. There are 2 boys for every 3 girls in Mrs. Sorrentino's class. If there are 30 students in
the class, what percentage are boys?

(Please show how to solve this question , step by step!)

Answer: The Inverse variation

Step-by-step explanation:

The phrase “ y varies inversely as x” or “ y is inversely proportional to x” means that as x gets bigger, y gets smaller, or vice versa. This concept is translated in two ways. yx = k for some constant k, called the constant of proportionality.

The domain is the set of x-values for which the equation is true.

The solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:

Given the set of inequalities expressed as;

x + 1 ≤ -3 or -4x < -8

For the inequality expression x + 1  ≤ -3

x  ≤ -3 - 1

x ≤ -4

For the inequality expression:

-4x < -8

Divide both sides by -4

-4x/-4 > -8/-4

x > 2

Hence the solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:

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Answer:

the first one i think sorry it im wrong

Step-by-step explanation:

Answer:

they each get 1/8 of a gallon of orange juice

Step-by-step explanation:

Answer:

x = [tex]\frac{5}{4} + \frac{ \sqrt{5} }{4}[/tex]

x = [tex]\frac{5}{4} - \frac{ \sqrt{5} }{4}[/tex]

Step-by-step explanation:

Quadratic equation:

[tex]x = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}[/tex]

The equation is:

[tex]4x^2 - 10x + 5 = 0\\[/tex]

So:

a = 4

b = -10

c = 5

Plug the variables into the quadratic equation:

[tex]x = \frac{-(-10) +- \sqrt{(-10)^2 - (4 * 4 * 5)} }{(2 * 4)}[/tex]

[tex]x = \frac{\sqrt{10 +- \sqrt{100 - 80} } }{8}[/tex]

[tex]x = \frac{10 + \sqrt{20} }{8}[/tex]

Divide both sides by 8:

10 ÷ 8 = [tex]\frac{5}{4}[/tex]

[tex]\sqrt{20}[/tex] ÷ 8 = [tex]\frac{\sqrt{5}}{4}[/tex]

[tex]\frac{5}{4}[/tex] +- [tex]\frac{\sqrt{5}}{4}[/tex]

This means that the solutions that satisfy the equation is:

x = [tex]\frac{5}{4} + \frac{ \sqrt{5} }{4}[/tex]

x = [tex]\frac{5}{4} - \frac{ \sqrt{5} }{4}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

1) Sum = - 9

Product = -36

Factors = -12 , 3     {-12 + 3 = -9  & -12*3 = -36}

3a²  - 9a - 12 = 3a² + 3a - 12a - 12

                    =3a(a + 1) - 12(a + 1)

                    = (a + 1) (3a - 12)

2) 4a² + 38a - 20 = 4a² + 40a - 2a  - 20

                            =4a(a + 10) - 2(a + 10)

                            =(a + 10)(4a - 2)

3) 11a² + 30a - 9 = 11a² + 33a - 3a - 9

                          = 11a(a + 3) - 3(a + 3)

                          =(a + 3)(11a - 3)

Answer:

8 bags

7 green marbles and 3 yellow marbles

Step-by-step explanation:

Find the GCF of 24 and 56

24 = 4 x 6

= 2 x 2 x 2 x 3

56 = 7 x 8

= 7 x 4 x 2

= 7 x 2 x 2 x 2

The common factors are - 2 x 2 x 2, which is 8.

So the greatest number of bags they can make is 8

Divide the amount of marbles by the number of bags

24 yellow marbles and 8 bags, so 24/8 is 3

56 green marbles and 8 bags, so 56/8 is 7

Hope this helps, let me know if you have any questions

Answer:

[tex]x = 2\sqrt{55}[/tex]  

Step-by-step explanation:

Given the values for the leg and hypotenuse:

a (leg) = 6 cm

c (hypotenuse) = 16 cm

Use the Pythagorean Theorem to find the value of the other leg, x:

[tex]x = \sqrt{c^{2} - a^{2} }[/tex]

[tex]x = \sqrt{16^{2} - 6^{2} }[/tex]

[tex]x = 2\sqrt{55}[/tex]  

Answer:

Your answer is [tex]\sqrt{220}[/tex] or 14.8323969...

Step-by-step explanation:

[tex]A^{2} +B^{2} =C^{2} \\x^{2} + 6^{2} =16^{2}[/tex]

[tex]x^{2} =16^{2} -6^{2} \\[/tex]

[tex]x^{2}[/tex] = 256 - 36

x = [tex]\sqrt{220}[/tex]

Answer:

If she runs for three hours, then she'll run 36 miles

Going at the speed she is going, Leila can travel a distance of 12(3 + t).

The distance that a person can travel is found by:

= Speed x time

The speed here is 12 miles per hour

Time = 3 more than t hours = (3 + t hours)

The distance Leila would have gone is therefore:

= 12 x (3 + t)

= 12 (3 + t)

In conclusion, as the question is not complete, the relevant expression to find the distance is 12 ( 3 + t)

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Answer:

Base

Step-by-step explanation:

A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

The solution to the given equations has infinitely many solutions

Given the following set of equations:

y = 9x - 5

y = 9x + 6

Equating both expressions

9x - 5 = 9x + 6

Collect the like terms

9x - 9x = 6 + 5

0x = 11

x = 11/0

x = ∞

This shows the solution has infinitely many solutions

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Answer: b

Step-by-step explanation: bc khan

Answer:

4%

Step-by-step explanation:

have a lovely day <3

Answer:

4% is 4/100 as a percent

just take the fraction and turn it into a fraction out of 100 which this already is and then the percent is the numerator

Answer:

The slope of Function A is less than the slope of Function B.

Step-by-step explanation:

Using the slope formula:

m = (y2 - y1)/(x2 - x1)

and the following ordered pairs from Function A:

(x1, y1) = (-5, -3)

(x2, y2) = (-10, -8)

m = (y2 - y1)/(x2 - x1)

[tex]m = \frac{-8 - (-3)}{-10 - (-5)} = \frac{-8 +3}{-10+5} = \frac{-5}{-5} = 1[/tex]

Since Function A's slope = 1, and Function B's slope = 4, then it means that the slope of Function A is lesser than the slope of Function B.

Answer: 28

Step-by-step explanation: A positive (+) and a negative (-) together make it a negative (-) which takes the positive away (+) making it 33 - 5 = 28

Answer:

28

Step-by-step explanation:

Subtract 33 - 5. You should get 28. But since the greater number is positive, the answer will be positive.

Answer:

the answer would be 40%.

The upper bound means the highest number that you can round up to the nearest unit, in this case meters. So the upper bound for the distance of 100 meters is 100.4 meters.

Answer:

bye

Step-by-step explanation:

Given :-

To find :-

Solution :-

As we know that ,

Substitute ,

Answer:16/20 equals 4/5

Step-by-step explanation:they are asking what is the probability that it is green so we know that 16 counters is green and total counters is 20 so it’s 16/20 and then you simplify it the answer is 4/5

Answer:

204

Step-by-step explanation:

Answer:

range 18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

1. The range of a data set is the difference between the largest and smallest number. In this case, the largest number is 28, and the smallest number is 10.

Therefore, the range is 18.

Answer:

Step-by-step explanation:

Let ABCD be a rhombus, all sides of the rhombus have equal length and its diagonal AC and BD are intersecting each other at a point O.

As we know that the diagonals in the rhombus bisect each other at 90°.

So, AO can be written as (AC/2)  

= 16/2  

= 8 cm

And, DO can be written as (BD/2)

= 30/2  

= 15 cm

Then, consider the triangle AOD and apply Pythagoras theorem,  

AD2 = AO2 + DO2

AD2 = 82 + 152

AD2 = 64 + 225

AD2 = 289

AD = √289

AD = 17 cm

Hence, the length of each side of the rhombus is 17 cm

Now,

The perimeter of rhombus = 4 × side of the rhombus

= 4 × 17

= 68 cm

Therefore, the perimeter of the rhombus is 68 cm.

Answer:

functions: first one, third one, fifth one, seventh one, eigth one

the rest are not function

Step-by-step explanation:

if it is a function it either passes the line test or it doesnt have two outputs

Answer:

y² = 7

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

The traingels are similar so we can conpare sides.

3 is to 18 as 2 is to 4x or

3/18 = 2/4x

1/6 = 1/2x

6 = 2x

3 = x

Answer:

7,58,406 ,   7,85,046 ,    7,85,460 ,   7,85,640  

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

70 minutes for 24 songs

70/2 minutes for 24/2 songs

35 minutes for 12 songs.

Answer:

35 minutes for 12 songs

Step-by-step explanation:

hope this helps

Answer: 13/14 = 169/182

Step-by-step explanation:

If you do 13 x 182 = 2,366

And then do 14 x 169 = 2,366

Making both sides equal if you multiple the numerator by denominator using cross multiplication

The fraction number 13/14 is equal to the fraction number 169/182. Then the true statement is A.

Algebra is the study of mathematical symbols, while logic is the manipulation of those icons.

The product is another name for it. If the same thing, n, is delivered to m different people, we merely multiply them.

The fraction number is given below.

⇒ 13/14 and 169/182

Multiply the fraction number 13/14 by 13 in numerator and denominator. Then the expression is written as,

⇒ (13 x 13)/(14 x 13)

⇒ 196 / 182

The fraction number 13/14 is equal to the fraction number 169/182. Then the true statement is A.

More about the Algebra link is given below.

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