The ratio of boys to girls in a classroom was 9:8. Half of the girls left the classroom, and then there were 15 more boys than girls. Part i.) How many children were in the classroom in the beginning?

Step-by-step explanation:

Given the equation;

3(x-2) = 4

A sequence of steps for solving the equation is as shown;

Step 1: Open the parenthesis by applying distributive law to distribute 3 over x and 2 as shown;

3(x-2) = 4

3(x)- 3(2) = 4

3x - 6 = 4

Step 2: Add 6 to both sides of the equation (Addition property)

3x-6+6 = 4+6

3x = 10

Step 3: Division property of equality. Divide both sides by 3;

3x = 10

3x/3 = 10/3

x = 10/3

Answer:

The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)

Step-by-step explanation:

Given quadratic polynomial is:

[tex]5x^2-14x+8[/tex]

To factor a quadratic polynomial with leading co-efficient has to be factorized, the leading co-efficient and the constant are multiplied and pairs(a,b) of the product are made so that their sum or subtraction is equal to the co-efficient of x

We get 40 by multiplying 8 and 5

And the pair we get are: 10 and 4

[tex]=5x^2-10x-4x+8\\=5x(x-2)-4(x-2)\\=(5x-4)(x-2)[/tex]

Hence,

The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)

Answer:

AB is parallel to CD - the reasoning looks right aswell although I don't know exactly what I'm answering here.. are you asking to check it?

Answer:

Step-by-step explanation:

-3x+4

-3(-4)+4

12+4

16

Answer:

3x+4

3(-4)+4

12+4

16

Step-by-step explanation:

Answer:

80 meals

Step-by-step explanation:

Set up an equation where x is the number of meals:

100x + 3000 = 70x + 5400

Solve for x:

100x + 3000 = 70x + 5400

30x + 3000 = 5400

30x = 2400

x = 80

So, at 80 meals, the cost of the 2 venues will be the same

Answer:

80 metals

Step-by-step explanation:

100x + 3000 = 70x + 5400

How to Solve for x:

100x + 3000 = 70x + 5400

30x + 3000 = 5400

30x = 2400

x = 80

So, at 80 meals, the cost of the 2 venues will be the exact same

Answer:

$12.60

Step-by-step explanation:

12/100 × 12 = 0.60

12 + 0.60 = 12.60

Answer:

[tex]\bold{\dfrac{63}{32}\ sq\ inches}[/tex]

Step-by-step explanation:

Given that:

Width of stamp = [tex]\frac{7}{8}[/tex] inches

Length of stamp = [tex]\frac{3}{4}[/tex] inches

It is well known that a stamp is in the form of a rectangular shape.

Area of a rectangular shape is given by the following formula:

[tex]Area = Width\times Length[/tex]

Also, there are 3 identical stamps on the envelop, therefore we need to find the area of one stamp and then multiply it with 3 to find the required area.

Required area:

[tex]3\times \dfrac{7}{8}\times \dfrac{3}{4}\\\Rightarrow \bold{\dfrac{63}{32}\ sq\ inches}[/tex]

Answer:

6.1555

Step-by-step explanation:

the 5 is infinite in 6.15 such as 6.155555555 it does not stop

Answer:

6 [tex]\frac{7}{45}[/tex]

Step-by-step explanation:

i have this question and this what i got its right

[tex]\huge\mathtt{Hello!}[/tex]

[tex](6x - 23) = (4x + 9)[/tex]

[tex]6x -4x = 9 + 23[/tex]

[tex]2x = 32[/tex]

[tex]x = 16[/tex]

It is because the sides are equal, so the angles opposite to them also are equal.

Have a nice day!

Given:

Initial population = 45,000

Decreasing rate = 2%

Time = 5 year

To find:

The population after a period of 5 years.

Solution:

Formula used:

[tex]f(t)=ae^{rt}[/tex]

where, a is initial population, r is rate and t is time.

[tex]r=\dfrac{2}{100}=0.02[/tex]

Decreasing rate represented by -0.02.

Substitute a=45000, r=-0.02 and t=5 in the above formula.

[tex]f(5)=45000e^{-0.02(5)}[/tex]

[tex]f(5)=45000e^{-0.1}[/tex]

[tex]f(5)=45000(0.904837418)[/tex]

[tex]f(5)=40717.68381 [/tex]

Approximate the value to the previous integer.

[tex]f(5)\approx 40717 [/tex]

Therefore, the population after 5 years is 40717.

Answer:

40,718

Step-by-step ex

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert. planation:

Answer:

12?

Step-by-step explanation:

Answer:

Iscoccecles

Sorry if i spelled it wrong.

Step-by-step explanation:

Answer:

66m

Step-by-step explanation:

perimeter is the distance all round a figure

perimeter(p)= 2( length(l) + width(w))  or  perimeter= 2 length + 2 width

p= 2(l + w)                                                 or      p =  2l  + 2w

p= 2(16.3 +16.7)                                        or      p=  2(16.3) + 2(16.7)

p=2(33)                                                      or     p=   32.6  +  33.4

p=66m                                                        or     p=  66m

1 foot = 12 inches:

1/72 = 12/x

Cross multiply:

1x = 72 * 12

x = 864 inches

Answer:

The answer is "25680.508"

Step-by-step explanation:

Use formula:

[tex]A=Pe^{rt}[/tex]

   [tex]=20000 \times e^{((0.05) \times (5))}\\\\=20000 \times e^{(.25)}\\\\=25680.508[/tex]

Answer:

0x + y = 6

Step-by-step explanation:

Equation of the Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be written as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It can be later converted to any other form of the line. For example, the standard form is:

[tex]Ax + By = C[/tex]

Let's find the equation by using the given points (0,6) (5,6):

[tex]\displaystyle y-6=\frac{6-6}{5-0}(x-0)[/tex]

Operating:

[tex]\displaystyle y-6=\frac{0}{5-0}(x-0)[/tex]

y - 6 = 0

Or, equivalently:

0x + y = 6

This corresponds to a horizontal line

Answer:

The area of a triangle is:

Step-by-step explanation:

Given the points of a triangle

A(1, 1)

B(2, 3)

C(4, 5)

[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Distance between AB:

[tex]AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}[/tex]

     [tex]=\sqrt{1+4}[/tex]

     [tex]=\sqrt{5}[/tex]

so

Distance between BC:

[tex]BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}[/tex]

     [tex]=\sqrt{2^2+2^2}[/tex]

     [tex]=\sqrt{2^3}[/tex]

     [tex]=2\sqrt{2}[/tex]

so

Distance between AC:

[tex]AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}[/tex]

    [tex]=\sqrt{3^2+4^2}[/tex]

   [tex]=\sqrt{5^2}[/tex]

    [tex]=5[/tex]

so

Semiperimeter = sum of sides ÷ 2            

                       [tex]s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224[/tex]

Area of the triangle:

[tex]A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}[/tex]

[tex]A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}[/tex]

[tex]A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}[/tex]

[tex]A=1[/tex]

Therefore, the area of a triangle is:

Answer:

B, D represent pairs of vertical angles.

___

Other pairs may be congruent, but they are not vertical angles. The lines that look parallel must be assumed to be NOT parallel, because they are not marked in the diagram as being parallel. Thus ∠8 ≠ ∠12, for example.

- sqdancefan

Answer:

booger

Step-by-step explanation:

bc

Answer:

The answer is D

Step-by-step explanation:

Answer:

RHS, RHA, RTS, RTA, BHS

Step-by-step explanation:

Step-by-step explanation:

you have to know how many inches make a foot or vice versa the you do simple proportion by equating the inches to the foot to get the answer. simple as abc

Answer:

Step-by-step explanation:

Answer:

y-intercept(0, -9)

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

Since all the angles are the same in this triangle, all the sides should be the same too.

Hence, 3x - 5 = 4x - 30

5 + -1x = -30

-1x = -35

x = 35

Hope this helped!

Answer:

Considering the fact that this is an equilateral triangle, x would equal 25

Step-by-step explanation:

since in an equilateral triangle all sides are equal, just pick 2 and solve for x

3x-5=2x+20

3x-2x=20+5

x=25

to check work,

4(25)-30=70

3(25)-5=70

2(25)+20=70

Answer:

317

Step-by-step explanation:

hope this helped:))))))

Answer:

100 minutes or 1 hour and 40 minutes

Step-by-step explanation:

3 miles in 30 minutes means 1 mile in 10 minutes

10 miles takes 100 minutes or 1 hour and 40 minutes.

1 hour and 40 minutes

Answer:

8.9

Step-by-step explanation:

Answer:

8.9

Step-by-step explanation:

8 9/10=8+9/10

=8/1+9/10

=(8/1×10/10)+9/10

=80/10+9/10=8 9/10

We know that

89/10

is the same as

89÷10

Then using

Long Division for 89 divided by 10

gives us

=8.9

Answer:

3\4

Step-by-step explanation:

hihihihihihihihihihi