MATHEMATICS HIGH SCHOOL

The cost of a book is twice that of a magazine.1 book and 4 magazines cost £ 24.
How much does a book cost?

Answers

Answer 1
Answer: The answer to your question is 8

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A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles? in cubic inches

Answers

To find out how much wax is needed for the candles we need to figure out the volume of each candle. We know radius r=0.5 inches and height h=3 inches of the smallest candle and we know that the middle candle has r2=2r=1 inch and h2=2h=6 inches and the biggest candle has r3=3r=1.5 inches and h3=3h=9 inches. So now we need the formula for volume: V=pi*r^2*h and we simply plug in the numbers. First candle is V=3.14*(0.5^2)*3=2.355 inches^3. Middle candle: V2=3.14*(1^2)*6=18.84 inches^3. Biggest candle: V3=3.14*(1.5^2)*9=63.585 inches^3. So overall wax needed to create all three candles is V+V2+V3=2.355 inches^3 + 18.84 inches^3 + 63.585 inches^3=84.78 inches^3.

Answer:

First candle is V=3.14*(0.5^2)*3=2.355 inches^3. Middle candle: V2=3.14*(1^2)*6=18.84 inches^3. Biggest candle: V3=3.14*(1.5^2)*9=63.585 inches^3. So overall wax needed to create all three candles is V+V2+V3=2.355 inches^3 + 18.84 inches^3 + 63.585 inches^3=84.78 inches^3.

Step-by-step explanation:

Which of the following is the equation of a line parallel to the line y=3x+2, passing through the point (10,1)?A. 3x - y=29
B. 3x + y=29
C. -3x-y=29
D. 3x + y=29

Answers

Answer:

Option A

Step-by-step explanation:

We have to find the equation of a line parallel to y = 3x + 2 and passing through (10, 1)

Slope of the given line y = 3x + 2 is 3

So line parallel to this line will have same slope = 3

Now we assume this line is y = 3x + c

It is given that a point ( 10,1 ) lies on this line.

So we put x = 10 and y = 1 in this equation to get

y-intercept

1 = 30 + c

c = - 29

Equation of the line will be y = 3x - 29

or   -3x + y = -29  ⇒ 3x - Y = 29

Option A is the answer.
I think it's A. One way you can identify if they are parallel is if both of the slopes are the same (also both have to have the same signs). 

Write the equation of the parabola with a focus (1,2) and directrix y = 1

Answers

since the y shifted and focus is above directix, parabola opens up
4P(y-k)=(x-h)^2
distance from focus to veretx=distance from vertex to directix=P

from focus to directix is
from 2 to 1 which is 1 distance
1/2=P since 1/2of 1=1/2
4(1/2)(y-k)=(x-h)^2
vertexis 1 higher than directix so add 1/2 to 1 to get 1.5
vertex=(1,1.5)
vertex=(h,k)

equation is
4(1/2)(y-1.5)=(x-1)^2
if you want vertex form
2(y-1.5)=(x-1)^2
divide 2
y-1.5=(1/2)(x-1)^2
add 1.5
y=(1/2)(x-1)^(2)+1.5

Aaron is solving the equation x2 – x = –2 with the quadratic formula. What values should he use for a, b, and c?a = 1, b = –1, c = –2
a = –1, b = 1, c = –2
a = 1, b = –1, c = 2
a = –1, b = 1, c = 2

Answers

A = 1
B = -1
C = 2 is your answer if you solve the equation. 

(And don't worry I didn't copy this person's answers. I just solved it out in my head that's all).
x² - x = -2
x² - x + 2 = 0

Comparing the given equation to Ax² + Bx + C = 0, we get,

A = 1
B = -1
C = 2

20x3 + 12x2 + 5x + 3

Answers

i hope this helps you

Answer: ( 5x+3) (4x2 (squared) + 1)

Step-by-step explanation:

What is the solution to 2x+12=5x-9

Answers

so 2x+12=5x-9
you want all of the unknowns on one side and all of  the known values on the other or
subtract 2x from both sides
12=3x-9
add 9 to both sides
21=3x
divide both sides by 3
7=x
2x+12=5x-9\ \ \ \ |combine\ like\ terms\n\n2x-5x=-9-12\ \ \ \ \ |simplify\n\n-3x=-21\ \ \ \ \ |:-3\n\nx=7
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