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3 years ago

Rst has vertices r(0,-4), s(-2,-1), and t(-6,1). Graph the image of rst for the translation (x,y). (X-4,y+7)

Mathematics

1 answer:

joja [24]3 years ago

4 0

You can directly plot the given points of the original image. As you can see in the attached picture, that would be the blue image. Now, to transform the points, simply follow the given instructions. For the x-coordinates, subtract 4 from the original x-coordinates. For the y-coordinates, add from the original y-coordinated. For example, Point R (0,-4) is transformed to Point R'(-4,3). The translated figure is the one in orange.

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What is the total area of the regions between the curves y = 6x2 − 18x and y = −6x from x = 1 to x=3?.

kvasek [131]

Using integration, it is found that the area between the two curves is of 22 square units.

<h3>What is the area between two curves?</h3>

The area between two curves y = f(x) and y = g(x), in the interval from x = a to x = b, is given by:

$A = \int_{x = a}^{x = b} |f(x) - g(x)| dx$

In this problem, we have that:

$f(x) = 6x^2 - 18x, g(x) = -6x, a = 1, b = 3$ .

Hence, the area is:

$A = \int_{1}^3 |6x^2 - 12x| dx$

$A = |x^3 - 6x^2|_{x = 1}^{x = 3}$

Applying the Fundamental Theorem of Calculus:

$A = |3^3 - 54 - 1^3 + 6|$

$A = 22$

The area between the two curves is of 22 square units.

More can be learned about the use of integration to find the area between the two curves at brainly.com/question/20733870

8 0

3 years ago

What is the Hypotenuse of 12mi and 16mi

stich3 [128]

20mi

H^2 = 12^2 + 16^2
H^2 = 144 + 256
H^2 = 400

H = square root of 400 = 20

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3 years ago

Brittany spent 68 hours in an 8-week period doing homework. what is the rate for the number of hours to the number of weeks

Amanda [17]

Answer: C- 17 hrs /2 weeks

Step-by-step explanation:

Write the number of hours in the numerator and the number of weeks in the denominator.

68 hrs/8 weeks

Simplify by dividing 4 into both the numerator and denominator.

68/8 = 17/2

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