MATHEMATICS MIDDLE SCHOOL

Given that (4p-5q)/(6p+q) = 1/4 , find the value of 2p : 7q in its lowest term.

Answers

Answer 1

Answer:

Answer 2

Answer:

Start from

$\cfrac{4p-5q}{6p+q} = \cfrac{1}{4}$

and cross multiply the denominators (i.e. multiply both sides by $4(6p+q)$

The result is

$4(4p-5q) = 6p+q$

Expand the left hand side:

$16p-20q = 6p+q$

Bring all terms involving p to the left, and all terms involving q to the right:

$16p-6p = 20q+q \implies 10p=21q$

Divide both sides by 21q:

$\cfrac{10p}{21q} = 1$

Now we have a ratio between multiples of p and q. It's not exactly the one we want, though. Nevertheless, we can keep multiplying both sides by approriate constants in order to get the ratio we want:

Divide both sides by 5:

$\cfrac{2p}{21q} = \cfrac{1}{5}$

Multiply both sides by 3:

$\cfrac{2p}{7q} = \cfrac{3}{5}$

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What is the surface area of a cube with faces that each have an area of 12 cm2?

Answers

a cube has 6 identical sides
if total surface area is the area of the sides added up
since 1 side=12 cm^2
then 6 sides=12 times 6 cm^2=72 cm^2

the total surface area=72 cm^2

Since a cube has 6 sides, and each side has an area of 12 cm² , just multiply 6 x 12 = 72
the surface area of the cube is 72 cm ².

How many 4-digit numbers can be created from the digits 6, 4, 2, 9, 7 and 1 without repeating any?

Answers

Total sets of 4-digits = 6
Total 4-digit numbers formed by one set of number = 4
So, total numbers that can be formed = 6 × 4 = 24

How many pints are in a gallon

Answers

It countains 8 pints

Which sets of numbers represent geometric sequences? Check all that apply.2/5,2/10,2/20,2/40...

11/12,8/12,5/12,2/12

25, 19, 13, 7, ...

4, 12, 36, 108, ...

–5, 5, –5, 5, ...

–3, 0, 3, 6, ...

–8, –2,1/2.1/8...

Answers

Answer:

2/5,2/10,2/20,2/40...

4, 12, 36, 108, ...

–5, 5, –5, 5, ...

Step-by-step explanation:

These 3 sets represent a geometric sequence.

A geometric sequence is a series of numbers where each number is obtained by MULTIPLYING the same fixed number to the previous number.

So, in the first sequence: 2/5,2/10,2/20,2/40...

The multiplying factor is 1/2.

In the second sequence: 4, 12, 36, 108, ...

The multiplying factor is 3

In the 3rd sequence: –5, 5, –5, 5, ...

The multiplying factor is -1.

Most of the other sequences are not geometric sequences, but arithmetic sequences (where the next term is obtained by ADDITION).

the one above me is correct

How do you find an equal ratio for example is 63:27 14:6 a equivalent ratio?

Answers

Answer:

Step-by-step explanation:

Find a common denominator or greatest common factor. 63 and 27 are both multiples of 9. When you divide each by 9 you get 7:3. 14 and 6 are both multiples of 2. When you divide each by 2 you get 7:3 again. So these ratios are equivalent.

Start with any set of numbers. Multiply them each by the same factor and the new set will be an equivalent ratio.

Write the rational number as a decimal -21/16

Answers

$- (21)/(16) = \boxed{\bf{1.3125}}$

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