During a football game, the parents of the players are selling pretzels and popcorn to make money. They charge $2.50 for a bag of popcorn and $2 for a pretzel. The parents collect $336 in sales. They sell twice as many bags of popcorn as pretzels.

Write a system of equations to represent the situation.

How many pretzels did they sell?

Answer:

A. Since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.

B. A'B' = 30

Step-by-step explanation:

A. Two triangles are said to be similar if their corresponding angles are congruent to each other.

To know whether ∆ABC and ∆A'B'C' are similar, let's find the measure of their angles each, and see if their corresponding angles are congruent to each other.

∆ABC:

m<A = 59°

m<B = 37°

m<C = 180 - (37 + 59) = 84°

∆A'B'C':

m<A' = 59°

m<B' = 180 - (59 + 84) = 37°

m<C' = 84°

As we can see,

Angle A is congruent to Angle A'

Angle B is congruent to Angle B'

Angle C is congruent to Angle C'

Therefore, since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.

B. AC = 8; A'C' = 12; AB = 20

Since ∆ABC is similar to ∆A'B'C', the ratio of their corresponding sides would be equal.

Therefore:

AC/A'C' = AB/A'B'

Plug in the values into the equation

8/12 = 20/A'B'

Cross multiply

A'B'*8 = 20*12

A'B'*8= 240

Divide both sides by 8

A'B' = 240/8

A'B' = 30

Answer:

x<−8

Step-by-step explanation:

4x+49−9<−x

4x+40<−x

40<−x−4x

−

​5

​

​40

​​ >x

−8>x

x<−8

This question is incomplete

Complete Question

An arts academy requires there to be 6 teachers for every 132 students and 4 tutors for every 44 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has 132 students​?

Answer:

a)How many students does the academy have per​ teacher?

22 students per teacher

b) Per​ tutor?

11 students per tutor

c) How many tutors does the academy need if it has 132 students​?

12 tutors

Step-by-step explanation:

a)How many students does the academy have per​ teacher?

6 teachers = 132 students

1 teacher = x

6 × x = 132 × 1

x = 132 × 1/6

x = 22 students

Hence, we have 22 students per tutor

b) Per​ tutor?

4 tutors = 44 students

1 tutor = x students

Cross Multiply

4 × x = 1 × 44

x = 44/4

x = 11 students

Hence, we have 11 students per tutor

c) How many tutors does the academy need if it has 132 students​?

44 students = 4 tutors

132 students = x tutors

Cross Multiply

44 × x = 132 × 4

44x = 132 × 4

x = 132 × 4/44

x = 12 tutors

The academy needs 12 tutors if they have 132 students.

Answer: A. f(x) = (x - 1)²

Step-by-step explanation:

Answer:

y = 1/4x + 5/2

Step-by-step explanation:

slope = rise over run

1 rise for 4 run

y intercept = 5/2

Answer:

Girls in Mr. Chang's class: 28 - 21 ; # girl students = # total students - # boy students ; 7 girl students.

Boys in Mr. Chang's class: 28 - 7 ; # boy students = # total students - girl students ; 21 boy students.

Answer:

b=74degrees

Step-by-step explanation:

First find angle a

180-112-33=35

use angle a to find b

180-35-71=74

Answer:

_3x>+31 but I am not sure

Step-by-step explanation:

-5x<-2x+8+23

-3x>+31

Answer:

x > -5

Step-by-step explanation:

1.) Add +5x on both sides

-5x + 8 < - 2x + 23

+5x         +5x      

8    <    3x + 23

2.) Subtract 23 from both sides

8    <    3x + 23

-23            -23

-15  <  3x

3.) Divide by 3 on both sides

-15 <  3x

 3        3

-5 < x

Because you divided by a negative, the sign flips

-5 > x

Answer:

The constant of proportionality is 3.50.

Step-by-step explanation:

We know that when y directly varies with x, such that

[tex]y=kx[/tex]

The number 'k' is called the constant of proportionality.

Given the equation

[tex]y=3.50x[/tex]

as

[tex]y=kx[/tex]

so

[tex]k=3.50[/tex]           ∵ [tex]y=kx[/tex]

Here the value of k = 3.50, which is the constant of proportionality.

Therefore, the constant of proportionality is 3.50.

Answer:

-2.50

Step-by-step explanation:

Using the formula for the expected value, it is found that the expected pay off is of -$1.

In this problem, the outcomes and probabilities are, considering the cost of the game of $5 and that there are 6 sides:

Hence:

[tex]E(X) = \frac{3}{6}(-5) + \frac{2}{6}(2) + \frac{1}{6}(5) = \frac{3(-5) + 2(2) + 1(5)}{6} = -\frac{6}{6} = -1[/tex]

The expected pay off is of -$1.

To learn more about expected value, you can take a look at https://brainly.com/question/24855677

Answer:

Step-by-step explanation:

Strawberry jelly:

120 ÷ 4 × 3 = 90 g

Sponge fingers:

8 ÷ 4 × 3 = 6

Custard:

420 ÷ 4 × 3 = 315 ml

Tinned fruit:

180 ÷ 4 × 3 = 135 g

I'm pretty sure you just multiply the 1 1/4 by 3 because if 1 1/4 makes 10 muffins you need to make 3 more dozens so 1 1/4 times 3 equals 3.75

Answer:

The solution is x=2 and y=-1

Step-by-step explanation:

(step 1)

4x + 2y = 6

x - y = 3 - then multiply by 2

4x +2y = 6

2x -2y = 6 then add

6x  x   = 12 x = 12/6 = 2

Substitue back in (step 1)

4 x 2 + 2y = 6

   8 + 2y = 6

Answer is = 2y = -2  y= -1

Solution: x= 2

               y= -1

Answer:

d and a

Step-by-step explanation:

Answer:

12 minutes I think question kinda confusing

Answer:

40% were satisfied

Step-by-step explanation:

You take 1120 and divide it by 2800 to get 0.4 and 0.4 in percent is 40%

Answer:

40%

Step-by-step explanation:

2,800 surveyed  

1,120 promised to buy that car again

Assuming that this promise show they are satisfied with the car

2,800.   and 1,120

100%               x%

crossmultipy and solve

x=100*1,120/2,800=40

Answer:

Step-by-step explanation:

company A = 28,000 + 3,000 (x)

company B = 36,000 + 2,000 (x)

where x = no. of years.

28,000 + 3,000 (x) = 36,000 + 2000 (x)

3,000 (x) - 2,000 (x) = 36,000 - 28,000

1,000 (x) = 8,000

x = 8,000

     1,000

company A = 28,000 + 3,000 (8)

company B = 36,000 + 2,000 (8)

Answer:

20

Step-by-step explanation:

since al = lb because it is midsegment and lb = 20 so AL = 20

Answer:

5:9

Step-by-step explanation:

There are 5 blue shapes out of 9 total shapes.

Answer:

700 calories

Step-by-step explanation:

1,750/5

=350

350colories per serving

So multiply 350 by 2

350x2

=700

Answer:

Elena eats 700 calories

Step-by-step explanation:

First, we need to find out how many calories are in one serving of granola. To do that, we will divide; 1750/5=350. We now know that there are 350 calories in one serving of granola. However, the problem is asking for how many calories are in two servings of granola. 350 x 2 = 700. Therefore, Elena eats 700 calories.

Answer:

Answer is D. 2 & -2

Answer:D

I THINK

Step-by-step explanation:

Hopefully this is the right one

Answer:

$20

Step-by-step explanation:

Two groups are going on a trip to a theater. The first group has 30 students and 4 adult chaperones. The second group has 25 students and 4 adult chaperones. The cost, in dollars, for each student ticket, s, and each adult ticket, a, can be determined using the system of equations below.

30s+4a=720

25s+4a=620

What is the cost for each student ticket?

Solution:

30s+4a=720

(1)

25s+4a=620 (2)

Subtract (2) from (1)

30s - 25s = 720 - 620

5s = 100

Divide both sides by 5

s = 100/5

= 20

s = $20

Substitute the value of s into (1)

30s + 4a = 720

30(20) + 4a = 720

600 + 4a = 720

4a = 720 - 600

4a = 120

a = 120 / 4

= 30

a = $30

Each student tickets cost $20

Answer:

9/10

Step-by-step explanation:

because it is

Answer:

18cm

Step-by-step explanation:

10        ?

25      45

cross multiply,

10*45

=450

then divide,

450/25

=18

Answer:

909

Step-by-step explanation:

I'm not sure if I'm right plz tell me if I'm wrong

Answer:

-4 for else the other sign as no value as of I knw

Answer:

(6, 3)

General Formulas and Concepts:

Pre-Alg

Alg I

Step-by-step explanation:

Step 1: Define systems

4x = 8y

2x + 5y = 27

Step 2: Rewrite systems

x = 2y

2x + 5y = 27

Step 3: Solve for y

Step 4: Solve for x

Plug in y into an original equation to find x.

Answer:

[tex](6,3)[/tex]

Step-by-step explanation:

[tex]4x = 8y\\4x/4 = x\\8y/4= 2y\\x=2y[/tex]

[tex]2(2y)+5y=27\\4y+5y=27\\9y=27\\9y/9=y\\27/9=3\\y=3[/tex]

[tex]x =2y\\x= 2(3)\\x=6[/tex]

Answer:

a pic of ur math?

Step-by-step explanation: