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3 years ago

LOTS OF POINTS Simplify the expression by factoring, showing the steps in your work

Mathematics

1 answer:

julia-pushkina [17]3 years ago

8 0

Answer:

$\frac{3x+7}{4x+1}$

Step-by-step explanation:

$\frac{12x^2+31x+7}{16x^2+8x+1}$

First you factor $12x^2+31x+7$ :

$=\left(12x^2+3x\right)+\left(28x+7\right)$

Then you factor out $3x$ from $12x^2+3x$ :

$12x^2+3x$

$=12xx+3x$

$=3\cdot \:4xx+3x$

$=3x\left(4x+1\right)$

Then you factor out 7 from $28x+7$ :

$28x+7$

$=7\cdot \:4x+7$

$=7\left(4x+1\right)$

$=3x\left(4x+1\right)+7\left(4x+1\right)$

Factor out common term $4x+1$ :

$=\left(4x+1\right)\left(3x+7\right)$

$\frac{\left(4x+1\right)\left(3x+7\right)}{16x^2+8x+1}$

Factor $16x^2+8x+1$ :

$=4^2x^2+8x+1$

$=4^2x^2+8x+1^2$

$=\left(4x\right)^2+8x+1^2$

$=\left(4x\right)^2+2\cdot \:4x\cdot \:1+1^2$

Use the perfect square formula:

$=\left(4x+1\right)^2$

$\frac{\left(4x+1\right)\left(3x+7\right)}{\left(4x+1\right)^2}$

Cancel out common factor $4x+1$ :

$=\frac{3x+7}{4x+1}$

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Step-by-step explanation:

If a cannonball is shot directly upward with a velocity of 160 ft per second. Its height as a function of time is given by :

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Acceleration is given by :

$a=\dfrac{dv}{dt}\\\\a=\dfrac{d(160-32t)}{dt}\\\\a=-32\ ft/s^2$

(b) For maximum height put $\dfrac{dh}{dt}=0$

i.e.

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Put t = 5 s in equation (1). So,

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h(t) = 0

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3 years ago

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gavmur [86]

Answer:

The answer is c

Step-by-step explanation:

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In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an. Then write the first three terms of the sequence.

Tresset [83]

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You know the first and third terms, $a_1$ and $a_3$ , so you just need to find the second term $a_2$ :

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neonofarm [45]

Answer:

Step-by-step explanation:

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