The value of P'(t) will be , P'(t) = -10t + 75 and value of P'(7) will be equal to 5 and rate of change of price will be $5 thousands per year in dollars.
It is given that median home price is represented by P(t) = -5t² + 75t - 30.
We have to find out the values of P'(t) and P'(7).
What is differentiation ?
Differentiation is a method in which the function's rate of change compared to the rate of change of the independent variable is calculated.
As per the question ;
The equation given is ;
P(t) = -5t² + 75t - 30
So ;
Differentiating the above equation with respect to t , we get ;
[tex]\frac{d}{dt}[/tex] (P(t)) = [tex]\frac{d}{dt}[/tex] ( -5t² + 75t - 30 )
[tex]\frac{d}{dt}[/tex] (P(t)) = P'(t) = -5 × 2 × t + 75
⇒ P'(t) = -10t + 75
And
The value of P'(7) will be ;
P'( t = 7) = -10 × 7 + 75
P'(7) = - 70 + 75
P'(7) = 5
Also ;
P(11) = 190
P(3) = 150
And
The rate of change of price will be ;
[tex]\frac{P(11) - P(3)}{11 - 3}[/tex]
= 190 - 150 / 8
= 40 / 8
= 5
Thus , the value of P'(t) will be , P'(t) = -10t + 75 and value of P'(7) will be equal to 5 and rate of change of price will be $5 thousands per year in dollars.
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what are the slope and the y intercept of the linear function represented by the equation y=9x-2
Answer:
the slope is 9 and the y-intercept is -2
∠A and \angle B∠B are vertical angles. If m\angle A=(5x+5)^{\circ}∠A=(5x+5)
∘
and m\angle B=(6x-8)^{\circ}∠B=(6x−8)
∘
, then find the value of x.
Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles. The value of x is 13.
What are vertical angles?Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles.
Given that ∠A and ∠B are vertical angles. Therefore, the measure of the two of the given angle will be equal to each other. Thus, we can write the measure of the two angles as,
∠A = ∠B
(5x + 5)° = (6x - 8)°
5x + 5 = 6x - 8
Bring the like terms on the same side of the equation,
5 + 8 = 6x - 5x
13 = x
x = 13
Hence, the value of x is 13.
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is it possible for a binomial and trinomial to have the same degree?
Answer:
No
Step-by-step explanation:
B/c trinomial has exactly 3 terms and binomial only have 2
what is the domain and range of the question below
domain=
range =
The Domain is [-4, -2] U [-1, 1) and range is [4, 0)
What is Domain and Range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
Given:
The left piece has its other endpoint at x = -2.
So, the interval for the domain is [-4, -2] and the other part is [-1, 1)
So, the domain is [-4, -2] U [-1, 1)
and the range is the vertical range of the right part.
So, range is [4, 0)
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Tatianna and Genesis are both saving money to buy new dolls. The
ratio of Tatianna's saving to Genesis's saving is 3:1. If they have
saved $400, how much has each girl saved?
Answer:
tianna has saved $300 and genesis has saved $100
Step-by-step explanation:
3 plus 1 is 4
400 divided by four is 100
3 times 100 is 300
1 times 100 is 100
tianna saved 300
genesis saved 100
solve the problem
(4 1/3) (-2) (5/13)
The solution of the given expression (4 1/3) (-2) (5/13) is -130/13.
According to the given question.
We have an expression (4 1/3) (-2) (5/13).
Here, we have to solve the given expression.
So, the solution of the expression (4 1/3) (-2) (5/13) is given by
(4 1/3) (-2) (5/13)
= (13/3)(-2)(5/-13) (by converting the mixed fraction into improper fraction)
= (-26/13)(5/13)
= -130/13
Hence, the solution of the given expression (4 1/3) (-2) (5/13) is -130/13.
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Find the vertex of the quadratic function f(x)=(x+3)2−4
The vertex of the quadratic function f(x) = (x + 3)² - 4 is (-3,-4)
How to find the vertex of the quadratic function?Given a quadratic function, the equation of the quadratic function in vertex form is given by f(x) = a(x - h)² + k where
h = x - coordinate of vertex and k = y-coordinate of vertex and (h, k) is the vertexNow, given the quadratic function f(x) = (x + 3)² - 4, we require the vertex of the quadratic function.
Comparing the function f(x) = (x + 3)² - 4 with f(x) a(x - h)² + k, we see that
a = 1, h = -3 and k = -4.Since the vertex of the quadratic function is (h, k), we see that the vertex of the quadratic function f(x) is (-3,-4)
So, the vertex of the quadratic function is (-3,-4)
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explain why the statement x < 3 or > 5 cannot be written 5 < x < 3
Answer:
This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.
Step-by-step explanation:
x < 3 or x > 5
This means, x is less than 3, but greater than 5.
Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.
Calculus 1 question
help please rn please help
Answer: the answer is MO=5
Step-by-step explanation:
One side of a rectangle is 4 m longer than four times another side. The area of the rectangle is 224 m².
Find the length of the shorter side.
m
Let the another side be x m.
Therefore, the longer side = (4 + 4x) m.
Now,
[tex]{\sf{→x \times (4 + 4x) = 224 \\ →4x + 4x {}^{2} - 224 = 0 \\→ x {}^{2} + x - 56 = 0 \\ →x {}^{2} + 8x - 7x - 56 = 0 \\ →x(x + 8) - 7(x + 8) = 0 \\ →(x - 7)(x +8 ) = 0 \\ →x = 7 \: or \: x = - 8 \\ \\ length \: cannot \: be \: negative \\ possible \: solution \: (x) = 7}}[/tex]
Length of shorter side = x = 7 metres.
[tex]{\sf{answer\: \\ss}}[/tex]
How can i upgrade now during the trial?
Rewrite using an exponent.
Answer:
2[tex] {}^{5} [/tex]
Step-by-step explanation:
2×2×2×2×2 = 2[tex] {}^{5} [/tex]
Which expression is equivalent to 3/2^3 HELP ASAP
Answer:
3rd option
Step-by-step explanation:
One of our exponent rules tells us that [tex](\frac{x}{y} )^{z}[/tex] = [tex]\frac{x^{z} }{y^{z} }[/tex]. So, knowing that exponent rule, we know that it has to be the third option. But what if we didn't know that rule? Then how could we solve this?
We know that 3/2 = 1.5. Do some math and you can figure out that 1.5^3 is 3.375. If we were to evaluate expression number 3, we would get 27/8, which, if you were to further evaluate it, you would also get 3.375.
Let me know if you have any questions!
Solve the equation by the zero factor property
b^2-8b+15=0
Answer:
(b-5)(b-3)
Step-by-step explanation:
To factor this equation we have to find 2 numbers that combine to equal -8 and multiply together to equal 15
these numbers would be -3 and -5
after that you just put them in an equation like so:
(b-5)(b-3)
you can check your work by just multiplying those back together
If you want future explanation on how to do this just ask
hope this helps :D
Use the diagram to find the following measures
A) triangle angle sum equation
B) value of x = ———- degrees
Answer:
x = 71°
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
The measure of two angles out of three is given, we will use the following equation to find the value of the missing angle:
82 + 27 + x = 180 add like terms
109 + x = 180 subtract 109 from both sides
x = 71
Which would increase an object’s temperature
Temperature is a physical quantity that expresses the hotness of matter or radiation. The heat increases an objects temperature.
What is temperature?
Temperature is a physical quantity that expresses the hotness of matter or radiation.
The temperature of the object increases due to the absorbed part of the heat. An object decreases its temperature by releasing energy in the form of heat to its surroundings. And an object increases its temperature by gaining energy in the form of heat from its surroundings.
So the temperature changes according to the heat of the surrounding.
Therefore the heat increases an objects temperature.
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Полоску бумаги разрезали на 7 частей. После этого самую большую
из полученных частей снова разрезали на 7 частей. Затем снова самую большую
из полученных частей разрезали на 7 частей. Так поступили много раз: на
каждом шаге самую большую часть разрезали на 7 частей. Могло ли в итоге
получиться 500 частей?
Answer:
2556285=68358556
Step-by-step explanation:
+58385-5838688(68589)8999=9858288
Make a conjecture about each pattern. Then write the next two items. 4. 1, 2, 2, 4, 8, 32, . . .
Answer:
256, 8192
{This is an educated guess}
Step-by-step explanation:
The problem seems to be a variation of the Fibonacci sequence: 1, 1, 2, 3, 5, 8...
1 ⇒ 2: 1*2
2 ⇒ 2: 2*1
2 ⇒ 4: 2*2
4⇒8:4*2
8⇒32:8*4
32⇒256: 32*8
256*32 = 8192
explain square root of 3 rational number
Answer:
[tex]\sqrt{4}[/tex], [tex]\sqrt{9}[/tex], [tex]\sqrt{16}[/tex]
Step-by-step explanation:
I think that you are asking for 3 examples of square roots that are rational. All perfect squares are rational. If the square root is not a perfect square then the number is irrational.
[tex]\sqrt{4[/tex] = 2 and -2. The number multiplied by itself is an integer. Integers are the whole numbers and their opposites: ...-3, -2, -1, 0, 1, 2, 3...
1/2 is not an integers. 0.75 is not an integer.
[tex]\sqrt{9}[/tex] is 3 and -3
[tex]\sqrt{16}[/tex] is 4 and -4
Numbers like:
[tex]\sqrt{3}[/tex] is irrational because this number in a decimal form never terminates or repeats.
Gina is making a scrapbook and is putting 6 pictures on each page. She has completed 12 pages so far. How many pictures has she used? What is the problem asking you?
PLS HELP 100 POINT QUESTION
how to simplify 4x5 / 1+9
Answer:
29
Step-by-step explanation:
Which shape has at least one pair of perpendicular sides?
Under his cell phone plan, William pays a flat cost of $54.50 per month and $3 per gigabyte. He wants to keep his bill at $66.20 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data William can use while staying within his budget.
Answer: 66.2=54.5+3gg
gg=3.9 gigabytes
Step-by-step explanation:
66.2=54.5+3gg
3gg=66.2-54.5
3gg=11.7
gg=3.9 gigabytes
3.9 number of gigabytes of data William can use while staying within his budget.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
William pays a flat cost of $54.50 per month and $3 per gigabyte.
He wants to keep his bill at $66.20 per month.
We need to solve this and to find number of gigabytes of data William can use while staying within his budget.
This can be written as equation
66.2=54.5+3gg
Subtract 54.5 from both sides
66.2=54.5+3gg
3gg=66.2-54.5
3gg=11.7
Divide both sides by 3
gg=3.9 gigabytes
Hence, 3.9 number of gigabytes of data William can use while staying within his budget.
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I need help to find x and y
The system of nonlinear equations have two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).
What is the solution of a system of nonlinear equations?In this problem we find a system of two nonlinear equations involving radical expressions. We proceed to resolve the system of nonlinear equations by algebra properties:
(2 · x - 1)² + 8√(2 · x · y) = 4
8√(2 · x · y) = 4 - (2 · x - 1)²
8√(2 · x · y) = 4 - 4 · x² + 4 · x - 1
8√(2 · x · y) = 4 · x - 4 · x² + 3
64 · (2 · x · y) = [(4 · x + 3) - 4 · x²]²
128 · x · y = (4 · x + 3)² - 8 · (4 · x + 3) · x² + 64 · x⁴
128 · x · y = 16 · x² + 24 · x + 9 - 32 · x³ - 24 · x² + 64 · x⁴ (1)
4 · y - √(8 · x · y - 1) = 1
4 · y - 1 = √(8 · x · y - 1)
(4 · y - 1)² = 8 · x · y - 1
16 · y² - 8 · y + 2 = 8 · x · y (2)
Now we plot two equations on a graphing tool and find that the system has the following two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).
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One state has a 6% sales tax on clothing items priced at $75 or higher, and no sales tax on clothing items priced under $75. What is the total tax on the items in the table above?
20 points!!!What is a two step problem with variables on each side equal 20? (Please help)
5x-15=5+4x
+15 +5
5x=20+4x
-4x -4x
x= 20
Step-by-step explanation:
the graph of function y
[tex]y = x ^{2} [/tex]
Given the graphs of f(x) and g(z) below, find the composition of functions f(g(-1)).
The composition of the functions, f(g(-1)) = 2.
How to Find the Composition of Functions?To find the composition of the functions, f(g(-1)), first, find the function, g(-1) by tracing the value of y that will give an x-value of -1 on the function graph.
The next step is to use the value you get in the first step to trace which value of y will give an x-value equivalent to what you got in the first step on the second function graph.
Thus, from the graph of g(x), g(-1) = 0. Using the graph of f(x), the value of y when x = 0 is 2.
Therefore, the composition of the functions, f(g(-1)) = 2.
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Express 88 kilometers per hour in miles per hour.
mi/hr
(Round to the nearest hundredth as needed.)
88 kilometers per hour in miles per hour is 54.68 mi/hr
Converting kilometers per hour to miles per hourNote that:
1 km = 0.6214 miles
The measurement to convert is 88 kilometers per hour
Multiply 88 kilometers per hour by 0.6214 to convert to miles per hour
88 kilometers per hour = 88 x 0.6214 miles per hour
88 kilometers per hour = 54.6832 miles per hour
88 kilometers per hour = 54.68 mi/hr
Therefore, 88 kilometers per hour in miles per hour is 54.68 mi/hr
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