 3 : 2 = x : 5

Expressed as fractions, the proportion is ...

  [tex]\dfrac{3}{2}=\dfrac{x}{5}\\\\5\times\dfrac{3}{2}=x\qquad\text{multiply by 5}\\\\\dfrac{15}{2}=x=7.5\qquad\text{simplify}[/tex]

7.5 parts yellow paint should be mixed with 5 parts violet paint.

__

Additional comment

If you kept the proportion as violet : yellow, then the unknown value would be in the denominator. The solution to that proportion requires another step. Here, we just needed to multiply by the denominator value to find the unknown.