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Pavel [41]
4 years ago
15

A rectangle is (2 x + 5) long and (x^2 - 3x + 1) wide. What is its area?

Mathematics
1 answer:
Stolb23 [73]4 years ago
3 0
Area of a rectangle is computed by multiplying its length and its width.

A = L * W
A = (2x+5)(x²-3x+1)
A = 2x(x²) + 2x(-3x) + 2x(1) + 5(x²) + 5(-3x) + 5(1)
A = 2x³ - 6x² + 2x + 5x² - 15x + 5
Group like terms:
A = 2x³ - 6x² + 5x² + 2x - 15x + 5
A = 2x³ - x² - 13x + 5   CHOICE A.

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Please help me! I really need help on this ASAP
andrey2020 [161]

Answer:

the vertex of the parabola is at the point; (5, -1)

which agrees with answer "B" in the list of options

Step-by-step explanation:

Notice that this is the equation of a parabola with branches that open horizontally (not vertically), since the variable the goes squared is the y-variable instead of "x".

By analyzing it we can then write it by isolating the term in "x" on one side of the equation, and use at the same time the fact that it is being written in "vertex" form:

-8\,(x-5)=(y+1)^2\\(x-5)=-\frac{1}{8} (y+1)^2

Therefore, the "y-value" of the vertex must be that which renders zero in the expression squared, that is y = -1. On the other hand, the x-value of the vertex is that which renders zero for the variable "x":  x=5.

Then, the vertex of the parabola is at the point; (5, -1)

8 0
3 years ago
What conic section is this 4x^2 +9y^2 =81?
Contact [7]
This follows the base equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

both of the variables are squared, and they're being added--you've got a circle.
3 0
4 years ago
A circle with area 81ㅠ has a sector with a central angle of 120°.
Mrac [35]

Answer:

<h2>84.78</h2>

Step-by-step explanation:

We have the area of a circle

A_O=81\pi

The sector with a central angle of

120^o

Calculate, what part of 360° is an angle 120°:

\dfrac{120^o}{360^o}=\dfrac{1}{3}

The same part of an area of a circle is an area of a segment.

Therefore:

A_S=\dfrac{1}{3}\cdot81\pi=27\pi

Use π ≈ 3.14

A_S\approx(27)(3.14)=84.78

4 0
4 years ago
Use the simple interest formula (I=PxRxT and Account= P+I) to find the interest joe will earn if he deposits $2500 in an account
OLEGan [10]

Answer:

$3175

Step-by-step explanation:

Substitute the equation with the numbers.

Interest = P x R x T

Interest = 2500 x 0.045 x 6

I = 675

Add the interest amount with the original amount.

675 + 2500 = 3175

I hope this helps and please mark me as brainliest!

8 0
2 years ago
Given that triangle LMN has side lengths of 20 inches, 10 inches, and 12 inches, prove triangle LMN is a right triangle. Explain
il63 [147K]

Answer:

It is not a right triangle. The hypotenuse is the biggest side so if you apply the Pythagorean Theorem formula it does not work.

Step-by-step explanation:

A² + B² = C² -------> 10² + 12²=20² --------> 100 + 144 = 400 ---> 244 = 400

8 0
3 years ago
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