Brianna went to Los Angeles for a vacation. She spent 5 nights at a hotel and rented a car for 6 days. Justin stayed at the same hotel, but spent 7 nights and rented a car for 8 days from the same company. If Brianna paid $1170 and Justin paid $1610, how much did one night at the hotel cost?
$150 per night
Use a system of equations using x (cost of hotel) and y (cost of car):
5x + 6y = 1170
7x + 8y = 1610
Solve for y in one of the equations and then use substitution to solve for x in the other:
6y = 1170 - 5x
y = (-5/6)x + 195
7x + 8((-5/6)x + 195) = 1610
7x + (-20/3)x + 1560 = 1610
(1/3)x +1560 = 1610
(1/3)x = 50
x = $150 a night
The graph of a proportional relationship contains the point (20, 4).
What is the corresponding equation?
Enter your answer as a fraction in simplest form
Please help
The corresponding equation is y = 1/5(x).
A graph of the equation is shown below.
In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:
y = kx
Where:
y represents the y-variable.
x represents the x-variable.
k is the constant of proportionality.
Next, we would determine the constant of proportionality (k) by using the various data points in table B as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 4/20
Constant of proportionality, k = 1/5.
In this context, the corresponding equation is given by;
y = 1/5(x)
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and x are related by the equation.
What is the change in the total cost for each book printed?
What is the cost to get started (before any books are printed)?
Equation: y=1250+25x
Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 3 years?
Round your answer to the nearest cent.
Enter your answer in the box.
Answer:
Step-by-step explanation:
7
64% of 596-estimate using a rate per 100
U.s. air has a net income before tax 60,000. it is expected 45% of net income will go to federal and state taxes. how much will u.s. air have left
Evaluate the integral (e^x)/((e^2x)+3) from 0 to infinity
A college class with 30 sophomores, 18 juniors, and 12 seniors is
divided into project groups where each group has the same number
of sophomores, juniors, and seniors. What is the greatest number of
groups that can be formed? How many sophomores, juniors, and
seniors are in each project group?
The maximum number of project groups can be formed is 5 and the number of sophomores, juniors, and seniors within each group will be 5, 3 and 2 respectively.
To find the greatest number of groups that can be formed with the given distribution of students,
Identify the common factor: The greatest common factor of 30, 18, and 12 is 6.
Calculate groups: Divide each class by 6: 30 sophomores ÷ 6 = 5, 18 juniors ÷ 6 = 3, and 12 seniors ÷ 6 = 2. Therefore, the maximum number of groups that can be formed is 5.
The sum of 8 and diane's savings is 56
which of the following is equivalent to 14x2+35x when it is completely factored?
A. 7x(2x+5)
B. 7(2x2+5x)
C. 14x(x+3)
D. x(14x+35)
The equivalent factored form is A. 7x(2x + 5).
How to determine the equivalent to 14x2+35x when it is completely factoredTo factorize the expression 14x^2 + 35x completely, we look for the greatest common factor (GCF) of the terms and apply the distributive property.
In this case, the GCF of 14x^2 and 35x is 7x.
So, we can factor out 7x from the expression:
14x^2 + 35x = 7x(2x + 5)
Therefore, the equivalent factored form is A. 7x(2x + 5).
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is square root 35 irrational or rational
The square root of 35 is an irrational number because it cannot be expressed as a precise fraction or whole number.
Explanation:The square root of 35 is an irrational number. Let me explain why. A number is rational if it can be expressed as a fraction of two integers, in other words, if it can be written in the form a/b where a and b are integers and b ≠ 0. The square root of a perfect square (like 9, 16, 25 and so on) is a rational number because it can be expressed as a whole number. But if a number is not a perfect square (like 35), its square root is generally an irrational number. The square root of 35 cannot be expressed as a whole number or as a precise fraction, hence it is an irrational number.
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A bunch of 6 bananas costs $3.54. What is the unit rate?
Sasha has some pennies, nickels, and dimes in her pocket. The number of coins is 16. The expression 0.01p+0.05n+0.10d represents the value of the coins, which is $1.22. She has twice as many nickles as pennies. How many of each coin does Sasha have?
Bob's team won 75% of its baseball games. it played 16 games in all. how many games did the team win?
Bob's team won 12 out of the 16 games it played, which is calculated by multiplying the total number of games (16) by the percentage of games won (75%).
Bob's team won 75% of its baseball games and played 16 games in all. To find out how many games the team won, we can use the formula:
Number of games won = (Percentage of games won / 100) x Total number of games played
Number of games won = (75 / 100) x 16
Number of games won = 0.75 x 16
Number of games won = 12
So, Bob's team won 12 out of the 16 games played.
What is the slopes for (8,2) and (11,3) (8,0) and (8, 6)
i need help asap
Your cell phone plan costs 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan.
F(x) = 55x + 0.35
F(x) = 55x + 15
F(x) = 0.35x + 55
F(x) = 35x + 55
it took Jill two hours to drive 100 miles. what was her average speed?
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
y = √x
(a) Find dy/dt, given x = 16 and dx/dt = 7.
dy/dt =
(b) Find dx/dt, given x = 64 and dy/dt = 8.
dx/dt =
...?
(a) The value of [tex]\frac{dy}{dt}[/tex] is [tex]\boxed{\dfrac{dy}{dt}=\dfrac{7}{8}}[/tex].
(b) The value of [tex]\frac{dx}{dt}[/tex] is [tex]\boxed{\dfrac{dx}{dt}=128}[/tex].
Further explanation:
Given that [tex]x[/tex] and [tex]y[/tex] are both differentiable functions of [tex]t[/tex].
The function is as follows:
[tex]\fbox{\begin\\\ \math y=\sqrt{x}\\\end{minispace}}[/tex]
Derivatives of parametric functions:
The relationship between variable [tex]x[/tex] and variable [tex]y[/tex] in the form [tex]y=f(t)[/tex] and [tex]x=g(t)[/tex] is called as parametric form with [tex]t[/tex] as a parameter.
The derivative of the parametric form is given as follows:
[tex]\fbox{\begin\\\ \dfrac{dy}{dt}=\dfrac{dy}{dx}\times\dfrac{dx}{dt}\\\end{minispace}}[/tex]
The above equation is neither explicit nor implicit, therefore a third variable is used.
Part (a):
It is given that [tex]x=16[/tex] and [tex]\frac{dx}{dt}=7[/tex].
To find the value of [tex]\frac{dy}{dt}[/tex] first find the value of [tex]\frac{dy}{dx}[/tex] that is shown below:
[tex]\begin{aligned}y&=\sqrt{x}\\\dfrac{dy}{dx}&=\dfrac{1}{2\sqrt{x}}\end{aligned}[/tex]
The value of [tex]\frac{dy}{dt}[/tex] is calculated as follows:
[tex]\begin{aligned}\dfrac{dy}{dt}&=\dfrac{dy}{dx}\times\dfrac{dx}{dt}\\&=\dfrac{1}{2\sqrt{x}}\dfrac{dx}{dt}\end{aligned}[/tex]
Now, substitute the value of [tex]x[/tex] and [tex]\frac{dx}{dt}[/tex] in above equation as shown below:
[tex]\begin{aligned}\dfrac{dy}{dt}&=\dfrac{1}{2\sqrt{16}}\times7\\&=\dfrac{1}{2\times4}\times7\\&=\dfrac{7}{8}\end{aligned}[/tex]
Therefore, the required value of [tex]\frac{dy}{dt}[/tex] is [tex]\frac{7}{8}[/tex].
Part (b):
It is given that [tex]x=64[/tex] and [tex]\frac{dy}{dt}=8[/tex].
To find the value of [tex]\frac{dx}{dt}[/tex] first find the value of [tex]\frac{dx}{dt}[/tex] that is shown below:
[tex]\begin{aligned}y&=\sqrt{x}\\\dfrac{dy}{dx}&=\dfrac{1}{2\sqrt{x}}\\\dfrac{dx}{dy}&=2\sqrt{x}\end{aligned}[/tex]
The value of [tex]\frac{dx}{dt}[/tex] is calculated as follows:
[tex]\boxed{\dfrac{dx}{dt}=\dfrac{dx}{dy}\times\dfrac{dy}{dt}}[/tex]
Now, substitute the value of [tex]\frac{dx}{dy}[/tex] and [tex]\frac{dy}{dt}[/tex] in above equation as shown below:
[tex]\begin{aligned}\dfrac{dx}{dt}&=2\sqrt{64}\times 8\\&=2\times8\times8\\&=2\times64\\&=128\end{aligned}[/tex]
Therefore, the required value of [tex]\frac{dx}{dt}[/tex] is [tex]128[/tex].
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Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Derivatives
Keywords: dy/dt, dx/dt, y=rootx, derivatives, parametric form, implicit, explicit, function, differentiable, x, y, t, x=16, x=64, dy/dx, dx/dy, differentiation.
Find the interest rate needed for an investment of $9,000 to quadruple in 15 years if interest is compounded quarterly. (round your answer to the nearest hundredth of a percentage point.)
40 is rounded to the nearest whole write down the maximum possible length it could have been
The maximum length the number could have been before being rounded down to 40 is just under 40.5 since that is the point at which it would round up to 41.
Explanation:The question pertains to rounding numbers to the nearest whole number. When rounding the number 40 to the nearest whole, we'd like to find the maximum length it could have been before rounding down. The process of rounding will round a number to the nearest whole number based on the decimal value. For instance, if you are rounding to the nearest whole number, a number with a decimal part of 0.5 or higher will round up, while a number with a decimal part of less than 0.5 will round down.
Given that 40 is already a whole number, this implies it could have been rounded down from a number up to one decimal less than 40.5 since any number 40.5 and above would round up to 41. Hence, the maximum possible length it could have been before rounding down is just under 40.5.
__
What is the length of PR?
The answer is 7 apex
Answer-
The length of PR is 7 units.
Solution-
Given,
in the ΔDEF,
m∠D = 25°, m∠E = 114°, DF = 21, DE = 15
in the ΔPQR,
m∠P = 25°, m∠Q = 114°, PR = x, PQ = 5
So, ΔDEF ~ ΔPQR by AA (Angle-Angle) similarity, as
m∠D = m∠P = 25°m∠E =m∠Q = 114°So, according to similarity
[tex]\Rightarrow \dfrac{DF}{PR}=\dfrac{DE}{PQ}=\dfrac{EF}{QR}[/tex]
Putting the values,
[tex]\Rightarrow \dfrac{21}{x}=\dfrac{15}{5}[/tex]
[tex]\Rightarrow x=\dfrac{21\times 5}{15}[/tex]
[tex]\Rightarrow x=7[/tex]
A _____ is a point that helps to define an ellipse.
...?
Annette rode her bike 6.8 miles at a constant rate for 90 minutes. To find how fast she traveled, she solved the equation 6.8= x⋅90. What does x represent?
a)The total distance after x minutes
b)Her speed in miles per minute
c)The amount of time it takes to travel 6.8 miles
d)The number of miles she has traveled so far
Answer:
x represents Annette speed in miles per minute. Hence, option b) is correct.
Step-by-step explanation:
Given that Annette rode her bike 6.8 miles at a constant rate for 90 minutes. Also to find how fast she traveled, she solved the equation [tex]6.8=x\times 90[/tex]. Now, we have to tell here what x represents.
As, [tex]Speed=\frac{Distance}{Time}[/tex]
Let speed of bike is x miles/min and given distance is 6.8 miles and at a constant rate for 90 minutes.
∴ [tex]x=\frac{6.8}{90}[/tex]
⇒ [tex]6.8=x\times 90[/tex]
which is the same equation as given.
Here x represents Annette speed in miles per minute. Hence, option b) is correct.
An angle measure is 6 degrees more than 3 times its compliment. find the measure of the angle.
The angle which is 6 degrees more than 3 times its complement is found to be 69 degrees.
Explanation:This problem is related to complementary angles in Mathematics. Complementary angles are two angles that add up to 90 degrees. If we denote one angle as x, its complement is 90 - x.
According to the question, an angle measure is 6 degrees more than 3 times its complement. So we write an equation from this: x = 3*(90 - x) + 6. By solving this equation, we can find the value of x which represents the angle.
First, distribute through the parenthesis: x = 270 - 3x + 6. Combine like terms: 4x = 276. Finally, divide both sides by 4 to solve for x: x = 69 degrees.
So, the angle is 69 degrees.
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How many fifths are the in 60/100
Ahmed is taking orders for lunch. A slice of pizza cost $2.9 and a chicken sandwich costs $3.9. He collects $25.3 for the group of 7 people.
Let x=number of pizza orders.Let y=number of chicken orders
An algebraic expression has parentheses with unlike terms inside. Explain how to simplify this algebraic expression if a minus sign is in front of the parentheses.
Answer:
The expression can be simplified by distributing the minus sign to each of the terms inside of the expression.
Step-by-step explanation:
What is tangent of 11/6?
Name the property of real numbers illustrated by the equation.
-3(x+4)=-3x-12
Answer:
distributive property (a)
Step-by-step explanation:
I got 100/100 so this should be correct for you too.
Is this sequence arithmetic, geometric or neither? 4, 8, 16, 32, 64,...
Answer:
geometric sequence