The graph represents the piecewise function:


100 POINTS !!!

Given:

In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).

The vertices of triangle A'B'C' are A'(-4,4), B'(8,4), C'(-4,-4).

To find:

The center of dilation and the scale factor.

Solution:

In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.

From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).

Therefore, the center of dilation is (0,0).

If a figure is dilated by factor k and the center of dilation is origin, then

[tex](x,y)\to (kx,ky)[/tex]

[tex]A(-2,2)\to A'(k(-2),k(2))[/tex]

[tex]A(-2,2)\to A'(-2k,2k)[/tex]

It is given that A'(-4,4). So,

[tex](-2k,2k)=(-4,4)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]2k=4[/tex]

[tex]k=\dfrac{4}{2}[/tex]

[tex]k=2[/tex]

Therefore, the scale factor is 2.

Answer:

y+x=k

Step-by-step explanation:

volume = 148 × 5.5 cube

= 24623.5 cubic cm

Answer:

Correct option is A

Step-by-step explanation:

According to given question,

[tex]sin 45^{0} =\frac{5\sqrt 2}{h} \\0.707=\frac{5\sqrt 2}{h} \\h=\frac{5\sqrt 2}{0.707} \\h=1[/tex]

Therefore, correct option is A.

Answer:

x = 2

Step-by-step explanation:

[tex]\frac{x}{x+1} =\frac{2}{x+1}[/tex]

x ≠ 0

x ≠ - 2

x ≠ - 1

[tex]\frac{x}{x+1}(x+1) =\frac{2}{x+1}(x+1)[/tex]

x = 2

Answer:

y = -0.7

Step-by-step explanation:

Reorder the terms:

-2.7 + y = -2.0 + 2y

Solving

-2.7 + y = -2.0 + 2y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2y' to each side of the equation.

-2.7 + y + -2y = -2.0 + 2y + -2y

Combine like terms: y + -2y = -1y

-2.7 + -1y = -2.0 + 2y + -2y

Combine like terms: 2y + -2y = 0

-2.7 + -1y = -2.0 + 0

-2.7 + -1y = -2.0

Add '2.7' to each side of the equation.

-2.7 + 2.7 + -1y = -2.0 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0

0.0 + -1y = -2.0 + 2.7

-1y = -2.0 + 2.7

Combine like terms: -2.0 + 2.7 = 0.7

-1y = 0.7

Divide each side by '-1'.

y = -0.7

Simplifying

y = -0.7

you are driving onajor highway 94 mp

Answer:

m<ACB  = 59degrees

Step-by-step explanation:

To get <ACB, first we need arcAB

arcAB + arcAC + arcBC = 360

arcAB + 89 + 153 = 360

arcAB+242 = 360

arcAB = 360 - 242

arcAB = 118

Also, m<ACB = 1/2arcAB

m<ACB = 1/2*118

m<ACB  = 59degrees

Answer:

Pythagoreas Theorem

Step-by-step explanation:

a^2+b^2=c^2

4^2+b^2=15^2

16+b^2=225

b^2= 209

14.45=b

Answer:

a. 38.5 square feet.

Step-by-step explanation:

11*7 = 77

77/2 = 38.5

Hope this helps! Good luck with your work.

Mark as brainliest if you'd like :D

Answer:

Circumference of circle = (15.5)π cm

Step-by-step explanation:

Missing information:

Area of circle = 60π cm²

Find:

Circumference of circle

Computation:

Area of circle = πr²

Area of given circle = π(Radius of circle)²

60π = πr²

60 = r²

Radius of circle = 7.75 cm  (Approx)

Circumference of circle = 2πr

Circumference of circle = 2(π)(7.75)

Circumference of circle = (15.5)π cm

Given : GH bisects ∠FGI

It means : ∠FGH and ∠HGI are equal

Given :

∠FGH = (5x - 8)°

∠HGI = (6x - 15)°

⇒  5x - 8 = 6x - 15

⇒  6x - 5x = 15 - 8

⇒  x = 7°

Substituting the value of x, We get :

∠FGH = 5(7) - 8 = (35 - 8) = 27°

∠HGI = 6(7) - 15 = (42 - 15) = 27°

∠FGI = ∠FGH + ∠HGI = (27 + 27) = 54°

Answer:

---

Step-by-step explanation:

(a+8)(a-3)

You multiply a*a and a*-3 first.

a²-3a

Then you multiply 8*a and 8*-3.

8a-24

Then combine.

a²-3a+8a-24

Combine like terms.

a²+5a-24

So dat the answer.

---

hope it helps

Answer:

See below

Step-by-step explanation:

(a+8)(a-3)

See image for extra explanation.

a * a = a^2

a * -3 = -3a

8 * a = 8a

8 * -3 = -24

a^2 - 3a + 8a - 24

a^2 + 5a - 24

Answer: 228 in3 (sorry I don’t know how to do the mini number at the top)

Answer:

its (0,-1) ...................................

Answer:

6 1/8 cups

Step-by-step explanation:

multiply both numbers together

Answer:

-25/3

Step-by-step explanation:

Answer:

a+52/3=9

a + 52/3 - 52/3 = 9 - 53/3

a=[tex]\frac{27- 53}{3}[/tex]

a= [tex]\frac{26}{3}[/tex]

Step-by-step explanation:

Answer:10

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

3^r = 19

Multiply each side by 3

3 * 3^r = 19 *3

We know that a^b * a^ c = a^ ( b+c)

3^1 * 3^r = 19 *3

3^(r+1) = 19*3

3^(r+1) = 57

Answer:

120 m squared

Step-by-step explanation:

Volume problems are very simple:

Just multiply the base x height x length

So 10 x 2 x 6, which is 120.

Therefore, the volume of this shape is 120 m squared.

Answer:

120 m

Step-by-step explanation:

Simply Multiply all the given measurements so

10m x 2m x 6m = 120m

So as simple as that.

Thank you! ^^

Answer:

5.78

19

Step-by-step explanation:

Let original population be, P = x

Growth in 12 years, A = 2x

Rate be = r

Time = 12years

Find the rate :

   [tex]A = P(1 + \frac{r}{100})^t[/tex]

 [tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]

The annual rate of increase of the population of this city is approximately 5.78.

Find  time in which the population becomes 3 times.

That is A = 3x

P = x

R= 5.78%

               [tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]

The population will grow to three times its current size in approximately 19years .

5.78% ,19 years are the answers.

2=(1+r)^12

r=(2)^(1÷12)−1

R=0.0578*100=5.78%

3=(1+0.0595)^t

t=log(3)÷log(1.0595)

t=19 years

Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky

exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.

The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.

Learn  more about exponential function here:https://brainly.com/question/2456547

#SPJ2

Answer:

= 140.544cm^2

Step-by-step explanation:

Given data

a is the radius=4cm

b is the lenght= 10cm

We two circles, hence the area of the circles is given as

Area= 2(πr^2)

Area= 2(3.142*4^2)

Area= 2(50.272)

Area= 100.544cm^2

Area of the rectangular shape= 4*10= 40cm^2

Hence the total area = 100.544+40

= 140.544cm^2

Answer:

Alternate Interior Angles

Step-by-step explanation:

Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.

Answer:

They are alternate interior angles

Step-by-step explanation:

<2 and <8 are inside the parallel lines and on opposite sides of the transversal

They are alternate interior angles

Answer:

I think it is 181m.

Step-by-step explanation:

[tex]by \: imagination \: you \: separate \: all \: the \: shapes[/tex]

you also name it .

I name the triangle area A

I name the rectangle area B

it is a triangle because it has different measurements on its sides.

I name the semi- circle area C.

[tex]area \: of \: a \: triangle \: = \\ \frac{1}{2} \times b \times h \\ \frac{1}{2} \times 5 \times 3 \\ \frac{1}{ 2} \times 15 \\ 7.5[/tex]

[tex]aea \: of \: a \: rectangle \: = l \times b \\ 5 \times 6 = \\ 30[/tex]

[tex]area \: of \: a \: semi \: circle \: = \frac{1}{2 } \times \pi \times {r}^{2} \\ \frac{1}{2} \times 3.14 \times 3 \times 3 \\ \frac{1}{2} \times 3.14 \times 9 \\ \frac{1}{2} \times \frac{314}{10} \times 9 \\ [/tex]

[tex]you \: then \: cancle \: 134 \: by \: 2[/tex]

[tex] = \frac{154}{10} \times 9[/tex]

[tex] = \frac{1431}{10} \\ 143.1[/tex]

[tex]you \: now \: add \: all \: the \: ares \: to \: get \: your \: full \: area \\ 7.5 + 30 + 143.1 \\ = 180.6 \\ to \: the \: nearest \: hundred \: will \: be \: 181m[/tex]

Answer:

A

Step-by-step explanation:

beacuse it is more reasonable hope this helps

Answer:

68

Step-by-step explanation:

4 out of 12 are blue.

Then 8 out 12 are not blue.

8 out of 12 is the same as the fraction 8/12 which can be reduced to 2/3.

2/3 of the birds are not blue.

2/3 of 102 = 2/3 * 102 = 68

Answer: 68

Answer:

13 degrees

Step-by-step explanation:

working out is attached

hope it helps:)

Answer:

look at picture.

Step-by-step explanation:

every angle in a triangle equals 180° and every straight line equals 180°. So you just take the angles given in each triangle and subtract from 180° to get the total of the 3rd angle.