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marishachu [46]
3 years ago
15

The polynomial 3x ^ 3 - 16x ^ 2 + 31x - 20 the area of a trapezoidal desktop . Of the bases of the x ^ 3 - 5x the height of the

trapezoid? Hins: Use long division , what is trapezoid represented by the expressions trapezoid
Mathematics
1 answer:
vaieri [72.5K]3 years ago
6 0

Answer:

Step-by-step explanation:

Given:

Area = 3x^3 - 16x^2 + 31x - 20

Base:

x^3 - 5x

Area of trapezoid, S = 1/2 × (A + B) × h

Using long division,

(2 × (3x^3 - 16x^2 + 31x - 20))/x^3 - 5x

= (6x^3 - 32x^2 + 62x - 40))/x^3 - 5x = 6 - (32x^2 - 92x + 40)/x^3 - 5x = 2S/Bh - Ah/Bh

= 2S/Bh - A/B

= (2S/B × 1/h) - A/B

Since, x^3 - 5x = B

Comparing the above,

A = 32x^2 - 92x + 40

2S/B = 6

Therefore, h = 1

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Solve for x. 3/4 = x/12 <br> I need work shown to
marta [7]

\frac{3}{4} = \frac{x}{12}

To solve for x you have to bring the 12 to the other side

How  do we do this?

Well if you think about it this is technically what the equation shows

\frac{3}{4} = x * \frac{1}{12}

This means to isolate x you can multiply both sides by 12 and that will cancel \frac{1}{12} from the right side

\frac{3}{4} * 12 = x * \frac{1}{12} * 12

\frac{36}{4} = x * 1\\\frac{36}{4}  = x

\frac{36}{4} can be further simplified to...

9

^^^This is the answer

Check:

3/4 = 9/12

3/4 = 3/4

Hope this helped!

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4 0
3 years ago
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Sean can spend at most $15.00 on snacks. He has already spent $5.00. Which inequality could be solved to determine how much mone
Lady bird [3.3K]

Answer:

5 + x ≤ 15

Step-by-step explanation:

4 0
3 years ago
Calculate pt3 such that a line from pt1 to pt3 is perpendicular to the line from pt1 to pt2, and the distance between pt1 and pt
Leni [432]
Let the point_1 = p₁ = (1,4)
and      point_2 = p₂ = (-2,1)
and      Point_3 = p₃ = (x,y)

The line from point_1 to point_2 is L₁ and has slope = m₁
The line from point_1 to point_3 is L₂ and has slope = m₂
m₁ = Δy/Δx = (1-4)/(-2-1) = 1
m₂ = Δy/Δx = (y-4)/(x-1)
L₁⊥L₂ ⇒⇒⇒⇒ m₁ * m₂ = -1
∴ (y-4)/(x-1) = -1 ⇒⇒⇒ (y-4)= -(x-1)
(y-4) = (1-x) ⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒ equation (1)

The distance from point_1 to point_2 is d₁
The distance from point_1 to point_3 is d₂
d = \sqrt{Δx^2+Δy^2}
d₁ = \sqrt{(-2-1)^2+(1-4)^2}
d₂ = \sqrt{(x-1)^2+(y-4)^2}
d₁ = d₂
∴ \sqrt{(-2-1)^2+(1-4)^2} = \sqrt{(x-1)^2+(y-4)^2} ⇒⇒ eliminating the root
∴(-2-1)²+(1-4)² = (x-1)²+(y-4)²
 (x-1)²+(y-4)² = 18
from equatoin (1)  y-4 = 1-x
∴(x-1)²+(1-x)² = 18            ⇒⇒⇒⇒⇒ note: (1-x)² = (x-1)²
2 (x-1)² = 18
(x-1)² = 9
x-1 = \pm \sqrt{9} = \pm 3
∴ x = 4 or x = -2
∴ y = 1 or y = 7

Point_3 = (4,1)  or  (-2,7)












8 0
3 years ago
3. What is the measure of angle B from the right triangle below?
Talja [164]

Answer:

angle B = 78.46°

Step-by-step explanation:

Use the cosine ratio

cosB=\frac{2}{10} =0.2

B=cos^{-1} (0.2)=78.46^{0}

Hope this helps

8 0
1 year ago
The radius of a circle is 42 inches. What is the circle's area?<br> Use 3.14 for ​.
Mazyrski [523]

Answer:

A =5538.96 in^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

We know the radius is 42 and pi is approximated by 3.14

A = 3.14 * 42^2

A =5538.96 in^2

3 0
2 years ago
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