A school is electing students for class officers. There are four offices: president, vice president, secretary, and treasurer. The student with the most votes becomes president, second highest number of votes is vice president, and so on. If there are students in this class, how many ways can students be elected?

Answer/Step-by-step explanation:

Since ∆PHS ≅ ∆CNF, therefore:

<P ≅ <C,

<H ≅ <N

<S ≅ <F

Thus:

Since, <P ≅ <C, therefore,

36° = (4z - 32)°

36 = 4z - 32

Add 32 to both sides

36 + 32 = 4z

68 = 4z

Divide both sides by 4

68/4 = z

17 = z

z = 17

Since <H ≅ <N, therefore:

6x - 29 = 115°

Add 29 to both sides

6x = 115 + 29

6x = 144

Divide both sides by 6

x = 114/6

x = 24

m<F + m<C + m<N = 180° (sum of ∆)

(3y - 1) + (4z - 32) + 115 = 180 (substitution)

Plug in the value of z and solve for y

3y - 1 + 4(17) - 32 + 115 = 180

3y - 1 + 68 - 32 + 115 = 180

3y + 150 = 180

Subtract 150 from both sides

3y = 180 - 150

3y = 30

y = 10

The value of x, y and z are 24, 10 and 17 respectively.

PHS≅CNF

Therefore,

∠P ≅ ∠C

∠H ≅ ∠N

∠S ≅ ∠F

36 = 4z - 32

36 + 32 = 4z

4z = 68

z = 68 / 4

z = 17

6x - 29 = 115

6x = 115 + 29

x = 144 / 6

x = 24

3y - 1 = 180 - 115 - (4z - 32)

3y - 1 = 180 - 115 - 4z + 32

3y - 1 = 97 - 4(17)

3y - 1 = 29

3y = 30

y = 30 / 3

y = 10

learn more: https://brainly.com/question/20502277?referrer=searchResults

Step-by-step explanation:

[tex]{:}\longrightarrow[/tex][tex]\sf 2 (x+4)+(x+1)=6 (2x)[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 2x+8+(x+1)=12x [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 2x+8+x+1=12x [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 2x+x+8+1=12x [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3x+9=12x [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 12x=3x+9 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 12x-3x=9 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 9x=9 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {9}{9}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=1 [/tex]

Answer:

x=3.5

Step-by-step explanation:

subract 5 on the other side, than divide by 2

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Work Shown:

Solve the given equation for y

2y = 3x - 10

y = (3x-10)/2 ..... divide both sides by 2

y = (3x)/2 - 10/2

y = (3/2)x - 5

The equation is in y = mx+b form with m = 3/2 as the slope.

The perpendicular slope is -2/3 because we flip the fraction and the sign from positive to negative.

Note how multiplying the original slope 3/2 and the perpendicular slope -2/3 leads to -1

(3/2)*(-2/3) = -1

This is true for any pair of perpendicular lines, assuming neither line is vertical.

Answer:

The first is 1:6 and the second one is 4

Step-by-step explanation:

Answer:

2775

Step-by-step explanation:

Hope this helped :)

Answer:

7

Step-by-step explanation:

[tex]\frac{10}{5} = \frac{14}{x}\\10x=70\\x=7[/tex]

Answer:

The solutions to the quadratic equation using the quadratic formula will be:

[tex]x=\frac{1}{2},\:x=\frac{1}{4}[/tex]

Step-by-step explanation:

Given the equation

[tex]8x^2-6x+1=0[/tex]

solving with the quadratic formula

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\mathrm{For\:}\quad a=8,\:b=-6,\:c=1[/tex]

[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}}{2\cdot \:8}[/tex]

as

[tex]\sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}=2[/tex]

so

[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:2}{2\cdot \:8}[/tex]

Separating the solution

[tex]x_1=\frac{-\left(-6\right)+2}{2\cdot \:8},\:x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}[/tex]

solving

[tex]x_1=\frac{-\left(-6\right)+2}{2\cdot \:\:8}[/tex]

    [tex]=\frac{6+2}{2\cdot \:8}[/tex]

   [tex]=\frac{8}{16}[/tex]

   [tex]=\frac{1}{2}[/tex]

and

[tex]x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}[/tex]

   [tex]=\frac{6-2}{2\cdot \:\:\:8}[/tex]

    [tex]=\frac{4}{16}[/tex]

    [tex]=\frac{1}{4}[/tex]

Therefore, the solutions to the quadratic equation using the quadratic formula will be:

[tex]x=\frac{1}{2},\:x=\frac{1}{4}[/tex]

Answer:

1/4 1/2

Step-by-step explanation:

Answer:

100 1/4

Step-by-step explanation:

Answer:

251.24$

Step-by-step explanation:

In order to find the answer to this question you just need to add the total cost together.

What we do know:

[tex]B=56.24[/tex]

[tex]NM=195[/tex]

[tex]56.24+195=251.24[/tex]

[tex]=251.24[/tex]

Hope this helps.

Answer:

1,061.64

Step-by-step explanation:

Im sorry if this is wrong

Answer:

32

Step-by-step explanation:

8 times 4 = 32

Answer: the answer is 32

Step-by-step explanation:

He made 8 key chains each week for 4 weeks 8*4 is 32 because if you make 8 key chains for 4 weeks it will add up to 32 hope this helps

Answer:

Television = $200 and DVD player = $450

Step-by-step explanation:

→ Make 2 equations

Televisions = t and DVD players = d

2t + 3d = 1750

4t + d = 1250

→ Multiply the bottom equation by 3 to make the same variable of d

2t + 3d = 1750

12t + 3d = 3750

→ Minus the two equations to isolate the d variable

-10t = -2000

→ Divide both sides by -10 to find the cost of one television

t = 200

→ Substitute t = 200 back into 4t + d = 1250

800 + d = 1250

→ Minus 800 from both sides to isolate d

d = 450

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

That's the rifgt answer for sure!!

Plz Mark brainliest...

Answer:

seven hundred and three dollars

Step-by-step explanation:

Answer:

seven hundred three

Step-by-step explanation:

just read it in hundreads

its 5=54                                            that is what i thsiknss

1 pound = 16 ounces

1 week = 7 days

0.1 x 7 = 0.7 pounds per week

0.7 x 16 = 11.2 ounces

0.1 lb/ day converts to 11.2 ounces / week

Answer:

HOPE THIS HELPS!!!

Step-by-step explanation:

To find the product,

✔ multiply

the numerators and

✔ multiply

the denominators.

The product is

✔ 2/15

Divide:  2

5

 ÷  3

5

To divide, multiply by the

✔ reciprocal

.

The quotient is

✔ 2/3

.

Answer:

Izzdebizz was right i am at teacher

Step-by-step explanation:

Answer:

Step-by-step explanation:

For number 1 the rate of change is 12 per 1  and for number 2 b is linear.

Answer: For my opinion, I think it's either A or B.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

$500 + $100x > 1200

x represents the months

Answer:

9/8

Step-by-step explanation:

1/2 = 4/8

5/8 + 4/8 = 9/8

Answer:

x = 6

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Set up equation

(8x + 2) + 70 + 60 = 180

Step 2: Solve for x

Answer:

what? there is nothing here... did you mean to attach a picture?

Step-by-step explanation:

Answer:

this is the Formel 4000:100×4=160

Answer:

Rigid transformations preserve segment lengths and angle measures.

Rigid transformations produce congruent figures.

If two figures are congruent, then there is a rigid transformation or a combination of rigid transformations that will map one onto the other.

Step-by-step explanation:

All of the answers are correct, meaning that A,B, and all true.