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pychu [463]
3 years ago
12

Determine the slope from the given graph below:

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
5 0
(0,-4) and (1,3)
3-1/-4-0
2/-4
-2
Your slope is -2
Hope that helped
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10. Determine the open interval(s) on which the function f(x) = 12x - x^3 is increasing.
Gre4nikov [31]

Answer:

\large\boxed{x\in(-2,\ 2)}

Step-by-step explanation:

f(x)=12x-x^3

Calculate the derivative of the function:

f'(x)=\left(12x-x^3\right)'=(12x)'-\left(x^3\right)'=12-3x^2

Calculate the zeros of the derivative:

f'(x)=0\Rightarrow12-3x^2=0\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2=12\qquad\text{divide both sides by 3}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2

Let's check the derivative sign:

f'(x)>0\iff12-3x^2>0\qquad\text{use the distributive property}\\\\-3(x^2-4)>0\\\\-3(x^2-2^2)>0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\-3(x-2)(x+2)>0\\^{\qquad x=2\qquad x=-2

Sketch a parabola open down

(before the brackets there is the number -3 < 0)

Look at the picture.

Where the derivative is negative, the function decreases.

Where the derivative is positive, the function increases.

Therefore your answer is:

x\in(-2,\ 2)

3 0
4 years ago
3. Suppose m4 = (3x + 5)º and m5 = (x +95), where x = 20. Are the lines parallel? Explain.
lions [1.4K]
No, 3(20)+5=65 and 20+95=115.
65 is not equal to 115; therefore they are not parallel because they are not congruent.
3 0
3 years ago
Find the value of y so that r⎹⎹ s A. 32 B. 56 C. 64 D. 124
Murrr4er [49]
Sorry i dont really understand this

5 0
3 years ago
Sarai wrapped a soccer
ololo11 [35]

Answer:

624 square inches of  cardboard were used to make the box.

Step-by-step explanation:

Slant height of the box = l = 20 inches

Side of the base of the box = s = 12 inch

Area of the base = s^2

Area of triangular face = \frac{1}{2}\times s\time l

There are 4 triangle faces, and single square base , so the total area is :

T=s^2+4\times \frac{1}{2}s\times h

=(12 inch)^2+4\times \frac{1}{2}\times 12 inch\times 20 inch

T=624 inch^2

624 square inches of  cardboard were used to make the box.

3 0
3 years ago
4.06 Question 5
AnnyKZ [126]
  • Adults be x
  • Campers be y

Total rooms =200

So inequality is given by

\\ \sf\longmapsto x+y\leqslant 200

Now

  • Adult costs 4$ and Camper costs 3\$

Inequality is given by

\\ \sf\longmapsto 4x+3y\leqslant 750

4 0
3 years ago
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