The **current yield** of the bond is 9.27%.

**What is current yield?**

**Current yield** is the bond **rate of return** computed as the **annual coupon** divided by the **current price** of the bond

The annual coupon is the coupon rate of 10% multiplied by the bond's par value of 100

**annual coupon**=10%*100

annual coupon=10

**current bond price**=107.87

current yield=annual coupon/current bond price

current yield=10/107.87

current yield=**9.27%**

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￼PLEASE HELP WITH SURFACE AREA!! This is my project and I need the awnser quick!! Pls help me marking brainliest if the awnsers r right !

The **surface areas** and **volumes** of the solids are listed below:

Case 1: A = 118 cm², V = 70 cm³

Case 2: A = 121.5 in², V = 91.125 in³

Case 3: A = 192 m², V = 144 m²

Case 4: A = 480 ft², V = 576 ft³

Case 5: A = 87.965 yd², V = 62.832 yd³

How to determine the surface area and the volume of solidsIn this problem we need to determine the **surface area** and the **volume** of each solid. The surface area is the sum of the areas of all faces. The area and volume formulas required to answer this question are shown below:

Area

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Circle

A = π · r²

Lateral face of a cylinder

A = 2π · r · h

Volumes

Prism

V = A · h

Where:

w - Widthl - Lengthh - Heightr - RadiusA - Base area.Now we proceed to determine the surface areas and volumes of the solids:

Case 1

A = 2 · [(5 cm) · (7 cm) + (5 cm) · (2 cm) + (7 cm) · (2 cm)]

A = 2 · (35 cm² + 10 cm² + 14 cm²)

A = 2 · 59 cm²

A = 118 cm²

V = (5 cm) · (7 cm) · (2 cm)

V = 70 cm³

Case 2

A = 6 · (4.5 in)²

A = 121.5 in²

V = (4.5 in)³

V = 91.125 in³

Case 3

A = 2 · 0.5 · (8 m) · (6 m) + (6 m) · (10 m) + (6 m)² + (8 m) · (6 m)

A = 192 m²

V = 0.5 · (8 m) · (6 m)²

V = 144 m²

Case 4

A = 2 · 0.5 · (12 ft) · (8 ft) + 2 · (10 ft) · (12 ft) + (12 ft)²

A = 480 ft²

V = 0.5 · (12 ft) · (8 ft) · (12 ft)

V = 576 ft³

Case 5

A = 2π · (2 yd)² + 2π · (2 yd) · (5 yd)

A = 87.965 yd²

V = π · (2 yd)² · (5 yd)

V = 62.832 yd³

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Estimate then find the product 34•12

**Answer:**

I estimate it is around 340 because 34 times 10 is 340 the product of 34 times 12 is 408

**Step-by-step explanation:**

7 in.

12 in.

6 in.

What is the surface area of this rectangular prism?

The **surface area **of the rectangular prism is 396 square inches

From the question, we have the following parameters that can be used in our computation:

7 in by 12 in by 6 in

The **surface area **of the **rectangular prism **is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the **area **is 396 square inches

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What is the mode of the data represented in this line plot?

Enter your answer in the box.

5 - xx

6 - xxxx

7 - xxx

8 - xxxxxx

9 - xx

10 - xxxx

11 - xx

The **mode **of the data represented in this **line plot **will be 8.

**Simply counting **how several times each number looks in the data set can help you identify the mode, which is the integer that **repeats **the **most frequently **in the collected data. The figure with the largest total is the mode.

The value that appears the **most frequently **in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's **mode**.

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Apples cost $1.29 per pound. How much would a bag of apples weighing 4.7 pounds cost? (Round your answer to the nearest cent.)

Answer:

$6.06

Step-by-step explanation:

$1.29 x 4.7 = 6.063

Round: 6.06

Identify the pairs of alternate exterior angles in the given figure.

A) ∠2 and ∠7; ∠1 and ∠8

B)∠3 and ∠6; ∠4 and ∠5

C) ∠3 and ∠5; ∠4 and ∠6

D) ∠1 and ∠7; ∠2 and ∠8

The pairs of **alternate exterior angles** in the given figure is **Option D) ∠1 and ∠7; ∠2 and ∠8**

Alternate exterior angles are a pair of angles formed by a **transversal line** intersecting two parallel lines and located on opposite sides of the transversal and on the exterior of the **parallel lines**. In other words, if two parallel lines are **intersected** by a third line (the transversal), then the pairs of angles on opposite sides of the transversal and outside the parallel lines are alternate exterior angles. These angles are **congruent** to each other.

In the given figure two parallel lines, which are crossed by a transversal line which forms angles.

Now according to the given figure

so, answer is **Option D) ∠1 and ∠7; ∠2 and ∠8**

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Focus: (-5,3); Directrix: y = 1

The **equation** of the **parabola** is: y = (1/4)(x-3)²+ 2

In Parabola mathematics, it is defined as a set of points that are **equidistant** from a fixed point called the focus and a fixed line called the directrix. In this case, we are given the focus (3,5) and the directrix y=1, y=1, and we need to find the equation of the parabola.

To find the equation of the parabola, we first need to determine the vertex. The **vertex** is the midpoint between the focus and the **directrix**, which in this case is (3,3). Since the parabola is symmetric, we know that the axis of **symmetry** passes through the vertex and is perpendicular to the directrix. Therefore, the equation of the **axis** of symmetry is x=3.

Next, we need to find the distance between a **point** on the parabola and the focus, as well as the **distance** between that same point and the directrix. Let (x,y) be a point on the parabola. The distance between (x,y) and the focus is given by the distance formula: √((x-3)² + (y-5)²)

The distance between (x,y) and the directrix is simply the **absolute value** of the difference between y and 1: |y-1|

Since the point (x,y) is equidistant from the focus and the directrix, we have: √((x-3)²+ (y-5)²) = |y-1|

Squaring both sides and simplifying, we get: (x-3)²= 4(y-2)

Therefore, the **equation** of the **parabola** is: y = (1/4)(x-3)²+ 2

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NOTE : I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.

**Complete Question : **Find the Parabola with Focus (3,5) and Directrix y=1 (3,5) , y=1

what is1+1+1 equal?

this is a not ur typical math problem try to get it right u will get brainliest

The **mathemematical** **s****u****m**** **of the three numbers 1+1+1 would give 3

**Addition** of numbers can involve 2 or more values using the **additive** sign '+'. For any given **sum** of values, the result obtained would be greater than any of the individual value in the **sum**.

Here, 1 + 1 + 1 means that we are **adding** 1 in three places. The value obtained would be 3.

Therefore, the **sum** of the 1+1+1 is 3

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4. The wheels of a bicycle have a

diameter of 22 inches. How many

full revolutions will the wheels need

to make to travel 300 feet? Use 3.14

for .

A 105 revolutions

B 10 revolutions

C164 revolutions

D 53 revolutions

no

53 **revolutions** will be needed by the **wheels** to make it travel 300 feet.

Option D is the correct answer.

We have,

To solve this problem, we can use the formula:

**Number** of **revolutions** = Distance / Circumference of the wheel

First, let's convert the distance from feet to inches:

300 feet = 300 x 12 = 3600 inches

Next, we need to calculate the **circumference** of the wheel using the given diameter:

Circumference = π x diameter

Circumference = 3.14 x 22 inches

Circumference ≈ 69.08 inches

(rounded to two decimal places)

Now we can calculate the number of revolutions:

**Number** of **revolutions** = 3600 inches / 69.08 inches

= 52.14 revolutions

Rounding to the nearest whole number.

= 52 revolutions.

Therefore,

53 **revolutions** will be needed by the **wheels** to make it travel 300 feet.

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The **bicycle **wheels will need 53 full **revolutions **to travel 300 feet.

The **circumference **of a wheel can be calculated using the formula:

circumference = π x diameter

So, circumference = 3.14 x 22

= 69.08 inches

Now, **converting **feet to inches

300 feet = 300 x 12 inches

300 feet = 3600 inches

So, number of **revolutions**:

revolutions = distance / circumference

= 3600 / 69.08

≈ 52.11

Therefore, the **bicycle **wheels will need 53 full **revolutions **to travel 300 feet.

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Please help me :(

What is the measure of p in the following diagram?

PS: Its in a Chapter 11 Go math book! Maybe... can you help me pls?

The **measure **of p in the **diagram **is,

m∠P = 45°

We have to given that;

PM is **perpendicular **to MO.

Now, If m ∠P = m∠2

then it's an **isosceles triangle.**

And, m ∠M = 90°, therefore it's an isosceles right triangle.

We know that,

the sum of measures of angles in a triangle is equal 180°.

Therefore we have the equation:

m∠P + m∠2 + m∠M = 180°

Substitute m∠M = 90° and m∠P = m∠2 = x:

x + x + 90° = 180°

substract 90° from both sides

2x = 90°

**divide** both sides by 2

x = 45°

m∠P = 45°

Thus, The **measure **of p in the **diagram **is,

m∠P = 45°

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PLEASSE HELP!!! MARKING AS BRAINLIST

The **area **of the figure as shown in the diagram is** 24 in².**

**Area **is the region bounded by a plane shape.

To calculate the **area **of the figure, we use the formula below

Formula:

A = lw+l'w'+l''w''.................. Equation 1Where:

A =From the question,

Given:

l = 4 inw = 2 inl' = 2 inw' = 4 inl'' = 4 inw'' = 2 inSubstitute these values into equation 1

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The total cost of a tie and a pair of pants was $87.18. If the price of the tie was $2.12 less than the pair of pants, what was the price of the tie?

**This is a linear equation problem with two variables. One way to solve it is by using the substitution method. Let x be the price of the tie and y be the price of the pair of pants. Then we have:**

**$$**

**\begin{aligned}**

**x + y &= 87.18 \\**

**x &= y - 2.12**

**\end{aligned}**

**$$**

**Substituting x into the first equation, we get:**

**$$**

**\begin{aligned}**

**(y - 2.12) + y &= 87.18 \\**

**2y - 2.12 &= 87.18 \\**

**2y &= 89.30 \\**

**y &= 44.65**

**\end{aligned}**

**$$**

**Therefore, the price of the pair of pants is $44.65. To find the price of the tie, we plug y into the second equation:**

**$$**

**\begin{aligned}**

**x &= y - 2.12 \\**

**x &= 44.65 - 2.12 \\**

**x &= 42.53**

**\end{aligned}**

**$$**

**Therefore, the price of the tie is $42.53.**

**Answer:**

42.53

**Step-by-step explanation:**

write equation

tie + pants = 87.18

since ties cost 2.12 less than pants,

tie = pants -2.12

now substitute back into first equation

pants - 2.12 + pants = 87.18

solve for pants by adding 2.12 to the other side

divide by 2 since there are 2 pants on one side

find pants and then substitute value into the tie equation to find the price of the tie

An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected malpractice suits, a 99% confidence interval was constructed for the true proportion of medical malpractice lawsuits that are dropped or dismissed. The confidence interval was (0.6633, 0.7308) find the Margin of error.

**Answer: I have this same exact question **

**Step-by-step explanation: So someone please help this person, or animal which ever you perfer**

100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!

The prove of the **statement** is described below.

First of all ,

Labeling the given figure

And draw a** diagonal**,

In the quadrilateral PQRS,

The side PQ is **equal** to the side RS.

Therefore,

PQ = RS

And also, the side PQ is** parallel** to the side RS.

Then,

PQ || RS.

Now, draw the **diagonal** PR.

We know that a** parallelogram's** diagonal divides the parallelogram into two **congruent **triangles.

By the rule of **Side-Angle-Side**,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a** parallelogram**.

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Below are two inequalities and the graphs of their without the shading. By imagining where the shading should be, identify which point would satisfy BOTH

inequalities

**Answer: C**

**Step-by-step explanation:**

**Answer:**

D. (-2, 10)

**Step-by-step explanation:**

Given **inequalities**:

[tex]y > -\dfrac{5}{3}x+2[/tex]

[tex]y > 3x+2[/tex]

Both inequalities have been given in **slope-intercept form**, y = mx + b, where m is the slope and b is the y-intercept.

The **first equation** has a **negative slope**, which means that as x increases, y decreases. Therefore, it is the dashed line that begins in quadrant II and ends in quadrant IV.

The **second equation** has a **positive slope**, which means that as x increases, y increases. Therefore, it is the dashed line that begins in quadrant III and ends in quadrant I.

When **graphing inequalities**, the inequality sign ">" indicates a **dashed **line and **shading above** **the line**.

As both inequalities should be shaded **above **the lines, the region where the **shaded regions overlap** is the upper "V" of the graph (see attachment).

A point that satisfies both inequalities is any point that is located in the overlapping shaded region, but *not* found on the dashed lines.

Therefore, the **point **that satisfies both inequalities is **(-2, 10)**.

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

**Answer:**

B, C, E

**Step-by-step explanation:**

For a rectangle,

area = length × width

Let length = y.

Then the width is y - 5.

A = LW

750 = y(y - 5)

y(y - 5) = 750

y² - 5y - 750 = 0

All equations that can be put in the form above are correct.

A) y(y + 5) = 750

y² + 5y - 750 = 0

**No**

B) y² – 5y = 750

y² - 5y - 750 = 0

**Yes**

C) 750 – y(y – 5) = 0

750 - y² + 5y = 0

y²- 5y - 750 = 0

**Yes**

D) y(y – 5) + 750 = 0

y² - 5y + 750 = 0

**No**

E) (y + 25)(y – 30) = 0

y² + 25y - 30y - 750 = 0

y² - 5y - 750 = 0

**Yes**

Consider this equation.

cos(0) = 4/41

If 0 is an angle in quadrant IV, what is the value of sin(0)

**Answer: sin(0) = 40.804/41**

**Step-by-step explanation:**

Function

�

gg can be thought of as a scaled version of

�

(

�

)

=

�

2

f(x)=x

2

f, left parenthesis, x, right parenthesis, equals, x, squared.

A parabola labeled f represents the equation y equals x squared. A parabola labeled g passes through the point negative 1, 4, through the origin, and through the point 1, 4.

Write the equation for

�

(

�

)

g(x)g, left parenthesis, x, right parenthesis.

The **equation **for g (x) is,

⇒ g(x) = x² -3

Since, The **function **is,

⇒ f (x) = x²

when x = 0, f(x) = 0

hence it has vertex at (0,0)

Since, g(x) is shifter **version **of f(x) and has vertex at (-1, 4),

Then, g(x) must be shifted along y axis.

So, We get;

g(x)= x²+c

when x = - 1, g(x)= 4

4 = (-1)² + c

4 = 1 + c

c = 3

Thus, The **equation **for g (x) is,

g(x) = x² -3

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According to the graph, what is the value of the constant in the equation

below?

Constant/ Width=Height

O A 3

OB. 75

O C. 15

OD. 25

The calculated **value **of the **constant **in the equation is 75

From the question, we have the following parameters that can be used in our computation:

The **graph**

Where we have

(3, 25) and (5, 15)

The value of the **constant **in the equation is calculated as

Constant = **Width *** **Height**

So, we have

Constant = 3 * 25

Evaluate

Constant = 75

Hence, the **value **of the **constant **in the equation is 75

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Find the midpoint (-3,-5)(4, 5)

The midpoint of this **line segment** (-3, -5) and (4, 5) is (0.5, 0).

In order to determine the **midpoint **of a **line segment** with two (2) **end points**, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

By substituting the given **end points** into the formula for the **midpoint** of a **line segment**, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(-3 + 4)/2, (-5 + 5)/2]

Midpoint = [(1)/2, 0/2]

**Midpoint **= (0.5, 0).

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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!

**Answer:**

∆ABC ~ ∆QPR by SSS since 6/8 = 9/12.

please help! math: find the perimeter of the polygon below. use the correct formula!

the width is 3.8 and the length is 6.3

The **perimeter **of the **rectangular **polygon is given by P = 20.2 units

Given data ,

Let the **perimeter **of the **polygon **be represented as P

Now , the value of P is

Perimeter P of **rectangle **= 2 ( Length + Width )

Now , width is 3.8 and the length is 6.3

On simplifying , we get

P = 2 ( 3.8 + 6.3 )

P = 20.2 units

Hence , the **perimeter **is P = 20.2 units

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ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)

Karen measures the width of a garden plot and records that it is 40 meters. Its actual width is 42 meters.

What is the percent error in the measurement?

A: 2%

B: 3%

C: 4%

D: 5%

Explanation:

The error is 42-40 = 2 meters

Divide this over the actual width

2/42 = 0.0476 = 4.76% approximately

This rounds to **5%**

**Answer:**

D. 5%

**Step-by-step explanation:**

Percent Error = (|40 - 42| / 42) × 100

Percent Error = (2 / 42) × 100

Percent Error ≈ 4.76%

Find the line parallel to y = 7x+2

that includes the point (3, -1).

**Answer:**

? = 7

**Step-by-step explanation:**

The equation of the line parallel to another line will have the same slope. The given line y = 7x + 2 has a slope of 7.

To find the equation of the line that passes through the point (3, -1) and is parallel to the given line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

So, the equation of the line parallel to y = 7x + 2 and passing through the point (3, -1) is:

y - (-1) = 7(x - 3)

Simplifying this, we get:

y = 7x - 21 - 1

y = 7x - 22

So, the equation of the line is y = 7x - 22.

Given the form of the equation y + 1 = ?(x -3). We then know the answer is y + 1 = 7 (x - 3)

**The line's equation is :**

**Solution:**

If two lines are** parallel then their slopes are equal.**

The **slope** of [tex]\sf{y=7x+2}[/tex] is 7, so the slope of the line parallel to it is 7.

Now, we should plug the slope and the point into the point slope equation. See, we're even given a hint :

**Remember : y - y₁ = m(x - x₁).**

This hint tells us the point slope equation.

Wherem = slopeSo I plugin :

[tex]\bf{y-(-1)=7(x-3)}[/tex]

Simplify.

[tex]\bf{y+1=7(x-3)}[/tex]

This is it, we don't have to simplify all the way to slope intercept.

Hence, the equation is y + 1 = 7(x - 3)HELP ASAP PHOTO INCLUDED

The volume of the **cylindrical **shaped **pool **with water is V = 75.4 feet³

Given data ,

Let the diameter of the **pool **be d = 8 feet

So , radius r = 4 feet

And , the height of the **cylindrical **pool is h = 3 feet

Now , the water is half full

So , Volume of **Cylindrical pool **is V = ( 1/2 ) πr²h

V = ( 1/2 ) ( 3.14 ) ( 4 )² ( 3 )

On simplifying , we get

V = 75.4 feet³

Hence , the amount of **water **in **pool **is V = 75.4 feet³

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Which system is equivalent to

O

O

O

[5-x=9x²

y = 5-x

[y=9y²-90y+225

1x=y-5

[5+x=9x²

y = 5+x

y = 3x

x+3x=5

y=9x²?

x+y=5

The first equation is a quadratic equation, and the second equation is a** linear equation. **The solution to the system is x = -2 and y = 7, which satisfies both equations.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

The system that is **equivalent** to:

O

O

O

[5-x=9x²

y = 5-x

is: x = -2, y = 7

In the given system, the first equation is a **quadratic equation**, and the second equation is a** linear equation. **The solution to the system is x = -2 and y = 7, which satisfies both equations.

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a sphere has a diameter of 9 and find the volume in terms of Pi and volume to the nearest tenth

**Answer:**

V = 381.7 or 121π

**Step-by-step explanation:**

V=4/3πr³

Radius is half the diameter so, 9/2 = 4.5

r=4.5

V = 4/3π(4.5)³

V=4/3π(91.125)

V = 381.7 or 121π

Find the value of the unknown variable. -c/6 = -4

The value of the **unknown** c in the **algebraic** **fraction** equation is equal to -24

To solve the simple **algebraic** fraction equation, we cross multiply to eliminate the **fractions**, then simplify by solving for the **unknown**

Given the **algebraic** equation:

-c/6 = 4

(-c/6) × 6 = 4 × 6

-c = 4 × 6

-c = 24

multiply both sides by -1

-1 × -c = -1 × 24

c = -24

Therefore, the value of the **unknown** c in the **algebraic** **fraction** equation is equal to -24

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Can someone help me find the plume of these shapes, then round the answer to the nearest whole number please?

The **volume **for each **cone **in this problem is given as follows:

**11)** V = 94 in³.

**12) **V = 367 ft³.

**13) **V = 1005 in³.

The volume of a cone of **radius r and height h** is given by the equation presented as follows:

V = πr²h/3.

For **item 11**, the dimensions are r = 3 in and h = 10 in, hence the volume is given as follows:

V = π x 3² x 10/3

V = 94 in³.

For **item 12**, the dimensions are r = 5 ft and h = 14 ft, hence the volume is given as follows:

V = π x 5² x 14/3

V = 367 ft³.

For **item 13**, the dimensions are r = 8 in(half the diameter) and h = 15 in, hence the volume is given as follows:

V = π x 8² x 15/3

V = 1005 in³.

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PLEASE ANSWER BOTH QUESTIONS!

The correct statement regarding the **transformation **is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the **dilation **are given as follows:

A dilation can be defined as a transformation that **multiplies **the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the** scale factor**.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the **scale factor** is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also **reflected **over the x-axis.

More can be learned about **dilation **at brainly.com/question/3457976

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