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2 years ago

The ratio of boys to girls in a group is 7:2. If there are 60 more boys than girls, work out how many girls there are.

Mathematics

1 answer:

zimovet [89]2 years ago

7 0

Answer:

Step-by-step explanation:

So, kids are divided into 8 total parts.

7 - 1 = 6 more parts that are boys. The 48 extra boys are those 6 parts.

48/6 = 8 boys per part

All parts have the equal number of kids, so one part girls also has 8.

There are 8 girls (and 56 boys. 8:56 = 1:7).

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Which angle pairs are supplementary? Check all that apply. ∠1 and ∠2 ∠4 and ∠3 ∠4 and ∠5 ∠7 and ∠5 ∠3 and ∠6.

Alla [95]

Answer:

∠4 and ∠3

∠4 and ∠5

∠3 and ∠6.

Step-by-step explanation

Find the diagram attached

First you must note that the sum of two supplementary angles is 180°

Also, since the sum of angle on a straight line is 180°, the angles that are supplementary must lie on the same straight line.

Based on the diagram, the pair of angles that lies on the same straight line are ∠4 and ∠3, ∠4 and ∠5 and ∠3 and ∠6. If that is the case, hence this angles are supplementary.

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2 years ago

Try this hard Math Problem if you dare!!

Dennis_Churaev [7]

Answer:

a. $(x - 3)^2 + 16$

b. $8(x -7)^2$

c. $(a^2 - 1)(7x - 6)$ or $(a+1)(a-1)(7x-6)$

d. $(x^2-4)(x^2+3)$ or $(x-2)(x+2)(x^2+3)$

e. $(a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})$

Step-by-step explanation:

$a.\ (x + 1)^2 - 8(x - 1) + 16$

Expand

$(x + 1)(x + 1) - 8(x - 1) + 16$

Open brackets

$x^2 + x + x + 1 - 8x + 8 + 16$

$x^2 + 2x + 1 - 8x + 24$

Collect Like Terms

$x^2 + 2x - 8x+ 1 + 24$

$x^2 - 6x+ 25$

Express 25 as 9 + 16

$x^2 - 6x+ 9 + 16$

Factorize:

$x^2 - 3x - 3x + 9 + 16$

$x(x -3)-3(x - 3) + 16$

$(x - 3)(x - 3) + 16$

$(x - 3)^2 + 16$

$b.\ 8(x - 3)^2 - 64(x-3) + 128$

Expand

$8(x - 3)(x - 3) - 64(x-3) + 128$

$8(x^2 - 6x+ 9) - 64(x-3) + 128$

Open Brackets

$8x^2 - 48x+ 72 - 64x+192 + 128$

Collect Like Terms

$8x^2 - 48x - 64x+192 + 128+ 72$

$8x^2 -112x+392$

Factorize

$8(x^2 -14x+49)$

Expand the expression in bracket

$8(x^2 -7x-7x+49)$

Factorize:

$8(x(x -7)-7(x-7))$

$8((x -7)(x-7))$

$8(x -7)^2$

$c.\ 7a^2x - 6a^2 - 7x + 6$

Factorize

$a^2(7x - 6) -1( 7x - 6)$

$(a^2 - 1)(7x - 6)$

The answer can be in this form of further expanded as follows:

$(a^2 - 1^2)(7x - 6)$

Apply difference of two squares

$(a+1)(a-1)(7x-6)$

$d.\ x^4 - x^2 - 12$

Express $x^4$ as $x^2$

$(x^2)^2 - x^2 - 12$

Expand

$(x^2)^2 +3x^2- 4x^2 - 12$

$x^2(x^2+3) -4(x^2+3)$

$(x^2-4)(x^2+3)$

The answer can be in this form of further expanded as follows:

$(x^2-2^2)(x^2+3)$

Apply difference of two squares

$(x-2)(x+2)(x^2+3)$

$e.\ a^{4n} -b^{4n}$

Represent as squares

$(a^{2n})^2 -(b^{2n})^2$

Apply difference of two squares

$(a^{2n} -b^{2n})(a^{2n} +b^{2n})$

Represent as squares

$((a^{n})^2 -(b^{n})^2)(a^{2n} +b^{2n})$

Apply difference of two squares

$(a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})$

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3 years ago

write a decimal between 0.5 and 0.75. then write it as a fraction in simplest form and as a percent. (PLZZ HELP MEH)

crimeas [40]

Decimal 0.6
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fracrion 3/5

4 0

2 years ago

How long does it take to drive 272 miles going 68mph

DedPeter [7]

272mi/68mi/hr= 4 hr

Example:
Calculate the acceleration of a boat that has been cruising at 15 m/s but speeds up to 45 m/s in about 6 seconds. Don’t forget your units, m/s2. In order to calculate the acceleration of the boat we first have to identify the suited formula for acceleration in this scenario. 

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Solution: 
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3 years ago

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Misha Larkins [42]

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3 years ago