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2 years ago

HELP WITH MY MATH EXAM i don't know what to do and my head hurts a lot

Mathematics

1 answer:

gogolik [260]2 years ago

8 0

Answer:

x = 154/13

Step-by-step explanation:

You are given the measures of all three angles in a triangle

so according to the Triangle Sum Theorem:

∠MNO + ∠OMN + ∠NOP = 180

1. Substitute the measures of the angles into the equation:

(3x + 11) + (2x + 20) + (8x - 5) = 180

2. Combine like terms:

(3x + 2x + 8x) + (11 + 20 -5) = 180

13x + 26 = 180

3. Isolate x by subtratcing 26 from both sides

13x + 26 -26 = 180 -26

13x = 154

4. Solve for x by dividing both sides by 13

13x/13 = 154/13

x = 154/13

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3 years ago

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Identify the expression with nonnegative limit values. More info on the pic. PLEASE HELP.

marshall27 [118]

Answer:

$\lim _{x\to 2}\:\frac{x-2}{x^2-2}\\\\ \lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}\\\\ \lim _{x\to \frac{5}{2}}\left\frac{2x^2+x-15}{2x-5}\right$

Step-by-step explanation:

a) $\lim _{x\to 3}\:\frac{x^2-10x+21}{x^2+4x-21}=\lim \:_{x\to \:3}\:\frac{\left(x-7\right)\left(x-3\right)}{\left(x+7\right)\left(x-3\right)}=\lim \:_{x\to \:3}\:\frac{x-7}{x+7}=\frac{3-7}{3+7}=-\frac{4}{10}=-\frac{2}{5}$

b) $\lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=\lim \:_{x\to -\frac{3}{2}}\:\frac{\left(2x+3\right)\left(x-4\right)}{\left(2x+3\right)}=\lim \:\:_{x\to \:-\frac{3}{2}}\:\left(x-4\right)=-\frac{3}{2}-4\\ \\ \lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=-\frac{11}{2}$

c) $\lim _{x\to 2}\:\frac{x-2}{x^2-2}=\frac{2-2}{\left(2\right)^2-2}=\frac{0}{4-2}=0$

d) $\lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}=\lim _{x\to 11}\:\frac{\left(x-11\right)\left(x+17\right)}{\left(x-11\right)\left(x+14\right)}=\lim _{x\to 11}\:\frac{\left(x+17\right)}{\left(x+14\right)}=\frac{11+17}{11+14}=\frac{28}{25}$

e) $\lim _{x\to 3}\:\frac{x^2-8x+15}{x-3}=\lim \:_{x\to \:3}\:\frac{\left(x-3\right)\left(x-5\right)}{x-3}=\lim _{x\to 3}\left(x-5\right)=3-5=-2$

f) $\lim _{x\to \frac{5}{2}}\left(\frac{2x^2+x-15}{2x-5}\right)=\lim \:_{x\to \:\frac{5}{2}}\frac{\left(2x-5\right)\left(x+3\right)}{2x-5}=\lim \:\:_{x\to \:\:\frac{5}{2}}\left(x+3\right)=\frac{5}{2}+3=\frac{11}{2}$

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2 years ago

A town has a population of 20000 and grows at 4% every year. What will be the population after 6 years, to the nearest whole num

zaharov [31]

Answer:

25306

Step-by-step explanation:

a=starting value = 20000

r=\text{rate = }4\% = 0.04

r=rate = 4%=0.04

\text{Exponential Growth:}

Exponential Growth:

b=1+r=1+0.04=1.04

\text{Write Exponential Function:}

Write Exponential Function:

y=20000(1.04)^x

y=20000(1.04)

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=20000(1.04)^{6}

y=20000(1.04)

y= 25306.38037

y=25306.38037

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2 years ago