Answers
Answer:
(i) The axis of symmetry is [tex]x = -4[/tex].
(ii) The axis of symmetry is [tex]x = 4[/tex].
(iii) The axis of symmetry is [tex]x = 1[/tex].
Step-by-step explanation:
We proceed to explain how we determine the expression for the axis of symmetry for each case:
(i) [tex]f(x) = 3\cdot (x+4)^{2}+1[/tex]
The expression depicts a vertical parabola, meaning that axis of symmetry is vertical, that is, a function of the form [tex]x = a,\,\forall\,a\in \mathbb{R}[/tex]. This line passes through the vertex of the parabola. The component [tex]x+4[/tex] contains the information of the horizontal component of the vertex, where the axis passes through. Therefore, the axis of symmetry is [tex]x = -4[/tex].
(ii) [tex]f(x) = 2\cdot x^{2} -16\cdot x +15[/tex]
At first we complete the square and factor the perfect square trinomial:
[tex]f(x) = 2\cdot \left(x^{2}-8\cdot x +\frac{15}{2} \right)[/tex]
[tex]f(x) = 2\cdot \left[(x^{2}-8\cdot x +16) +\frac{15}{2}-16 \right][/tex]
[tex]f(x) = 2\cdot (x-4)^{2}-17[/tex]
By applying the approach used in (i), we find that the axis of symmetry is [tex]x = 4[/tex].
(iii) First, we locate the vertex of the parabola, which is (1,-3). The first component of the ordered pair contains all the needed information to determine the equation of the axis of symmetry, which is [tex]x = 1[/tex].
Related Questions
pweeez help me :3
How long does it take for the ball to reach its maximum height (or its vertex)?
A. 4 seconds
B. 2.5 seconds
C. 0.6 seconds
D. 2 seconds
Answers
Answer:
The vertex, (1.5, 40), tells us that it takes 1.5 seconds for the ball to reach its maximum height of 40 feet.
Step-by-step explanation:
...i think..
Akoshia has more money than Komley. If Akoshia gave Komley 20, they would have the same amount. While if Komley gave Akoshia ¢22, Akoshia would then have twice as much as Komley. How much does each one actually have?
Answers
Answer:
Aksohia has $146 and Komley has $106
Step-by-step explanation:
The computation of the amount does each one have is shown below:
Let us assume Akoshia money be x
And, komley money be y
x>y
x - 20 = y + 20
x - y = 40
x = 40 + y.........(i)
2(y - 22) = x + 22
2y - 44 = x + 22
Now put the value of x in the above equation
2y - 44 = 40 + y + 22
2y - 44 = 62 + y
y = 62 + 44
= 106
And, x = 40 + 106
= 146
What is the area of a circle with a diameter of 4
Answers
Answer:
12.57
Step-by-step explanation:
Answer:
I think its 12.56637.
Now use the length of the vertical line segment and the horizontal line segment to find the distance between G and H. Substitute these values in the equation for the Pythagorean Theorem.
Answers
Answer:
please first tell me the numbers written
Triangles 2.0........
Answers
N=2m so 3m=1.5n then we can plug in that to get 1.5n+5=n+8 to get the value of n then we do our magic and get n=6 n+9 is 15 and it’s the same length as TU
Answer:
triangle STU and WEK are CONGRUENT
ST=WK SIDE OF A CONGRUENT TRAINGLE ARE EQUAL
2M=N.....1
SU=WE
3M+5=N+8
3M+5=2M+8
3M-2M=8-5
M=3
NOW
N=2M=2×3=6CM
TU=WK=N=6CM.
Can someone help and explain what the student did wrong and what the correct answer is
Answers
Answer: (x-6)(x+4)
Step-by-step explanation:
So firstly everything in the table is correct however this isn't the way to factor this equation. The way I use is if the what multiplies to get the third number(-24) and what adds to get the second number (-2) so the numbers 6 and 4 work but now we have to look at our signs (positive/negative). So lets look at the students answer (x+6)(x-4) although 6*-4= -24 if you add 6 and -4 you get 2 which doesn't equal -2. So the factor answer should be
(x-6)(x+4)
because -6 times 4= -24(third number) and -6 plus 4= -2(second number)
Tom had 216 marbles. First, he divided them into 3 equal groups. Then he put two groups into a 2 separate bags. He took the remaining group of marbles and shared it equally with his 3 friends. How many marbles did each of his friends get ?
Answers
Answer: each of his friends got 24 marbles
Step-by-step explanation:
216 / 3 = 72
72 / 3 = 24
30. Write and solve an equation for the
following situation:
Marshall earns a salary of $36,000, and each
year he receives a $4,000 raise. Jim earns a
salary of $51,000, and each year he receives
o $1,500 raise. How many years will it take
before Marshall and Jim earn the same
salary?
Equation:
Volue of x:
Answers
Answer:
equation: 36000 + 4000x = 51000 + 1500x
value of x: 6
Step-by-step explanation:
Marshall:
36000 + 4000x
Jim:
51000 + 1500x
36000 + 4000x = 51000 + 1500x
360 + 40x = 510 + 15x
25x = 150
x = 6
Answer:
equation: 36000 + 4000x = 51000 + 1500x
value of x: 6
please help i don't know what I'm doing
Answers
Answer:
11 is the answer
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
to find one of the addend
subtract another one of the addend by the sum
eg : 9 + __= 20
20 - 9 = 11
now we can check
9 + 11 = 20
hope this helps
thanks bye
Please help me quickly
Answers
Step-by-step explanation:
5: -7=x,-1=y so (-7,-1)
6. 7=x,8=y so (7,8)
Hope that helps :)
In three days, the chickens on Nigel's farm can lay 33 eggs. How many eggs will they lay in 11 days?
Answers
Answer:
Eggs laid by chicken in 11 days = 121 eggs
Step-by-step explanation:
Eggs laid by the chickens in 3 days = 33
Average rate at which the chickens are laying the eggs = [tex]\frac{33}{3}[/tex]
= 11 eggs per day
At the same rate number of eggs laid by the chickens in 11 days = Rate × Number of days
= 11 × 11
= 121 eggs
Therefore, eggs laid by chicken in 11 days = 121 eggs
If gorge had a gf for 4 mo. then on their 5 mo he dumped her. how long did gorge have a gf?
Answers
Answer:
For 4 months. Also, is this a real life problem that happened to you??
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
what is the expression for this:
12 less than 4 times a number
Answers
Answer:
It would be 4n - 12.
From her home, Glera traveled 5.8 miles north to the grocery stare, then 2.1 mlles west to the library. What is the distance thom her home to the library
Answers
Answer:
6.16 miles
Step-by-step explanation:
When solving word problems like these, I like to start by drawing a picture.
So, Glera starts at her home and moves north by 5.8 miles. Then, she walks west by 2.1 miles to the library. The problem wants you to find the distance from her home to the library.
I've attached a drawing I made to help me visualize the problem. The distance from her home to the library is the hypotenuse of the triangle. To solve for it, you would use the equation [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].
a and b are the sides of the triangle, and c is the hypotenuse.
[tex]5.8^{2}[/tex] + [tex]2.1^{2}[/tex] = [tex]c^{2}[/tex]
33.64 + 4.41 = [tex]c^{2}[/tex]
38.05 = [tex]c^{2}[/tex]
To find c, you would take the square root of 38.05, which is about 6.16 if you use a calculator.
So, the distance from her home to the library is 6.16 miles!
can anyone please help thank yall so much!!
Answers
Answer: 1.No, 2.Yes, 3.No, 4.22, 25, 28, 5.-29, -34, -39, 6. 9/10, 1, 1 and 1/10, For the last three you are on your own. Good luck :)
Step-by-step explanation:
Nb gn njjrndndnfnfjdjfjfi
Answers
Answer:
jkbgf7jhfdt7jceru9onvdtihdr
HELP ASAP PLEASE EXPLAIN THOUGH
Answers
Answer:
35 times, or D
Step-by-step explanation:
A bag contains 5 red marbles, 6 blue marbles, 3 green marbles, 4 black marbles, and 2 yellow marbles. A marble will be drawn from the bag and replaced 100 times. What is a reasonable prediction for the number of times a green or black marble will be drawn?
A quick lesson on probability:
The probability of an event is: (the number of ways what you want can happen) / (total number of outcomes possible). For example, in a coin flip, there is 1 way to get heads, and 2 possible outcomes. Thus, the possiblity of flipping a coin and getting heads is:
(1 way to get heads) / (2 possible outcomes) = 1/2
Then, if we were to flip the coin 100 times, we would expect about 1/2 of the times to be heads, so we should expect heads 50 times.
On to the problem.
There are 3 green marbles and 4 black marbles, so there are 7 ways to draw a green or black marble.
Then, there are 5 + 6 + 3 + 4 + 2 = 20 possible outcomes.
Using the formula to find the probability, substitute the values we just found.
(the number of ways what you want can happen) / (total number of outcomes possible) =
(7 ways to draw a green or black marble) / (20 marbles that can be drawn) = 7/20 chance of getting a green or black marble.
Then, because there is a 7/20 chance of getting what we want, and there are 100 draws, we can say that an we should get green or black
7/20 * 100 = 35 times, or D
Feel free to ask any questions! :)
Mara has no money. In order to buy a gift, she borrowed $35 from her mom. When her birthday came, she received $125 dollars. If she repays her mom, how much money will she have?
Answers
Answer:
She will have $90 left over!
Step-by-step explanation:
Hope this is correct!
Which is a true statement about the transformation shown?
Answers
Answer:
A
Step-by-step explanation:
It's not a reflection because then it would be flipped and M and N would switch places
It's a translation and everything is the same length in terms of each other so
A translation with the pre and after image being congruent
Choice A
Is this linear or nonlinear?
y + 7 = 2x + 3
Answers
Answer:
I think it is tho
let's wait for another answer
EXPLANATION-
Need help with this please will give you the brainliest
Answers
Answer:
5m
Step-by-step explanation:
The volume doesnt count so do height × width
Answer:
SA = 50
Step-by-step explanation:
Formula for surface area of a rectangular prism : A=2(wl+hl+hw)
hope this helps :)
A right triangle has one side that measures 4 in. The angle opposite that side measures 80o.
What is the length of the hypotenuse of the triangle? Round to the nearest tenth.
3.9 in.
4.1 in.
22.7 in.
23.0 in.
Answers
Answer:
The answer is option B. 4.1 !
Step-by-step explanation:
Hop this helps :)
Brainliest would be greatly appreciated :D
Using the graph, predict the y-value when the x-value is 13
A) 17
B) 18
C) 19
D) 20
Answers
9514 1404 393
Answer:
D) 20
Step-by-step explanation:
Each point marked on the graph is 3 units higher and 2 units to the right of the one before. The last dot is at x=9, so a dot at x=13 will be 2×2=4 units to the right. At the same rate of increase, it will be 2×3=6 units higher than 14.
The y-value is predicted to be 20 at x=13.
find the volume of the sphere
Answers
Answer:
113.04 units³Step-by-step explanation:
Given that
radius (r) = 3 unitsπ value = 3.14Therefore the
Volume of sphere =
4/3 × π × r × r × r=
4/3 × 3.14 × 3 × 3 × 3 =
4/3 × 3.14 × 27 =
36 × 3.14 =
113.04 units³_________________
#StayPositive - kexcvi
a man gives 40 percent of his money to his children and 20% of the remaining to a trust if we still left with 9600 what did he originally have
Answers
Answer:
20000
Step-by-step explanation:
9600 = 80% after he gave 40% to his children
80%=4/5
9600 / 4 * 5 = 12000
12000 = 60% of the original
60%=3/5
12000 / 3 * 5 = 20000
A large group of friends needs to call a taxi service to get home. The taxi cab company charges $2 per mile
Answers
Answer:
36 dollars per person and they all will pay 2 dollars each the large group will hit a wall
Weekly wages at a
certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$250 and $300.
Answers
Answer:
2.35% chance
Step-by-step explanation:
in a normally distributed graph with a standard deviation of $50 $250 and $300 contain 2.35% of the data.
2.15% chance.
in a normally distributed graph with a standard deviation of $50 $250 and $300 contain 2.15% of the data.
How do you calculate probability?
The probability of an event can be calculated by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
Please check the attached file for a complete answer.
Learn more about probability at
https://brainly.com/question/24756209
#SPJ2
Find the unknown value in the pair of equivalent fractions.
3/4 = ?/100
Answers
Answer:
75.
Step-by-step explanation:
100÷4= 25
25×3= 75
75/100
Answer:
75
Step-by-step explanation:
4 x 25 = 100
3 x 25 = 75
or
100/4 = 25
25 x 3 = 75
wich value from the set ( 0, 1/2, 2, 4) makes the equation 6-4x=4 true
Answers
Answer:
1/2
Step-by-step explanation:
6 - 4(0) = 6 (incorrect answer)
6 - 4(1/2) = 4 (correct answer)
6 - 4(2) = -2 (incorrect answer)
6 - 4(4) = -10 (incorrect answer)
I hope this helps :)
what if we are given 7:11? Can we write 2 equivalent ratios?
Answers
Answer:
yes we can write as follows :-
14:22
21:33
28:44
hope it helps