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pentagon [3]
3 years ago
8

George read 15 pages in a book in 12 minutes. At this rate, how long will it take him to finish the book if it has 85 pages?

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
3 0

Answer:

Step-by-step explanation:

Set up a ratio in the form of pages/minute:

\frac{pages}{minute} :

then fill in next to that how many pages per minute George can read:

\frac{pages}{minute}:\frac{15}{12}

Now we want to figure out how long (time is our unknown, so we call that x) it will take him to read 85 pages.  The 85 goes in a ratio on the same line as the other number of pages:

\frac{pages}{minute}:\frac{15}{12}=\frac{85}{x}

Cross multiply to get 15x = 1020

Now divide both sides by 15 to get x = 68 minutes, which is an hour and 8 minutes.

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Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.
Nezavi [6.7K]

Answer:

\displaystyle a = \frac{8}{5}.

Step-by-step explanation:

Two vectors (x_1,\, y_1) and (x_2,\, y_2) are parallel to one another if and only if the ratio between their corresponding components are equal:

\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}.

Equivalently:

\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}.

For the two vectors in this equation to be parallel to one another:

\displaystyle \frac{a}{4} = \frac{2}{5}.

Solve for a:

\displaystyle a = \frac{8}{5}.

\displaystyle \frac{8}{5} would be the only valid value of a; no other value would satisfy the \displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2} equation.

4 0
3 years ago
- Jimmy is 440 miles from home, but he is driving back at a speed of 60 mph. Which equation
Musya8 [376]

440d=60t            it would take jimmy 7.33 hours to get home if he drove at a constant rate of 60 Miles Per Hour

8 0
3 years ago
What is best estimate for 31.9 divide by 4
butalik [34]
Hi there.

The best way to estimate starts by rounding.

31.9 rounds up to 32.

32/4 = 8

The best estimate for 31.9 divided by 4 is 8.

Let me know if you spot any errors :)
3 0
3 years ago
Read 2 more answers
The center of a circle is located at (3, 8), and the circle has a radius that is 5 units long. What is the general form of the e
lana [24]
First we write equation that consist  coordinates of center and radius. That formula goes like this:
(x-x1)^2 + (y-y1)^2  = r^2

x and y are coordinates on any point on circle
x1 and y1 are coordinates of center of circle.
r is radius of that circle. now we need to express our values for center and radius andf square binoms and see what matches in our options.

(x-3)^2 + (y-8)^2 = 5^2
x^2 + y^2 -6x -16y +48 = 0

The answer is first option.
5 0
3 years ago
What is the value of ( h o k ) (2)<br><br>a -5<br><br>b 1<br><br>c -2<br><br>d -3
Bond [772]

Answer:

-3

Step-by-step explanation:

h(k(2)) = h(k(x=2)) = h(-2) = h(x= -2)= 3/( -2+1) = 3/-1= -3

sorry if I'm wrong.

3 0
3 years ago
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