The concession stand at the high school football stadium sells hot dogs and sodas. Jack bought 3 hotdogs and 2 sodas for a total of $12. Angie bought 1 hotdog and 4 sodas for $9. Solve a system of equations to determine the cost of 1 hotdog and 1 soda.


Answers

Answer 1

Answer: each soda costs $1.5 and each hotdog costs $3.

Step-by-step explanation:

If H is the price for one hotdog and S is the price for one soda, we have the equations:

for Jack.

3*H + 2*S = $12

For Angie.

1*H + 4*S = $9

Now we can isolate one of the variables in one of the equations and then replace it in the other equation, let's isolate H in the second equation:

H = $9 - 4*S

now we replace it in the first eq

3*H + 2*S = $12

3*($9 - 4*S) + 2*S = $12

$27 - 12*S + 2*S = $12

-10*S = $12 - $27 = -$15

S = $15/10 = $1.5

Now we can replace it in the equation for H and get:

H = $9 - 4*$1.5 = $3

So each soda costs $1.5 and each hotdog costs $3.

Answer 2

Answer: One hotdog cost $3 and One soda costs $1.5

Step-by-step explanation:

Let hotdogs be denoted by h

Let sodas be denoted as s

Jack bought 3 hotdogs and 2 sodas for a total of $12. This can be written as:

3h + 2s = 12

Angie bought 1 hotdog and 4 sodas for $9. This can be written as:

h + 4s = 9

3h + 2s = 12

h + 4s = 9

1 × (3h + 2s = 12)

3 × (h + 4s = 9)

3h + 2s = 12

3h + 12s = 27

Subtract the equation

-10s = -15

s = -15/-10

s = 1.5

One soda cost $1.5

Since h + 4s = 9

h + 4(1.5) = 9

h = 9 - 6

h = 3

One hotdog costs $3


Related Questions

Help! Stuck on this question (calculus)


If [tex]y=\frac{3}{x^2}[/tex]


work out [tex]\frac{dx}{dy}[/tex]

Answers

Answer:

[tex]\displaystyle \frac{dx}{dy} = \frac{3\sqrt{\frac{3}{y}}(y - 1)}{6y}[/tex]

General Formulas and Concepts:

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:                                                                                [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{3}{x^2}[/tex]

Step 2: Differentiate

Rewrite Function:                                                                                             [tex]\displaystyle yx^2 = 3[/tex][Implicit Differentiation] Basic Power Rule [Product Rule]:                            [tex]\displaystyle y^{1 - 1}x^2 + y(2x^{2 - 1})\frac{dx}{dy} = 3[/tex]Simplify:                                                                                                             [tex]\displaystyle x^2 + y(2x)\frac{dx}{dy} = 3[/tex]Isolate  [tex]\displaystyle \frac{dx}{dy}[/tex]  term:                                                                                               [tex]\displaystyle y(2x)\frac{dx}{dy} = 3 - x^2[/tex]Isolate  [tex]\displaystyle \frac{dx}{dy}[/tex]:                                                                                                         [tex]\displaystyle \frac{dx}{dy} = \frac{3 - x^2}{2xy}[/tex]Substitute in x²:                                                                                                 [tex]\displaystyle \frac{dx}{dy} = \frac{3 - \frac{3}{y}}{2xy}[/tex]Simplify:                                                                                                             [tex]\displaystyle \frac{dx}{dy} = \frac{3(y - 1)}{2xy^2}[/tex]Substitute in x:                                                                                                  [tex]\displaystyle \frac{dx}{dy} = \frac{3(y - 1)}{2y^2(\sqrt{\frac{3}{y}})}[/tex]Simplify:                                                                                                             [tex]\displaystyle \frac{dx}{dy} = \frac{3\sqrt{\frac{3}{y}}(y - 1)}{6y}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Marcus deposited his paycheck in the amount of $625.84. He’ll use the check register to record his transaction. What will be his new balance? A check register has a balance of 640 dollars and 31 cents.

Answers

Beginning balance: $640.31
Deposit of : $625.84
New Balance: $1,266.15

Answer:

His new balance will be $1,266.15

Step-by-step explanation:

Would side lengths 5,7, and 10 form a triangle?

Answers

Answer:

Yes

Step-by-step explanation:

Add any two sides and see if it is greater than the third   for all three sides

5+7 > 10  true

7+10 > 5  true

10+7 > 5  true

Then the three sides form a triangle

Isaac is constructing a circular pool that has a diameter of 20 ft and is 5 ft deep. Part A: Find the circumference of the pool to the nearest tenth of a foot. Use 3.14 for pi. Part B: Find the area of the circle formed by the pool to the nearest foot.

Answers

Answer:

The circumference of the pool is 62.8 foot long and the area of the circle formed by the pool is 314 ft².

Step-by-step explanation:

The circumference of the pool can be found by calculating the arc's length of the edges of the pool. This is done by using the following formula:

[tex]circumference = 2*\pi*r[/tex]

Where the radius is half the diameter, applying the data from the problem we have:

[tex]circumference = 2*3.14*10 = 62.8 \text{ ft}[/tex]

The area of the circle formed by the pool can be found using the following expression:

[tex]area = pi*r^2 = 3.14*(10)^2 = 314 \text{ ft}^2[/tex]

The circumference of the pool is 62.8 foot long and the area of the circle formed by the pool is 314 ft².

A counter recorded 254 revolutions of the bicycle wheel shown. How far did the bicycle travel? Use 22/7

Answers

[tex]C=\pi d[/tex]

[tex]22/7(5/4)[/tex]

[tex]=3.92857142857[/tex]

[tex]3.92857142857(254)[/tex]

[tex]=997.857142857[/tex]

In 254 revolutions , the bicycle will travel [tex]997.85m[/tex]

Circumference :

The circumference of bicycle is given as,

                        [tex]C=\pi d[/tex]

Where [tex]d[/tex] is diameter of bicycle.

Given that,[tex]d=\frac{5}{4} ,\pi=22/7[/tex]

Substitute values in above equation.

[tex]C=\frac{22}{7}*\frac{5}{4}\\ \\ C=\frac{110}{28}=3.93[/tex]

In 254 revolutions of the bicycle wheel is,[tex]C=254*3.93=997.85m[/tex]

In 254 revolutions , the bicycle will travel [tex]997.85m[/tex]

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Your question was incomplete , Complete question is here :

"A counter recorded 254 revolutions of the bicycle wheel shown below how far did the bicycle travel. Use 22/7 as pi and the diameter of the wheel is 5/4."

What’s c ? And I need explanation plz

Answers

Answer:

a

Step-by-step explanation:

the probablity of getting head when flipping a coin that hasn't been altered is 50/50, therefor it's a :) hope it helped

Answer:

A

Step-by-step explanation:

The probability scale shows how likely or unlikely something is going to happen. So when flipping an unbiased (fair) coin, the probability of getting a head is exactly 50%. Thus, A means "half" on the probability scale so A is the correct answer.

The cost of 4 bear toys and a lion toy is $70. If the cost of a lion toy and 2 bear toys is
$41, what is the cost of a lion toy?
$36
$28
$14.50
$12

Answers

Answer:

14.50 because you need to divide the total amount by 2 and then you have the remaining

The cost of a lion toy is $12

What is a linear equation?

An equation between two variables with a constant in the form of ax +by =c is called a linear equation.

Given the cost of 4 bear toys and a lion toy is $70.

And If the cost of a lion toy and 2 bear toys is $41,

Write a linear equation for the above equation

4B +1L =70

2B +1L =41

By solving the above equations we get B= $14.5 and L=12

Thus the cost of a bear is $14.5 and cost of a lion is $12.

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Lisa’s test grades are 79, 89, and 90.

What is Lisa’s test average?

Answers

So you do 79+89+90=258 then you take 258/3=9.3 so you would get a 93% test average
Hope this helps

Answer:

Lisa's text average is 86 :))

Step-by-step explanation:

add all numbers up then divide them by 3.

The ratio of boys to girls in a school is 4:5. How many boys are in the school if there are 720 students.

Answers

Answer:

There are 320 boys

Step-by-step explanation:

boys: girls : total

4         5         4+5 = 9

Take the total and divide by 9

720/9 = 80

Multiply each term by 80

boys: girls : total

4*80  5*80    9*80

320    400    720

There are 320 boys

Answer:

324 boys

Step-by-step explanation:

Add the ratio, 4+ 5 = 9 and divide 720 with nine. Then multiply that value, 81, with 4 to find the number of boys, and multiply with 5 to get the girls

Consider this system of linear equations: y = –3x + 5 y = mx + b Which values of m and b will create a system of linear equations with no solution?

Answers

Answer:

m = - 3 and b = - 3.

Step-by-step explanation:

A system of linear equations will not have solutions if the two lines are parallel.

Two equations are parallel:

1. if their slopes (m) are equal

2. the y-intercep (b) are different.

As y = - 3x + 5, the value of m of the other equation, y = mx + b, in order to make a system with no solution, needs to be  - 3, and the value of b need to be different to 5.

The only pair from the choices that meets that is the first option m = - 3 and b = -3.

Answer:

m = -3, b = 5

Step-by-step explanation:

The values m = -3 and b = 5, forms a linear equation: y = -3x + 5. This obviously coincides with the original equation given, and so will create a system of linear equations with no solution.

2. Find the value of V343 X V27​

Answers

Answer:

De value of v is 12

Step-by-step explanation:

v343×v27

343×27÷27

=12red 7

evaluate 3×-14, when ×=5​

Answers

Answer:

1

Step-by-step explanation:

Plug in the x value.

3(5)-14

3(5)=15

So then you do 15-14

Which equals to 1

Hope this helps! Plz mark brainliest!!

Answer:

1

Step-by-step explanation:

1. 3(5)-14     first substitute

2. 15-14

3. 1

Write the expression
Divide y by 9 then subtract z from the result

Answers

Answer:

Bruh its not that hard, but ill answer it. answer is below

Step-by-step explanation:

Divide y by 9 then subtract z from the result

We know that y divided by 9 is y/9

and the you subtract z from it: y/9-z

but i think that since it says "subtract z FROM THE RESULT"

I think it is

(y/9)-z

David leaves the house to go to school. He walks 200 meters west and
125 meters north. How far away is he from his starting point (the diagonal)?


Answers

Pythagorean Theorem, where a^2+b^2=c^2. Just plugging in the numbers:
200^2 + 125^2=C^2
40,000 + 15,625=C^2
55,625=C^2
Then just take the square root
C=235.8495
If the number needs to be rounded then 236 meters.

One night, it is 24 ℃ warmer in Tucson than it was in Minneapolis. If the temperatures in Tucson and Minneapolis are opposites, what is the temperature in Tucson?

Answers

Answer:

The temperature in Tucson is [tex]12\,^{\circ}C[/tex].

Step-by-step explanation:

Let be [tex]T[/tex] and [tex]-T[/tex] the temperatures registered in Tucson and Minneapolis, respectively. The difference between both temperatures is:

[tex]T - (-T) = 24\,^{\circ}C[/tex]

[tex]2\cdot T = 24\,^{\circ}C[/tex]

[tex]T = 12\,^{\circ}C[/tex]

The temperature in Tucson is [tex]12\,^{\circ}C[/tex].

Answer:

The temperature in Tucson is 12°C, and that of Minneapolis is -12°C.

Step-by-step explanation:

Let the temperature in Tucson = T

And the temperature in Minneapolis = -T. Because the temperatures are opposites.

Since we know that it is 24°C warmer in Tucson that it was in Minneapolis, then

T - (-T) = 24

T + T = 24

2T = 24

T = 24/2

= 12

Therefore, the temperature in Tucson is 12°C, and that of Minneapolis is -12°C.

What is the area of the given compound shape?

1. 19 sq cm
2. 25 sq cm
3. 34 sq cm

Answers

Answer:

(A)

Step-by-step explanation:

As you can see, the figure can be divided into a square of side 2cm and a rectangle of sides 5cm and 3cm so we find the area of both and add.

Area of the square

= 2x2 = 4cm^2

Area of the rectangle

= lxb

= 3x5

= 15 cm^2

Therefore the area of the entire figure

= Area of square + area of rectangle

= 15+4

= 19 cm^2

So the correct option is (a)

Hope this helps:)

Answer:

Option 1

Step-by-step explanation:

I broke the figure up into two shapes. One of them was a square and the other one was a big rectangle. I calculated the two areas and added them back together.  My work is attached in the picture.

Area of a square is: s^2

's' -side length

Area of a rectangle is: b * w

'b' - base or length

'w' - width

The area of the figure should be 19cm².

Mr. Nicholas invested $4,250 into an account that pays 3.5% interest, compounded annually. How much will Mr. Nicholas’s investment be worth after 8 years?

Answers

Answer:

$5596.44

Step-by-step explanation:

$4250*(1.035)^8= $5596.44

Solve for h.

–10 − 8h − 14h = –15h + 18

h =

Answers

Answer:

[tex] \boxed{h = -4} [/tex]

Step-by-step explanation:

[tex] = > - 10 - 8h - 14h = - 15h + 18 \\ \\ = > - 10 - 22h = - 15h + 18 \\ \\ = > - 22h + 15h - 10 = 18 \\ \\ = > - 7h - 10 = 18 \\ \\ = > - 7h = 18 + 10 \\ \\ = > - 7h = 28 \\ \\ = > 7h = - 28 \\ \\ = > h = - \frac{28}{7} \\ \\ = > h = -4[/tex]

What is the purpose and structure of a proof in Geometry?

Answers

Answer: A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.

The number of flowers, f, that a gardener can plant along a border of a garden varies inversely with the distance d (in inches) between the flowers. If the gardener can fill the border with 30 flowers planted 12 inches apart, how far apart should the gardener plant 36 flowers instead?

Answers

Answer:

d=20

       

Hope it helps :]!!!!!!!

Tyron made 60 cakes. He gave 1/6 of the 60 cakes to Lilly. What fraction of the cakes does he have left?

Answers

Answer:

38/60 or 19/30

Step-by-step explanation:

The question isn't fully attached as stated by the person who submitted it.

The fraction of the cakes he has left is ( 5 / 6 ). The remaining number of cakes is 50.

What is a fraction?

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

The fraction is calculated as:-

The remaining fraction = 1 - ( 1 / 6 )

                                      = ( 6 - 1 ) / 6

                                      = 5 / 6

The remaining number of cakes,

Remaining number = 60 x ( 5 / 6 )

Remaining number = 50

Hence, the remaining number of cakes is 50.                                                          

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What is the answer of the Fractions listed? Will give Brainliest 20 points

Answers

Answer:

- 6 1/2

Step-by-step explanation:

-4 - 2 1/2

Since the signs are the same, we add them together and take the signs

4+2 1/2 = 6 1/2

Take the sign

- 6 1/2

Answer:

(-4) - 2 1/2 = -6.5

Step-by-step explanation:

( −4 ) − 2 1/2 = -13/2

-13/2 = -6 1/2  

Rania is riding the ferris wheel. Her vertical height H(t)H(t)H, left parenthesis, t, right parenthesis (in \text{m}mstart text, m, end text) off the ground as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\cos(b\cdot t)+da⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. At t=0t=0t, equals, 0, when she starts moving, she is at a height of 10\text{ m}10 m10, start text, space, m, end text off the ground, which is as low as she goes. After 20\pi20π20, pi seconds, she reaches her maximum height of 30\text{ m}30 m30, start text, space, m, end text. Find H(t)H(t)H, left parenthesis, t, right parenthesis.

Answers

Answer:

  H(t) = -10·cos(t/20) +20

Step-by-step explanation:

The range of heights is ...

  30 m - 10 m = 20 m

The amplitude of the cosine function is half that, or 10 m. Here, the function starts off at a minimum, whereas the parent cosine function starts at a maximum. That means the parent function is reflected vertically, so the amplitude coefficient in H(t) is negative.

The midline of the cosine function is the average of the extreme heights, so is ...

  midline = (30 m +10 m)/2 = 20 m

The period of the function is double the time it takes to go from a minimum to a maximum, so is ...

  p = 2(20π) = 40π . . . . seconds

In the given function form ...

  H(t) = a·cos(bt) +d

the amplitude is a=-10; the coefficient b is 2π/p = 1/20; and the midline is d = 20. Then the function is ...

  H(t) = -10·cos(t/20) +20

Which inequality is represented by this graph?

Answers

Answer: C

Step-by-step explanation:

We can say that the equaiton of the line is -1/6x+1, considering that is in each answer choice. Than main part is the shading and inequality. If you look closely at the graph, the shading line is a dashed/dotted line. This means the shaded part does not equal the actual line. We can eliminate B and D.

Now, we are left with A and C. A is saying y< while C is saying y>. C is the correct answer because if you look at the shading, it it above the line, which is greater than. Therefore, the answer is C.

Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!

Answers

Answer:

-5x=-11

Step-by-step explanation:

[tex]-4x-2y=-2 \\\\x-2y=9[/tex]

Subtract the second equation from the first:

[tex]-4x-(x)-2y-(-2y)=-2-(9)\\\\-5x=-11[/tex]

Hope this helps!

what is 8.92 x 106 in standerd form

Answers

[tex]8.92 \times 10^6[/tex]

[tex]8920000[/tex]

Answer: 945.52

Step-by-step explanation:

help please? what is the following quotient?

Answers

Answer:

√(30) - 3√(2) + √(55) - √(33) / 2

Step-by-step explanation:

please answer thanks























i have 4 more questions after this

Answers

Answer:

Step-by-step explanation:

[tex]V= ?\\r = 2\\h = 5\\\pi = 3.14\\\\V = \frac{1}{3} \pi*r^{2} *h\\\\V = \frac{1}{3} *3.14*2^{2} *5\\\\V= \frac{1}{3} *12.56*5\\\\V= \frac{1}{3}* 62.8\\\\V = 20.93333333\\\\\\V = 20.93[/tex]

In terms of pi

[tex]V= ?\\r = 2\\h = 5\\V = \frac{1}{3} \pi*r^{2} *h\\\\V= \frac{1}{3} *\pi*2^{2} *5\\\\V = \frac{1}{3} \pi*20\\V= 6.67\pi\\[/tex]

What is the equation of the line of best fit for the following data round the slope and Y intercept of the line to three dimensional places. Please help ASAP thank you so much.

Answers

Answer:

y = 1.56 x - 4.105

which agrees with answer "B" in your list of possible options.

Step-by-step explanation:

Notice that you are expected to use some type of regression tool for this problem. either a computer program or a handheld graphing calculator with such functionality.

I have entered the set of data points in two separate lists, one for the x-values,and another one for the y-values, and run the linear regression tool in order to get the best fitting line. See what I obtained using this tool in the screen capture I am attaching below.

Notice that the line of best fit reads:

y = 1.56015038 x - 4.10526316

showing clearly the slope and y-intercept of the line of best fit.

Rounding slope and y-intercept to the third decimal, we get:

y = 1.56 x - 4.105

which agrees with answer "B" in your list of possible options.

I’m not so sure but I think the answer is B. If it’s wrong I’m sorry:(.
.
.
.
You can also use Desmos for these kinds of questions. (It’s a graphing app)

Telephone pole breaks and falls as shown. To the nearest foot, what was the

original height of the pole? they are 7 ft and 10 ft pls explain how u got the answer and the choices r a.19ft. b.17ft. c.20ft. d.18 ft pls find the answer for me

but its a triangle and in the bottom it has number 10 and in the long side of the triangle is 7

Answers

Answer:

Length of the pole = 12.2ft

Step-by-step explanation:

Hello,

According to your description, the pole against a wall of height 7ft and the distance between the base of the pole to the wall is 10ft.

See attached document for better illustration.

To solve this problem, we'll have to make use of pythagorean theorem

According to pythagorean theorem,

X² = y² + z²

X = ?

Y = 10ft

Z = 7ft

X² = 10² + 7²

X² = 100 + 49

X² = 149

X = √(149)

X = 12.2ft

The length of the pole is 12.2 ft

Unfortunately, the length of the pole does not corresponds with any of the answers above, but this is actually the right answer.

Good luck

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Please help me!!!!!! k (t) = 10t - 19 k(-7) = A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow. Model Price ($) Model Price ($) Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard 1 39 27 5 40 30 2 39 29 6 39 35 3 46 35 7 35 29 4 38 31 The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10. a.Calculate the value of the test statistic (to 2 decimals).b.What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)? Why do you think the patriots won the American revolution?need done by 11:20! thanks! Mr. Henry spent $15 on a new hat this week. He learned that the same hat available on sale at $12 last week. What was the percentage increase in the price of the hat this week?*please help:)-must haves:).right answer.step-by-step.makes sense.^I will mark someone the brainiest if more than one person answers this :) Two small plastic spheres each have a mass of 2.0 g and a charge of 50.0 nC. They are placed 2.0 cm apart (center to center). What is the magnitude of the electric force on each sphere? By what factor is the electric force on a sphere larger than its weight? Would the world be a better place or a worse place without the internet? Please explain in CER. Thank youuu Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!! A bag of trail mix shrugged 1.625 pounds round 1.625 to the nearest tenth.use the number line for help can anyone please explain me this,would be appreciated Brian, a scientist, is writing a research paper on projectile motion. during one of his experiments, he throws a ball from a point marked as point a, with a certain velocity in the horizontal direction. the ball travels a horizontal distance of 0.6 meter in the 1st second, 1.2 meters in the 2nd second, 1.8 meters in the 3rd second, and so on. it hits the ground on the 8th second. brian marks the point where the ball landed as point b. calculate the distance between point a and point b. When may a scientific theory be revised PLEASE HELP I HAVE LIMITED TIME!!How many particles of water (H20) are in a collection of snowflakeswith a mass of 0.005 g? 3x-2y Practice using experimental probability.AsmentThe experimental probability of getting a 3 on a number cube is 5/36. Which of the following is true about the event'sexperimental probability?The number 5 was rolled 36 times.O The number 3 was rolled 5 times in 36 trials.o The number cube was rolled 41 timesAfter 5 trials, the number 3 was rolled 36 times.IntroDone Which expression is a polynomial? a. 9x^7 y^-3z b. 4x^3 - 2x^2 + 5x - 6+ 1/x c. - 13 d. 13x ^-2 Before graduating this year, a senior homeroom was given a survey. Of those surveyed, 24% felt they learned better at home. Of this group, 80% said they plan on taking an online course in college. Of the students who felt they did not learn better at home, 40% said they plan on taking an online course in collegePart AWhat is the probability a person who does not plan on taking an online course felt they learned better at home?A : 2/21 B : 24/125C : 38/125D : 19/31E :None of thesePart BWhat is the probability a person who does plan on taking an online course felt they did not learn better at home? A : 2/21B : 24/125 C : 38/125D : 19/31E : None of these Factoring Quadratics - Please help; will mark Brainliest! Por una espira de 0.5 m2 de rea circula una corriente de 5 A. Calcula la densi- dad de flujo magntico B considerando que la espira considera la permeabilidad del medio es la del aire Which angle in ADEF has the largest measure? Which sentence describes the etymology of a word?O A. Synonyms of rubbish include garbage, trash, waste, and refuse.O B. Arboreal describes anything related to trees or tree dwellers.C. In biology, bio comes from the Greek bios, which means "life."O D. The ch in chimera is pronounced like the kin kite or kangaroo.