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3 years ago

Graph a line through the point (-3, 2) with a slope of -2/5 .

Mathematics

1 answer:

alexira [117]3 years ago

7 0

Answer:

y = $-\frac{2}{5} x$ $-\frac{16}{5}$

Some of the points on the graph are: (0,-3.2),(-8,0),(2,-4), and (-3,-2)

Step-by-step explanation:

https://www.d esmos.com/calculator/jx7d3ews7b

Brainly has been acting up. It won't let us paste links.

So when copying and pasting the link above, remove the space between d and e to get the graph.

Hope that helps!

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Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet

frosja888 [35]

There seems to be one character missing. But I gather that f(x) needs to satisfy

• $x^3$ divides $f(x)$

• $(x-1)^3$ divides $f(x)^2$

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

$f(x) = x^5 + \cdots$

Since $x^3$ divides $f(x)$ , and

$f(x) = x^3 p(x)$

where $p(x)$ is degree-2, and we can write it as

$f(x)=x^3 (x^2+ax+b)$

Now, we have

$f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2$

so if $(x - 1)^3$ divides $f(x)^2$ , then $p(x)$ is degree-2, so $p(x)^2$ is degree-4, and we can write

$p(x)^2 = (x-1)^3 q(x)$

where $q(x)$ is degree-1.

Expanding the left side gives

$p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2$

and dividing by $(x-1)^3$ leaves no remainder. If we actually compute the quotient, we wind up with

$\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}$

If the remainder is supposed to be zero, then

$\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}$

Adding these equations together and grouping terms, we get

$(a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1$

Then $b=-1-a$ , and you can solve for a and b by substituting this into any of the three equations above. For instance,

$2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1$

So, we end up with

$p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}$

6 0

3 years ago

Nia answered 80% of the 40 questions on a test correctly. How many correct answers did she have?

Step2247 [10]

Nia answered correct answers = 80% of the 40 questions

When we remove % sign from a number, we divide that number by 100

= $\frac{80}{100}$ of 40

= $\frac{80}{100} \times 40$

Cancelling the two zeroes from numerator and denominator,

= $8 \times 4$

= 32.

Total correct answers answered by Nia = 32

3 0

3 years ago

Read 2 more answers

Please help this is urgent

Sergio [31]

Answer is
B 1/4 W = 6

----------------------------

4 0

3 years ago

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Suppose j varies jointly with g and v, j=1 when g=6 and v=3. Find j when g=8 and v=11

Lady bird [3.3K]

j=4.88 when g=8 and v=11

Further explanation:

When the increase/decrease in one quantity cause increase/decrease in other quantity, it is called direct variation.

Variation is always accompanied by a variation constant.

Given

g and v vary directly with j

IT can be written as:

j∝gv

Putting the variation constant k

j = kgv

Putting g = 6 and v=3

$j = kgv\\1 = k * 6 * 3\\1 = 18k\\k = \frac{1}{18}$

So the value of k is 1/18 which makes the equation

$j = \frac{1}{18}gv\\ Putting\ g=8\ and\ v=11\\j = \frac{1}{18} * 8 * 11\\j = \frac{88}{18}\\ j =4.88$

So, j=4.88 when g=8 and v=11

Keywords: Variation, Direct Variation

Learn more about variation at:

#LearnwithBrainly

8 0

3 years ago

What happens to the volume of a cylinder when the radius is doubled?

wlad13 [49]

When the radius is doubled, the volume of a cylinder quadruple

5 0

3 years ago

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