1. At a fundraiser breakfast, the bill for 3 glasses of orange juice and 5 pancake specials is $7.60, whereas the bill for 1 glass of orange juice and 2 pancake specials is $2.90. a. Write a system of 2 equations to model this problem. Let j stand for the price of a glass of juice and let p stand for the price of a pancake special. b. Use the substitution method to solve the system of equations. c. What would the bill be for 1 glass of orange juice and 1 pancake special?

Answers

Answer 1

Answer: a.
If:
j - the price of a glass of juice
p - the price of a pancake special
Then:
3j + 5p = 7.60
j + 2p = 2.90

b.
If:
j + 2p = 2.90
Then:
j = 2.90 - 2p
We can substite j in the first equation.
If:
3j + 5p = 7.60
j = 2.90 - 2p
Then:
3×(2.90-2p) + 5p = 7.60
8.70 - 6p + 5p = 7.60
8.70 - p = 7.60
⇒ p = 8.70 - 7.60
⇒ p = 1.10

If:
j = 2.90 - 2p
p = 1.10
Then:
j = 2.90 - 2×1.10
j = 2.90 - 2.20
j = 0.70

Thus, the price of a glass of juice is $0.70 and the price of a pancake special is $1.10.

c.
If:
p = 1.10
j = 0.70
Then:
j + p = 1.10 + 0.70 = 1.80

Thus, the bill for 1 glass of orange juice and 1 pancake special is $1.80.

Related Questions

What is the answer for 4⁴÷4³=
Write 0.27 as a fraction
A set of equations is given below: Equation C: y = 5x + 10 Equation D: y = 5x + 2 Which of the following best describes the solution to the given set of equations? One solution No solution Two solutions Infinitely many solutions
Find the point of intersection between y=5x-6 and y=6x+5
Y = 2x + 4 is this exponential or linear?

Order from least to greatest 1/8, 7/8, 4/8

Answers

first 1/8 then 4/8 and lastly 7/8

Answer:

1/8 = 0.125

7/8 = 0.875

4/8 = 0.5

The order from least to greatest is :

1/8, 4/8, 7/8

Step-by-step explanation:

A foot is 12 inches long. If an inch is about 2.54 centimeters long, how many centimeters are in a foot?

Answers

This is a question that needs understanding. The calculation part is comparatively easy. We should first concentrate and write down all the important information's that are given in the question.
1 foot = 12 inches
1 inch = 2.54 centimeters
The thing that needs to be determined is
1 foot = ? centimeters
Now
1 foot = 12 inches
= (12 * 2.54) centimeters
= 30.48 centimeters
So from the above deduction we can clearly see that 1 foot is equal to 30.48 centimeters. I hope the procedure is simple enough for you to understand.

Answer: 30.48

Step-by-step explanation: There are 2.54 centimeters in an inch so of you multiply that by 12 you get 30.48

Select two polynomials that have a sum of 16n^3+13n^2+7n-10 A. 8n^3 - 5n +11n^2 - 5 B. 7n^2 + 8n - n^3 + 2 C. 15n^2 - 10n + 3n^3 - 4 D. 2n^2 + 12n - 5 + 8n^3

Answers

Option A and Option D are correct, $8n^3 - 5n +11n^2 - 5$ and $2n^2 + 12n - 5 + 8n^3$ are added to form the polynomial $16n^3 + 13n^2 + 7n - 10.$

To find two polynomials that have a sum of $16n^3 + 13n^2 + 7n - 10.$

Add the coefficients of the corresponding terms in each polynomial and see if they match the coefficients of the given polynomial.

In the given options, let us consider two polynomials:

$8n^3 - 5n +11n^2 - 5$ and $2n^2 + 12n - 5 + 8n^3$

Add these two polynomials:

$8n^3 - 5n +11n^2 - 5 + 2n^2 + 12n - 5 + 8n^3$

Group the like terms:

$8n^3+8n^3+11n^2+2n^2-5n+12n-5-5$

Combine like terms:

$16n^3 + 13n^2 + 7n - 10.$

Hence, the two polynomials that have a sum of $16n^3 + 13n^2 + 7n - 10$ are $8n^3 - 5n +11n^2 - 5$ and $2n^2 + 12n - 5 + 8n^3$ . Option A and D are correct.

To learn more on Polynomials click:

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Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.y = –2x + 4

6x + 3y =

A: –12

B: –4

C: 0

D: 4

E: 12

Answers

For this case we have the following system of equations:

Rewriting equation 1 we have:

Therefore, the equivalent system is:

The system will have no solution, if we write equation 2 as a linear combination of equation 1.

Therefore, since both lines have the same slope, they are parallel.

Parallel lines do not intersect when they have different cut points.

Therefore, there is no solution for:

-12, -4, 0, 4

The system has inifinites solutions for:

This is because the lines intersect at all points in the domain.

Answer:

The values, when placed in the box, would result in a system of equations with no solution are:

A: -12

B: -4

C: 0

D: 4

Answer:

Thus, option (a), (b) , (c) , (d) are correct.

The system will have no solution for all values except 12.

Step-by-step explanation:

Given a system of equation y = –2x + 4 and 6x + 3y = ?

We have to check for which value the '?' would result in a system of equations with no solution.

Consider a system of equation $a_1x+b_1y+c_1=0 \n\na_2x+b_2y+c_2=0$

For the system to have no solution the condition is,

$(a_1)/(a_2)=(b_1)/(b_2)\neq (c_1)/(c_2)$

For the given system of equation ,

Let unknown quantity be v.

y = –2x + 4 ⇒ 2x +y - 4 = 0

and 6x + 3y = v ⇒ 6x + 3y - v =0

On comparing, we get,

$a_1=2 , b_1=1,c_1=-4\n\n\a_2=6,b_2=3,c_3=-v$

Substitute the values in condition for no solution , we get ,

$(2)/(6)=(1)/(3)\neq (-4)/(-v)$

Consider second and third ratio, we get,

$(1)/(3)\neq (-4)/(-v)$

Solve for v , we get,

$(1)/(3)\neq (-4)/(-v) \n\n \Rightarrow v \neq 12$

Thus, for all values v except v = 12

The system will have no solution

at v = 12 the system will have infinite many solution.

Thus, option (a), (b) , (c) , (d) are correct.

Help with number 11? Please

Answers

m(<BAC) = 180 - 70 - 65 = 45 degrees;
but, m(<A) < m(<B) < m(<C) => BC < AC < AB (3);

Find the distance between (11, 10) and (1,3). Round your answer to
the nearest tenth.

Answers

Answer:

12.2

Step-by-step explanation:

$d=√((x_2-x_1)^2+(y_2-y_1)^2)\n\nd=√((1-11)^2+(3-10)^2)=√((-10)^2+(-7)^2)=√(149)\n\nd=12.2065...\approx12.2$

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