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2 years ago

14

The PTA at Newberg High School is having its annual dinner and auction to raise money for music and art programs. Last year, the

event raised $84,240. This year, it raised $54,756. What is the percent of decrease in the amount raised?

1 answer:

Zinaida [17]2 years ago

8 0

Percent of change = absolute value of the original amount minus new amount divided by the original amount.

The answer is a 35% decrease

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Select the correct answer.

9966 [12]

Answer:

C

Step-by-step explanation:

Because c has the variables in the right spot and the other ones don't make scene

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3 years ago

Mark the statements that are true.

qaws [65]

Answer:

Hi there!

The correct choices are: A, B, C

Step-by-step explanation:

π in radians equals to 180°

A is correct because 180/3 = 60

C is correct because 180/4 = 45

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3 years ago

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

3 years ago

What is the number of solutions of 4x^2+12x+9=0?

Gwar [14]

Answer:

One Real number solution

Step-by-step explanation:

check the discriminant

12^2 - 4*4*9

b^2 - 4ac

...

144 - 16*9 = 0

one double root

7 0

2 years ago

What value of t is the solution of the above equation?

mel-nik [20]

Answer:

15/4, or 3 3/4 is your answer.

Step-by-step explanation:

Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Multiply 3/2 to both sides.

(3/2)(2/3)t = (5/2)(3/2)

t = (5/2)(3/2)

t = 15/4

15/4, or 3 3/4 is your answer.

~

7 0

3 years ago