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and 45 points

The scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

Point c is the center of dilation. Line segment BA is dilated to create line segment b prime, a prime.  The image of the given problem is attached below. The length of CA is 4.

[tex]CA=4[/tex]

The length of a prime is 16.

[tex]AA'=16[/tex]

The new dimension will be,

[tex]CA'=CA+AA'\\CA'=4+16\\CA'=20[/tex]

Now, the scale factor is the ratio of the new dimension to the original dimension. Thus, the scale factor of the dilation is,

[tex]r=\dfrac{20}{4}\\r=5[/tex]

This will be the same for the line segment BA. Thus, the scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

Learn more about the dilation of the figure here;

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Answer:

the answer is 5

Step-by-step explanation:

D

Answer:

34? Idek

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

To maximize the length of the third side, which I'll call x, it needs to be the longest side.

So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.

Answer:

Add 1 unit to the X coordinates and Y coordinates for each new pair.

step-by-step explanation:

X: 10 + 1 = 11 + 1 = 12

Y: 20 + 1 = 21 + 1 = 22

Answer:80.8%

Step-by-step explanation:

£1200=100%

£970=

£970*100%/£1200=80.8333333

80.8%

Answer:

19.2%.

Step-by-step explanation:

Reduction = 1200-970 = £230,

% reduction = 230*100/ 1200

= 19,2%

Dimensions : 16 x 20

solving steps:

So we found Width = 16 feet

Length:

Answer:

width = 16 ft

length = 20 ft

Step-by-step explanation:

Let width = x

If the length is 4 ft longer than the width, then

⇒ length = x + 4

Area of a rectangle = width × length

Given:

Substituting these values into the equation for the area of a rectangle and solving for x:

⇒ 320 = x(x + 4)

⇒ 320 = x² + 4x

⇒ x² + 4x - 320 = 0

⇒ (x - 16)(x + 20) = 0

⇒ x = 16, -20

As distance is positive, then x = 16 only.

Therefore, width = 16 ft and length = 20 ft

Since v is a vector of magnitude 4 and makes angle 30° with the positive x axis, vector v in component form is v = 2√3i + 2j

To find vector v in component form, we need to know what a vector is

A vector is a physical quantity that has both magnitude and direction.

A vector can be resolved into perpendicular components along the x, y and z axis.

Since vector v has a magnitude of 4 making an angle of 30 with the positive x - axis, its x-component is V = (vcos30°)i

= (4cos30°)i

= (4 × √3/2)i

= 2√3i.

The y-component of v is V' = (vsin30°)j

= (4 × sin30°)j

= (4 × 1/2)j

= 2j

So, vector v in component form is v = V + V'

= 2√3i + 2j

So, since v is a vector of magnitude 4 and makes angle 30° with the positive x axis, vector v in component form is v = 2√3i + 2j

Learn more about vectors here:

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n²= 7²+3²

=49+9

=58

n= V58

=7.62m

Answer:

-12

Step-by-step explanation:

h(x) = ½x - 14 where x = 4:

h(4) = ½(4) - 14

= 2 - 14

= -12

Based on the amount that Noel cashed in each of her most recent paychecks, the amount she spent in total is $10.99.

The bank directory shows that you are charged 1.99% of the amount being cashed as well as a check processing fee of $1.39.

The amount Noel spent is therefore:

= (1.99% x 100.53) + (1.99% x 119.38) + (1.99% x 122.52) + (1.39 x 3 checks)

= 2.00 + 2.38 + 2.44 + 4.17

= $10.99

Find out more on bank charges at https://brainly.com/question/26494219.

Answer:

For the last three years, the National Post has greeted the yuletide season by publishing the video above. With a simple message of maximizing charitable giving by donating money to the food bank instead of canned goods, it is one of our most popular videos of all time, reaching virtually every corner of the English-speaking world.

Step-by-step explanation:

The object attached to a string illustrates a sinusoidal trigonometric function

The trigonometric function is H(t) = 5sin(π/2(t-0.2))-20, and the object's height after 0.6 seconds is  -17.06 cm

The trigonometry model of the object is a sine function represented by:

H(t) = Asin(B(t - c)) + D

The maximum height is 5 cm.

So, we have:

Amplitude, A = 5

The average height is - 20 cm.

So, we have

Vertical shift, D = -20

Its first average height is at t = 0.2.

So, we have:

Horizontal shift, C = 0.2

The period B is then calculated as:

B = π/t

The object reaches the maximum height every 2 seconds.

So, we have:

B = π/2

Substitute these values in H(t) = Asin(B(t - c)) + D

H(t) = 5sin(π/2(t-0.2))-20

Hence, the trigonometric function is H(t) = 5sin(π/2(t-0.2))-20

Substitute 0.6 for t in H(t)

H(0.6) = 5sin(π/2(0.6-0.2))-20

Evaluate

H(0.6) = -17.06

Hence, the object's height after 0.6 seconds is  -17.06 cm

Read more about trigonometric functions at:

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Answer:

What is the importance of biology laboratory?

Biological Science Laboratory Apparatus is essential for meeting our basic needs of food, clothing, shelter, health, energy, clean air, water and soil. Biological Science Laboratory Apparatus enrich the quality of life in numerous ways by providing new solutions to problems in health and materials and energy usage.

Answer:

Step-by-step explanation:

Area of triangle = 1/2 * base * height

Use the side of length 5.6cm as base, the height will be a perpendicular line from the base to the tip of the triangle.

From the right-angle triangle formed by the height and the side of length 3.9cm,

sin(56°45') = height / 3.9

height = 3.9*sin(56°45')

Substituting back into the area equation:

Area = 1/2*5.6*3.9*sin(56°45')

= 9.0cm^2

= 9cm^2

Use sine rule for Area

[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}absinC[/tex]

[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}(3.9)(5.6)sin56°45'[/tex]

[tex]\\ \rm\rightarrowtail Area=10.92(0.836)[/tex]

[tex]\\ \rm\rightarrowtail Area=10.22cm^2[/tex]

Answer:

10°

Step-by-step explanation:

According remote interior angles, 4k + 5 + 6k + 10 = 115.

10k + 15 = 115

10k = 100

k = 10

Hope this helps :)

Have a nice day!

Answer:

k = 10°

Step-by-step explanation:

      According to the exterior angle theorem, the exterior angle will be equal to the two opposite inside angles added together. It will look like the following, and we solve for k from there.

115° = (4k + 5)° + (6k + 10)°

115° = 4k° + 5° + 6k° + 10°

115° = 6k° + 4k° + 10°  + 5°

115° = 10k° + 15°

100° = 10k°

10° = k

k = 10°

Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.

In △ABC,

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{AB}{AC}[/tex]

[tex]\longrightarrow[/tex]sin 30⁰ = [tex]\sf \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = \dfrac{10\sqrt{2}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = 5\sqrt{2}\:units[/tex]

[tex]\\[/tex]

In △ABC,

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{Base}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{BC}{AC}[/tex]

[tex]\longrightarrow[/tex]cos 30⁰ = [tex]\sf \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2\times 3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{6}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = 5\sqrt{6}\: units[/tex]

Thus , the length of other two sides of triangles are 5√2 and 5√6 units.

Answer:

273cm

Step-by-step explanation:

21 times 13 is 217. That is how you find out the area of parallelogram, (base times peperndicular heigh)

The volume of the half part of a cylinder of 60 cm high and 14 cm in diameter is 1470π cm³.

volume of a cylinder = πr²h

where

Therefore,

r = 14 / 2 = 7 cm

h = 60 cm

volume of the cylinder = π × 7² × 60

volume of the cylinder = π × 49 × 60

volume of the cylinder = 2940π cm³

The volume of the half part = 2940π / 2 = 1470π cm³

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Answer: 13 [tex]\frac{1}{3}[/tex] pounds

Step-by-step explanation:

     We will set up a proportion. I will have the weight, in pounds, on the top (numerator) and the length, in inches, on the bottom (denominator).

[tex]\frac{12}{36} =\frac{x}{40}[/tex]

     Cross-multiply:

36 * x = 12 * 40

36x = 480

     Divide both sides of the equation by 36:

x = 13 [tex]\frac{1}{3}[/tex] pounds

Answer:

Step-by-step explanation:

First find unit weight.

1 foot = 12 inches

3 ft = 3*12 = 36 inches

3ft 4 inches = 36 + 4 = 40inches

Weight of 36 inches  long bar =   12  pounds

Weight of 1 inch bar = 12/36

[tex]\text{Weight of 40 inches long bar = $\dfrac{12}{36}*40$}[/tex]

                                             = 13.3 pounds

Answer:

Isosceles right triangles are half squares, and if the length of one side is 6cm, that is the length of the other side since both segments are equal. Take the formula to find the area of a square (base times height), apply the side measurement of the triangle (6cm) and divide it in half to find the area of half of it (therefore, finding the area of the isosceles triangle.) (6x6) / 26x6 = 3636 / 2 = 18 The area of the isosceles triangle is 18 square centimeters.

Step-by-step explanation:

Answer:

[tex]y = {4}^{x} [/tex]

is the answer

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2\implies A=2121.8[/tex]

Answer:

2,121.8

Step-by-step explanation:

2000(1.03)^2

please rate and mark as brainlest.

Answer:

N = -1

explanation:

x = N

solving steps:

[tex]\sf f(x)=x^2+2x-15[/tex]

To find symmetry of a quadratic function.

                                                                   vertex formula    :   [tex]\sf x=\dfrac{-b}{2a}[/tex]

[tex]a=1,\:b=2[/tex]

[tex]\sf x=\dfrac{-2}{2\cdot \:1}[/tex]

[tex]\sf x = -1[/tex]

Then,

N = -1

Answer:

answer is 16.5

Step-by-step explanation:

answer is 16.5

Answer:

B=5

Step-by-step explanation:

If 7 plus a equals 9 then a would equal 2.

2+8=b+5

10=b+5

Ask yourself what number plus 5 equals 10

B is 5 because 5 plus 5 is 10

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \:48200[/tex]

[tex]\qquad \sf  \dashrightarrow \:4.82 \times 10 {}^{4} [/tex]

Answer:

Sorry let me try to understand the question

Step-by-step explanation:

The domain of the function r(x) is (0, 200).

The revenue earned when the price is $30 is $20400.

The rule for the function r(x) is x(800 - 4x).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Demand:

d(x) = 800 - 4x

Price = x

Revenue = Price x demand

Revenue = r(x)

A)

The rule for r(x).

r(x) = x d(x) = x(800 - 4x)

The domain of r(x) is 0 < x < 200 i.e (0, 200).

B)

x = 30

r(x) = 30(800 - 4 x 30)

r(x) = 30(800 - 120) = 30 x 680 = 20400

C)

r(x) = x(800 - 4x)

Thus,

The answers are given above.

Learn more about functions here:

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Answer:

see my question and come there now I want to talk with you

Step-by-step explanation:

Goal: illustrates radius, diameter, chord, center, arc, central angle, and

inscribed angle.

Role: Garden Designer/Landscape Architect

Audience: Math Teacher

Situation: A certified plantita and backyard owner plans to have a unique

garden. As a Landscape Architect, you are asked to make a sample layout of

a circular garden. She asks you to include the following on her garden:

● well

● pond

● bridge

● fountain

● walkways

● benches or chairs

● entrance and exit gates.

● trees, ornamental plants, and herbs

Procedure:

1. Draw a circle.

2. Conceptualize a circular garden and layout using the specified

items mentioned above.

What I Can Do

9

DISCIPLINE • GOOD TASTE • EXCELLENCE

3. Label the parts of circle formed on the garden layout

Please I'm looking for a serious answer. I need to pass this on monday. Thank you.