A window in the shape of a parallelogram has the dimensions given.

What is the area of this window?




20 ft²

24 ft²

28 ft²

40 ft²

Answer:

✓ ✓ ✓

-6 X X✓ ✓ ✓

-6 X X

Given:

The scale factor is [tex]s=\dfrac{1}{3}[/tex] and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

[tex](x,y)\to (k(x-a)+a,k(y-b)+b)[/tex]

According to the given information, the scale factor is [tex]\dfrac{1}{3}[/tex] and the center of dilation is at (4,2).

[tex](x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)[/tex]            ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

[tex]C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)[/tex]

[tex]C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)[/tex]

[tex]C(-2,11)\to C'(-2+4,3+2)[/tex]

[tex]C(-2,11)\to C'(2,5)[/tex]

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

[tex]A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)[/tex]

From the given figure it is clear that the image of point A is (8,4).

[tex]A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)[/tex]

On comparing both sides, we get

[tex]\dfrac{1}{3}(m-4)+4=8[/tex]

[tex]\dfrac{1}{3}(m-4)=8-4[/tex]

[tex](m-4)=3(4)[/tex]

[tex]m=12+4[/tex]

[tex]m=16[/tex]

And,

[tex]\dfrac{1}{3}(n-2)+2=4[/tex]

[tex]\dfrac{1}{3}(n-2)=4-2[/tex]

[tex](n-2)=3(2)[/tex]

[tex]n=6+2[/tex]

[tex]n=8[/tex]

Therefore, the coordinates of point A are (16,8).

Answer:

y = -x + 30

Step-by-step explanation:

You will want to put the equation in the form y = mx + b where m is the slope and b is the y-intercept (an example is y = 2x - 1).

First, to find the slope you want to find how much x goes up by when y goes up by 1. You know from the table that when y goes up by 5, x goes up by -5 (using the points (10, 20) and (5, 25))

Then, you can divide each value by 5, so it would be when y goes up by 1, x goes up by -1. That means the slope is -1.

So far, the equation is y = -x + b. To find b, you can plug in one of the points you have and solve for b. For example, substitute in x = 10 and y = 20, so:

20 = -10 + b

add 10 to both sides

30 = b

So you know the equation is y = -x + 30

Please let me know if any parts of these explanation are confusing, I definitely think this concept can be confusing at time. Good luck with your work! :)

Answer:

To create an equation, you need to find the slope first. The slope formula is [tex]\frac{y^2-y^1}{x^2-x^1}[/tex]. Let's use two random coordinates: (10,20) and (5,25). Plug in these digits into the formula to get [tex]\frac{25-20}{5-10}[/tex]. Simplify to get [tex]\frac{5}{-5}[/tex] or -1. The equation would look like y=-x+b. Now we need to find b. Again, let's use a random coordinate: (10,20). Plug in the digits into the variables to get 20=-10+b. Add 10 on both sides to get 30=b. So, the equation would be y=-x+30.

Answer:

option A is the answer hope you find it helpful

Answer:

WHY?

Step-by-step explanation:

i need 1 MORE BRAINLIEST!!!

Answer:

D, 180.

Step-by-step explanation:

2400 divided by 200 is 12, which means 2400 is 12 times 200

Next, times 15 by 12 which is 180.

Answer:

1. Given

2. Reflection property of congruence

3. Definition of a a midpoint

4. Reflexive property of congruence

5. CPCTC

Step-by-step explanation:

Answer:

7.4% increase (approximated)

Step-by-step explanation:

✔️Dimension of the original rectangle:

Length = 30 cm

Width = 20 cm

Perimeter = 2(L + W) = 2(20 + 30) = 2(50) = 100 cm

✔️Dimension of new rectangle:

Length is increased by 10% = 10/100 × 30cm = 3 cm

New length = 30 + 3 = 33 cm

Width is increased by 5% = 5/100 × 20cm = 1 cm

New width = 20 + 1 = 21 cm

✔️Perimeter of New rectangle = 2(L + W) = 2(33 + 21) = 2(54) = 108 cm

✔️Percentage increase in the perimeter of the rectangle = (perimeter of New rectangle - perimeter of original rectangle)/perimeter of original rectangle × 100

= (108 - 100)/108 × 100

= 8/108 × 100

≈ 7.4% increase

Answer:

Step-by-step explanation:

discount = 65% of $37.35 = 0.65×37.35 ≅ $24.28

sale price = $37.35 - 24.28 = $13.07

Answer:

4567890

Step-by-step explanation:

this is not correct

Answer:

2

Step-by-step explanation:

Answer:

4.50r + 6.00f ≤ 35.00

Step-by-step explanation:

5x³ - 45x

5x(x² - 9)

Or 5x(x-3)(x+3)

[tex]\tt{} {5x}^{2} - 45x[/tex]

[tex]\tt{}5x \times ( {x}^{2} - 9)[/tex]

[tex]\tt{}5x \times (x - 3) \times ( x + 3)[/tex]

Answer:

9

Step-by-step explanation:

i did the same thing on k12

Answer:

$1456.25

Step-by-step explanation:

Given data

P= $1,250

t= 3 years

r=5.5%

The compound interest expression is given as

A= P(1+r)^t

substitute

A=  1250(1+0.055*3)

A=  1250(1+ 0.165)

A= 1250(1.165)

A= 1456.25

Hence the amount after 3 years is $1456.25

Answer:

#1

Zeroes: x = 4, x = -6

The vertex is at ( -1 , 50 )

Step-by-step explanation:

I'll do the first one, you try the rest

All of these are written in y = a(x - x1)(x - x2) where x1 and x2 are given and x are the two different zeroes (or x-intercepts)

f(x) = -2(x-4)(x+6)

The zeroes are x - 4 = 0 and x + 6 = 0 if you solve, you get 4 and -6

Zeroes: x = 4, x = -6

The x value of the vertex can be found using -b/2a (in the form ax^2 + bx + c)

First expand f(x)

-2(x^2 + 2x - 24) => -2x^2 - 4x + 48

b = -4 and a = -2

-(-4)/2(-2) = 4/-4 = -1

the x-value of the vertex is -1

Now substitute -1 as x to find the y-value of the vertex

-2(-1-4)(-1+6) = -2(-5)(5) = 50 <= y-value of vertex

The vertex is at ( -1 , 50 )

Answer:

7. b = 3

8. m = -2

9. c = -5

Step-by-step explanation:

1. There would be 2 slices as the denominator is 2.

2. There would be 5 slices as the denominator is 5.

3. As each slice gets smaller, the denominator gets bigger, because the bigger the denominator is, the more pieces it needs to make a whole.

Hope this helps :)

There are 2 pieces if each slice is 1/2 of a loaf, and 5 pieces if each slice is 1/5 of a loaf, and the total number of pieces get increases if each slice gets smaller.

When fractions are represented on a number line, we can plot them on a number line just like we can with whole numbers and integers. Parts of a whole are represented by fractions. In order to depict fractions on a number line, equal pieces of a whole are divided.

Given A loaf of bread is cut into slices.

1. If each slice is 1/2 of a loaf, how many slices are there,

here slices are  1/2 of the loaf so the loaf is divided into two equal parts,

1/2 + 1/2 = 1

2. If each slice is 1/5 of a loaf, how many slices are there,

here loaf has 5 equal parts,

1/5 + 1/5 + 1/5 +1/5 + 1/5 = 1 loaf

3. What happens to the number of slices as each slice gets smaller?

the value of the denominator in fraction goes on increasing and since the value is increasing the number of slices also gets increases.

Hence there are 2 pieces for 1/2 of the loaf,

5 pieces for 1/5 of the loaf,

and the number of slices increases when each slice gets smaller.

Learn more about fractions on number lines;

https://brainly.com/question/17658856

#SPJ5

Answer: it would be B "4.05"

Step-by-step explanation:

2.5 x 1.8 x 0.9 = 4.05

Answer:

4.05 m^3

Step-by-step explanation:

Calculate volume with this formula:

LxWxH (length x width x height)

0.9 x 2.5 x 1.8 = 4.05

Don't forget the unit! It's m^3 or m³ since we are finding the volume of a three-dimensional figure.

So our answer is 4.05 m^3.

Answer:

(-.5)

Step-by-step explanation:

Answer:

Please find attached the required triangle drawn with Microsoft Visio

Step-by-step explanation:

The isosceles triangle ΔPQR we are to construct has the following parameters;

∠PQR = 90°

Length of side hypotenuse PR = 4 cm

Therefore, given that the triangle is right triangle is an isosceles triangle the length of each of the side legs are equal

Therefore, we have;

Length of PQ = Length of QR

The length of the legs , [tex]\overline {PQ}[/tex] and [tex]\overline {QR}[/tex], are given by Pythagoras's theorem as follows;

[tex]\overline {PR}[/tex] = √([tex]\overline {PQ}[/tex]² + [tex]\overline {QR}[/tex]²) = √([tex]\overline {PQ}[/tex]² + [tex]\overline {PQ}[/tex]²) = [tex]\overline {PQ}[/tex]·√2

∴ [tex]\overline {PQ}[/tex] = 4 cm/(√2) = 2·√2 cm = [tex]\overline {QR}[/tex]

The required triangle drawn with Microsoft Visio is attached

Answer:

4/35, 0.114, 11.4%

Step-by-step explanation:

Answer:

x = -1.791 and x = 2.791

Step-by-step explanation:

Graphing x^2 - x - 2 = 3

we got 2 intersects at x = -1.791 and x = 2.791

Answer:

I dont know if this is the right answer hehe

Answer:

51.2 dollars

Step-by-step explanation:

you have to multiply 6.40 by 8

Answer:

1.50x+10=34

Step-by-step explanation:

Answer:

0.15

Step-by-step explanation:

6 divided by 24 equals 0.25

12 divided by 30 equals 0.4

0.4 minus 0.25 is 0.15

Answer:

8.5

Step-by-step explanation:

BF * EF = CF * DF

7 * 17 = CF * 14

119 = CF * 14

CF = 119 / 14

CF = 8.5

Answer:

area of the rectangle =8*15=120sq.m

area of semi circle =1/2*π*4*4

=1/2*22/7*4*4=22/7*8=176/7=2.51sq.m

Answer:

5544cm (squared)

Step-by-step explanation:

Surface area of a sphere=4πr  (squared) =4×  7/ 22 ×21×21cm  (squared)  

Surface area of the sphere=5544cm  

.

Answer:

Area = 5164.8 cm; volume = 38792.4 centimeters

Step-by-step explanation:

Since the radius is known, we can substitute it for r in the first formula.

A = 4πr²

A = 4π(21)²

A = 4π(411)

A = 12.566370614359 * 411

A = 5164.8

V = 4/3πr^3

V = 4/3π21^3

V = 4/3π(9261)

V = 4.1887902047863 * 9261

V - 38792.4