Find the value of x in the image

Mathematics

1 answer:

Ber [7]3 years ago

4 0

Answer:

Step-by-step explanation:

a pentagon has a total of 540 degrees

105, 115, 110, 180-2x, 180-3x are the interior angles (subtract each from 180 because they're on lines)

540= 105+115+110+(180-2x)+(180-3x)

540=330 +(180-2x)+(180-3x)

210=360-5x

-150=-5x

50=x

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(3 3/4) divided by (-2 1/2)

GalinKa [24]

Answer:

-1 1/2

same as -1.5 but since you are dealing with fractions you should put it in fraction form unless told otherwise.

3 0

3 years ago

If f(x)=2x+sinx and the function g is the inverse of f then g'(2)=

Alexxx [7]

$\bf f(x)=y=2x+sin(x)
\\\\\\
inverse\implies x=2y+sin(y)\leftarrow f^{-1}(x)\leftarrow g(x)
\\\\\\
\textit{now, the "y" in the inverse, is really just g(x)}
\\\\\\
\textit{so, we can write it as }x=2g(x)+sin[g(x)]\\\\
-----------------------------\\\\$

$\bf \textit{let's use implicit differentiation}\\\\
1=2\cfrac{dg(x)}{dx}+cos[g(x)]\cdot \cfrac{dg(x)}{dx}\impliedby \textit{common factor}
\\\\\\
1=\cfrac{dg(x)}{dx}[2+cos[g(x)]]\implies \cfrac{1}{[2+cos[g(x)]]}=\cfrac{dg(x)}{dx}=g'(x)\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}$

now, if we just knew what g(2) is, we'd be golden, however, we dunno

BUT, recall, g(x) is the inverse of f(x), meaning, all domain for f(x) is really the range of g(x) and, the range for f(x), is the domain for g(x)

for inverse expressions, the domain and range is the same as the original, just switched over

so, g(2) = some range value
that means if we use that value in f(x), f( some range value) = 2

so... in short, instead of getting the range from g(2), let's get the domain of f(x) IF the range is 2

thus 2 = 2x+sin(x)

$\bf 2=2x+sin(x)\implies 0=2x+sin(x)-2
\\\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}\implies g'(2)=\cfrac{1}{2+cos[2x+sin(x)-2]}$

hmmm I was looking for some constant value... but hmm, not sure there is one, so I think that'd be it

5 0

3 years ago

James has worked full time as an entry-level web designer since earning his certification. He

Norma-Jean [14]

A budget is a periodical compilation of the estimated revenue earned and expenses incurred within a given time period

Monthly income calculation

James monthly income is calculated as follows;

Monthly income = $\dfrac{\$47,000}{12} \approx \$ 3,916.\overline 6$

The required <u>James' monthly personal budget </u>is presented as follows;

Based on the above monthly income, the monthly personal budget is found by entering the given values in a budget template as follows;

$\begin{array}{lllc}& Incone &\$3,916.6 \\&Rent&\$950\\&Insurance \ (renter's)&\$25\\&Insurance \ (health)&\$185\\&Retirement \ (401 (k))&\$157\\&Car \ insurance &\$120 \\Fixed \ expenses&Utilities&\$100 &\\&Cell \ phone &\$85 &\\&Cable \ TV& \$70 &\\&Credit \ card& \$150 \\&Car \ payment&\$554\\&\underline{ \mathbf{Total \ fixed \ expenses}}& \$2,396 \\&&\\&Clothing& \$80 & \\Variable \ expenses&Groceries& \$300 \\&Entertainment&\$196 \\&\underline{ \mathbf{ Total \ variable \ expenses}}&\$576 \end{array}$