What is the fastest way to solve the following question:
The ratio of boys to girls in Mr. Brown's class is 2:3. If there are 30 students in the class, how many more girls than boys are in the class?

Hello there! :)

The first step is to use the Distributive Property.

It states that

a(b+c)=ab+ac

Let's distribute 3, using this property:

3(x-6)=3x-18

Now, our inequality looks like so:

12+x≤3x-18

The next step is to move the variables to the left, using the opposite operation:

12+x-3x≤-18

12-2x≤-18

Now, move all the numbers to the right, using the opposite operation:

-2x≤-18-12

-2x≤-30

Divide both sides by -2 to isolate x.

Remember that when we divide by a negative variable, we change the inequality sign:

x≥15

Therefore, x≥15

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

Answer:

answer 215 nickels

Step-by-step explanation:

Answer:

18 meters by 9 meters (or 9 meters by 18 meters)

Step-by-step explanation:

lets say the dimensions are x and y. we have x*y=162, and 2x+2y=54. from the second equation we have x+y=27 so y=27-x. plug this into the first equation to get x(27-x)=162 or -x^2 + 27x = 162. x^2 - 27x + 162 = 0. simplify to get (x-18)(x-9)=0. so x=18 or x=9. when x=18, y=9, when x=9, y=18 so the dimensions are 18 by 9 meters

Answer:

check online for more information

Answer:

7

Step-by-step explanation:

(x - 5)(x + 2) = 0

x = 5 & -2

Now,

given

r > s

r = 5, s = -2

Now,

=> r - s

=> 5 - (-2)

=> 5 + 2

=> 7

Answer: no

Step-by-step explanation:

the angle is too steep

Step-by-step explanation:

please mark me as brainlest

Arlen already established that ΔRST and ΔUTS has two pairs of congruent angles and a pair of congruent included sides, which meet the ASA Congruence Criterion. Therefore:

The ASA Congruence Criterion states that for two triangles to be considered congruent to each other, both triangles must have a pair of congruent included sides and two pairs of congruent angles.

Thus, the two-column proof that shows that RS ≅ TU that Arlen is trying to write, has already established that ΔRST and ΔUTS has the following:

Two pairs of congruent angles - ∠RST ≅ ∠UTS and ∠RTS ≅ ∠UST.

A pair of congruent included sides - ST ≅ S.

These satisfy the ASA Congruence Criterion. Therefore:

Learn more about the ASA Congruence Criterion on:

https://brainly.com/question/11637992

Answer:

The total cost for two packets of Fig rolls is £1.62

Step-by-step explanation:

Answer: 102

Step-by-step explanation:

Answer:

$2.10

Step-by-step explanation:

Answer:

$2.1

Step-by-step explanation:

2 x 0.05 = 0.1

5+0.1 = $2.1

Answer:

[tex]\huge\boxed{\sf p = 48\°}[/tex]

Step-by-step explanation:

Since, interior angles of a triangle add up to 180 degrees.

So,

S + Q + R = 180°

S + 44 + 40 = 180

S + 84 = 180

Subtract 84 to both sides

S = 180 - 84

S = 96°

Since S is divided into two p angles because ST is an angle bisector (dividing the angle into two "equal" parts)

So,

S =  p + p

S = 2p

96 = 2p

Divide both sides by 2

48 = p

OR

p = 48°

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

[tex]y = x-5~~....(i)\\\\y =x^2-5x+3~~.....(ii)\\\\\text{Substitute}~ y= x-5 ~\text{in equation (ii):}\\\\x-5 = x^2 -5x +3\\\\\implies x^2 -5x -x +3 +5 =0\\\\\implies x^2 - 6x + 8 =0\\\\\implies x^2 --4x -2x +8 =0\\\\\implies x(x-4) -2(x-4) =0\\\\\implies (x-4)(x-2)= 0\\\\\implies x =4~~ \text{or}~~ x = 2\\\\\text{Substitute x = 4 in equation (i):} \\\\y = 4-5 = -1\\\\\text{Substitute x = 2 in equation (i):} \\\\y = 2-5 = -3\\\\\text{Hence,}~ (x,y) = (4,-1)~ \text{and}~ (x,y) = (2,-3)}[/tex]

Answer:

y = 65 degrees

Step-by-step explanation:

You can use a vertical angle to figure this out. Since 65 is a vertical angle to y, it equals the same amount. I have attached an image of an example of vertical angles. They are on the opposite side of the line.

Answer:

A

Step-by-step explanation:

Answer: I don't really know because there is no picture of what coordinate A was before it was reflected across x-axis.

Answer:

Hope this helps

Step-by-step explanation:

a) x^2 + 3x = x(x+3)

b) 2x^2 - 8x = 2x(x - 4)

c) 6x + 9x^3 = 3x(2 + 3x^2)

d) 12x^3 - 4x^2 = 4x^2(3x - 1)

Answer:

They are both correct but they rounded to different places. Scrooge rounded to the nearest whole number while Bon rounded to the nearest tenth.

Step-by-step explanation:

Scrooge rounded up to the next whole number which was three because the tenth place value was 5 or greater.

While Bob on the other hand rounded to the nearest tenth. Which resulted in the number going down because the number in the hundredth place value was less than 5.

Answer:

Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two. Notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). Dilations involve multiplication! Dilation with scale factor 2, multiply by 2.

Step-by-step explanation:

Make me brainlest.

Answer:

False

That is an equation as shown by the = sign.

An inequality has an inequality sign like '<' .

Answer:

15,000 liters

Step-by-step explanation:

First, find the volume in meters. 5*3*1=15 meters

1 meter = 1000 liters

(x15)

15 meters = 15000 liters

Hope this helped :D

Answer:

y=4x-5

Step-by-step explanation:

8x-2y=10

-8

-2y=-8x+10

-2= -2   -2

y=4x-5

Answer: the answer is inside the triangle

Answer:

x=17

Step-by-step explanation:

angle O is equal to angle M.

This means (5x-10)=75

add 10 degrees to both sides

5x=85

divide both sides by 5

x=17

They would meet 30 times after 10 minutes.

Since Nick and Sally run on the 100m straight track, and Nicks's speed is 3m / s, while Sally's speed is 2m / s, if they both start from two sides of the track, running towards each other continuously, to determine how many times they would meet each other after 10 minutes the following calculation should be performed:  

Therefore, they would meet 30 times after 10 minutes.

Learn more about maths in https://brainly.com/question/25849676

Answer:

157.8

Step-by-step explanation:

so since its on a 80% discount we want to see how much 80% is on $790 which was its initial price. To find out the percentage of $790 we need to multiply $790 by 0.80 which will equal to 631.2.

the answer is 157.8

you have to subtract 790 with 631.2

Answer:

2.829 mm

Step-by-step explanation:

Correct:  2.83 mm

Measured(mm)    Difference (mm)

2.837             0.007

2.829            -0.001  Smallest deviation from actual.

2.812            -0.018

2.805            -0.025

The measurement of the piece of metal that is the most accurate is 2.837 cm.

A piece of metal with a length of 2.83 cm was measured using four different devices.

Which of the following measurements is the most accurate?

A piece of metal with a length of 2.83 cm was measured using four different devices.

Accuracy is the degree to which the measured value is close to the correct value.

The difference between the accepted value and the measured value of the quantity is called the error of measurement.

The measurement for the first device is,

[tex]=2.83 - 2.837\\\\=-0.007[/tex]

The measurement of the first device is -0.007.

The measurement for the second device is,

[tex]=2.83 - 2.829\\\\=-0.001[/tex]

The measurement of the second device is -0.001.

The measurement for the third device is,

[tex]=2.83 - 2.812\\\\=-0.018[/tex]

The measurement of the third device is -0.018.

The measurement for the fourth device is,

[tex]=2.83 - 2.805\\\\=-0.025[/tex]

The measurement of the fourth device is -0.02.

Hence, The measurement that is the most accurate is 2.837 cm.

For more details about Substitution refer to the link given below.

https://brainly.com/question/2785991

Answer:

The angles are supplementary meaning they equal 180 degrees so the angles have to equal 180.

p + 7 + 3p + 1 = 180

4p + 8 = 180

-8          -8(subtracting 8 from both sides)

4p = 172

/4     /4(dividing by 4 on both sides)

p = 43

Answer:

(p + 7) + (3p + 1) = 180

p + 7 + 3p + 1 = 180

4p + 8 = 180

4p = 180 - 8

4p = 172

•°• p = 172/4 = 43

Answer:

d + 8/hr

Step-by-step explanation:

Step-by-step explanation:

female workers:2250

% female workers:?

First, find the percentage of workers who aren't men since we are told the number of workers who aren't men

100-55=45

Therefore 45% of workers aren't men

Let the total number of workers =x

Now form an equation for the problem

[tex]x \times \frac{45}{100} = 2250[/tex]

[tex]x = 2250 \div \frac{45}{100} [/tex]

[tex]x = 5000[/tex]

Therefore, there are 5000 workers in total