The integral represents the volume of a solid. describe the solid. π π 0 sin(x) dx

Use scalar multiplication to determine the coordinates of the vertices of the dilated figure. Then graph the pre-image and the i

Luba_88 [7]

Answer:

The coordinates of the vertices of the dilated figure are:

A' is (-2 , 4), B' is (4 , 8), C' is (4 , -2), D' is (-2 , -6) ⇒ the answer is (d)

Step-by-step explanation:

* Lets study the matrix of the dilation

- If we dilate any point by scale factor k we multiply the

coordinates of the point by k

- The matrix of the dilation by scale factor k is

$\left[\begin{array}{ccc}k&0\\0&k\end{array}\right]$

* Now lets solve the problem

- We will multiply the matrix of dilation by the matrix of the

vertices of the quadrilateral

- The dimension of the matrix of the dilation is 2×2 and the

dimension of the matrix of the vertices of the quadrilateral

is 2×4 then the dimension of the matrix of the image of the

quadrilateral is 2×4

∵ The scale factor is 2

∴ The matrix of dilation is $\left[\begin{array}{cc}2&0\\0&2\end{array}\right]$

∵ The matrix of the vertices of the quadrilateral is

$\left[\begin{array}{cccc}-1&2&2&-1\\2&4&-1&-3\end{array}\right]$

∴ The image of the quadrilateral is :

$\left[\begin{array}{cc}2&0\\0&2\end{array}\right]\left[\begin{array}{cccc}-1&2&2&-1\\2&4&-1&-3\end{array}\right]=$

$\left[\begin{array}{cccc}(2)(-1)+(0)(2)&(2)(2)+(0)(4)&(2)(2)+(0)(-1)&(2)(-1)+(0)(-3)\\(0)(-1)+(2)(2)&(0)(2)+(2)(4)&(0)(2)+(2)(-1)&(0)(-1)+(2)(-3)\end{array}\right]=$

$\left[\begin{array}{cccc}-2&4&4&-2\\4&8&-2&-6\end{array}\right]$

∴ The image of point A' is (-2 , 4)

∴ The image of point B' is (4 , 8)

∴ The image of point C' is (4 , -2)

∴ The image of point D' is (-2 , -6)

* The right answer is figure (d)

3 0

3 years ago

A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme

Ipatiy [6.2K]

Answer:

See below

Step-by-step explanation:

Gas in liquid state at

- 40° F < t < 140° F

The graph is the line segment from the point -40 to 140 on the number line, with both points open circles and shaded in between those 2 points

Solution set is all numbers greater that -40 and smaller than 140.

-49° F is smaller than -40° F, so the gas would freeze

8 0

4 years ago

Need help please, Algebra 1/Polynomials

expeople1 [14]

It's the first choice. If you multiply the first equation by 3, your y term is a +12, and if you multiply the second equation by 4, your y term is a -12. When you add them the y terms cancel each other out.

3 0

3 years ago

a triangle has sides 35cm, 54cm and 61cm long. find it's area, also find the smallest of its altitudes

KiRa [710]

Whats the length, base and height of the triangle

4 0

3 years ago

A point P lies on the line with equation y= 4-3X. The point P is a distance √34 from the origin. Find the two possible positions

Oksi-84 [34.3K]

The two possible positions of point P are:

(3, -5) and (0.6, 5.8)

<h3>How to find the two possible positions of point P?</h3>