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Nina [5.8K]
2 years ago
10

Two groups of bikers leave the same camp heading in different directions. Each group travels 4 miles, then changes direction and

travels 1.4 miles. Group A starts due east and then turns 48° toward north. Group B starts due west and then turns 32° toward south. Which group is farther from camp?
1. Group A is farther from camp.
2. Group B is farther from camp.
3. Group A and Group B are the same distance from camp.
4. Not enough information is given.
Mathematics
1 answer:
devlian [24]2 years ago
7 0

Group B is farther from camp.

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Answer:

How can the solution be located?

find the intersection

Which integers is the x-coordinate between?

0 and 1

Which integers is the y-coordinate between?

2 and 3

What is the solution approximated to the tenths place?

(0.4,2.8)

Step-by-step explanation:

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If you need $8000 to travel to Europe after you graduate in 4 year. How much would your monthly deposits need to be if your acco
lina2011 [118]
\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\
\left. \qquad \qquad \right.(\textit{payments at the end of the period})
\\\\
A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]

\bf \qquad 
\begin{cases}
A=
\begin{array}{llll}
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\end{array}\to &
\begin{array}{llll}
8000
\end{array}\\
pymnt=\textit{periodic payments}\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
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\textit{times it compounds per year}\\
\textit{monthly, thus twelve}
\end{array}\to &12\\
t=years\to &4
\end{cases}

\bf 8000=pymnt\left[ \cfrac{\left( 1+\frac{0.05}{12} \right)^{12\cdot 4}-1}{\frac{0.05}{12}} \right]
\\\\\\
\cfrac{8000}{\left[ \frac{\left( 1+\frac{0.05}{12} \right)^{12\cdot 4}-1}{\frac{0.05}{12}} \right]}=pymnt\implies \cfrac{8000}{\frac{\left( \frac{241}{240} \right)^{48}-1}{\frac{1}{240}}}=pymnt
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\cfrac{8000}{53.0148852}\approx pymnt\implies 150.9010152318\approx pymnt
6 0
3 years ago
If f(x)=3x-2 and g(x)=x^2+1, find f(g(-1)) and g(f(3))
julsineya [31]

Answer:

f(g(-1))=4

g(f(3))=50

Step-by-step explanation:

We know the definition of both functions: f(x)=3x-2, and g(x)=x^2+1

A) In order to evaluate what f(g(-1)) is, let's first investigate what g(-1) is using the definition for this function:

g(x)=x^2+1\\g(-1)=(-1)^2+1\\g(-1)=1+1\\g(-1)=2

Now let's find what f(2) is using f(x) definition: f(x)=3x-2\\f(2)=3(2)-2\\f(2)=6-2\\f(2)=4

B) In order to evaluate what g(f(3)) is, let's first investigate what f(3) is using the definition for this function:

f(x)=3x-2\\f(3)=3(3)-2\\f(3)=9-2\\f(3)=7

Now let's find what g(7) is using the definition for this function:

g(x)=x^2+1\\g(7)=(7)^2+1\\g(7)=49+1\\g(7)=50

4 0
2 years ago
What is the variable x in 40+10x=5x-30
konstantin123 [22]

40 + 10x = 5x - 30

To begin isolating x, subtract 40 from both sides.

40 + 10x - 40 = 5x - 30 - 40

10x = 5x - 70

Subtract 5x from both sides.

10x - 5x= 5x - 70 - 5x

5x = -70

Finally, divide both sides by 5.

5x/5 = -70/5

x = -14

Answer:

x = -14

4 0
3 years ago
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