The cost y (in dollars) to rent a camping tent is proportional to the number x of days that the tent is rented. It costs $56 to rent a tent for 7 days. Write an equation that represents the cost to rent a camping tent for x days.
Answer:
[tex]y=8x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem the linear equation represent a proportional variation
Let
x------> the number of days
y-----> the cost to rent a camping tent
The linear equation is equal to
[tex]y=kx[/tex]
we know that
It costs [tex]\$56[/tex] to rent a tent for [tex]7[/tex] days
Find the value of k
[tex]56=7k\\ \\k=56/7\\ \\k=8\frac{\$}{day}[/tex]
substitute
The linear equation is equal to
[tex]y=8x[/tex]
Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Which of the following are true? Select all that apply.
A. One pound of pistachios plus 1 pound of almonds cost $20.
B. The pistachios cost twice as much per pound as the almonds.
C. Reducing the number of pounds of almonds by one results in a total cost of $40. D. The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48. E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
We want to find a system of equations, and by solving that system we will be able to see which statements are true.
We will see that options A, C, and E are true.
We know that:
Venetta buys 2lb of pistachios
Venetta buys 3 lb of almonds.
Let's define the variables:
x = price per pound of pistachios
y = price per pound of almonds.
Now we also know that:
"The pistachios cost $4 more per pound than the almonds."
This can be written as:
[tex]x = y + \$4[/tex]
"She pays a total of $48"
This can be written as:
[tex]2*x + 3*y = \$48.[/tex]
So a system of equations:
[tex]x = y + \$4[/tex]
[tex]2*x + 3*y = \$48.[/tex]
To solve this system, the first thing we need to do is isolate one of the variables in one of the equations, particularly we can see that x is already isolated in the first equation, so we can skip that step.
Now we can replace the isolated variable in the other equation to get:
[tex]2*(y + \$4) + 3*y = \$48[/tex]
now we can solve this for y:
[tex]2*y + \$8 + 3*y = \$48[/tex]
[tex]5*y + \$8 = \$48[/tex]
[tex]5*y = \$48 - \$8 = \$40[/tex]
[tex]y = \$40/5 = \$8[/tex]
now that we know this, we can use:
[tex]x = y + \$4 = \$8 + \$4 = \$12[/tex]
now that we know:
y = $8
x = $12
Let's see which statements are true:
A) One pound of pistachios plus 1 pound of almonds cost $20.
True, $8 + $12 = $20.
B) The pistachios cost twice as much per pound as the almonds.
False, $12 is not the double of $8.
C) Reducing the number of pounds of almonds by one results in a total cost of $40.
True, one pound less of almonds means $8 less in the price.
D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48
Simplifying the expression we get:
2*(a - 4) + 3a = -8 + a = 48
a = 48 + 8 = 52
This clearly does not model the price of one pound of almonds, this statement is false.
E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Solving the equation we get:
2*p + 3*p - 12 = 48
5*p = 48 + 12 = 60
p = 60/5 = 12
This is true.
If you want to learn more, you can read:
https://brainly.com/question/20067450
15(−22.38−10.12) HELP PLEASE!!!
lots of points
what is 118/13 = 59/z?
whats the exact value of tan (300°)
Answer:
[tex]Tan(300^{\circ})= - \sqrt{3}[/tex]
Step-by-step explanation:
Tan (300°) can be written as Tan (360°-60°) ---1
Using identity :
[tex]Tan(360^{\circ}-\theta)=- Tan\theta[/tex]
Using 1
So, [tex]Tan(360^{\circ}-60^{\circ})= - Tan60^{\circ}[/tex]
The value [tex] Tan60^{\circ}=\sqrt{3}[/tex]
So, [tex]Tan(300^{\circ})= - \sqrt{3}[/tex]
Thus the exact value of [tex]Tan(300^{\circ})= - \sqrt{3}[/tex]
Answer:
[tex]-\sqrt{3}[/tex] or Option A on E2020 Quiz
Step-by-step explanation:
The area of the parallelogram is 45 square miles. Find its base and height
Final answer:
The student's question involves finding the base and height of a parallelogram given its area. Without additional information, there are infinite base-height combinations possible. The formula used is base multiplied by height equals the area of the parallelogram.
Explanation:
The student is asking about the relationship between the base, the height, and the area of a parallelogram. To find the base and height from the area, the formula for the area of a parallelogram is used, which is base x height = area. With an area of 45 square miles, if we have the measurement of either the base or the height, we can divide the area by that measurement to find the other dimension. However, with only the area given, the base and height can't be uniquely determined; there are infinitely many combinations of base and height that yield the same area. For instance, if the base is 9 miles, the height would be 5 miles, or if the base is 15 miles, the height would be 3 miles, and so on.
THIS IS MY LAST ONE BROS.
Mrs. Lamb is going to make a 3 question true false test. She wants to see how many different answer keys would be possible. What could she do to simulate this quiz? What would the sample space be?
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $10 million after 4 years while profits increased $7.5 million per year. Select the correct graph of this function.
Erik bought a savings bond. He could have invested in a mutual fund and earned 2 percent more. The 2 percent he could have earned is the _____.
Answer:
The 2 percent he could have earned is the opportunity cost.
Step-by-step explanation:
Erik bought a savings bond. He could have invested in a mutual fund and earned 2 percent more.
The 2 percent he could have earned is the opportunity cost.
The opportunity cost is defined as the loss of potential gain from other alternatives when one alternative is chosen.