The equation of the new parabola, that is, the image of the parabola f(x) = x² is g(x) = - (1 / 8) · x².
What is the equation of the image of a parabola?
In this problem we must determine the image of the parabola f(x) = x², which is the result of a sequence of two rigid transformations: (i) Reflection across the x-axis, (ii) Dilation. Each kind of rigid transformation is described below:
Reflection across the x-axis
f'(x) = - f(x)
Dilation
g(x) = k · f'(x), where k is the scale factor.
Now we proceed to determine the equation of the new parabola:
Step 0
f(x) = x²
Step 1
f'(x) = - x²
Step 2
g(x) = - (1 / 8) · x²
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A ball is thrown from a height of 3 meters with an initial downward velocity of 5 m/s The ball's height h (in meters) after t seconds is given by the following. how long after the ball is thrown does it hit the ground
The ball hits the ground at a time of 1.433 seconds.
How to calculate the time until the ball hits the ground
In this problem we have the case of a ball that experiments a free fall, that is, an uniform accelerated motion due to gravity. The position of the ball in time is described by a quadratic equation:
y = y' + v' · t + 0.5 · g · t²
Where:
y' - Initial position, in meters.v' - Initial speed, in meters per second. t - Time, in seconds. g - Gravitational acceleration, in meters per square second.y - Final position, in meters.If we know that y' = 3 m, v' = 5 m / s, g = - 9.807 m / s², y = 0 m, then the time of the ball until it hits the ground is:
0 = 3 + 5 · t - 4.904 · t²
Then, by the quadratic formula:
t = - v' / g ± (1 / g) · √[v'² - 2 · g · y']
t = - 5 / (- 9.807) ± [1 / (- 9.807)] · [5² - 2 · (- 9.807) · 3]
t₁ = 1.433 s. or t₂ = - 0.424 s.
The hitting time of the ball is 1.433 seconds.
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● 4.Harsh purchased 6kg 025g of fruits and 4 kg 325of vegetables and put them in a bag. The bag with its contents weighs 12 kg. What is the weight of the empty bag?
Step-by-step explanation:
6kg025g = 6025g
4kg 325g = 4325 g
6025+4325= 10350 g
12kg = 12000g
12000-10350 = 1650g = 1 kg 650 g
-6 1/4x= -3 1/8
Whats the value of x
Answer:
Step-by-step explanation:
-25/4(x)= -25/8
x= -(25/8) X (4/-25)= 1/2
2:8=12:_____________
48 let the unknown part be x. And make it 2/8=
Give the degree of the polynomial.
Answer: 7
This is a seventh degree polynomial.
Step-by-step explanation:
The degree of the polynomial is the highest exponent.
Step-by-step explanation:
7 is the degree of the polynomial
7 is the highest exponent.
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I need help with this Please been struggling all day
Answer:
x-intercepts: -0.16 and 3.16
vertex: (1.5, 5.5)
Step-by-step explanation:
A rectangle has a length of 72cm and a width of 56cm. A second rectangle has the same area as this one, but its width is 21cm. What is the constant of variation.
192 cm is the length of rectangle.
What is rectangle?
An example of a quadrilateral with opposite sides that are both equal and parallel is a rectangle.
There are four 90-degree angles on its four sides, making it a four-sided polygon. A rectangle is a shape with only two dimensions.
Area of rectangle = 72 * 56
= 4032 cm²
the second rectangle's area is same as first rectangle .
4032 = x * 21
x = 4032/21
x = 192 cm
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3. Find the length of the bridge.
20 ft
160 ft
32.5 ft
74 % of 315
estimate using the rate per 100
Answer:
23.4920634921
Step-by-step explanation:
74/315 x 100% = 23.4920634921
HELP ME PLEASE THANKS
Answer: Answer choice B
Step-by-step explanation:
f(x) = 3x² + 2x - 20 for x = 3
help please?
When we're given f(x) and x, we can evaluate the function by replacing every x with the given value, and simplifying.
Solving the Question[tex]f(x) = 3x^2 + 2x - 20[/tex]
⇒ Replace every x with 3:
[tex]f(3) = 3(3)^2 + 2(3) - 20\\\\f(3) = 3(9) + 6 - 20\\\\f(3) = 27 + 6 - 20\\\\f(3) = 13[/tex]
Answer[tex]f(3) = 13[/tex]
Step-by-step explanation:
A function is a relationship bound to one output for every single input the value of F(3) for the given function F(x)=3x²+2x-20 is 13.
What is a function?
The function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
A certain kind of relationship called a function binds inputs to essentially one output.
As per the given function,
F(x)=3x²+2x-20
Substitute, x = 3
F(3) = 3(3)^2 + 2(3) - 20
F(3) = 3(9) + 6 - 20
F(3) = 13
Hence "A function is a relationship bound to one output for every single input the value of F(3) for the given function F(x)=3x²+2x-20 is 13".
For more about the function,
I WILL GIVE BRAINLY TO WHOEVER HELPS!!
Select all the equations that represent the bar diagram.
Answer:
A and C
Step-by-step explanation:
Find the values of x, y, and z in the triangle.
(Image attached.)
I need assistance on This question
Answer: it would be A.
Step-by-step explanation: I did the quiz
You have saved $16,000 for a down payment on a house. Your bank requires a minimum down payment of 15%.
What is the maximum price you can offer for a home in order to have enough money for the down payment?
an equation for the direct variation function of the points (-8, -6) and (12, 9)
Answer:
Your answer is [tex]y=0.75x[/tex] or [tex]y=\frac{3}{4} x[/tex]
Step-by-step explanation:
Using the formula [tex]\frac{y1-y2}{x2-x1}[/tex] we get [tex]\frac{3}{4}[/tex]
Using the formula [tex]y=kx[/tex] we get [tex]y=\frac{3}{4} x[/tex]
Explain why the equation cos(x) = x has at least 1 solution
There exists a point c ∈ [0, 2π], therefore, f(c) =0, Hence cos x = x has at least one solution.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
cos(x) = x (1)
For the given interval [0, 2π],
By intermediate theorem, for c ∈ [0, 2π], for which f(c) =0
Or we can say that, at x = 0, f(0) = 0
Therefore, cos(x) has at least one solution, in the interval [0, 2π]
So, given equation cos(x) = x has one solution.
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What is x when x=2-4+5
Which statement describes the relationship between the function and its inverse? The range of both f(x) and f–1(x) is all real numbers. The domain of both f(x) and f–1(x) is all real numbers. The range of f(x) is y > 0 and the domain of f–1(x) is x > 0. The domain of f(x) is x > 0 and the range of f–1(x) is y > 0.
The true statement about a function and its inverse is, the range of both f(x) and f⁻¹(x) is all real numbers.
What is an inverse function?The inverse of a function f is denoted by f⁻¹ and it exists only when f is both one-one and onto function.
f⁻¹ isn't the reciprocal of f. The composition of the function f and the reciprocal function f⁻¹ gives the domain value of x.
The true statement about a function and its inverse is,
The range of both f(x) and f⁻¹(x) is all real numbers.
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Can you please help me with this question
Answer: I can’t read it
Step-by-step explanation:
THE ONE PIECE IS REAL
Answer: im going to be king of the pierates
Step-by-step explanation: :)
When you apply the method to complete the square to find the solution to the equation
2x^2 +3x +3=4
What term should we sum/add on both sides of the equation?
A. 9
B. 9/4
C. 3/2
D. 9/16
Answer:
B
Step-by-step explanation:
2x²+3x=4-3=1
2x²+3x=1
to make it a perfect square we divide the coeff of X by 2 then square it and add it to both sides
=(3/2)²=9/4
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
The income on day 31 would be $21,1474,836.48 and the total income for working 31 days would be $42,949,672.94.
The company pays one penny on the first day, 2 cents on the second day, 4 cents on the third day, and so on.
This situation represents the geometry sequence below as
0.02, 0.04, 0.08,..
Here first-term a₁ = 0.02
And common ratio r = 0.04/0.02 = 2
The income on day 31 would be:
⇒ a₁ (r)ⁿ⁻¹
⇒ 0.02 (2)³¹⁻¹
⇒ 0.02 (2)³⁰
⇒ 21,1474,836.48
Total income for working 31 days would be:
⇒ a₁ (1-rⁿ) / 1 - r
⇒ 0.02 (1-2³¹) / (1 - 2)
⇒ 42,949,672.94
Thus, the income on day 31 would be $21,1474,836.48 and the total income for working 31 days would be $42,949,672.94.
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Sandpiper Company has 25,000 shares of cumulative preferred 1% stock, $150 par and 50,000 shares of $5 par common stock. The following amounts were distributed as dividends:
20Y1 $75,000
20Y2 15,000
20Y3 112,500
Determine the dividends per share for preferred and common stock for each year. Round all answers to two decimal places.
If Sandpiper Company has 25,000 shares of cumulative preferred 1% stock.
Dividends per share for preferred
Year 1 = $3 per shareYear 2 = $4.5 per shareYear 3 = $1 per shareCommon stock
Year 1 = $0Year 2 = $1.95Year 3 =$1.75How to find the dividends per share and common stock?The arrear $75,000 of unpaid dividends from year 1 will be paid to preferred stockholders in year 2
= ($150 x 1% x 25,000) +$75,000
= ($37,500 + $75,000)
= $112,500
Year 1 Year 2 Year 3
Distributed $75,000 $15,000 $112,500
Preferred $75,000 $112,500 $25,000
Common $0 $97,500 $87,500
Dividends per share for preferred
Year 1 = $75,000/25,000 shares
Year 1 = $3 per share
Year 2 = $112,500 /25,000 shares
Year 2 = $4.5 per share
Year 3 = $25,000/$25,000 shares
Year 3 = $1 per share
Common stock
Year 1 = 0/ 50,000 shares
Year 1 = $0
Year 2 =$97,500 / 50,000 shares
Year 2 = $1.95
Year 3 = $87,500 /50,000 shares
Year 3 =$1.75
Therefore the dividends per share for preferred is $3 per share, $4.5 per share, $1 per share and the common stock $0, $1.95, $1.75.
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Graph the function (fx) = 2√ + 3 on the coordinate plane
The graph of the function y = 2√x + 6 is plotted and attached.
What is the general equation of a Straight line? What are the points of intersection of the graph of y = x and y = √x? Which curve is more diverged?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The points of intersection of the graph of y = x and y = √x are (0, 0) and (1, 1). The curve y = √x diverges more.
We have the following equation -
y = 2√x + 6
Given is the following equation as -
y = 2√x + 6
Refer to the graph of the function attached.
Therefore, the graph of the function y = 2√x + 6 is plotted and attached.
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The exponential form of log5 25 = 2 when written exponentially is 25 = 25.
False
True
Answer: never mind
Step-by-step explanation:
Find the HCF of 2, 4 and 4/5.
(A) 1/20 (B) 1/40 (C) 20 (D) 15
Answer:
1/20
Step-by-step explanation:
You can find the HCF (Highest Common Factor), also known as GCF, by dividing the numbers by the list of answers. And, if they all come out as whole numbers, then the answer you chose will be the answer. But, if there is another answer that also comes out as whole numbers for all of them, we choose the biggest one (HCF):
2 ÷ 1/20 = 40
4 ÷ 1/20 = 80
4/5 ÷ 1/20 = 16
So, 1/20 is definitely one of the answers, but we should check the other ones too:
2 ÷ 1/40 = 80
4 ÷ 1/40 = 160
4/5 ÷ 1/40 = 32
So, even though we also got whole numbers for this one, it isn't the answer because 1/20 is bigger than 1/40 so far. Let's try the last two answers:
2 ÷ 20 = 0.1
So, we already got our answer. We don't need to check the rest of the numbers, because the first one is already not a whole number. Let's try the final answer:
2 ÷ 15 = 0.13333333
This is not the right one either. So, our answer is 1/20 because it is the biggest one that came out as all whole numbers.
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Find the product.
(wz + 8)³ =
We are given:
Find the product.
[tex](wz+8)^3[/tex]
Solution:
[tex]w^3z^3+24w^2z^2+192wz+512[/tex]
Hope this helps!
Answer:
Step-by-step explanation:
Graph the equation. y = -(x-4)^2+4
Please help me I need help
Answer:
El intercepto en y es 6,1
Step-by-step explanation:
Espero que esto ayude