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HACTEHA [7]
3 years ago
7

What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15 ?

Mathematics
2 answers:
Sladkaya [172]3 years ago
6 0

3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15\frac{3}{4x+3} +\frac{21}{8x^2 +26x+15}

factor the quadratic expression

⇒\frac{3}{4x+3} +\frac{21}{8x^2 +20x+6x+15}= \frac{3}{4x+3} +\frac{21}{4x(2x+5)+3(2x+5)}

=\frac{3}{4x+3} +\frac{21}{(2x+5)(4x+3)}

Find LCD , and make the denominators same by multiplying first expression by (2x+5) both in numerator and denominator

=\frac{3(2x+5)}{(4x+3)(2x+5)} +\frac{21}{(2x+5)(4x+3)}

Simplify

=\frac{3(2x+5) +21}{(4x+3)(2x+5)}

=\frac{6x+15 +21}{(4x+3)(2x+5)}

=\frac{6x+36}{(4x+3)(2x+5)}

Factor the numerator

=\frac{6(x+6)}{(4x+3)(2x+5)}

Option D

nekit [7.7K]3 years ago
4 0

Answer:

-4x + 14

Step-by-step explanation:

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wariber [46]

Answer:

PQ = 20

QR = 15

Step-by-step explanation:

PQ^2 = 16^2 + 12^2

PQ^2 = 400

PQ = √400 = 20

QR^2 = 12^2+9^2

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QR = √225 = 15

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3 years ago
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Stells [14]

Answer:

2.0 x 10^11

Step-by-step explanation:

2.6 divide it by 1.3 and get 2.0. 9+2 = 11. Together with the, it would be 10^11. That how I got 2.0 x 10^11

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7 0
3 years ago
Which measurements for the capacity of the ice cream carton?
nalin [4]

Answer:

  • 1 cup
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Step-by-step explanation:

In retail grocery stores in the US, you can find ice cream packaged in sizes of 1 cup (half pint), 1 pint, 1 quart, 1/2 gallon, 1 gallon, and perhaps some odd sizes in between. For commercial purposes, ice cream may be packaged in tubs of 3- or 5-gallons or more.

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6 0
3 years ago
Tom and Becky can paint Jim's fence together in 12 hours. If all people paint at the same rate, how many hours would it take to
Delvig [45]

Answer: 8 hours

Step-by-step explanation:

Let x be the time taken by each person to paint the fence.

Given: Tom and Becky can paint Jim's fence together in 12 hours.

Since all people paint at the same rate, then we have the following equation ;-

\dfrac{1}{x}+\dfrac{1}{x}=\dfrac{1}{12}\\\\\Rightarrow\ \dfrac{2}{x}=\dfrac{1}{12}\\\\\Rightarrow\ x=24

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\dfrac{1}{t}=\dfrac{1}{24}+\dfrac{1}{24}+\dfrac{1}{24}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3}{24}\\\\\Rightarrow\ t=\dfrac{24}{3}=8\text{ hours}

Hence, it would take 8 hours if all three paint together.

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3 years ago
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expeople1 [14]

Answer:

5%

Step-by-step explanation:

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

0.05 × 100/100

= (0.05 × 100) × 1/100 = 5/100

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