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3 years ago

How many boys are there in a group of 27 students if there are four-fifths as many girls as there are boys?

Mathematics

1 answer:

tekilochka [14]3 years ago

4 0

Answer:

15 boys

Step-by-step explanation:

There are 27 students. The number of girls is only 4/5 of the number of boys. I started by splitting the class. 14 boys and 13 girls doesn't work, so I changed it to 12 and 15. If it was 12 girls and 15 boys, the girls would have 4/5 of the boys, so it must be 12 girls and 15 boys.

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Write the equation of the function whose graph is shown. y = (x + )2 +

Deffense [45]

Quadratic form is given in the form
$y= ax^{2}+bx+c$ , where a, b, and c are constants

We substitute the value (8, 12) and (5,3) in turn

$12= a(8)^{2}+b(8)+c$
$12=64a+8b+c$ ... Equation 1

$3=a(5)^{2}+b(5)+c$
$3=25a+5b+c$ ... Equation 2

Equation 1 - Equation 2 gives
$39a+3b=9$ , we call this Equation 3

We also know that (5, 3) is the turning point of the curve, where the value of $x$ is given by $x=- \frac{b}{2a}$
Substitute $x=5$
$5=- \frac{b}{2a}$
$10a=-b$
$b=-10a$ ... Equation 4

Substitute Equation 4 into Equation 3
$39a+3b=9$
$39a+3(-10a)=9$
$39a-30a=9$
$9a=9$
$a=1$

Now we need to work out the value of $b$ and $c$

Substitute $a=1$ back into equation 4
$-10a=b$
$-10(1)=b$
$b=-10$

Substitute $a=1$ and $b=-10$ into either equation 1 or equation 2

$64a+8b+c=12$
$64(1)+8(-10)+c=12$
$64-80+c=12$
$c=12+80-64$
$c=28$

Hence the equation of the quadratic curve is
$y= x^{2} 10x+28$

8 0

3 years ago

Read 2 more answers

A sector of a circle has a central angle of 60°. find the area of the sector if the radius of the circle is 6 mi.

professor190 [17]

The entire circle has a central angle of 360°.
Because the radius is 6 mi, the area of the circle is
π(6)² = 36π mi².

The sector has a central angle of 60°, therefore it occupies 60/360 = 1/6 of the area of the circle.
The area of the sector is
(1/6)*36π = 6π mi² = 18.85 mi²

Answer: 6π mi² or 18.85 mi².

8 0

3 years ago

(x4 − 9x + 5x7) + (5x − 10 + 3x4 − 2x2)

Svetlanka [38]

Answer:

(x^4 - 9·x + 5·x^7) + (5·x - 10 + 3·x^4 - 2·x^2)

x^4 - 9·x + 5·x^7 + 5·x - 10 + 3·x^4 - 2·x^2

5·x^7 + x^4 + 3·x^4 - 2·x^2 - 9·x + 5·x - 10

5·x^7 + 4·x^4 - 2·x^2 - 4·x - 10

4 0

3 years ago

HELP please its the 4.06 Linear Functions if you know it please help broo and girl or whoever!

MissTica

y= 1/2x +2

if x=0 y=2 (0,2)

if x=2 y = 1/2 *2 +2 =1+2 =3 (2,3)

you now have two points so you can plot the line

4 0

3 years ago

Which equation represents the statement: Three times the sum of a number and 5 is –30?

castortr0y [4]

Answer:

3(n+5)=-30

Step-by-step explanation:

Three times the sum of a number and 5 is - 30

Vocabulary:

times = multiplication, represented with *

sum = addition, represented by +

unknown number = n

Three * the sum of a number and 5

The sum of a number and 5 is the same as saying n + 5

So we are multiplying 3 by n + 5

Because n is an unknown variable we have to separate the sum of n and 5 from being multiplied by 3 with parenthesis. We do this because if we want to multiply 3 by the sum of n and 5. If we put 3 * n + 5 we are only multiplying the unknown variable by 3 not including the 5 that is added to it.

So we get 3( n + 5 ) is -30

3(n+5)=-30 is the answer.

3 0

2 years ago

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