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3 years ago

7

A rental car company charges $35 a day plus $.15/mi for a mid-size car. A customer owes $117.25 for a three-day rental. How many

miles did the customer drive?

1 answer:

Molodets [167]3 years ago

8 0

The base charge is 35 dollars per day. He rented the car for 3 days, so before you add in the mileage you have to multiply 35 x 3 days for 105 dollars. Then you have to take the remaining charge and divide it by the charge per mile to get the number of miles driven. Lets set up the equation.

d= number of days rented
m= number of miles driven

35(d) + .15(m) = 117.25
35(3) + .15m = 117.25
105 + .15m = 117.25
.15m = 117.25 - 105
.15m = 12.25
m = 12.25/.15
m = 81.67

So he drove 81.67 miles

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PLEASE HELP FASTTT!!!

nirvana33 [79]

Answer:

5 seconds

Step-by-step explanation:

Looking at your function (h(t) = -16t^2 + 48t + 160), I see that the peak height will be 196 feet, and that is achieved in 1.5 seconds.

h(1.5) = -16(1.5)^2 + 48(1.5) + 160

h(1.5) = -16(2.25)+ 48(1.5) + 160

h(1.5) = -36 + 48(1.5) + 160

h(1.5) = -36 + 72 + 160

h(1.5) = 36 + 160

h(1.5) = 196

Going down from that height, it would take 3.5 more seconds, so it would take 5 seconds in total

h(5) = -16(5)^2 + 48(5) + 160

h(5) = -16(25) + 48(5) + 160

h(5) = -400 + 48(5) + 160

h(5) = -400 + 240 + 160

h(5) = -400 + 400

h(5) = 0

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2 years ago

The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

<h3>1.</h3>

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

<h3>2.</h3>

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

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Lelu [443]

Answer:

AX : XB as AB : AC

AX = 5

XB = 4

AC = 6

AB = x

Step-by-step explanation:

5 : 4 as to x : 6

ratios can also be written as fractions...

5/4 = x/6 ..now we have a proportion...so we cross multiply

(4)(x) = (5)(6)

4x = 30

x = 30/4

x = 15/2 <==== AB = 15/2

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Answer:

5.72

Step-by-step explanation:

(-16.75 + 16.75) = 0

0 + 5.72= 5.72

Therefore, the answer is 5.72

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3 years ago

If f(x) = -5x+3 when x=-2 what’s f(x)?

WINSTONCH [101]

Answer:

f(x)=13

Step-by-step explanation:

f(x)= -5 × -2= 10 + 3 = 13

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