Jessie paid $43.75 for 5 movie tickets. Each ticket cost the same amount. What was the cost of each movie ticket in dollars and cents?

Answers:

x = 2.40

y = 1.60

This means 1 hot cocoa costs $2.40 and 1 pretzel costs $1.60

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Work Shown:

x = cost of 1 cup of hot cocoa

y = cost of 1 pretzel

5x = cost of 5 cocoas

4y = cost of 4 pretzels

5x+4y = cost of 5 cocoas+4 pretzels

5x+4y = 18.40

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2x = cost of 2 cocoas

4y = cost of 4 pretzels

2x+4y = cost of 2 cocoas+4 pretzels

2x+4y = 11.20

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The system of equations we have is

[tex]\begin{cases}5x+4y = 18.40\\2x+4y = 11.20\end{cases}[/tex]

Note how 4y shows up twice. This is handy to be able to get rid of the y terms completely.

How? By subtracting the equations straight down

The x terms subtract to 5x-2x = 3x

The y terms subtract to 4y-4y = 0y = 0 and they go away

The right hand sides subtract to 18.40 - 11.20 = 7.20

After those three separate subtractions, we have this new equation:

3x = 7.20

Divide both sides by 3 to isolate x

3x/3 = 7.20/3

x = 2.40

Each hot cocoa costs $2.40

Now use this x value to find y. You can pick any equation you want as long as it has x,y in it. I'll pick the first equation

5x+4y = 18.40

5(2.40)+4y = 18.40

12+4y = 18.40

4y = 18.40-12

4y = 6.40

y = 6.40/4

y = 1.60

Each pretzel costs $1.60

If we picked on the second equation, we should get the same y value

Let's find out

2x+4y = 11.20

2(2.40)+4y = 11.20

4.80+4y = 11.20

4y = 11.20-4.80

4y = 6.40

y = 6.40/4

y = 1.60

We get the same result as before.

To check the answers, you need to plug those values back into the two original equations and simplify. You should get the same thing on both sides.

Answer:

A.

Step-by-step explanation:

Answer:

Im not sure but go with 24

exterior angle = sum of its opposite interior angles

Which means :-

[tex]x + 21 + 63 = 3x[/tex]

[tex]21 + 63 = 3x - x[/tex]

[tex]21 + 63 = 2x[/tex]

[tex]84 = 2x[/tex]

[tex]2x = 84[/tex]

[tex]x = 84 \div 2[/tex]

[tex]x = 42°[/tex]

Therefore , the correct option is :-

Answer:

y=mx

Step-by-step explanation:

i think thats the equation am pretty sure tho

Answer:

25/2 or 12 1/2 or 12.5

Step-by-step explanation:

Answer:

48s plus 12p - 18

Step-by-step explanation:

Answer:

Add 48 + 12 and Subtract the sum from 18 (14+12-18)

Step-by-step explanation:

Sorry if I'm confusing you ;(

Answer:

what are the other ways two straight lines could intersect in the coordinate plane How many solutions would each of these options haver

Answer:

Step-by-step explanation:

On the 2nd equation, turn the slope the -3x. This creates two parralel lines.

Two linear equations will always be parallel and never intersect if their y-intersect is different and their slope is the same.

Answer:

every 8 mins

Step-by-step explanation:

bus b

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Explanation:

We're adding terms in the form (2n+5)

The first term is when n = 3, so

2n+5 = 2*3+5 = 6+5 = 11

The next term is when n = 4, so

2n+5 = 2*4+5 = 8+5 = 13

The next term is when n = 5, so

2n+5 = 2*5+5 = 10+5 = 15

And so on

This means,

[tex]\displaystyle \sum_{n=3}^{\infty} (2n+5) = 11+13+15+17+\ldots[/tex]

which matches with choice C. The three dots indicates the pattern goes on forever.

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Choice B does not have these dots, so that's why choice B is not the answer. If we replaced the infinity symbol with 7, then choice B would be the answer.

I.e,

[tex]\displaystyle \sum_{n=3}^{7} (2n+5) = 11+13+15+17+19[/tex]

Answer:

8/5-12x

Step-by-step explanation:

-4(-2/5+3x)

Multiply each term inside the parentheses by -4

-4 * -2/5 + -4 * 3x

8/5-12x

Answer:

-1.6+12x

Step-by-step explanation:

First you do -4*2/5 + -4*3x. Which will give you -1.6+ 12x

Answer:

14

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

x+7+7=4x+2 simplify

Answer:

10 is the answer. 1:50 is 10:500 simplified

Step-by-step explanation:

500÷50=10.

Answer:12x+10y-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

C=-3t+30

Step-by-step explanation:

Given:

[tex]\dfrac{2}{5}[/tex] of the ice sticks are blue raspberry.

Of the remaining ice sticks, [tex]\dfrac{1}{3}[/tex] are grape, and the rest are cherry.

There are 48 blue raspberry and cherry flavored ice sticks altogether.

To find:

The total number of ice sticks.

Solution:

Let x be the total number of ice sticks.

[tex]\dfrac{2}{5}[/tex] of the ice sticks are blue raspberry.

Blue raspberry [tex]=\dfrac{2}{5}x[/tex]

Remaining raspberry [tex]=x-\dfrac{2}{5}x[/tex]

                                   [tex]=\dfrac{3}{5}x[/tex]

Of the remaining ice sticks, [tex]\dfrac{1}{3}[/tex] are grape, and the rest are cherry.

Grape [tex]=\dfrac{1}{3}\times \dfrac{3}{5}x[/tex]

          [tex]=\dfrac{1}{5}x[/tex]

Cherry [tex]=\dfrac{3}{5}x-\dfrac{1}{5}x[/tex]

           [tex]=\dfrac{2}{5}x[/tex]

There are 48 blue raspberry and cherry flavored ice sticks altogether.

[tex]\dfrac{2}{5}x+\dfrac{2}{5}x=48[/tex]

[tex]\dfrac{4}{5}x=48[/tex]

[tex]x=48\times \dfrac{5}{4}[/tex]

[tex]x=60[/tex]

Therefore, the total number of ice sticks is 60.

Answer:

-4 Degrees Fahrenheit

Step-by-step explanation:

Given

[tex]Initial\ Temperature = 8[/tex] ---- at 10am

[tex]Difference = -3[/tex]

Required

Determine the final temperature at 2pm

First, we need to determine the hour from 10am to 2pm (Both inclusive)

[tex]Interval = 2pm - 10am + 1hr[/tex]

[tex]Interval = 4hr + 1hr[/tex]

[tex]Interval = 5hr[/tex]

To solve further, we make use of the following Arithmetic Progression formula:

[tex]T_n = a + (n - 1)d[/tex]

Where

[tex]a = 8[/tex] --- Initial

[tex]d = -3[/tex] --- difference

[tex]n = 5[/tex] -- 5th term

[tex]T_n[/tex] --- Final temperature at 2pm

So: we have:

[tex]T_n = 8 + (5 - 1) * -3[/tex]

[tex]T_n = 8 + (4) * -3[/tex]

[tex]T_n = 8 + 4 * -3[/tex]

[tex]T_n = 8 -12[/tex]

[tex]T_n = -4[/tex]

Hence:

The temperature is -4 Degrees Fahrenheit

Answer: 2

Step-by-step explanation: First, multiply 7/8 by 4/5 which equals to 7/10. Then, divide 7/10 by 7/20. Finally, you should end up with a result of 2.

Answer:

3.81

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens

P = 2*L + 2*W

P = 70

w = 16

Solution

70 = 2L + 2*16

70 = 2L + 32

70-32 = 2L

38 = 2L

38/2 = 2L/2

L = 19

Answer:33,325,000

Step-by-step explanation:95,976,000÷2.88=33,325,000

Answer:

Alex needs to walk for 45 minutes.

Step-by-step explanation:

2.25 / 3 = 0.75 hours

0.75 hours = 45 minutes

Answer:

185

Step-by-step explanation:

distance formula is d=√((x_2-x_1)²+(y_2-y_1)²

so it would be d=[tex]\sqrt{(-3-5)^{2} + (7-(-4))^{2} }[/tex]

where we see [tex](7-(-4))^{2}[/tex] will turn into [tex](7+4)^{2}[/tex]

[tex](-3-5)^{2} =64[/tex]

[tex](7+4)^{2} =121[/tex]

64+121= 185

Hope this helps...sorry if i'm wrong.

Answer:

(4, -3)

Step-by-step explanation:

It says my answers need to be at least 20 characters long so I had to write this.

Answer:

(x-5)(2x-3)

Step-by-step explanation:

key words:

product = multiplication

minus - subraction

x-5

and = first phrase times next phrase

less than = a number minus the number before the 'less than'

twice = 2 times a number

if we put it together we get x-5 times 2x-3. we put parenthesis because we dont want to multiply only 5 and 2x so our answer is (x-5)(2x-3).

i hope this helped :))

The equation of the problem is [tex]5(n+7)[/tex]

The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.

Answer:

y - 5 = 3(x - 1)

Step-by-step explanation:

Let the equation of the line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is represented by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (0, 2) and (1, 5) is,

m = [tex]\frac{5-2}{1-0}[/tex] = 3

Now equation of the line passing through a point (1, 5) and slope = 3 will be,

y - 5 = 3(x - 1)

Option (4) is the answer.

Answer:

y−5=3(x−1)

Step-by-step explanation: