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3 years ago

Solve 3x 2 + 2 = 11 - x 2

1 answer:

4 0

$3x^2 + 2 = 11 - x^2\\\\ 3x^2+x^2=11-2\\\\ 4x^2=9\\\\(2x)^2=3^2\\\\ |2x|=3\\\\ 2x=3 \ or \ 2x=-3\\\\ x=\frac{3}{2} \ or \ x=-\frac{3}{2}$

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Find the limit, if it exists (picture below)

valentinak56 [21]

Answer:

c. $\frac{1}{2 \sqrt{7} }$

Step-by-step explanation:

When plugging in zero into the given equation:

$\lim_{x \rightarrow 0} \frac{\sqrt{x + 7} - \sqrt{7} }{x} = \frac{0}{0}$

Answer is in indeterminate form = use L'Hospital's Rule:

(Derivative of the top / Derivative of the bottom)

$\lim_{x \rightarrow 0} \frac{ \frac{1}{2} (x + 7)^{ \frac{-1}{2}} - 0 }{1}$

Rearranged equation:

$\lim_{x \rightarrow 0} \frac{1}{2 \sqrt{x + 7} }$

Plug zero back into equation:

$\lim_{x \rightarrow 0} \frac{1}{2 \sqrt{x + 7} } = \frac{1}{2 \sqrt{0 + 7} } = \frac{1}{2 \sqrt{7} }$

Answer:

$\lim_{x \rightarrow 0} \frac{\sqrt{x + 7} - \sqrt{7} }{x} = \frac{1}{2 \sqrt{7} }$

5 0

2 years ago

Given that D is the midpoint of AB and B is the midpoint of AC, which statement must be true?

abruzzese [7]

Answer:

AC =4DB

Step-by-step explanation:

D is midpoint of AB .So, AD = DB

AB = 2DB ---------- (i)

B is the midpoint of AC.So, AB = BC

AC = 2AB

= 2*2DB {FROM 1}

=4DB

4 0

3 years ago

On the first 7 statistics tests of the semester, Jamal

lubasha [3.4K]

Balls are good that’s the answer

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2 years ago

9x - y = 15 2x + 8y = 28

faust18 [17]

9x - y = 15
2x + 8y = 28

Use the substitution method.
Solve for y in the first equation.

9x - y = 15
-y = 15 - 9x
y = -15 + 9x

Now plug in y into the second equation.
2x + 8(-15 + 9x) = 28
2x - 120 + 72x = 28
74x - 120 = 28
74x = 148
x = 2

Plug x back into the rewritten first equation.
y = -15 + 9(2)
y = -15 + 18
y = 3

x = 2, y = 3

5 0

3 years ago

Calculate the unit price of the following item:

Vikki [24]

10 lol that’s the answer.

7 0

3 years ago