A prop assistant needs to rent a telescope to use for a scene in a movie. One company charges $57 per day plus a flat fee of $32 to rent a telescope. Another company charged $62 per day with no flat fee. For how many days would the total cost of renting a telescope be the same at both companies? Justify your answer by writing and solving an equation.

Fill in the blanks with the correct answers.

62x = 58x + 32, when x = ____. The total cost of renting a telescope would be the same at both companies for _____ day(s).

Answer:

12/5 or 2,2/5

Step-by-step explanation:

[tex]3 \times \frac{4}{5} [/tex]

[tex] = \frac{12}{5} [/tex]

[tex] = 2 \frac{2}{5} [/tex]

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Answer:64.62

Step-by-step explanation:

Step-by-step explanation:

Answer:

[tex]b)\ 6\frac{1}{4}[/tex]

Step-by-step explanation:

Which is the product of 15 and 5/12

[tex]15*\frac{5}{12} \\\\\frac{15}{1} *\frac{5}{12}\\\\\frac{5}{1}*\frac{5}{4}\\\\ \frac{25}{4} \\\\6\frac{1}{4}[/tex]

Hope this helps!

Hi!

Your answer is B.

Given:

[tex]15*\dfrac{5}{12}[/tex]

Change [tex]15[/tex] into a fraction by putting it over [tex]1[/tex]

[tex]\dfrac{15}{1} * \dfrac{5}{12}[/tex]

Multiply the numerators and the denominators by each other:

[tex]\dfrac{15*5}{12*1} =\dfrac{75}{12}[/tex]

Simplify:

[tex]\dfrac{75/3}{12/3} = \dfrac{25}{4}[/tex]

Mixed number form = [tex]6\dfrac{1}{4}[/tex]

point slope equation formula: y - y1 = m (x - x1)

(-1,4) (-2,1)

answer:

1 -4 = 3 (-2+1)

Step-by-step explanation:

since it's an isosceles triangle, DE = EF

i.e. 8x-13 = 5x+ 17

or 8x -5x = 17 +13

or 2x = 30

or X = 15

The third graph is the only one that is an an odd-degree polynomial with a positive lead coefficient.

An even number of total minimums/maximums of the Polynomial is classified as an odd-degree polynomial. Now, we see that only the 3rd and 4th graphs are odd-degree polynomials because they have four total minimums/maximums.

For the polynomial to have a positive leading coefficient, the line must go up in the positive direction. This means that only the 1st and 3rd graphs have a positive leading coefficient due to the fact that their right-most line is going upwards.

Thus, we can say that the third graph is the only one that is an an odd-degree polynomial with a positive lead coefficient.

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Answer:

5 log₅ x − ¼ log₅ (8−x)

log₅ x⁵ − log₅ (8−x)^¼

log₅ x⁵ − log₅ ∜(8−x)

log₅ (x⁵ / ∜(8−x))       is the answer

Step-by-step explanation:

hope this helps

Answer:

[tex]log_5\biggr(\frac{x^5}{(8-x)^{\frac{1}{4}}}\biggr)[/tex]

Step-by-step explanation:

[tex]5log_5(x)-\frac{1}{4}log_5(8-x)\\ \\log_5(x^5)-log_5((8-x)^{\frac{1}{4}})\\\\log_5\biggr(\frac{x^5}{(8-x)^{\frac{1}{4}}}\biggr)[/tex]

Step-by-step explanation:

first, let's bring everything to the same fraction denominator, which would be 1/8 to cover all.

so, he jogs

3 2/8 miles on Monday

5 5/8 miles on Tuesday

8 0/8 miles on Wednesday

the difference from day to day is

5 5/8 - 3 2/8 = 2 3/8 (subtract the whole numbers and then also the fractional part).

to control :

5 5/8 + 2 3/8 = 7 8/8 = 8

so, he adds every day 2 3/8 miles.

that means in 2 days (from Wednesday to Friday) this will be additional 2×(2 3/8) = 4 6/8 = 4 3/4 miles.

so, he will jog

8 + 4 3/4 = 12 3/4 miles

on Friday.

don't forget, when we write something like 2 3/8. we actuality mean (2 + 3/8). and all rules about handling, transforming and calculating expressions apply.

therefore, e.g

2×(2 3/8) = 2×(2 + 3/8) = 4 + 6/8 = 4 6/8 = 4 3/4

Answer:

400 = 1600 ( 6 -0.5x )

distruibite

9600-800x=400

-9600

-800x=-9200

get rid of negitive

800x=9200

divide by 800

x=11.5

Hope This Helps!!!

Answer:

$2.10

Step-by-step explanation:

To get this answer all you have to do is, $1.05 x 2 = $2.10

Answer:

The answer is True

Answer:

Step-by-step explanation:

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Answer:

- 1/2

Step-by-step explanation:

I did the math and got the answer -1/2

The first step to solve the equation 1 1/2 + 2 1/3 = ? is (a) First, you should convert the mixed numbers to improper fractions.

The equation is given as:

1 1/2 + 2 1/3 = ?

The terms in the equation are mixed numbers.

So, the first stem is to convert the mixed numbers to improper fractions

Hence, the true statement is (a) First, you should convert the mixed numbers to improper fractions.

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Answer:

Step-by-step explanation:

y= john's balls

y+2+y = 18

2+2y = 18

Answer:

76.

Step-by-step explanation:

Forty "more" implies that you are adding forty to thirty-six. Making it seventy-six.

The number that is 36 more than 40 will be 76.

Algebra is the analysis of abstract symbols, while reasoning is the manipulation of all those views.

The definition of unsophistication is making something simpler to achieve or grasp while also making it a little less difficult.

Let 'x' be the number that is 36 more than 40. Then the equation is given as,

x = 36 + 40

Add the number 36 and 40, then we have

x = 36 + 40

x = 76

The number that is 36 more than 40 will be 76.

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The area covered if the side measures 5 meters. is 34.68 m²

The area of the shown figure is given as:

Area of the figure = area of square + area of a semicircle

Area of square = 5^2 = 25 square meters

Area of semicircle = πr²/2

Area of semicircle = (3.14)(2.5)²/2

Area of semicircle =9.6875 square meter

Area of the figure = 25 + 9.6875

Area of the figure = 34.68 square metres

Hence the area covered if the side measures 5 meters. is 34.68 m²

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The degree of the polynomial P(x) is the highest power of the polynomial P(X)

A possible formula for P(x) is [tex]P(x) =(x + 5)x^2(x - 1)^2 \\[/tex]

The given parameters are:

Roots of multiplicity 2 at x=1 and x=0

Root of multiplicity 1 at x= -5

Write out the roots

x=1 and x=0 ------- Multiplicity 2

x = -5  ------- Multiplicity 1

Equate the roots to 0

x - 1 = 0 and x = 0 ------- Multiplicity 2

x + 5= 0  ------- Multiplicity 1

Place the multiplicities as the exponents of the roots

(x - 1)^2 = 0 and x^2 = 0

(x + 5)^1 = 0

Multiply the expressions

[tex](x - 1)^2 * x^2 * (x + 5)^1 = 0 * 0 * 0[/tex]

This gives

[tex](x - 1)^2 * x^2 * (x + 5) = 0[/tex]

Rewrite as:

[tex](x + 5)x^2(x - 1)^2 = 0[/tex]

Replace 0 with P(x)

[tex]P(x) =(x + 5)x^2(x - 1)^2[/tex]

Hence, a possible formula for P(x) is [tex]P(x) =(x + 5)x^2(x - 1)^2 \\[/tex]

Read more about polynomials at:

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Answer:

398 * 1.034^t

Step-by-step explanation:

P = 398(1 + 3.4%)^t = 398 * 1.034^t

Answer:

C

Step-by-step explanation:

Label the two equations:

-2x -y= 9 -----(1)

2x -9y= 1 -----(2)

(1) +(2):

-2x -y +2x -9y= 9 +1

-2x +2x -y -9y= 10

Simplify:

-10y= 10

y= 10 ÷(-10)

y= -1

Substitute y= -1 into (2):

2x -9(-1)= 1

2x +9= 1

2x= 1 -9

2x= -8

x= -8 ÷2

x= -4

Thus, the solution is (-4, -1).

Answer: y = 2x -7

Step-by-step explanation:

The equation of a line is in the form y = mx + b

We know m = 2

So, y = 2x + b

we need to find b, and we can use either point given to find it:

lets use (2, -3):

-3 = 2(2) + b

-7 = b

now we know, the line's equation is y = 2x -7

Answer:

length

Step-by-step explanation:

because 9/10 will be:

9 divided by 10= 0.9

and 0.85 is greater than 0.9

Answer:

196.25in^3

Step-by-step explanation:

[tex]diameter(d) = 5in \\ radius(r) = 2.5in \\ height(h) = 10in \\ \\ volume = \pi {r}^{2} h \\ volume = 3.14 \times {2.5in}^{2} \times 10in \\ volume = 196.25 {in}^{3} [/tex]

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of a straight line we only need two points off of it, hmmm let's use from the table (-1 , 13) and (2 , 1)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{13})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{13}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}}\implies \cfrac{-12}{2+1}\implies \cfrac{-12}{3}\implies -4[/tex]

The required rate of change in the slope-intercept form is -4. Option A is correct.

The slope of the line is the tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Two coordinates from the table,
(-2, 17) and (-1, 13)
Now,
Rate of change = slope of the function = (13 - 17) / (-1 - (-2))
                                                                 = -4 / 1
                                                                 = -4

Thus, the required rate of change in the slope-intercept form is -4. Option A is correct.

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The velocity of the rock is the number of feet traveled per second

The velocity of the rock is a linear function of time

From the question, we understand that the velocity increases by 32 feet per second for each second

This means that we have the following rates:

Velocity = 0, 32, 64, 96, 128....

Notice that the difference between adjacent numbers is 32.

This means that the velocity changes at a constant rate or slope

Hence, the velocity of the rock is a linear function

Read more about linear functions at:

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Answer:

9.1

Step-by-step explanation:

I went into my calculator and typed in [tex]\sqrt{82}[/tex] and I was given:

9.055385...

So to round the nearest tenth, you look at the tenths place (which is 0) and go one number behind that (which is 5). Since the number behind the tenths place is 5 or higher, you round up to 1

Answer:

1/7 of 21 is 3.

Step-by-step explanation:

If we multiply 1/7 by 21/1, we can 21/7. 21/7 is equivalent to 3.