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PIT_PIT [208]
3 years ago
9

6a^2 -12a equals what

Mathematics
1 answer:
Wittaler [7]3 years ago
4 0
Factor out the GCF
6a(a-2)
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Noah has just purchased a previously owned home. he put $5,000 towards a down payment and took out a $65,000 mortgage. noah know
cricket20 [7]
The answer to your question is B) $700 because 1% of the $5,000 down payment and the $65,000 mortgage so $70,000 is $700.
5 0
2 years ago
Help help help if u can answer this I’ll mark u brainliest (6) (the one in the middle)
Hoochie [10]

You just have to plug in each thing:

So f(0):

3(0)^2 - 4 = -4

so its not A

f(-2) and f(2):

3(-2)^2 - 4

3(2)^2 -4

now we don't even have to calculate these, anything to the power of an even number is a positive number so -2^2 and 2^2 both equal 4

B is correct, so you can do the others if you want to check, but if B is true the others shouldn't be true.

4 0
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
1. Give another name for liner r.
nirvana33 [79]

Answer:

1) A line can be defined by two points that are connected by the given line.

We can see that the line r connects the points A and B, then we can call this line as:

AB (the notation usually uses a double arrow in top of the letters)

2) In the image we can see that lines r and s intersect at the point B, then another name for that intersection is: B.

3) 3 colinear points are 3 points that are connected by a single line, an example of this can be the points A, B and C.

4) A plane can be defined by a line and a point outside the line.

For example, we can choose the line AB and the point D, that does not belong to the line.

Then we can call the plane as ABD.

6 0
3 years ago
Tank a has a capacity of 9.5 gallons. 6 1/3 gallons of the tank's water are poured out. how many gallons of water are left in th
Advocard [28]

Answer:

Water left in tank is 3\frac{1}{6} gallons.

Step-by-step explanation:

Given :

Capacity of tank = 9.5 gallons  =\frac{95}{10}

Water taken out of tank =6\frac{1}{3}=\frac{19}{3} gallons

We have to find the water left in the tank.

Water left in the tank = Total capacity of tank - water taken out of tank

                                    =\frac{95}{10}-\frac{19}{3}

Taking LCM of (3,10)= 30

\Rightarrow \frac{95 \times 3-19 \times10}{30}

Solving further, we get,

\Rightarrow \frac{285-190}{30}

\Rightarrow \frac{95}{30}=\frac{19}{6}=3\frac{1}{6}

Thus, Water left in tank is 3\frac{1}{6} gallons..

5 0
3 years ago
Read 2 more answers
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