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3 years ago

Find x, round to the nearest tenth degree.

Mathematics

1 answer:

Romashka [77]3 years ago

5 0

Answer:

Step-by-step explanation:

Use the Law of Cosines

A = arccos[(10²+14²-9.6²)/(2×10×14) ≅ 43.3°

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Ben jogged 4 and 1/2 miles in 1 and 1/4 hours at a constant rate. How far did Ben jog in one hour? *

Mrac [35]

let's firstly convert the mixed fractions to improper fractions and then proceed.

$\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill$

$\begin{array}{ccll} miles&hours\\ \cline{1-2} \frac{9}{2}&\frac{5}{4}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{9}{2}~~}{x}=\cfrac{~~ \frac{5}{4}~~}{1}\implies \cfrac{~~ \frac{9}{2}~~}{\frac{x}{1}}=\cfrac{5}{4}\implies \cfrac{9}{2}\cdot \cfrac{1}{x}=\cfrac{5}{4} \\\\\\ \cfrac{9}{2x}=\cfrac{5}{4}\implies 36=10x\implies \cfrac{36}{10}=x\implies \cfrac{18}{5}=x\implies 3\frac{3}{5}=x$

7 0

2 years ago

Please help ASAP If f(x) = x^2-6x+2 and g(x) =sqrt x find a.) (fog) (x) b.) (gof) (-2)

Rudik [331]

$\large\begin{array}{l} \left\{\!\begin{array}{l} \mathsf{f(x)=x^2-6x+2}\\ \mathsf{g(x)=\sqrt{x}}\\ \end{array}\right. \end{array}$

$\large\begin{array}{l} \textsf{a) }\mathsf{(f\circ g)(x)}\\\\ =\mathsf{f\big[g(x)\big]}\\\\ =\mathsf{\big[g(x)\big]^2-6\cdot g(x)+2}\\\\ =\mathsf{\big[\sqrt{x}\big]^2-6\sqrt{x}+2}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(f\circ g)(x)=x-6\sqrt{x}+2} \end{array}}\qquad\checkmark \end{array}$

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$\large\begin{array}{l} \textsf{b) }\mathsf{(g\circ f)(-2)}\\\\ =\mathsf{g\big[f(-2)\big]}\\\\ =\mathsf{\sqrt{f(-2)}}\\\\ =\mathsf{\sqrt{(-2)^2-6\cdot (-2)+2}}\\\\ =\mathsf{\sqrt{4+12+2}}\\\\ =\mathsf{\sqrt{18}}\\\\ =\mathsf{\sqrt{3^2\cdot 2}}\\\\ =\mathsf{3\sqrt{2}}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(g\circ f)(-2)=3\sqrt{2}} \end{array}}\qquad\checkmark \end{array}$

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$\large\textsf{I hope this helps. :-)}$

Tags: composite function composition evaluate algebra

7 0

3 years ago

At a basketball game, a team made 57 successful shots. They were a combination of 1- and 2-point

levacccp [35]

Answer:

2-point shots = 41, 1-point shots = 16

Step-by-step explanation:

Let the number of 1-point shots is x and 2-points shots is y.

The system as per question is

x + y = 57
1*x + 2*y = 98

Solve it by elimination, subtract the first equation from the second

x + 2y - x - y = 98 - 57
y = 41

Find the value of x

x + 41 = 57
x = 16

4 0

2 years ago

Simplify -4 1/4 - (-9 1/2)

Andreas93 [3]

The answer is D) 5 1/4.

7 0

3 years ago

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If a die is rolled one time, what is the probability of getting a 4

BaLLatris [955]

Answer:

1/6

Step-by-step explanation:

You have one die, with one 4 and six sides. The probability of getting a 4 with one roll is 1/6.

5 0

3 years ago

Read 2 more answers