If g(x)=4x^(2)-16 were shifted 7 units to the right and 3 down, what would the new equation be?
Answers
The equation of the transformed function is h(x) = 4(x - 7)² - 19 option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
g(x) = 4x² - 16
The above function shifted 7 units to the right and 3 down.
Applying transformation:
x → (x - 7)
G(x) = 4(x - 7)² - 16
G(x) → G(x) - 3
h(x) = 4(x - 7)² - 16 - 3
h(x) = 4(x - 7)² - 19
Thus, the equation of the transformed function is h(x) = 4(x - 7)² - 19 option (C) is correct.
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Related Questions
Please Help Me! What is cos B?
Answers
Answer:
cos B = 0.4706
Step-by-step explanation:
The cosine of an angle in a right-angled triangle is the ratio of its adjacent side and the hypotenuse, so:
[tex]cos B = \frac{adjacent}{hypotenuse}\\\\cos B = \frac{8}{17} \\\\cos B = 0.4706[/tex]
Option B
Consider the function f(x) = 10x and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)?
Answers
The function g(x) gets shifted toward right by 6 units. Then the correct option is C.
The complete question is attached below.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
The function f(x) is given below.
f(x) = 10ˣ
And the function g(x) is given as
g(x) = f(x – 6)
Then the function can be written as
[tex]\rm g(x) = 10^{x - 6}[/tex]
The function g(x) gets shifted toward right by 6 units.
Then the correct option is C.
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Ted is trying to change 0.43 to a fraction. Evaluate teds method so far
Answers
Step-by-step explanation:
[tex] = 0,43[/tex]
[tex] = \frac{0,43}{1} [/tex]
[tex] = \frac{0,43}{1} \times \frac{100}{100} [/tex]
[tex] = \frac{43}{100} [/tex]
both of the drop menus have the same options
Answers
Answer:
The slope of line p is 3 and the slope of line q is -3
On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2). Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line? a rise of 6 and a run of 8 a rise of 8 and a run of 6 a rise of 6 and a run of 5 a rise of 5 and a run of 6
Answers
A rise of 8 and a run of 6. Then the correct option is B.
What is a coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).
The distance between AB will be
AB² = (-5 + 5)² + (-2 + 4)²
AB² = 4²
AB = 4
The distance between BC will be
BC² = (-2 + 5)² + (-2 + 2)²
BC² = 3²
BC = 3
Then the rise and run will be
rise / run = 4 / 3
Then this can be written as
rise / run = 8 / 6
Then the correct option is B.
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Do this for me pls its mdths
Answers
Answer:
A = -1
B = -3
C = -7
Step-by-step explanation:
See attached image.
What is the mean of the data set?
85, 97, 84, 88, 95, 100,81
Answers
Answer:
90
Step-by-step explanation:
Add up all the numbers in the data set and divide that number by the amount of numbers in the data set
85 + 97 + 84 + 88 + 95 + 100 + 81 = 630
630/7 = 90
Expand . ( 3x –2 ) 2 please help me with this.
Answers
Answer:
6x-4
Step-by-step explanation:
3x•2= 6x
-2•2=-4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(3x - 2)}^2[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number. If so the following steps would be followed.
Expand
[tex]\textsf{(3x - 2)}^2[/tex][tex]\textsf{(3x - 2)(3x - 2)}[/tex][tex]\textsf{(3x * 3x) + (3x * (-2)) + (3x * (-2)) + (-2 * (-2))}[/tex]Simplify
[tex]\textsf{9x}^2\textsf{ - 6x - 6x + 4}[/tex][tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.
Pls someone help me on this question
Answers
Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]
Step-by-step explanation:
All radii of a circle are congruent, so by the base angles theorem
z = y = (180-50)/2 = 65.Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.
Find the range for the given domain: {-2, 0, and 1}and the function is y = 3x + 1.
Answers
Answer:
It's the first option: -5, 1 and 4
how to apply Trigonometry in cricket?
Answers
Answer:
as we know that in cricket there is use of tan while doing bating
Points
Find f(−2)
given f(x)=−x3−3x2+8
Answers
Answer:
12 :D
Step-by-step explanation:
First we substitute all x's for -2 :)
f(-2)=−-2^3−3(-2)^2+8
Now we solve :)
f(-2)=−-2^3−3(-2)^2+8
f(-2)=− -8 −3(-2)^2 + 8
f(-2) = -8 - 3(-4) + 8
f(-2) = - 8 + 12 + 8
f(-2) = 4 + 8
f(-2) = 12 :)
f will equal 12 :)
Have an amazing day!!
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can you write 3/5 as a recurring decimal?
can i also have an explanation please :)
Answers
Answer:
0.6
Step-by-step explanation:
You can literally put 3/5 into a calculator and you would get the answer 0.6, so I don't know what else to say. Whoever asked you this question, give them the above answer ask them what they were on, because the person was probably way high on LSD.
from a practice assignment:
solve the following differential equation given initial conditions
Answers
If [tex]y' = e^y \sin(x)[/tex] and [tex]y(-\pi)=0[/tex], separate variables in the differential equation to get
[tex]e^{-y} \, dy = \sin(x) \, dx[/tex]
Integrate both sides:
[tex]\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C[/tex]
Use the initial condition to solve for [tex]C[/tex] :
[tex]-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2[/tex]
Then the particular solution to the initial value problem is
[tex]-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2[/tex]
(A)
a researcher in north america discovers a fossil that contains 40% of its original amount of C-14
Answers
Using an exponential function, it is found that the substance is 7,535 years old.
What is the exponential function for the amount of a substance?
The function is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which:
A(0) is the initial amount.k is the rate of exponential decay.Carbon-14 has a half life of 5700 years, that is, A(5700) = 0.5A(0), hence we use this to find k.
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.5A(0) = A(0)e^{-5700k}[/tex]
[tex]e^{-5700k} = 0.5[/tex]
[tex]\ln{e^{-5700k}} = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{5700}[/tex]
k = 0.00012160476
Hence:
[tex]A(t) = A(0)e^{-0.00012160476t}[/tex]
It was 40% of the amount when A(t) = 0.4A(0), hence we solve for t.
[tex]A(t) = A(0)e^{-0.00012160476t}[/tex]
[tex]0.4A(0) = A(0)e^{-0.00012160476t}[/tex]
[tex]\ln{e^{-0.00012160476t}} = \ln{0.4}[/tex]
[tex]t = -\frac{\ln{0.4}}{0.00012160476}[/tex]
t = 7535.
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Investor Lucas just bought a large amount of stock in Company Y. What may have motivated his behavior? (5 points)
Lower shares prices
O Low real returns
O Higher shares costs
O High total ear
Answers
What must have motivated the behavior of the Investor to commit to such a large stock is; Option C: High Total Earnings
How to know the value of investing in stocks?A) Low real returns; This cannot be his motivation to buy large shares because real return is what is earned on an investment after accounting for taxes and inflation. Thus, the lower, the less encouraging to investors.
B) Higher shares costs; This only means that the share cost is currently high which indicates strength of the company but it does not guarantee that it will scale up at a very fast rate again.
C) High total earnings; Thus would be an encouragement to the investor because the higher the total earning potential of an investment, the more the profitability and the more attractive to others.
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What is the discriminant of the quadratic equation 2x² - x - 3=0?
A. -25
B. 25
C. -23
D. 23
Answers
The given quadratic equation is
[tex]2 {x}^{2} - x - 3 = 0[/tex]
comparing with
[tex] {ax}^{2} + bx + c = 0[/tex]
We get ,
[tex]a = 2 \\ b = - 1 \\ c = - 3[/tex]
formula :
[tex]D = {b}^{2} - 4ac \\ \\ D = {( - 1)}^{2} - 4 \times 2 \times ( - 3) \\ \\ D = 1 - ( - 24) \\ \\D = 1 + 24 \\ \\D = 25.[/tex]
Discriminant of given quadratic equation is 25 .
option (B) 25 ✔
FW = 6 units, X = 3 units, and Y = 5 units, what is the surface area of the figure?
Answers
The surface area of the figure is approximately: 178 units².
How to Find the Surface Area of a Figure?The surface area of any figure is the area of all its faces.
Find the area of each face as shown below:
Area of base = w² = 6² = 36 units²
Area of the 4 rectangular faces = 4(6)(3) = 72 units²
Area of the 4 triangular faces = 4[1/2bh]
b = w = 6 units
h = √(y² + (w/2)²) = √(5² + (6/2)²) = 5.8 units
Area of the 4 triangular faces = 4[1/2(6)(5.8)] = 69.6 units²
Surface area = 36 + 72 + 69.6 ≈ 178 units²
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When the expression 3(x²+6-3x) - (2x²-8) + 3(x² + 4x) is simplified, the coefficient
of x is
A. 7
B. 4
C. 3
D. 2
Answers
The correct answer is option C which is 3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression will be solved as follows:-
E = 3( x² +6 -3x)- ( 2x² - 8 ) +3(x² + 4x )
E = 3x²+18-9x-2x²+8+3x²+12x
E= 4x² +3x+8
We can see the coefficient of x is 3.
Therefore the correct answer is option C which is 3.
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How much weight does the women in the video lose in a year? 80 pounds 90 pounds 50 pounds 20 pounds
Answers
Medical practitioners recommend losing around 365 pounds or 730 pounds per year.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Medical practitioners recommend losing around 1–2 pounds (0.5–0.9 kg) per week.
Hence for a year:
Amount of weight loss = (1 * 365) or (2 * 365)
Medical practitioners recommend losing around 365 pounds or 730 pounds per year.
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What is the speed of a wave with a wavelength of 10 meters
Answers
Any wave's speed is equal to its frequency times wavelength. Now, the question doesn't specifically state what kind of wave it is. Thus, there might be two distinct scenarios: If the wave is elastic (sound is an example), you can't calculate its speed unless you also know its frequency and wavelength. However, the speed in vacuum is constant (3*108 m/s) if the wave is electromagnetic (for instance, light). In order to maintain constant velocity, frequency must shift in response to variations in wavelength. The frequency of light rays is constant in all other optical media (apart from vacuum and air), although their velocity and wavelength change correspondingly. However, that is not the case here since if it must be an EM wave with a wavelength of 10 m, then it must be a radio wave that travels uniformly through all medium at a speed of 3*108 m/s.
A pair of dice is rolled. What is the probability that the sum is 9 or that the first number is a 2?
Answers
Answer:
9/2 or 6/2
Step-by-step explanation:
The sum of nine should be amended by adding 6 + 2 +1 = 9
so when adding these numbers you will get the sum of 9
Given: a and b are parallel and c is a transversal.
Prove: ∠2 ≅ ∠7
Parallel lines b and a are cut by transversal c. On line b where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 5, 6, 2. On line a where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 3, 7, 8, 4.
Use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent.
We know that lines a and b are parallel and that line c is a transversal because that is given. We can tell that angles 2 and 5 are congruent because
angles are congruent. Angles 5 and 7 are congruent because angles by parallel lines cut by a transversal are congruent. Therefore, angles 2 and 7 are congruent based on the
.
Answers
The missing words to complete the proof are respectively; Vertical Angles; Corresponding angles; Transitive Property
How to prove congruent angles?The image of the transversal line is attached.
1) We know that lines a and b are parallel and that line c is a transversal because that is given.
2) We can tell that angles 2 and 5 are congruent because vertical angles are congruent.
3) Angles 5 and 7 are congruent because corresponding angles by parallel lines cut by a transversal are congruent.
4) Therefore, angles 2 and 7 are congruent based on the transitive property.
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Answer: vertical, corresponding, and transitive property
Step-by-step explanation: I got the correct answer on Edge 2022. The answer is correct trust me! Proof is shown down below.
Find y in terms with x
Help me pleaseee thank uu:)
Answers
Answer:
y = 90 -5/2 x
Step-by-step explanation:
The angle on the left equals x+3x+x = 5x
The angle on the right equals 2y
The two angles are same side interior angles which are supplementary because the lines are parallel
5x+2y = 180
Solving for y
2y = 180-5x
Divide by 2
2y/2 = 180/2 -5x/2
y = 90 -5/2 x
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\tt y = 90 \degree - \cfrac{5x}{2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The two lines are parallel, henceforth we can apply Angle pair rules.
[tex]\qquad \tt \rightarrow \:(x + 3x + x) + 2y = 180[/tex]
[ Co - interior angles ]
[tex]\qquad \tt \rightarrow \:5x + 2y = 180[/tex]
[tex]\qquad \tt \rightarrow \:2y = 180 - 5x[/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{180 - 5x}{2} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{180 }{2} - \cfrac{5x}{2} [/tex]
[tex]\qquad \tt \rightarrow \:y = 90 \degree - \cfrac{5x}{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
From a hot-air balloon, Brody measures a 39^{\circ}
∘
angle of depression to a landmark that’s 532 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
335.16 ft
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $280 to spend on parking and admission. Parking is $19.50, and tickets cost $33.75 per person, including tax. Which inequality can be used to determine semanticsp, the maximum number of people who can go to the amusement park?
Answers
The number of people who can go to the amusement park is 8.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given: the group of friends had $280.
For parking= $19.50
Remaining will be,
=$(280-19.50)
= $ 260.5
Cost of ticket per person = $33.75
Thus, number of tickets they can buy
=260.5 / 33.75
=7.718 = 8 peoples
Hence, number of people who can go to the amusement park is 8.
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Alison has three times as many dimes as quarters in her purse. She has $9.35 altogether. How many coins of each type does she have?
Answers
========================================================
Work Shown:
x = number of quarters
3x = number of dimes
0.25x = value of just the quarters, in dollars
0.10(3x) = 0.30x = value of just the dimes, in dollars
0.25x+0.30x = 0.55x = total value in dollars
0.55x = 9.35
x = (9.35)/(0.55)
x = 17
Alison has 17 quarters and 3x = 3*17 = 51 dimes
17 quarters = 17*0.25 = $4.25
51 dimes = 51*0.10 = $5.10
17 quarters + 51 dimes = $4.25 + $5.10 = $9.35
The answers are confirmed.
The graphs below are both absolute value functions. The equation of the red
graph is f(x) = xl. Which of these is the equation of the blue graph, g(x)?
a. g(x)=|x-2|
b.g(x)=|x+2|
c. g(x)=1/2|x|
d. g(x)=2|x|
Answers
Answer:
c
Step-by-step explanation:
Graph the linear equation. Find three points that solve the equation, then plot on the graph.
-3x + 2y = 2
Answers
Step-by-step explanation:
I have done it go and check it once
Quayleen wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?
Answers
[tex]\bullet\:{\boxed{\tt{\red{{Given :}}}}}[/tex]
• Length of the wooden box [tex](l)[/tex] = 80cm.
• Breadth of the wooden box [tex](b)[/tex] = 40cm.
• Height of the wooden box [tex](h)[/tex] = 20cm.
• Side of the square sheet paper = 40cm.
[tex]\bullet\:{\boxed{\tt{\red{{To : Find :}}}}}[/tex]
The number of sheets required.
[tex] \bullet\:{\boxed{\tt{\red{{Formula \: \: used :}}}}}[/tex]
[tex] \star{\underline{\boxed{{\sf{{{TSA}} = \underline{\underline{{\purple\sf 2(lb+bh+hl)}}}}}}}} \star[/tex]
[tex]\star{\underline{\boxed{{\sf{{{Area \: of \: square}} = \underline{\underline{{\purple{\sf side \times side }}}}}}}}}\star[/tex]
[tex]\star{\underline{\boxed{{\sf{{{Number \: of \: sheets \: required} = {{{\purple{\sf \dfrac{TSA}{area \: of \: one \: sheet}}}}}}}}}}} \star[/tex]
[tex] \bullet\:{\boxed{\tt{\red{{Concept :}}}}}[/tex]
As Quayleen wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. So for knowing the number of sheets required, we need two things one the TSA and Area of one sheet. Once, we will get the values we will divide them to get the answer. Let's Start !!
[tex] \bullet\:{\boxed{\tt{\red{{Solution :}}}}}[/tex]
As we know that ::
Total surface area of cuboid [tex]\large[ \sf 2(lb+bh + hl)][/tex]
Here,
✧ Length [tex](l)[/tex] = 80cm
✧ Breadth [tex](b)[/tex] = 40cm
✧ Height [tex](h)[/tex] = 20cm
Now, by putting the values we get :
[tex] \longrightarrow 2 \bigg[ (80 \times 40) + (40 \times 20) + (20 \times 80) \bigg]\sf {cm}^{2}[/tex]
[tex]\longrightarrow 2 \bigg[ (3200) + (800) + (1600) \bigg] \sf {cm}^{2} [/tex]
[tex] \longrightarrow 2 \bigg[ 5600 \bigg] \sf {cm}^{2} [/tex]
[tex] \longrightarrow 11200 \: \sf {cm}^{2}[/tex]
Hence, the total surface area of the wooden box is 11200 cm²
Now,
The area of each sheet of paper will be :
[tex] \sf \longrightarrow side \times side[/tex]
[tex]\sf \longrightarrow (40 \times 40) \: {cm}^{2} [/tex]
[tex]\longrightarrow \sf (1600) \: {cm}^{2} [/tex]
Hence, the area of each sheet of paper is 1600 cm²
Now,
For finding the number of sheets required
[tex] \longrightarrow \tt \dfrac{total \: surface \: area \: of \: box}{ area \: of \: one \: sheet} [/tex]
[tex]\longrightarrow \sf\dfrac{ \cancel{11200}_{7}}{\cancel{1600}_{1}}[/tex]
[tex] \longrightarrow \purple{ \sf 7}[/tex]
Therefore, Quayleen requires 7 sheets.
[tex]\rule{280pt}{2pt}[/tex]