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3 years ago

Simplify: 3u2 + 21u2

1 answer:

7 0

If you would like to simplify 3 * u^2 + 21 * u^2, you can calculate this using the following steps:

3 * u^2 + 21 * u^2 = (3 + 21) * u^2 = 24 * u^2

The correct result would be 24 * u^2.

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The point-slope form of a line that has a slope of –2 and passes through point (5, –2) is shown below.

Ilya [14]

Answer:

y =-2x+8

Step-by-step explanation:

We have a point and a slope

(5,-2) and m =-2

The slope intercept form of a line is

y = mx+b

y = -2x+b

Substitute in the point

-2 = -2(5)+b

-2 = -10+b

Add 10 to each side

-2+ 10 = -10+10 +b

8 = b

The equation is

y =-2x+8

8 0

3 years ago

Read 2 more answers

» Alexander has some watermelons. He gathers 13 more watermelons. He now has 62 watermelons.

Vilka [71]

Yeah but what is the question?

3 0

3 years ago

What is the slope between (-4,0) and (0,2)

zaharov [31]

The slope is y=1/2x + 2 or y= 0.5x+2

3 0

3 years ago

Read 2 more answers

Find sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B).

Reil [10]

Answer:

Part A) $sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}$

Part B) $tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) $sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}$

Step-by-step explanation:

Part A) Find $sin(\alpha)\ and\ cos(\beta)$

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sin(\alpha)=cos(\beta)$

Find the value of $sin(\alpha)$ in the right triangle of the figure

$sin(\alpha)=\frac{8}{14}$ ---> opposite side divided by the hypotenuse

simplify

$sin(\alpha)=\frac{4}{7}$

therefore

$sin(\alpha)=\frac{4}{7}$

$cos(\beta)=\frac{4}{7}$

Part B) Find $tan(\alpha)\ and\ cot(\beta)$

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$tan(\alpha)=cot(\beta)$

<em>Find the value of the length side adjacent to the angle alpha</em>

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

$14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132$

$x=\sqrt{132}\ units$

simplify

$x=2\sqrt{33}\ units$

Find the value of $tan(\alpha)$ in the right triangle of the figure

$tan(\alpha)=\frac{8}{2\sqrt{33}}$ ---> opposite side divided by the adjacent side angle alpha

simplify

$tan(\alpha)=\frac{4}{\sqrt{33}}$

therefore

$tan(\alpha)=\frac{4}{\sqrt{33}}$

$tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) Find $sec(\alpha)\ and\ csc(\beta)$

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sec(\alpha)=csc(\beta)$

Find the value of $sec(\alpha)$ in the right triangle of the figure

$sec(\alpha)=\frac{1}{cos(\alpha)}$

Find the value of $cos(\alpha)$

$cos(\alpha)=\frac{2\sqrt{33}}{14}$ ---> adjacent side divided by the hypotenuse

simplify

$cos(\alpha)=\frac{\sqrt{33}}{7}$

therefore

$sec(\alpha)=\frac{7}{\sqrt{33}}$

$csc(\beta)=\frac{7}{\sqrt{33}}$

6 0

4 years ago

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −3 and a local minimum value of 0 at

Vinvika [58]

The formula is f(x) = a x ^ 3 + b x ^ 2 + c x + d
f '(x) = 3ax^2 + 2bx + c.
f(- 3) = 3 ==> - 27a + 9b - 3c + d = 3
f '(- 3) = 0 (being a most extreme) ==> 27a - 6b + c = 0.
f(1) = 0 ==> a + b + c + d = 0
f '(1) = 0 (being a base) ==> 3a + 2b + c = 0.
-
Along these lines, we have the four conditions
- 27a + 9b - 3c + d = 3
a + b + c + d = 0
27a - 6b + c = 0
3a + 2b + c = 0
Subtracting the last two conditions yields 24a - 8b = 0 ==> b = 3a.
Along these lines, the last condition yields 3a + 6a + c = 0 ==> c = - 9a.
Consequently, we have from the initial two conditions:
- 27a + 9(3a) - 3(- 9a) + d = 3 ==> 27a + d = 3
a + 3a - 9a + d = 0 ==> d = 5a.
Along these lines, a = 3/32 and d = 15/32.
==> b = 9/32 and c = - 27/32.
That is, f(x) = (1/32)(3x^3 + 9x^2 - 27x + 15).

8 0

3 years ago