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3 years ago

Need help with dilation with a scale factor of 1/2 centered at (−1, 3)

Mathematics

1 answer:

Studentka2010 [4]3 years ago

4 0

A scale factor of 1/2 makes the triangle half the size of the original.

The original is 4 units tall, so 1/2 scale makes the new one 2 units tall.

It is 6 units long, so 1/2 would be 3 units long.

Now since the scale factor is centered at (-1,3) fine the midpoint between The top left corner of the triangle and the center point:

Midpoint ( -1-5/2 , 3+7/2)

Midpoint = (-6/2 , 10/2)

Midpoint = -3,5

This is where the top left corner of the scaled triangle would be.

See attached picture:

You might be interested in

one night a theater sold 548 movie tickets. an adult’s costs $6.50 an child’s cost $3.50. in all, $2,881 was takin in. how many

gavmur [86]

Answer:

321 adult tickets
227 child tickets

Step-by-step explanation:

This sort of problem is easily solved by defining a variable to be the quantity of the higher-value contributor. Here, we can let x represent the number of adult tickets. Then total revenue is ...

6.50x +3.50(548-x) = 2881

3x +1918 = 2881 . . . . . . . . . . . . eliminate parentheses, collect terms

3x = 963 . . . . . . . . . . . . . . . . . . subtract 1918

x = 321 . . . . . . . . . . . . . . . . . . . . divide by 3

548-x = 548 -321 = 227 . . . . . .number of child tickets

321 adult tickets and 227 child tickets were sold.

3 0

2 years ago

What is 36 divided by 1.5 in long division

Tatiana [17]

Answer: 24

To calculate with long division when the divisor is a decimal, add zeroes in both the dividend and divisor. This means you get 360 ÷ 15.

From here, just do normal calculation and you get 24 as your answer.

4 0

2 years ago

Ewen has 48 whistle tiles and 16 blue tiles the cost of each white tile was £2 and the cost of each blue tile was £4 Work out th

AnnZ [28]

Answer:

3:2

Step-by-step explanation:

Ewen has 48 white tiles and 16 blue tiles

The cost of each white tile was £2

The cost of each blue tile was £4

Therefore the total cost of 48 white tiles is

= 48×2

= £96

The total cost of 16 blue tiles is

= 16×4

= £64

The ratio of the total cost of the white tiles and blue tile can be calculated by dividing the cost of both tiles by their greatest common factor

The greatest common factor of £96 and £64 is 32

96/32 = 3

64/32= 2

Ratio= 3:2

Hence the ratio of the total cost of the white tiles to the blue tiles is 3:2

6 0

2 years ago

Here is a rectangle which has a width of x cm. x cm

miskamm [114]

Answer:

278.25 cm2

Step-by-step explanation:

If the width of the rectangle is x (cm), as the length is 8cm longer, so that the length of the rectangle is: x + 8 (cm).

In the attached image, we can see the length of each side. Total length of the sides are 90 cm.

=> (x + x + 8) + x + 8 + (x+8) + (x + x + 8) + x + 8 + (x +8) = 90

=> 8x + 48 = 90

=> 8x = 90 - 48 = 42

=> x =42/8 = 5.25 (cm)

=> The width of the rectangle is 5.25cm

=> The length of the rectangle is: 5.25 + 8 = 13.25 cm

=> The area of one rectangle is: Length x Width = 5.25 x 13.25 = 69.5625 cm2

As the 8-sided shape is made from 4 rectangles, so that:

Area of 8 sided shape = 4 x Area of the rectangle = 4 x 69.5625 = 278.25 cm2

6 0

2 years ago

What is the value of b in the equation (y)*

KonstantinChe [14]

Answer:

b = -6

Step-by-step explanation:

Apply the exponent rule that $\frac{1}{x^{n}} = x^{-n}$

In this case, $\frac{1}{y^{24}} = y^{-24}$

Set that equal to $(y^{b})^{4}$ :

$(y^{b})^{4} = y^{-24}$

Apply the exponent rule that $(x^{m})^{n} = x^{mn}$ so now you get:

$y^{4b} = y^{-24}$

Since the base is y for both sides of the equation, just set the exponents equal to each other and solve for b.

4b = -24

divide each side by 4 to get:

b = -6

6 0

2 years ago