MATHEMATICS HIGH SCHOOL

A copier prints 80 pages in 5 minutes. Which unit rate represents this ratio?

A.80 pages per 5 minutes

B.40 pages per 2.5 minutes

C.32 pages per minute

D.16 pages per minute

Answers

Answer 1
Answer: The correct answer is D, 16 pages per minute. A unit rate is a ratio of something to one; in this case, the ratio is 16:1, or 16 pages to 1 minute. To get the unit rate for this problem, divide both numbers by 5 to get how many pages will be printed per 1 minute. 80/5 = 16, so the copier prints 16 pages in 1 minute. Answer choices A and B are not unit rates, and answer choice C is the incorrect unit rate.

Hope this helps!

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Which point lies on a circle that is centered at A(-3, 2) and passes through B(1, 3)?C(-1, -2)

D(-6, 3)

E(-3, -3)

F(-2, 6)

Answers

The equation of a circle:
(x-h)^2+(y-k)^2=r^2
(h,k) - the coordinates of the center
r - the radius

\hbox{the center: } A(-3,2) \nh=-3 \n k=2 \n \n\hbox{the equation:} \n(x+3)^2+(y-2)^2=r^2 \n \n\hbox{the circle passes through B(1,3)} \nx=1 \n y=3 \n \Downarrow \n(1+3)^2+(3-2)^2=r^2 \n4^2+1^2=r^2 \n16+1=r^2 \n17=r^2 \n \n\hbox{the equation is:} \n(x+3)^2+(y-2)^2=17

Plug the coordinates of the points into the equation and check:
C(-1,-2) \n(-1+3)^2+(-2-2)^2=17 \n2^2+(-4)^2=17 \n4+16=17 \n20=17 \nnot \ true \n \nD(-6,3) \n(-6+3)^2+(3-2)^2=17 \n(-3)^2+1^2=17 \n9+1=17 \n10=17 \nnot \ true

E(-3,-3) \n(-3+3)^2+(-3-2)^2=17 \n0^2+(-5)^2=17 \n25=17 \nnot \ true \n \nF(-2,6) \n(-2+3)^2+(6-2)^2=17 \n1^2+4^2=17 \n1+16=17 \n17=17 \ntrue

The answer is F(-2,6).

The product of the first and last digit is equal to 48The sum of the last two digits is greater than 7

The sum of the first two digits is equal to 9

Answers

a,b,c,d\ \rightarrow\ digits\ of\ number\n\n a\cdot d=48\nc+d=7\ \ \Rightarrow\ \ c \leq 7\ and\ d \leq 7\ \ \ (*)\na+b=9\n\na\cdot d=48\ \ \Rightarrow\ \ (*)\ a=8\ and\ d=6\n\na=8\ \ \Rightarrow\ \ 8+b=9\ \ \Rightarrow\ \ b=1\n\nd=6\ \ \Rightarrow\ \ c+6=7\ \ \Rightarrow\ \ c=1\n\nAns.\ number:\ \ 8116

Five eighths added to Q number is 4. Determine the number.

Answers

Yes five eights added to Q is 4!

How to find the area and circumference of a circle given the radius or diameter

Answers

circumference = 2 × pi × radius
area = pi × radius^2

Write an equation in standard form for the line.
Slope is 3, and (1, 6) is on the line.

Answers

Answer:

Step-by-step explanation:

m = 3

(1 , 6)

y - y1 = m(x -x1)

y - 6 = 3(x - 1)

y - 6 = 3x - 3

    y = 3x - 3 + 6

    y = 3x +3

Standard form:

-3x + y - 3 = 0

How do you divide A number with a remainder

Answers

We set up our problem with the long division symbol or the long division bracket. ...Divide the first number of the dividend by the divisor. ...The whole number result, 0, is placed on top to start the quotient. ...Next, subtract the bottom number from the top. ...Next, we bring down the next number of the dividend. hope i helped
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