A rectangle has vertices at P (16,16), Q(16,-16), R(-16,-16) and S(-16,16). The origin is the center of dilation and the rule of a dilation is (x,y)→(1/4x, 1/4y) What is P' of the dilated image, PQ’R’S’?

Answer:

Lateral areas have ratio of 4:1

Volumes have ratio of 8:1

Step-by-step explanation:

There is a rule in 3D geometry that when two solids are similar, and their edges are in the ratio of [tex]a:b[/tex], the ratio of any surface area type measure is always [tex]a^2:b^2[/tex] this includes the lateral area, which is just a surface area minus the base, which is not important for this problem. The ratio of volumes of those similar solids is in the ratio of [tex]a^3:b^3\\[/tex].

Now, to solve this, we need to find the ratio of any corresponding length of these similar pyramids. We have both the heights, so if we form a ratio of [tex]\frac{5\frac{1}{2} }{2\frac{3}{4} }[/tex] which if you simplify it, it is [tex]\frac{5.5}{2.75}[/tex], which is [tex]2[/tex]. The ratio of the heights are [tex]2:1[/tex].

Now we can apply those rules to this ratio, the ratio of lateral areas would then be [tex]2^2:1^2[/tex], which is [tex]4:1[/tex]. the ratio of volumes would be [tex]2^3:1^3[/tex], which is [tex]8:1[/tex]

Answer:

u equals 3.43 because you subtract from both sides.

Answer:

FG = 44

EG = 80

Step-by-step explanation:

For FG:

1) 5z - 16 = 3z + 8

2) 5z = 3z + 24

3) 2z = 24

4) z = 12

5) 3(12) + 8 = 44

For EG:

1) 2w + 22 = 4w + 4

2) 2w = 4w - 18

3) -2w = -18

4) w = 9

5) 4(9) + 4 + 2w + 22 = 80

Answer:

all these answer choices are wrong? if there are 8 female students and 20 students total then it will be 8/20 which can be simplified to 4/10 or 2/5.  

Step-by-step explanation:

8 females/ 20 students

Question

( 10 + 5x )7

Lets solve this easily.

So, basically, 10 + 5x is 15 but we still didn't

get rid of the x so therefore it's still 15x and then there's 7 so we multiply 15 x 7 giving us 105x.

Hence, the answer is.

(C), 70 + 35x is the answer.

Answer:

no

Step-by-step explanation:

Its not possible to make 5 pieces with only 2 cuts. Anyway you use your two cuts would not result in 5 pieces

Answer:

No It's Not Possible To Make It 5 Pieces And 2 cuts

Answer:

i dont see the angles but heres how to solve for X

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

[tex] - 5(4x - 2) = - 2(3 + 6x)[/tex]

[tex]20x - 10 = 6 + 12x[/tex]

[tex]8x = 16[/tex]

[tex]x = 2[/tex]

Answer:

x=2

Step-by-step explanation:

-5(4x-2)=-6-12x

-20x+10=-6x-12x

-8x=-16 | : (-8)

x= 2

Answer:

Arc RP is 125 degrees, arc QS is also 125 degrees, and I think the ast one would be 110 degrees

Step-by-step explanation:

Answer:

None.

Step-by-step explanation:

let's check it

- 2a + 2a + 7 = 8

7≠ 8

So there's no solution for the given equation.

Answer:

Yes its correct!

Step-by-step explanation:

The number in question is 7.5

Step-by-step explanation:

15 ÷ 2 = 7.5

Why divide by 2? Because dividing by 2 is the inverse of multiplying by 2. To double-check our solution, just multiply 7.5 by 2... and 15!!

Answer:

is there any more information you could give?

Step-by-step explanation:

**i promise to provide a real answer**

Answer:

7 children and 3 adults

Step-by-step explanation:

We should set up a system of equations for this problem, so let's say that:

x represents the number of children

y represents the number of adults

We know there is a total of 10 people, so:

x + y = 10

We also know that each adult had to pay $22.50 and each child had to pay $12.50. Their total amount paid is $155.00, so:

12.50x + 22.50y = 155.00

Simplifying this a bit:

12.5x + 22.5y = 155

Now, we can use the substitution method to solve this system of equations:

x + y = 10

y = 10 - x

12.5x + 22.5y = 155

12.5x + 22.5 (10 - x) = 155

12.5x + 225 - 22.5x = 155

12.5x - 22.5x = 155 - 225

-10x = 155 - 225

-10x = -70

x = [tex]\frac{70}{10}[/tex]

x = 7 children

Now we substitute back into the system of equations:

x + y = 10

7 + y = 10

y = 10 - 7

y = 3 adults

Answer:

Answer is 5

Step-by-step explanation:

x+2x+3x=30

6x=30

x=5

Answer:

a.(89-5)divided by 6 = 14 b. 14

Step-by-step explanation:

a.

Answer:

thanx

Step-by-step explanation:

Answer:

Sample space is the collection of all possible events.

So, sample space of tossing two coins, S=(H,T),(T,T),(T,H),(H,H)

Step-by-step explanation:

Answer:

y=-7x+9

Step-by-step explanation:

Answer:

2/3 of the class are boys

Step-by-step explanation:

16+8 is the total class which is 24 students.

To write it as a fraction it would be 16/24 (simplified is 2/3)

Answer:

equivalent

Step-by-step explanation:

when you divide the second one by 2 you'll get the first one

Answer:

1/7

Step-by-step explanation:

Formula for 2 perpendicular lines: m1 * m2 = -1,

where m1 is gradient of 1st line and m2 is gradient of 2nd line

Application:

-7 * m2 = -1

m2 = 1/7

Answer:

X》55

Step-by-step explanation:

hope it helps u

have a great day!!

Answer:

Step-by-step explanation:

A line can be defined by any two points on the line andhas the form

y=mx+b

Where m=slope and b=y intercept (value of y when x=0)

Slope is defined as

m=(y2-y1)/(x2-x1), we have points (0,7) and (1,4)

m=(4-7)/(1-0)

m=-3/1

m=-3 so the line is thus far

y=-3x+b, since we have the point (0,7) we know that b=7 so the line is

y=-3x+7

Answer:

x = 8.92 units

Step-by-step explanation:

From the triangle given in the picture,

Missing side of the triangle is the opposite side of the angle measuring 28°

And hypotenuse measuring 19 units has been given.

So, we will use sine ratio for the given angle.

sin(28°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

sin(28°) = [tex]\frac{x}{19}[/tex]

x = 19sin(28°)

x = 8.92 units

Answer:

-5 degrees! If you did 20-25 it would get you -5! Hope this helps :)

Step-by-step explanation:

Answer:

4/100

Step-by-step explanation:

0.04 = 4/100

Answer:

no it is not

Step-by-step explanation:

i drew the line bc in order for it to be a function there would have to be only one point in each line

hopefully this helps :)

have a nice day !!

Answer:

A and F are both correct

Step-by-step explanation:

0 and -1 are both greater than -3

Answer:

Around 5.5 or 5 1/2

Step-by-step explanation: