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Triss [41]
3 years ago
10

Find x. Round to the nearest tenth if needed.

Mathematics
2 answers:
alexdok [17]3 years ago
5 0

Answer:

x = 16

Step-by-step explanation:

Use that the addition of all internal angles of a triangle must add up to 180, and the fact that the two given triangles are similar:

51 + 65 + 4 x = 180

combine and solve for "x"

116 + 4 x = 180

4 x = 180 - 116

4 x = 64

x = 64 / 4

x = 16

arsen [322]3 years ago
3 0

Answer:

x = 16

Step-by-step explanation:

A triangle is 180 degrees. Since two of the angles are congruent to each other, the third angle must be congruent as well. This means that the third measure for both triangles is 4x. Knowing all of this, we can solve for x:

65 + 51 + 4x = 180

116 + 4x = 180

4x = 64

x = 16

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3 years ago
Answer the questions below about the quadratic function.f(x) = -2x² - 4x
Juli2301 [7.4K]

We are given the function below;

f(x)=-2x^2-4x

PART A

We then proceed to find if the function has a minimum or maximum value. To find if the function has a minimum or maximum value. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.

ANSWER: From the above, we can see that x^2 is negative, hence the function has a maximum

PART B and C

To find the minimum or maximum value, we would plot the graph of the f(x). The graph can be seen below.

From the graph, the black point helps answer part A and part B.

ANSWER: The function's maximum value is f(x)=2.

This is the point where the slope of the graph is equal to zero

ANSWER: The maximum value then occurs at x= -1

We can also solve this by differentiating the function.

\begin{gathered} f(x)=-2x^2-4x \\ f^{\prime}(x)=-4x-4 \\ At\xi maxmum\text{ }f^{\prime}(x)=0 \\ -4x-4=0 \\ -4x=4 \\ x=-\frac{4}{4} \\ x=-1 \\ \therefore\text{The max}imum\text{ value occurs at x=-1} \\ \text{Inserting the value of x into the function, we have} \\ f(x)=-2(-1)^2-4(-1) \\ f(x)=-2+4 \\ f(x)=2 \\ \therefore\text{The function max}imum\text{ value is 2} \end{gathered}

5 0
1 year ago
Ther are 10 girls and 8 boys in Mr. Augello's class. If 5 more girls and 5 more boys join the class, will the ratio of girls to
NISA [10]
Presently ratio is at 10:18 = 1.25
With 5 more girls & guys joining, ratio would change to 15:13 = 1.153846154
Therefore, the ratio of girls to boys would change rather not remain the same.
6 0
3 years ago
What is the area of a trapezoid that has the following dimensions?
Grace [21]
A=1/2 × (a+b) × h
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I hope this helps.
8 0
3 years ago
Read 2 more answers
A customer deposits $500 in an account that pays 5% annual interest.
skelet666 [1.2K]

~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=500\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=500(1.05)^3\implies A\approx 578.81

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2 years ago
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