Consider the function f(x) = (x+ 1)2 - 1. Which of the following functions stretches
fo) vertically by a factor of 4?
O A) f0 - (/ax+ 1)2 +3
O B) f9 = 1/ax+ 1)2 -4
Oo fo-4(x+ 1)2 - 1
OD) fo = 4(4x+ 1)2- 1
Answers
Answer:
C
Step-by-step explanation:
A coefficient of 4 would have to be added in front of (x+1)^2 in order to vertically stretch the function by a factor of 4.
The answer that demonstrates this is choice C: [tex]f(x) = 4(x+1)^2-1[/tex]
The functions stretches vertically by a factor of 4 will be f(x) = 4(x+ 1)² - 1. Then the correct option is C.
What is the equation of the parabola?Let the point (h, k) is the vertex of the parabola and a is the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The quadratic function is given below.
f(x) = a(x+ 1)² - 1
If the value of the leading coefficient lies between 0 to 1. Then the parabola is stretched horizontally.
And if the value of the leading coefficient is greater than one. Then the parabola is stretched vertically.
The functions stretches vertically by a factor of 4. Then the value of the leading coefficient is 4. Then the equation will be
f(x) = 4(x+ 1)² - 1
Then the correct option is C.
More about the equation of parabola link is given below.
https://brainly.com/question/20333425
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Related Questions
Please help! I’ll give brainliest to whoever gets it right!
Answers
Answer:
3.62
Step-by-step explanation:
I am big brain and very smort
Answer:
362/ 100 or 3 62/100
Step-by-step explanation:
Please hurry no clown answers and please do the whole thing
You are a member of your local movie theater’s club. Every time you see a movie at the theater, you earn 2 advantage points. When you earn 100 points, you get a free movie pass. Currently, you have 40 advantage points.
Write an equation to model the number of movies m you have to watch before you earn a free movie pass.
Solve the equation. Show your work.
Answers
100=40+2m
100-40=60
2m=60
60 divided by 2=30
30 movies
Answer:
2m+40=100, 30 movies
Step-by-step explanation:
1 movie = 2 points
1 pass= 100 points
curently have 40 points so
100points = 40points +2points *m
solve for m:
2m+40 =100 subtract 40 from both sides
2m = 100-40
2m=60 divide both sides by 2
m=60/2
m=30
somebody please help me thansk
Answers
Answer:
y=-2x-1
Step-by-step explanation:
You have to check the distance the points are apart from eachother
if the transformation was a rotation, tiffany..... be certain the trapezoids are congruent
A. can
B. cannot
Answers
Two figures are congruent when their corresponding angles are equal and they have the same shape and size.
A figure can go thorugh 3 types of transformations:
Rotation: the figure is turned around a fixed point;
Reflection: is created by fliping over the figure over a line;
Translation: move the figure to another location, without changing its size;
As long the figure doesn't change its size or shape, it doesn't matter if it's rotated, reflected or translated, they will be congruent.
When the trapezoid was rotated creating another one, the two shapes didn't change its size or shape, so Tiffany can be certain they are congruent.
A jewelry store is having a going out of busniess sale. All merchandise is marked 40% off the reguler price. The regualr price of a watch is $59.95. Find the amount of the discount and the sale price.
Answers
Answer:
Amount of the Discount: $23.98
Sale Price: $35.97
Step-by-step explanation:
In order to calculate the discount we first need to turn this percentage into a decimal by dividing it by 100. Once we have it in decimal form we subtract that value from 1. Finally, we multiply this new decimal by the original price in order to obtain the sale price like so...
40 / 100 = 0.40
1 - 0.40 = 0.60
0.60 * 59.95 = 35.97
Now we have the sale price which is $35.97 now we can subtract this value from the original price to calculate the amount of the discount.
59.95 - 35.97 = 23.98
Sally put dots on a place value chart to show a number. She had a total of 10 dots. She put 3 in the tens place, 5 in the hundreds place, and 2 in the thousands place. Which of these is Sally’s number?
A.
253
B.
2503
C.
2530
D.
25,300
Answers
A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week. 1. Create a system of equations or inequalities that models the situation. Define the variables you use.
Answers
Answer:
15x=300, x=20
20x=300, x=15
Step-by-step explanation:
Answer:
:)
Step-by-step explanation:
15x=300
x will equal 20
20x=300
x will equal 15
Match each inequality to the correct graph.
Answers
Answer: Hope this helps
A vector in standard position has its terminal point at (7, –4). What is the magnitude of the vector?
Answers
Answer:
Square root of 65
Step-by-step explanation:
Edge
The magnitude of the vector will be 8.0622 units.
What exactly is a vector?A vector is a quantity with a magnitude, and direction that follows the law of vector addition.
Given data;
u = (7, –4)
The magnitude of the vector is, R found as;
[tex]\rm R = \sqrt{7^2+(-4^2)} \\\\ R = \sqrt {65} \\\\ R = 8.0622 \ units[/tex]
Hence the magnitude of the vector will be 8.0622 units.
To learn more about vectors, refer;
https://brainly.com/question/13322477
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Jorge's family arrived home at 8:00 at night after traveling in the car for 5 hours and 15 minutes. What time did Jorge's family leave?
Answers
Answer:
2:45 P.M
Step-by-step explanation:
Answer:
3:45
Step-by-step explanation:
8:00-5 hours and 15 min=3:45
Which values could be the values of x and y?
Answers
Answer:
1 3/4, 9 1/4
Step-by-step explanation:
continue the pattern
How many solutions does 5 - 2x = 4 - 2x + 4 + x have?
A. Infinitely many solutions
B. Two solutions
C. One solution
D. No solutions
Answers
Answer:
One solution, being x = -3
Step-by-step explanation:
2(4 + 7) − 8 ÷ 2 whats the answer
Answers
Answer:
your answer is 18 look below for an explanation!
Step-by-step explanation:
please just trust me i know for a fact its right plz leave a thx and may i please have brainliest?
because 2(4+7)= 8+14= 22. 8/2= 4. 22-4=18.
find the sum of 10x^2-6 and x +6
Answers
Answer:
10x2+x
Step-by-step explanation:
(x + 3)(x^2 - 5x + 7)
write in standard form once you find answer.
Answers
x^3-2x^2-8x+21
Find the value for x for which r ll s. Then find m<1 and m<2. m<1 = (60-2x)to the zero power m<2 = (71 - 3x)to the zero power. The value for x for which r || s is ?
Answers
2x + 22 = 4(x + 3)
Please help me
Answers
Answer: x=5
Step-by-step explanation:
2x+22=4(x+3)
First distribute
2x+22=4x+12
Now intractable 2x from both sides
22=2x+12
Now subtract 12 from both sides
10=2x
Now divide by 2 to get x alone
5=x
So
x=5
Answer:
The answer is x = 5, see comments for explanation.
The least common denominator of[tex]\frac{1}{6} and \frac{5}{12}[/tex] is 12.
TrueFalse
Answers
what is 3 tenths plus 8 tenths?
Answers
Answer:
1.1
Step-by-step explanation:
What is 1+2+3+4+5+6+7+8+9+10=?
have a great day!! :)
Answers
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
Answer:
55
Step-by-step explanation:
9 + 1 = 10
8 + 2 = 10
7 + 3 = 10
6 + 4 = 10
5 + 10 = 15
10 + 10 + 10 + 10 + 15 = 55
It cost $20 plus $1.50 per hour to rent a golf cart. Write an equation showing the relationship between the cost of renting a cart (y) and the number of hours it was rented (x).
Answers
Answer:
y=20+1.5x
Step-by-step explanation:
The cost of renting a golf cart is equal to $20 plus $1.50 per hour.
let y=the cost of renting a golf cart
let x=the # of hours
y=20+1.5x
We are standing on the top of a 1680 ft tall building and throw a small object upwards. At every second, we measure the distance of the object from the ground. Exactly seconds after we threw the object, it’s height, (measured in feet) is
ℎ= -16^2 + 256 + 1680
a.) Find ℎ when = 3.
b.) How much does the object travel during the two seconds between 5 seconds and 7 seconds?
c.) How long does it take for the object to reach a height of 2640 ft?
d.) How long does it take for the object to hit the ground?
Answers
Answer:
a) The height of the small object 3 seconds after being launched is 2304 feet.
b) The small object ascends 128 feet between 5 seconds and 7 seconds.
c) The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.
d) The object will take 21 seconds to hit the ground.
Step-by-step explanation:
The correct formula for the height of the small object is:
[tex]h(t) = -16\cdot t^{2}+256\cdot t+1680[/tex] (1)
Where:
[tex]h[/tex] - Height above the ground, measured in feet.
[tex]t[/tex] - Time, measured in seconds.
a) The height of the small object at given time is found by evaluating the function:
[tex]h(3\,s)= -16\cdot (3\,s)^{2}+256\cdot (3\,s)+1680[/tex]
[tex]h(3\,s) = 2304\,ft[/tex]
The height of the small object 3 seconds after being launched is 2304 feet.
b) First, we evaluate the function at [tex]t = 5\,s[/tex] and [tex]t = 7\,s[/tex]:
[tex]h(5\,s)= -16\cdot (5\,s)^{2}+256\cdot (5\,s)+1680[/tex]
[tex]h(5\,s) = 2560\,s[/tex]
[tex]h(7\,s)= -16\cdot (7\,s)^{2}+256\cdot (7\,s)+1680[/tex]
[tex]h(7\,s) = 2688\,s[/tex]
We notice that the small object ascends in the given interval.
[tex]\Delta h = h(7\,s)-h(5\,s)[/tex]
[tex]\Delta h = 128\,ft[/tex]
The small object ascends 128 feet between 5 seconds and 7 seconds.
c) If we know that [tex]h = 2640\,ft[/tex], then (1) is reduced into this second-order polynomial:
[tex]-16\cdot t^{2}+256\cdot t-960=0[/tex] (2)
All roots of the resulting equation come from the Quadratic Formula:
[tex]t_{1} = 10\,s[/tex] and [tex]t_{2}= 6\,s[/tex]
The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.
d) If we know that [tex]h = 0\,ft[/tex], then (1) is reduced into this second-order polynomial:
[tex]-16\cdot t^{2}+256\cdot t +1680 = 0[/tex] (3)
All roots of the resulting equation come from the Quadratic Formula:
[tex]t_{1} = 21\,s[/tex] and [tex]t_{2} = -5\,s[/tex]
Just the first root offers a solution that is physically reasonable.
The object will take 21 seconds to hit the ground.
Question in picture solve
Answers
Answer:
Bike 1
Step-by-step explanation:
If you look at the graph, you'll see that Bike 1 went 9 feet but Bike 2 is at about 7.5 feet in 6 seconds.
Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse functions
Answers
Answer:
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
Step-by-step explanation:
Given
[tex]a(d) = 5d - 3[/tex]
Solving (a): Write as inverse function
[tex]a(d) = 5d - 3[/tex]
Represent a(d) as y
[tex]y = 5d - 3[/tex]
Swap positions of d and y
[tex]d = 5y - 3[/tex]
Make y the subject
[tex]5y = d + 3[/tex]
[tex]y = \frac{d}{5} + \frac{3}{5}[/tex]
Replace y with a'(d)
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
Prove that a(d) and a'(d) are inverse functions
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex] and [tex]a(d) = 5d - 3[/tex]
To do this, we prove that:
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
Solving for [tex]a(a'(d))[/tex]
[tex]a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})[/tex]
Substitute [tex]\frac{d}{5} + \frac{3}{5}[/tex] for d in [tex]a(d) = 5d - 3[/tex]
[tex]a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3[/tex]
[tex]a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3[/tex]
[tex]a(a'(d)) = d + 3 - 3[/tex]
[tex]a(a'(d)) = d[/tex]
Solving for: [tex]a'(a(d))[/tex]
[tex]a'(a(d)) = a'(5d - 3)[/tex]
Substitute 5d - 3 for d in [tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
[tex]a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}[/tex]
Add fractions
[tex]a'(a(d)) = \frac{5d - 3+3}{5}[/tex]
[tex]a'(a(d)) = \frac{5d}{5}[/tex]
[tex]a'(a(d)) = d[/tex]
Hence:
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
help me real quickhahahahaha
Answers
Answer:
19
Step-by-step explanation:
2d= 2 x 8= 16
16+3= 19
Answer:
Step-by-step explanation:
2d + 3 (d=8)
(2*8) + 3 =
16 + 3 =
19
Janka si vložila 3200 eur na termínovaný účet s 1,2 úrokovou mierov koľko bude mať po 1 roku
Answers
Answer:
the present value is 3,162 euros
Step-by-step explanation:
The computation of the present value is shown below:
As we know that
Future value = Present value × (1 + rate of interest)^number of years
3,200 euros = Present value × (1 + 0.012)^1
3,200 euros = Present value × 1.012^1
Present value is
= 3,200 euros ÷ 1.012
= 3,162 euros
Hence, the present value is 3,162 euros
2. Solve (x – 4)(x + 7). (2 points) O x = 4, X= 7 X = =4, x = -7 x = 4, X = -7 X = -4, X = 7
Answers
Answer:
X = 4, x = -7
Step-by-step explanation:
You can set each equation in the parenthesis Equal to 0.
x - 4 = 0 and x + 7 = 0
start with x - 4 =0
add 4 to both sides
x = 4.
then do x +7 =0. subtract 7 from both sides.
x = -7
so x =4, and x = -7
There are 85 girls and 70 boys in the sixth grade. Of these students, 14
girls and 8 boys take piano lessons. What percentage of the sixth
graders at this school take piano lessons?
Answers
Answer:
14.2%
Step-by-step explanation:
85+70= 155
155=100%
22=?
22×100%÷155
= 14.1935
hence answer is 14.2%
WILL CHOOSE BRAINLIEST!!!!!!!!!!!!!
30 points!!!!!!!!!!
12x^2 y for x=–0.3,y= 1/6
Answers
Answer:
0.18
Step-by-step explanation:
A store had a sale where you could get 5 bags of cashews for $4. If you
wanted to buy 50 bags, how much would it cost?
Answers
Answer:
$40
Step-by-step explanation:
50/5=10, 10•4=40
50 bags divided by 5 is 10
10 x $4 is $40