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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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Answer:

C

Step-by-step explanation:

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4 years ago
In the diagram, the measure of angle 3 is (23x)°, and the measure of angle 4 is (7x)°.
Sophie [7]
Angles three and four are a linear pair, meaning that they they form a line. When two angles make a line, the measures add up to 180°. Adding the two values together, we see that 3x+27x=180. Simplifying and solving for x, we get 30x=180 ⇒ x=6.

The question, however, is asking for the measure of angle 4. Thus, we plug x=6 into 7x to get 6(7)=42.

Hope this helped!
3 0
4 years ago
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A basketball player made 80 out of 100 attempted free throws. What percent of free throws was​ made?
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5 0
3 years ago
A sprinter who weighs 706 N runs the first 5.5 m of a race in 1.6 s, starting from rest and accelerating uniformly. What are the
zhenek [66]

Answer:

(a) Speed = 6.875 m/s

(b) Kinetic Energy = 1.70 kJ

(c) Average power =  1.06 kW

Step-by-step explanation:

Given:

d = 5.5 m

t = 1.6 s

W = 706 N

Part (a)

Using the equation of motion with the assumption of zero initial speed:

d = \frac{1}{2} ({v-0})t

5.5= \frac{1}{2} (1.6v)

The speed of the sprinter then become:

v = 6.875 m/s

Part (b)

Convert the weight of the sprinter to mass:

m = \frac{w}{g}

m = \frac{706}{9.8}

m = 72 kg

KE (Kinetic Energy) can then be calculated as:

KE = \frac{1}{2} mv^{2}

KE = \frac{1}{2} (72)(6.875)^{2}

KE = 1701.56 J = 1.70 kJ

Part (c)

The change of the kinetic energy is equivalent to the work done by the sprinter. The average power P is the rate of the work done and can be calculated as

P = \frac{KE}{t} \\\

P = \frac{1701.56}{1.6}

P = 1063.48 W = 1.06 kW

5 0
3 years ago
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