64% of 596-estimate using a rate per 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
How many fifths are the in 60/100
What is the slopes for (8,2) and (11,3) (8,0) and (8, 6)
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
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.
Can you use PEMDAS without parenthesis, exponents, division, or subtraction? Example: 5+1x10=?
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
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.
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.
__
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]
it took Jill two hours to drive 100 miles. what was her average speed?
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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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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A line segment has endpoints at (–1, 4) and (4, 1). Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4)?
a reflection of the line segment across the x-axis
a reflection of the line segment across the y-axis
a reflection of the line segment across the line y = x
a reflection of the line segment across the line y = –x
Answer:- A reflection of the line segment across the line y = –x .
Explanation:-
A reflection over the line y = -x, the x-coordinate and y-coordinate interchange their places and they are negated (the signs are changed).
Given :- A line segment has endpoints at (–1, 4) and (4, 1) such that it reflects produce an image with endpoints at (–4, 1) and (–1, –4).
(-1, 4)→(-4, 1) and
(4, 1)→(-1, -4)
Thus this shows a reflection of the line segment across the line y = –x.
Answer:
A reflection of the line segment across the line y = –x.
Step-by-step explanation:
Given : A line segment has endpoints at (–1, 4) and (4, 1).
To find : Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4).
Solution : We have given that endpoints at (–1, 4) and (4, 1).
After reflection endpoints become (–4, 1) and (–1, –4).
Reflection: (–1, 4) →→ (–4, 1)
(4, 1)→→→ (–1, –4).
We can see x coordinate become -y coordinate and y coordinate become -x coordinate.
(x ,y) →→ (–y, -x)
This is the a reflection of the line segment across the line y = –x rule of reflection .
Therefore, a reflection of the line segment across the line y = –x.
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?
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
Two angles in a triangle are 30° and 35°. What type of angle is the other?
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)
in a chess match, a win counts 1 point, a draw counts 1/2 point, and a loss counts 0 points. After 15 games, the winner was 4 points ahead of the loser. How many points did the loser have? ...?
The loser had 5.5 points in the chess match.
Explanation:To find out how many points the loser had in the chess match, we can set up an equation. Let's say the loser had x points. The winner was 4 points ahead, so the winner had x + 4 points. Since there were 15 games in total, we can set up the equation:
x + (x + 4) = 15
Combining like terms, we get:
2x + 4 = 15
Subtracting 4 from both sides, we get:
2x = 11
Dividing both sides by 2, we get:
x = 5.5
Therefore, the loser had 5.5 points in the chess match.
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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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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
Did I do this correctly and if any errors just tell me in the comments
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
The sum of 8 and diane's savings is 56
A _____ is a point that helps to define an ellipse.
...?
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.)
Evaluate the integral (e^x)/((e^2x)+3) from 0 to infinity
A bunch of 6 bananas costs $3.54. What is the unit rate?
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.