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3 years ago

Need help with both plz help me it is turn in by 12:10

Mathematics

2 answers:

Bumek [7]3 years ago

7 0

The first question is the 64 trucks and 80 cars. The second is the ratio 3:5

NNADVOKAT [17]3 years ago

5 0

Answer:

The first question is the 64 trucks and 80 cars. The second is the ratio 3:5

Step-by-step explanation:

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Will mark brainliest!!! Solve for x and plz do both

sladkih [1.3K]

Answer:

8. 64.23

10. 51.317

Step-by-step explanation:

tan^-1(29/14) = 64.23

cos^-1(25/40) = 51.317

7 0

3 years ago

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

A company has $14,000 in liabilities and $15,000 in equity. Calculate the company's debt to equity ratio as a percentage.

liberstina [14]

The required debt-equity ratio is 14:15

Solution:

Given:

Liabilities of the company = $14000

Equity of the company = $15000

To calculate: The debt-equity ratio

Here, the liabilities are included in the debt of the company. The debt-to-equity (D/E) ratio is calculated by dividing a company's total liabilities by its shareholder equity. Therefore, the debt equity ratio is as follows,

$\text { Debt Equity ratio }=\frac{\text { Debt }}{\text { Equity }}=\frac{14000}{15000}=\frac{14}{15}$

$\text { Debt Equity ratio }=\frac{14}{15} \rightarrow 14: 15$

The debt-equity ratio reflects the ability of shareholder equity to cover all outstanding debts in the event of a business downturn.

5 0

3 years ago

Pls help on this too

Nata [24]

Is there more of the picture you can show us?

5 0

2 years ago

Add these mixed numbers -Thanks!

alina1380 [7]

1. 6 1/2
2.4 1/2
3. 9 1/3
4. 9 1/2
5. 9 6/8
6. 6 1/2
(For the adding ones ) I also simplified them.

7 0

3 years ago