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3 years ago

Question from my math test.

Mathematics

2 answers:

zmey [24]3 years ago

7 0

Answer:

$5.50

Step-by-step explanation:

We can list out some values and continue this pattern until we reach 11 pages.

2 pages costs $1

4 pages costs $2

6 pages costs $3

8 pages costs $4

These are all points described by your graph. We will notice that every two pages costs $1, which also means that each additional page costs $0.50

This means that:

10 pages costs $5

and

11 pages costs $5 + $0.50 = $5.50

zavuch27 [327]3 years ago

4 0

Answer:

5.5

Step-by-step explanation:

1 = 0.5

2 = 1

x1/2

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A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m². The surface area of the image is 315 m². T

Westkost [7]

The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

<h3>How does dilation affect length, area, and volume of an object?</h3>

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly,

Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that;

Surface area of pre-image = 35 m²
Surface area of dilated image = 315 m²
Height of pre-image = 5.8 m
Height of dilated image.

Let the scale fator of dilation be k.

Then:

So area of pre-image = k² × area of dilated image

Thus, we get:

$35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3$

(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)

Thus, we get:

Height of pre-image = (1/3) × Height of dilated image (say h)

$5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m$

Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

Learn more about dilation here:

brainly.com/question/3266920

4 0

2 years ago

Read 2 more answers

Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*

Veronika [31]

Answer:

The area of the triangle DEF is 10.

Step-by-step explanation:

Area of a Triangle:

A triangle of base B and height H (both must be perpendicular) has an area of:

$\displaystyle A=\frac{BH}{2}$

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

$\displaystyle A=\frac{5*4}{2}=10$