Answers
Answer:
[tex]\displaystyle y = x^2 + 6x + 12[/tex]
Step-by-step explanation:
To begin with, to define the stretch factour [tex]\displaystyle [A],[/tex]from the standard quadratic equation of [tex]\displaystyle y = Ax^2 + Bx + C,[/tex]find the rate of change between the vertex of [tex]\displaystyle [-3, 3][/tex] and either [tex]\displaystyle [-4, 4][/tex]or [tex]\displaystyle [-2, 4].[/tex]It really does not matter which ordered pair you choose to pair with the vertex because one result will be negative, and the other result will be positive, so it is as though you are taking the absolute value of the rate of change, but not entirely. Anyhow, let us get to wourk:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-4 + 3}{2 - 3} \hookrightarrow \frac{-1}{-1} \\ \\ 1 = m[/tex]
OR
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-4 + 3}{4 - 3} \hookrightarrow \frac{-1}{1} \\ \\ -1 = m[/tex]
So, both oppocite rate of changes tell you that the stretch factour of this quadratic function is [tex]\displaystyle 1,[/tex]ESPECIALLY sinse the graph opens upward.
Now, to determine the quadratic equation for this graph, you need to write this in vertex form first. Remember to base the equation off the vertex:
[tex]\displaystyle y = A[x - h]^2 + k \\ \\ y = [x + 3]^2 + 3[/tex]
So, −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, and sinse the vertex [tex]\displaystyle [(h, k)][/tex]is at [tex]\displaystyle [-3, 3],[/tex]there MUST BE a plus sign inside those brackets. Anyway, let us continue:
[tex]\displaystyle y = [x + 3]^2 + 3 \hookrightarrow y = x^2 + 6x + 9 + 3 \\ \\ \boxed{y = x^2 + 6x + 12}[/tex]
You now have your quadratic equation.
I am delighted to assist you at any time.
Related Questions
Three members of a teen hiking group hiked 3 5 of the entire Appalachian trail. The hikers took turns carrying a backpack of supplies. If each teen carried the backpack the same distance, what part of the total distance did each hiker carry the backpack? In this problem, the numerator is the same number as the . So the answer will be a . Each hiker carried the backpack for of the total trail distance.
Answers
Answer:
divisor,unit fraction,1/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
2. Five pigs were weighed daily to regulate caloric
intake before the stock show. The weight
gain/loss for each pig after one week is shown in
the table below.
Pig
Porky
Gumball
Wilbur
Roscoe
Chance
Weight Changes
Weight Gain/Loss (lbs.)
0.17
-1.48
0.10
-1.409
0.07
Which list shows the values in the table from least
to greatest?
Answers
Hope this helps
80/91 + 5/9 plz help
Answers
Answer:
1.43467643468
Step-by-step explanation:
Answer:
I think the answer is 1.44
Step-by-step explanation:
this is a simplified version of 1.43467643
A recipe for orange water says, "Mix 3 teaspoons yellow water with 1 teaspoon red water." For this recipe, we might say: "The ratio of teaspoons of yellow water to teaspoons of red water is 3:1 ." Write a ratio for 2 batches of this recipe and explain how you know it is equivalent to 3:1.
Answers
Answer:
The ratio of 2 batches of recipe is 6:2. Which is equivalent to 3:1 because if we multiply the ratio with same number it would give us equivalent ratio.
Step-by-step explanation:
When mix 3 teaspoon of Yellow water with 1 teaspoon of red water, we get ratio as 3:1
If we use 2 batches of recipe, the ratio is multiplied twice.
That's ratio of yellow water to red water is 3*2 :1*2 , which gives 6:2
But, if we simplify the ratio, by dividing both by common factor, we would get 3:1
That's [tex]\frac{6}{2} :\frac{2}{2}[/tex] simplified to 3:1
Rewrite the expression in the form 3^n.
Answers
Explanation:
Cross off four copies of '3' in both the numerator and denominator. Each pair cancels because 3/3 = 1, and 1 times any number is the same number. See the diagram below.
The numerator will be left with two copies of '3'. The denominator won't have anything left.
So we have 3*3 = 3^2
A car can travel 80 miles on 4 gallons of gasoline. If the gas tank, which can hold about 15 gallons, is half full, how many miles can the car travel before it runs out gas?
Answers
Answer: 150
Step-by-step explanation: A car can travel 80 miles on 4 gallons of gas if the gas tank can hold about 15 gallons is half full there will be 7.5 gallons of gas in the can so multipy the 80 miles by 1.875, 150
A 6 foot tall man makes a shadow that is 3 1/2 feet long. How tall is a building that makes a 14 7/8 foot shadow?
A) 52.06 feet
B) 8.68 feet
C) 25.5 feet
D) 1.41 feet
Answers
6/3.5 = 14.875/x
6 x 14.875 = 89.25
89.25/3.5 = 25.5
A survey asked 200 people which sports they play regularly. It revealed that
30 played tennis,
25 played golf,
40 played softball,
10 played tennis and golf,
20 played tennis and softball,
15 played golf and softball,
and 8 played all three sports.
How many of those surveyed played golf or softball?
Answers
Answer:
15
Step-by-step explanation:
How do you know whether two quantities x and y are proportional? Every ratio yx for related pairs of x and y is equivalent. Every sum x + y is the same for related pairs of x and y. Every x term is a multiple of the previous term. Every difference x – y is the same for related pairs of x and
Answers
Answer:
Two quantities x and y are said to be proportional if ratio yx for related pairs of x and y is equivalent.
Step-by-step explanation:
Two quantities x and y are said to be proportional if ratio [tex]yx[/tex] for related pairs of [tex]x[/tex] and y is equivalent.
The symbol ∝ is used to denote the proportionality. For example, if [tex]x[/tex] is proportional to y, then it is represented as [tex]x[/tex]∝y and if [tex]x[/tex] is inversely proportional to y, then it is represented as [tex]x[/tex] ∝ 1/y
given: y is the midpoint of XZ
prove: XY 1/2XZ
Answers
Given:
Y is the midpoint of XZ.
To prove:
[tex]XY=\dfrac{1}{2}XZ[/tex]
Proof:
It is given that Y is the midpoint of XZ. It means Y divides the line segment XZ in two equal parts XY and YZ.
[tex]XY=YZ[/tex] ...(i)
Point Y lines on the segment XZ, so by segment addition theorem, we get
[tex]XY+YZ=XZ[/tex]
[tex]XY+XY=XZ[/tex] [tex][Using (i)][/tex]
[tex]2XY=XZ[/tex]
Divide both sides by 2.
[tex]XY=\dfrac{1}{2}XZ[/tex]
Hence proved.
After school one night, I had to stop at the local office supply store and pick up a few items. I bought 2 packages of page dividers. They each cost $3.79. I bought one package of Post-It Tabs that cost $6.79. Finally, I bought a large binder for $11.99. Sales tax was 7.5% and I paid with a 50 dollar bill. How much change did I receive?
Answers
Answer:
$21.66
Step-by-step explanation:
Add up all of the costs
3.79 + 3.79 + 6.79 + 11.99 = 26.36
Then multiply by the sales tax
26.36 x 7.5% = 1.98
Add the total cost and the tax
26.36 + 1.98 = 28.34
Subtract 28.34 from 50
50 - 28.34 = 21.66
That is how much change you recieve after your purchase.
14^7/14^2 simplify expression
Answers
Answer:
537824
Step-by-step explanation:
[tex]14^{7}[/tex]/ [tex]14^{2}[/tex]
[tex]14^{7}[/tex] = 105413504
[tex]14^{2}[/tex] = 196
105413504 / 196
537824
A bag contains 56 marbles: 7 red, 8 green, 11 yellow, 17 brown, and 13 blue.
If a marble is chosen at random, what is the probability that the marble is green?
А. 1/5
B. 1/6
C. 1/7
D. 1/8
Answers
Answer:
D
Step-by-step explanation:
1/8
Answer: D
Step-by-step explanation:
Graph the inequality.
[tex]y \leqslant 2[/tex]
Answers
Riley bought a plant and planted it in a pot near a window in her house. The
initial height of the plant was 6 inches and it grew at a rate of 2 inches per
month. Write an equation for H, in terms of t, representing the height, in
inches, of the plant t months after Riley bought the plant.
Answers
Answer:
6+2t=h
Step-by-step explanation:
Answer:
H = 6 + 2t
Step-by-step explanation:
H = your solution
6 = initial height of the plant
+ = the height of the plant grows each month
2 = the rate at which the plants grows per month
t = the number of recorded months the plant will grow for
Hope this Helps! :)
-SGO
i need help with this equation can someone please help me
Answers
Answer:
d= 24
Step-by-step explanation:
-2= d/3 - 10
-6= d-30
-d=-30+6
-d= -24
d= 24
What is Three-fourths divided by one-sixth? A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 6 boxes containing one-sixth. Under the 6 boxes are 12 boxes containing StartFraction 1 Over 12 EndFraction. 3 4 4 and StartFraction 1 Over 12 EndFraction 4 and one-half
Answers
Answer:
4 and one-half
Step-by-step explanation:
Given the expression (3/4)÷(1/6), we are to simplify it. See the workings below;
(3/4)÷(1/6)
= 3/4 × 6/1
= (3×6)/4
= 18/4
= 9/2
Write as a mixed fraction
= 4 1/2
Hence the correct answer is 4 and one-half
Answer:
D
Step-by-step explanation:
Shona cycles at an average speed of 8km/h. How far has she travelled if she cycles for 4 hours
Answers
Answer:
32km
Step-by-step explanation:
Solve for x.
Зxy = W
Answers
Answer:
[tex]\huge\boxed{x=\frac{W}{3y}}[/tex]
Step-by-step explanation:
If we have the equation [tex]3xy=W[/tex] and we want to solve for x, our goal is to isolate x one one side of the equation.
The question we have to ask ourself is ”What’s stopping x from being isolated?”
That would be the 3 and the y.
Since we’re multiplying x by the 3 and the y, we can divide both sides by the 3 and the y to get x isolated.
[tex]3xy \div 3y = w \div 3y[/tex]
[tex]x = \frac{W}{3y}[/tex]
Hope this helped!
Max Quimby picks Raspberries for his grandmother every Tuesday during 2 points
the summer. She pays him $0.75 per quart. If he were able to pick 93
quarts how much he be paid?
Answers
Answer:
Would be paid $69.75
Step-by-step explanation:
Since he is paid $0.75 per quart, and he has picked up 93 quarts, you would multiply 0.75 by 93. Which would give you $69.75.
Your friend spent $7 in two days on lunch. He says that
he will need $21 for 6 days to spend on lunch. Is your
friend correct? Explain your reasoning.
Answers
Answer:
Yes
Step-by-step explanation:
Because he spent 3.50 in those two days and he will spend 3.50 in 6 days. 3.50×6= 21.
please help quickly
Answers
the first option because you multiply both sides,move the constant to the right, calculate,then divide on both sides
Help me o my I think I’m going to cry so please help
Answers
Answer:
The final answer in the most simplest form is 3/32
Step-by-step explanation:
3/8(3/4+5/6)-1/2
3/8( 38/24)-1/2
114/192-1/2=36/184
Divide by 12 for the 36 and 184
the final answer should be 3/32
Which equation fits the situation? Mikes test score was 20 points lower than marks if mark scored a 95 on the test which equation would give mike’s score
Answers
Answer:
95 - 20 = t
Step-by-step explanation:
Let's start with the facts. You know that Mike's test score is 20 points lower than Mark's. You know that Mark's score was 95.
If we are trying to find Mike's test score, t, the equation would be this:
The equation would be 95 - 20 = t
I hope this helps :)
Five more than four times a number
Answers
Answer: 4x +5
Step-by-step explanation:
If a problem says “(five) more than” that means your adding.
“(four) times” means your multiplying.
“a number” is your variable.
your answer would be 5+4n. *n* being a number.
Greg drove 300 miles at a constant speed in 5. The speed limit was 70 miles per hour. Was his rate greater than the speed limit?
Answers
The average speed of Greg will be 60 miles per hour.
To answer this question, we need to calculate Greg's average speed during the trip.
We can use the formula:
Average Speed = Total Distance / Total Time
In this case, Greg drove 300 miles in 5 hours, so:
Average Speed = 300 miles / 5 hours = 60 miles per hour
Since Greg's average speed was 60 miles per hour, which is less than the speed limit of 70 miles per hour, his rate was not greater than the speed limit.
Learn more about inequalities here:
https://brainly.com/question/30231190
#SPJ1
8 less then a number n is -13
Answers
Answer:
equation: 8-n=13
answer: n = 21
Step-by-step explanation:
I really need help with this one
Answers
Answer:
28
Step-by-step explanation:
Since B is the midpoint of AC, that means AB = BC. That means 3x+4 = 5x-6. We can now set up an equation to solve for x:
3x+4 = 5x-6
3x+10 = 5x
10 = 2x
x = 5
Now that we know what x is, we can just plug x into the expression of AB and multiply it by 2:
(3*(5)+4)*2
=(15+4)*2
=19*2
=28
(side note: we could have plugged x into the expression of BC as well, but in this case plugging it into AB tends to be easier to solve)
Therefore, the length of AC is 28.
Is 285 as a perfect square
Answers
Answer:
no
Step-by-step explanation:
the square root of 285 is not a whole number. 285 is not a perfect square.
Answer:
No , it is not a perfect square number of any numbers..
mark BRAINLIEST
Thank you ☺️☺️☺️
Factor
• 1/343 x3 - 1/125
• 0.001b3 - 8
- send help •-•'
Answers
Answer:
[1/7 x - 1/5][(1/49 x²)+(1/35 x)+(1/25)]
(0.1b - 2)[0.01b²+0.2b+4]
Step-by-step explanation:
a³-b³=(a-b)(a²+ab+b²)
So
1/343 x³ - 1/125
[(1/7)x]³ - [1/5]³
[1/7 x - 1/5][(1/7 x)²+(1/7 x)(1/5)+(1/5)²]
[1/7 x - 1/5][(1/49 x²)+(1/35 x)+(1/25)]
And
0.001b3 - 8
(0.1b)³-(2)³
(0.1b - 2)[(0.1b)²+(0.1b)(2)+2²]
(0.1b - 2)[0.01b²+0.2b+4]