Suppose the constant rate of change of y with respect to x is 8.5, and the value of y is 5 when the value of x is 11. what is the value of y when the value of x is 19? what is the value of y when the value of x is –1? what is the value of x when the value of y is 7?
Answers
Answer:
(x, y) = (19, 73)(x, y) = (-1, -97)(x, y) = (11 4/17, 7)Step-by-step explanation:
You are given a point and a slope, so you can write the linear equation relating x and y using the point-slope form of the equation for a line. That form for slope m and point (h, k) is ...
y = m(x -h) +k
For your given values, m = 8.5, and (h, k) = (11, 5), the equation relating x and y can be written ...
y = 8.5(x -11) +5
___
Evaluating this for several different x-values can be done with a spreadsheet or calculator. I like to write the function into a graphing calculator and let it do the tedious arithmetic. (See the attachment.)
However, to show you what is involved in doing this by hand, we can ...
let x = 19, then ...
y = 8.5(19 -11) +5 = 8.5·8 +5 = 73
__
let x = -1, then ...
y = 8.5(-1-11) +5 = 8.5·(-12) +5 = -97
____
To find the value of x for y=7, we can realize that to make y go up by 2 (from the given point of 5), we need to have x go up by 2/8.5 (from the given point of 11). That is ...
for y = 7 ...
x = 11 + 2/8.5 = 11 + 4/17 = 11 4/17
To determine values for y based on x in a linear function, use the equation derived. For x = 19, y equals 73; for x = -1, y equals -97. Solving for x when y is 7 gives approximately 11.24.
To solve the given problem, we use the concept of a linear function which states that the change in y with respect to x is constant. Here, the constant rate of change (slope) is given as 8.5.
We can express the linear relationship in the form of the equation:
y = 8.5x + b
We are also given a point on the line: (11, 5). Plugging these values into the equation to find b:
5 = 8.5(11) + b
5 = 93.5 + b
Subtract 93.5 from both sides:
b = 5 - 93.5 = -88.5
So, the equation becomes:
y = 8.5x - 88.5
Now, let's find the values of y for the given x values:
When x = 19: y = 8.5(19) - 88.5 = 161.5 - 88.5 = 73When x = -1: y = 8.5(-1) - 88.5 = -8.5 - 88.5 = -97To find the value of x when y = 7, we can rearrange the equation:
7 = 8.5x - 88.5
Add 88.5 to both sides:
95.5 = 8.5x
Divide by 8.5:
x = 95.5 / 8.5 = 11.2353 (approximately)
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A water tank holds 24000 gallons. How many hours will it take for 2/3 of the water to be used if the water is used at an average rate of 650 gallons a day?
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Next, divide this 18000 gallon amount by 650 gallons/da:
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A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals. Integers are the set of whole numbers and their negatives, rationals can be expressed as a fraction of two integers, irrationals cannot be expressed as a fraction, and reals represent all possible numbers on the number line.
Explanation:A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals.
Integers are the set of whole numbers and their negatives, including zero. They don't include fractions or decimals.
Rationals are the set of numbers that can be expressed as a fraction of two integers, like 3/4 or -5/2.
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Help me asap!!! :) please
Mark you a brainly!
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usually, the "r" above, is used as a "rate of increase".
but 1+r combined, can be referred as the "rate for the new size".
so, for example, if something is increasing at a rate of 25%, 1+0.25 or 1.25, the new size wil be 1.25 or 125% of the old size.
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61°
67°
69°
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Answer:
52° is ur answer
Step-by-step explanation:
I just did the quiz so i know
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I hope you found this helpful! :)
1.A system of two linear equations is graphed on a coordinate plane. If the system of equations has infinitely many solutions, which statement must be true?
A.On the graph, there is exactly one point (x,y) that satisfies both equations.
B.On the graph, any point (x,y) that satisfies one of the equations cannot satisfy the other equation.
C.On the graph, there are no points (x,y) that satisfy both equations.
D.On the graph, any point (x,y) that satisfies one of the equations must also satisfy the other equation.
2.Mark drank a total of 10 glasses of water and iced tea yesterday.
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x + y = 10
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How many glasses of water did Mark drink yesterday?
A.3 glasses
B.4 glasses
C.5 glasses
D.6 glasses
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A disc jockey must allow time for 24 minutes of commercials every hour, along with 4 minutes for news, 3 minutes for weather, and 2 minutes for public-service announcements. If each record lasts and average of 3 minutes, how many records per hour can the DJ play?
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Hello!
your answer is 75 • $6 - $35
next time add the answers too for these questions that's why the other guy didn't give you the right answer
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Is m=0.75d-2 proportional?
Answers
If m = 0.75d, then ratio m/d = (0.75d)/d = 0.75
In this example, the ratio is (.75d-2)/d = 0.75 - (2/d).
Therefore, it is not proportional.
Answer:
No, the equation m=0.75d-2 does not represent proportional relationship.
Step-by-step explanation:
The given equation is
[tex]m=0.75d-2[/tex]
We need to check whether the given equation represents proportional relationship or not.
If variable y is proportional to variable x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is the constant of proportionality.
At x=0 the value of y is 0. It means, if a linear equation represents proportional relationship then it must be passes though the origin.
Substitute d=0 in the given equation.
[tex]m=0.75(0)-2[/tex]
[tex]m=-2[/tex]
The line passes through the point (0,-2).
Since the line does not pass through the origin, therefore it does not represent proportional relationship.
For integer values of a and b, b^a = 8. The ratio of a to b is equivalent to the ratio of c to d, where c and d are integers. What is the value of c when d = 10?
Answers
3:2 = c:10
c is then equal to 10/2 *3
15
To find the value of c when d = 10, we first need to determine the values of a and b. Given that b^a = 8, we know that 8 is the result of raising b to the power of a.
Since the question states that a and b are integers, there are a limited number of possibilities to consider. Let's examine the possible combinations of a and b that satisfy this equation: [tex]1^3 = 1 2^3 = 8 3^2 = 9[/tex](which is not 8) [tex]4^2 = 16[/tex] (which is not 8) [tex]5^1 = 5 6^1 = 6 7^1 = 7 8^1 = 8[/tex]From these calculations, we find that the only combination that satisfies the equation is a = 3 and b = 2. Now, let's consider the ratio of a to b and the ratio of c to d.
The ratio of a to b is a/b = 3/2. The question states that the ratio of a to b is equivalent to the ratio of c to d, which means: a/b = c/d Given that d = 10, we can substitute the value into the equation: [tex]3/2 = c/10[/tex] Next, we can cross-multiply to solve for c: [tex]3 * 10 = 2 * c 30 = 2[/tex] c Dividing both sides by 2, we get: c = 15 Therefore, when d = 10, the value of c is 15. In conclusion, when d = 10, the value of c is 15 based on the given equation and calculations.
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What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?
Answers
-1-11
---------
1--5
Answer:-2
Step-by-step explanation:
Which equation can be used to find the number of wolves in the state on January 1? A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier. What is the number of wolves in the state on January 1? w−84=−23 w−23=84 23−w=84 w + 23 = 84
Answers
w - 23 = 84
is your answer
because there were 107 wolves the previous year
hope this helps
Answer: w - 23 = 84
Step-by-step explanation:
The number of Adult tickets is the same as the number of Child (age 5-12) tickets. A total of 38 tickets was purchased. What is the total cost of the tickets? Explain.
Data: Adult Tickets $23
Child Tickets $17
Under 5 $8
Answers
A=C=19
A*19 +C*17 = cost
19*19+19*17=684
It is estimated that there are 10^20 grains of sand on a beach in Florida in April. The beach is heavily eroded by tourists over the peak summer holiday season. Approximately one hundredth of the beach is removed as a result of this erosion. How many grains of sand are removed from the beach?
Answers
Answer:
c
Step-by-step explanation:
You are standing above the point (5,4)(5,4) on the surface z=15−(2x2+3y2)z=15−(2x2+3y2). (a) in which direction should you walk to descend fastest? (give your answer as a unit 2-vector.)
Answers
[tex]u= \frac{-\nabla z(5,\ 4)}{||\nabla f(5,\ 4)||} \\ \\ = \frac{-\ \textless \ -4x,\ -6y\ \textgreater \ |_{(5,\ 4)}}{||\ \textless \ -4x,\ -6x\ \textgreater \ ||_{(5,\ 4)}} \\ \\ = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{\sqrt{(-20)^2+(-24)^2}} = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{\sqrt{400+576}} \\ \\ = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{\sqrt{976}} = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{4\sqrt{61}} = \frac{\ \textless \ 5,\ 6\ \textgreater \ }{\sqrt{61}} [/tex]
To descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), you should walk in the direction of the negative gradient vector, normalized to be a unit vector, which is approximately <0.640, 0.768>.
Explanation:To determine the direction in which you should walk to descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), we can find the gradient of the surface at that point. The gradient vector will point in the direction of the steepest ascent, so the direction of the steepest descent is the opposite direction of the gradient vector.
First, calculate the partial derivatives of z with respect to x and y:
∂z/∂x = -4x
∂z/∂y = -6y
Next, evaluate these derivatives at the point (5,4):
∂z/∂x(5,4) = -4(5) = -20
∂z/∂y(5,4) = -6(4) = -24
The gradient vector at (5,4) is <-20, -24>. To get the direction of steepest descent, we take the negative of the gradient vector, which is <20, 24>.
Finally, normalize this vector to make it a unit vector (so it has a length of 1):
Length of gradient vector = √(20^2 + 24^2) = √(400 + 576) = √976 ≈ 31.24
The unit vector in the direction of steepest descent is <20/31.24, 24/31.24> ≈ <0.640, 0.768>.
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A hollow ball is made of rubber that is 1 centimeter thick. The ball has a radius of 5 centimeters at the outside surface.
What is the approximate volume of rubber used to make the ball?
Answers
The approximate volume of rubber used to make the ball is given by the volume of the ball at the outside surface minus the volume of the ball at the inside surface.
i.e.
[tex]Volume\ of\ rubber= \frac{4}{3} \pi\left(5^3-4^3\right) \\ \\ = \frac{4}{3} \pi(61)= \frac{244}{3} \pi\approx255.5\ cm^3[/tex]
Answer: I got the same answer. It's 255.4 cm3
Step-by-step explanation:
whats the awnser is it 600
Answers
3600/300 = 12
4800/400 = 12
the common ratio is 12 so divide pounds of milk by 12 to get pounds pf ice cream
6000 / 12 = 500
Answer is B
What does −2/3(12c−9)+14c simplify to?
Answers
Answer:
The simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{-2}{3}(12c-9)+14c[/tex]
Use the distributive property:
[tex]a(b+c)=ab+ac[/tex]
By using the above property we can simplify it as shown:
[tex]\frac{-2}{3}\times 12c-\frac{-2}{3}\times 9+14c[/tex]
[tex]-2\times 4c+2\times 3+14c[/tex]
[tex]-8c+6+14c[/tex]
Add or subtract the like terms.
[tex]6c+6[/tex] or [tex]6(c+1)[/tex]
Thus, the simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]
The simplest form of expression by applying distributive property would be, 6 (c + 1)
Given that,
The expression is,
[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]
Now, used the concept of distributive property to simplify the expression,
[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]
Apply distributive property,
[tex][\dfrac{- 2}{3} \times 12c - (\dfrac{- 2}{3} )\times 9] + 14c[/tex]
[tex][- 2 \times 4c + 2 \times 3] + 14c[/tex]
[tex][- 8c + 6] + 14c[/tex]
Combine like terms,
[tex]- 8c + 14c + 6[/tex]
[tex]6c + 6[/tex]
Take 6 as a common term,
[tex]6 (c + 1)[/tex]
So, the solution of expression 6 (c + 1).
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1/4 + -2/3 (SIMPLIFY)
Answers
Answer:
[tex]\large\boxed{\dfrac{1}{4}+-\dfrac{2}{3}=-\dfrac{5}{12}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{4}+\left(-\dfrac{2}{3}\right)=\dfrac{1}{4}-\dfrac{2}{3}\\\\\text{You must find the common denominator.}\\\\\text{List of multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ \boxed{12},\ 15,\ ...\\\text{List of multiples of 4:}\ 0,\ 4,\ 8,\ \boxed{12},\ 16,\ ...\\\\\text{The common denominator is}\ \boxeed{12}.\\\\3\cdot4=12\\\\\dfrac{1}{4}=\dfrac{1\cdot3}{4\cdot3}=\dfrac{3}{12}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}\\\\\\\dfrac{1}{4}-\dfrac{2}{3}=\dfrac{3}{12}-\dfrac{8}{12}=\dfrac{3-8}{12}=-\dfrac{5}{12}[/tex]