Expand and simplify 2(5x+4)+ 3(2x-1)

Mathematics

1 answer:

tester [92]3 years ago

3 0

10x+8+6x-3
answer
16x+5

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Find the limit of the function algebraically. limit as x approaches negative 2 of quantity x squared minus four divided by quant

lakkis [162]

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The limit is -4

EXPLANATION

$\displaystyle\lim_{x\to -2} \dfrac{x^2-4}{x+2}$

The numerator factors into (x-2)(x+2)

$\displaystyle\lim_{x\to -2} \dfrac{(x-2)(x+2)}{x+2}$

The (x+2) cancel out

$\displaystyle\lim_{x\to -2} (x-2)$

By direct substitution

$\displaystyle\lim_{x\to -2} (x-2) = -2 -2 = -4$

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Ilia_Sergeevich [38]

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Step-by-step explanation:

$\frac{2}{3}$ is between 0 and 1

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Can someone please clearly and correctly solve and show me how to work out QUESTION 3 AND 4??

vredina [299]

There are 2 options to solve that.
1. The first one is by derivatives.
f(x)=x^2+12x+36
f'(x)=2x+12
then you solve that for f'(x)=0
0=2x+12
x=(-6)
you have x so for (-6) solve the first equation, then you find y
y=(-6)^2+12*(-6)+36=(-72)
so the vertex is (-6, -72)
2. The second option is to solve that by equations:
for x we have:
x=(-b)/2a
for that task we have
b=12
a=1
x=(-12)/2=(-6)
you have x so put x into the main equation
y=(-6)^2+12*(-6)+36=(-72)
and we have the same solution: vertex is (-6, -72)

For next task, I will use the second option:
y=x^2-6x
x=(-b)/2a
for that task we have
b=(-6)
a=1
x=(6)/2=3
you have x so put x into the main equation
y=3^2+(-6)*3=(--9)
and we have the same solution: vertex is (3, -9)

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3 years ago

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