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3 years ago

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Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus \$6$6 for each hour of work. He

r total fee for a 44-hour job, for instance, is \$32$32. Let F(t)F(t) denote Carolina's fee for a single job FF (measured in dollars) as a function of the number of hours tt it took her to complete it.

2 answers:

maksim [4K]3 years ago

8 0

Answer:

$F(t)=6t+8$ .

Step-by-step explanation:

Let t represent number of hours.

We have been given that Carolina charges $6 for each hour of work. So amount charged for t hours of work would be $6t$ .

Let us find initial cost by subtracting charges for 4 hours from 32 as:

$\text{Initial cost}=32-4\times 6$

$\text{Initial cost}=32-24$

$\text{Initial cost}=8$

The total cost for t hours of work would be initial cost plus cost per hour: $6t+8$ .

Our required function would be $F(t)=6t+8$ .

GenaCL600 [577]3 years ago

4 0

Answer:

y=8+6t

Step-by-step explanation:

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Answer:

Length:8 m

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Step-by-step explanation:

<u><em>The complete question is</em></u>

If the perimeter of a rectangle is 22 meters, and the perimeter of a right triangle is 12 meters (the sides of the triangle are half the length of the rectangle, the width of the rectangle, and the hypotenuse is 5 meters). How do you solve for L and W, the dimensions of the rectangle.

step 1

<em>Perimeter of rectangle</em>

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

we have

$P=22\ m$

so

$22=2(L+W)$

Simplify

$11=L+W$ -----> equation A

step 2

Perimeter of triangle

The perimeter of triangle is equal to

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$P=12\ m$

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$12=\frac{L}{2}+W+5$

Multiply by 2 both sides

$24=L+2W+10$

$L+2W=14$ ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (8,3)

see the attached figure

therefore

The dimensions of the rectangle are

Length:8 m

Width:3 m

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3 years ago

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Alecsey [184]

Answer:

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Step-by-step explanation:

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3 years ago

Evaluate each expression if a = 6, b = 3, and c = 2.

My name is Ann [436]

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Step-by-step explanation:

1. 6 x 3 = 18

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3 years ago

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Answer:

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3 years ago

Read 2 more answers

Can you please help with this question about exponential equations?

RSB [31]

Since $t$ represents the number of years passed since 2005, in 2005 we have $t=0$ , and in 2015 we have $t=10$ . Let $P_J(y),P_D(y)$ represent the profits of Jones and Davis, respectively, at year y.

We have

$P_J(2005) = 10(0.99)^0 = 10,\quad P_J(2015) = 10(0.99)^{10}\approx 9$

$P_D(2005) = 8(1.01)^0 = 8,\quad P_D(2015) = 8(1.01)^{10}\approx 9$

Choosing the best company somehow depends on how much time you can wait: Jones start with a higher value (10 vs 8), but it has a descending trend, because the multiplicative factor $0.99^t$ goes to zero as t grows.

On the other hand, Davis starts with a smaller value, but $1.01^t$ tends to infinity as t grows.

So, if you need an immediate result, the most valuable company is Jones, otherwise you're certain can Davis will eventually become bigger.

More precisely, we have

$8\cdot 1.01^t = 10\cdot 0.99^t \iff 0.8 = \left(\dfrac{0.99}{1.01}\right)^t \iff t\approx 11$

So, after 11 years, Davis will overcome Jones.

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3 years ago