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aleksklad [387]

3 years ago

15

Use the set of clues in the equations below to find the value of each variable .

1 answer:

soldier1979 [14.2K]3 years ago

4 0

There are many ways to solve this problem. All you have to do is simple algebraic manipulation. Solve for b and h with the two simpler equations:
2b = 12; divide 2 on both sides to get b = 6
h - x = 2; add x to both sides to get h = (2 + x)

Plug this stuff into the first equation to solve for x. Once we solve for x, we can plug that x value into the equation for h. Because you can see we didn’t get an actual numerical value for h. So:
x + (2+x) + 6 = 14
Subtract 6 from both sides and distribute that plus sign to get rid of the parenthesis. Then combine the like terms to get:
2x + 2 = 8
Subtract 2 from both sides and divide by 2 to get x = 3

Finally plug it into the equation for h:
h = 2+3 = 5

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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.

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2 years ago

What is the equation of the line that has a slope of 1/2 and passes through the point (6,4)? Write your answer in slope intercep

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Answer:

A

Step-by-step explanation:took it on edge!

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2 years ago

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Alinara [238K]

Answer:

12

Step-by-step explanation:

12 parts

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

13.1: Equivalent Expressions

scoundrel [369]

Distributive Property: a ( b + c) = (a*b) + (a*c)

b) x(x + 9) = x*x + 9*x

= x² + 9x

c) x² - 18x

x² = x * x

18x = 18 *x

G C F = x

Greatest common factor in both the terms is 'x'.Take the common variable from both the terms.

x² - 18x = x*x - 18*x

= x (x - 18)

Standard form. Factored form

x² x*x

x² + 9x x(x +9)

x² - 18x x(x - 18)

-x² + 10x x(-x + 10) = x(10 -x)

-x² - 2.75x -x(x + 2.75)

3 0

1 year ago