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2 years ago

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Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x.

Add: x 5 - 4x 4 + 7x 3 + 8, 9x 3 + 7x 2 - 10, and -2x 5 + 7x 4 - 3x + 8.

1 answer:

CaHeK987 [17]2 years ago

6 0

Answer:

$-x^5+3x^4+16x^3+7x^2-3x+6$

Step-by-step explanation:

Given polynomials are:

$x^5-4x^4+7x^3+8$ , $9x^3+7x^2-10$ and $-2x^5+7x^4-3x+8$

Now we need to add the given polynomials, then place the answer in the proper location on the grid. Also we need to write answer in descending powers of x.

So let's add them by combining like terms:

$x^5-4x^4+7x^3+8+9x^3+7x^2-10-2x^5+7x^4-3x+8$

$-x^5+3x^4+16x^3+7x^2-3x+6$

Hence final answer in descending order is $-x^5+3x^4+16x^3+7x^2-3x+6$

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i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

<u>Solving the trigonometry functions</u>

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

2 years ago

A rectangle with a width of 3 units and a length of x +5

Luden [163]

Answer:

The area is 45 units squared

Step-by-step explanation:

If the rectangle's width is 3 units, and the length is 5 times then:

5 x 3 = 15

So the length is 15 units

The area is length times width

15 x 3 = 45

The area is 45 units squared

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3 years ago

Add and round to the correct number of significant digits: 13.8 + 60 A.70

ArbitrLikvidat [17]

The correct answer is C

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What is 2937082 in expanded form

AnnZ [28]

The expanded form for this problem is <span><span> 200,000 </span><span>+90,000 +30,000</span><span>+7,000 </span><span>+50 </span><span>+8<span> </span></span></span>

7 0

2 years ago

What is the factorization of 3x^2 – 8x + 5?

I am Lyosha [343]

Answer:

Step-by-step explanation

Step 1: multiply the coefficient a and the constant c. Given that the general expression of a parabolic equation is ax^2+bx+c

3*5=15

Step 2: examine the coefficient b and try to find 2 numbers which you can multiply to get 15, add or subtract and get - 8

In this Case: - 3*-5=15 and - 3+(-5)= - 8

Step3:

You separate the equation in terms of the two factors you have found

3x^2-3x-5x+5=0

Step 4:Factorise

3x(x-1)-5(x-1)=0

(3x-5)(x-1)=0

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2 years ago