At the local Dairy Mart, you can buy one ice cream sandwich and two ice cream cones for $8 or one ice cream sandwich and one ice cream cone for $5. This situation can be represented with the system 2x+y=8
and x+y=5
, where x
represents the cost of an ice cream cone and y
represents the cost of an ice cream sandwich.Use the system of equations to determine the cost of one ice cream sandwich and one ice cream cone.

Answers

Answer 1

The solution for the system of linear equations is given by ( 2,3) with cost of one ice cream cone as $2 and cost of one ice cream sandwich as $3.

What are linear equations?

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The system of linear equations are 2x+y=8

and x+y=5

Solving the system of linear equations by the method of elimination we get

2x+y=8

2x+2y=10

__________

-y=-2

Thus y=2 and x=8-2 / 2

Hence, The solution for the system of linear equations is given by ( 2,3)

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Related Questions

Amy will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. The second plan has no initial fee but costs $0.90 per mile driven.

For what amount of driving do the two plans cost the
same?

What is the cost when the two plans cost the same?

Answers

The two plans cost the same when the amount is $200.

What are equations?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the miles driven = x.

Given that,

The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. This is represented as:

A = 40 + 0.70x

The second plan has no initial fee but costs $0.90 per mile driven.

B = 0.90x

The two plans cost the same when A = B:

40 + 0.70x = 0.90x

40 = 0.90x - 0.70x

40 = 0.20x

x = 200

The two plans cost the same when the amount is $200.

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Trigonometric Identities (HELP)
Use the Reciprocal and Quotient Identities for 1&2

1: Find cscX if sinX= 2√5/5

2: Find cosA if tanA= √2/2 and sinA= -√3/3

Use the Pythagorean Theorem identities for 3&4

3: Find sinX if cotX= -√3/2 and cosX < 0

4: Find cotθ if cosθ= 1/7 and sinθ < 0

Use the cofunction and even-odd identities for 5&6

5: Find tan(-x) if cot(π/2 -x)= -1.84

6: Find cos(θ-π/2) if sinθ= -0.57

Simplify the Trigonometric expressions

7: secX ⋅ sin^2X + cosX

8:(sinθ + 1)(tanθ - secθ)

Prove the Trigonometric expression

1+sec^2X / 1+tan^2X= 1+cos^2X

Answers

1: cscX = 1/sinX = 5/2√5.

2: Using the reciprocal identity of tanA and sinA,

tanA/sinA = 1/cosA

√2/2 / -√3/3 = 1/cosA

-2√2/2√3 = 1/cosA

cosA = -2√3/2√2.

What are the responses to other questions?

3: Using the Pythagorean theorem, sinX = √(1 - cos^2X)

√(1 - cos^2X) = √((1/cot^2X) - 1) = √((√3/2)^2 - 1) / (-√3/2)

sinX = √2/2.

4: Using the Pythagorean theorem,

cotθ = cosθ / sinθ = 1 / tanθ = 1 / (√(1 - cos^2θ) / cosθ) = cosθ / √(1 - cos^2θ) = 1 / (√(1 - (1/7)^2)) = √(48) / 7.

5: Using the cofunction identity, tan(-x) = -tan(x).

Using the identity that tan(π/2 -x) = cot(x),

-tan(x) = -1/cot(π/2 -x) = -1/(-1.84) = 1.84.

6: Using the even-odd identity, cos(-θ) = cos(θ), and

sin(-θ) = -sin(θ),

cos(θ-π/2) = cosθcos(π/2) + sinθsin(π/2) = 0cos(π/2) + (-0.57)sin(π/2) = -0.57.

7: Using the identity sin^2X + cos^2X = 1,

secX ⋅ sin^2X + cosX = secX ⋅ (1 - cos^2X) + cosX = secX - secXcos^2X + cosX = secX + cosX.

8: Using the identity 1 + tan^2θ = sec^2θ,

(sinθ + 1)(tanθ - secθ) = (sinθ + 1)(tanθ - 1/cosθ) = (sinθ + 1)(tanθcosθ - 1) = (sinθ + 1)sinθ(tanθ/sinθ) - (sinθ + 1) = sinθ + sin^2θ - sinθ - 1 = sin^2θ - 1.

Proof:

Using the identity tan^2X = sin^2X / cos^2X,

1+sec^2X / 1+tan^2X = (1 + 1/cos^2X) / (1 + sin^2X / cos^2X) = cos^2X / (cos^2X + sin^2X) = cos^2X / (1) = 1 + cos^2X.

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According to this diagram, what is sin 28°?
28°
OA. 17
15
OB.
B. 15
8
O C. 17
D. 15
OE
F.
8
15
8
17-
15
62°
90°
00
8

Answers

Sin =p/h

Hence

Sin(28)= 8/17

Option C

Answer:

sin 28 = 8 /17

Step-by-step explanation:

Since this is a right triangle, we can use trig functions.

sin theta = opp side / hypotenuse

sin 28 = 8 /17

Demarco and Tanya have received information about three separate mortgage offers. In two or three paragraphs, describe your recommendation for the best financial choice in their situation. Evaluate each of the three offers, compare and contrast their effectiveness, and explain the offer that works best. As you explain your answer, support it using reasons and evidence from the calculations you made based on the information provided in this guide for Analyzing Mortgage Options. pls try to be original

Answers

Best Mortgage Option 3 because this mortgage option offers a lower interest rate.

Why Option 3 was recommended

After reviewing all three mortgage options available to Demarco and Tanya, I would recommend that they choose option 3. This option offers a lower interest rate compared to the other two options and a longer loan term, which means that their monthly payments will be lower and more manageable for their budget. Additionally, option 3 offers a fixed interest rate, which provides them with more stability and predictability in their mortgage payments, as opposed to options 1 and 2 that offer adjustable interest rates.

Option 1 has the highest interest rate and the shortest loan term, making their monthly payments the highest of all three options. Option 2 offers a slightly lower interest rate, but it still higher compared to option 3, and has a shorter loan term compared to option 3, making their monthly payments still relatively high.

In conclusion, the best financial choice for Demarco and Tanya would be option 3. Its lower interest rate, longer loan term, and fixed interest rate make it the most affordable and stable option for them in the long run.

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Instructions Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay. 1) In your own words, write a definition for sales tax. 2) If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes? - Explain in detail, the steps you would take to solve this sales tax question.

Answers

1) The sales tax is an additional rate that is paid along with the cost of the meal.

2) The amount paid in taxes for a meal costing $15.00 and a rate of 7% is given as follows: $1.05.

How to obtain the sales tax?

The sales tax is obtained applying the proportions in the context of this problem.

A proportion is applied as the sales tax is obtained with the multiplication of the cost of the meal by the decimal equivalent of the percentage of tax.

The decimal equivalent for a percentage of 7% is given as follows:

7/100 = 0.07.

Hence the amount of tax paid is given as follows:

0.07 x 15 = $1.05.

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A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. A 3-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. What is the mean difference (A – B) and the standard deviation of the differences?

Answers

I think that it could be b but I'm not 100 percent sure

Eli's basketball team is having a Free-Throw Challenge in order to raise money for new uniforms. Eli's grandma pledges to give $10 as well as $2 for every free throw he makes. Which equation represents how much money (M) Eli's grandma will give depending on how many free throws (f)
Eli makes?

Answers

Answer:

M = 10 + 2f

Step-by-step explanation:

Please see the attachment for detail explanation

Given a2 = 6 and a5 = –384 of a geometric sequence, what is the recursive equation for the nth term?

an = –4(an – 1), a1 = –1.5
an = –4(an – 1), a1 = 1.5
an = 4(an – 1), a1 = –1.5
an = 4(an – 1), a1 = 1.5

Answers

Answer:

[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]

Step-by-step explanation:

[tex] a_1 = a_1 [/tex]

[tex] a_2 = a_1 \times r [/tex]

[tex] a_3 = a_1 \times r^2 [/tex]

[tex] a_4 = a_1 \times r^3 [/tex]

[tex] a_5 = a_1 \times r^4 [/tex]

[tex] a_1 \times r = 6 [/tex]

[tex] a_1 \times r^4 = -384 [/tex]