Simplify, answer should have only positive exponents.

If the Kramers spent $2,905 on their auto expenses,auto expenses are 7% of house hold expenses, what was their total income for

dimaraw [331]

37,300.20 Because 7% is 0.07 and then you multiply that by 2905 which is 203.35 and add that by 2905 which is 3108.15 then multiply that by 12 months

8 0

3 years ago

The points (7,r) and (8,9) fall on a line with a slope of 5. What is the value of r?

mrs_skeptik [129]

Answer:

r = 4

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to 5

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (7, r ) and (x₂, y₂ ) = (8, 9)

m = $\frac{9-r}{8-7}$ = $\frac{9-r}{1}$ = 9 - r = 5 ( subtract 9 from both sides )

- r = - 4 ( multiply both sides by - 1 )

r = 4

7 0

3 years ago

Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)

Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial $p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17$ . The polynomial is in standards when has the form $p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}$ , where $n$ is the order of the polynomial. The example has the following information:

$n = 3$ , $a_{0} = 17$ , $a_{1} = -6$ , $a_{2} = 2$ , $a_{3} = 5$ .

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials $p_{1}$ and $p_{2}$ such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$ and $p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}$ , where $m \geq n$

$p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}$

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be $p_{1}$ a polynomial such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$

And $\alpha$ an scalar. If the polynomial is multiplied by the scalar number, then:

$\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}$

Lastly, the following expression is constructed by distributive property:

$\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}$

Hence, polynomials are closed with respect to multiplication.

4 0

3 years ago

The product of a number and 7, decreased by the number is equal to 42. Find the number.

evablogger [386]

$7$
this is the answer, its pretty simple. I'm not sure the mathematical procedures but if you plug in 7 you get 49. Then all you got to do is subtract by 7, because the question states the number is the same. So basically,
$7(7) - 7 = 42$

8 0

3 years ago

Why is - t - 3 written as 3 - t? Is it wrong if it is left as -t -3?

Eddi Din [679]

-t-3 and 3-t are not the same since t-3 would result in a negative answer since both -t and -3 are negative. While in t-3 t is positive and -3 is negative. it is wrong if its left as t-3 since -t-3=3-t is false.

4 0

3 years ago