Answers
Answer:
Option 1: y = (x - 2)² + 2
Step-by-step explanation:
Given the vertex, (2, 2), of an upward-facing parabola, and using the y-intercept of the graph, (0, 6):
Definitions:The vertex form of the quadratic equations is:
y = a(x - h)² + k
where:
(h, k) is the vertex.
The value of h represents the horizontal translation of the graph. h > 0 represents the horizontal shift of the graph h units to the right. h < 0 shifts the graph |h | units to the left. The value of k represents the vertical translation of the graph. k > 0 shifts the graph k units upward. k < 0 shifts the graph |k | units down.The sign of a determines the direction of the graph's opening. The value of a also determines the vertical stretch or shrink of the graph.
If a is positive (or a > 1), then the graph opens upward. The value of a > 1 also represents the vertical stretch of the graph. If a is negative (or a < 0), then the graph opens down.The value of 0 < a < 1 represents the vertical shrink or compression of the graph. Solution:Substitute the values of the vertex (2, 2) and the y-intercept, (0, 6) into the vertex form to solve for the value of the coefficient, a:
y = a(x - h)² + k
6 = a(0 - 2)² + 2
6 = a(-2)² + 2
6 = 4a + 2
Subtract 2 from both sides
6 - 2 = 4a + 2 - 2
4 = 4a
Divide both sides by 4 to solve for a :
[tex]\displaytext\mathsf{\frac{4}{4} \:=\frac{4a}{4}}[/tex]
a = 1
Quadratic Equation in Vertex Form:Therefore, given the vertex, (2, 2) and a = 1, the quadratic equation in vertex form is: y = (x - 2)² + 2, thereby matching Option 1.
Related Questions
In a recent year, 39% of all college students were enrolled part-time. If 5.8 million college students were enrolled part-time that year, what was the total number of college students?
Round your answer to the nearest million.
Answers
Answer:
15 million
Step-by-step explanation:
39% of all college students enrolled part-time.
5.8 million college students enrolled part-time.
Let x = the total number of college students.
39/100 • x = 5.8
x = 5.8 • 100/39
x = 14.87
=15 million
Hope this helps :)
y=-x-6 input (x) = -3 find (y) output
Answers
-(-3) =+3
Because negative number multiplied by a negative number equals positive
Answer:
[tex]y=-3[/tex]
Step-by-step explanation:
[tex]y=-x-6[/tex]
Plug in the given value for x:
[tex]y=-(-3)-6[/tex]
Simplify:
[tex]y=3-6[/tex]
[tex]y=-3[/tex]
There is 358 pieces of pumpkin pie by the time dessert comes around there are only 7 guest left how many pieces can each person get if it is shared equally how many will be left over
Answers
sales tax is 7% what is the amount of sales tax you would pay this bill
Answers
% means per 100
so when figuring out percents it's good to use 100
so
on $100 7% would mean $7
on $50 7% would mean $3.5
in $200 7% would mean $14
Larry needs 45 ounces of graph juice for 6 guests. Later, he finds out that 26 guests are coming. how much graph juice does he need to purchase?
A. 196 Ounces
B. 270 Ounces
C. 40.3 Ounces
D. 1170 Ounces
Answers
Based on the amount of juice needed for 6 guests, the amount of juice Larry will need for 26 guests is A. 196 ounces.
First find out the amount of juice a single guest will need:
= Quantity of juice / Number of guests
= 45 / 6
= 7.5 ounces
If a guest needs 7.5 ounces, 26 guests would need:
= 25 x 7.5
= 195 ounces
In conclusion, 196 ounces of juice is needed.
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Please help!! I’m taking a math course a grade above mine but since i’m on break my teacher isn’t able to help me.
Answers
Answer:
Slope = ½
Step-by-step explanation:
Given the two points on the graph, (-4 , 0) and (0, 2):
Let (x₁, y₁) = (-4 , 0)
(x₂, y₂) = (0, 2)
Substitute the given points into the following slope formula:
[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]
[tex]\LARGE\mathsf{m = \frac {2\: -\:0}{0\: -\:(-4)}}[/tex]
[tex]\LARGE\mathsf{m = \frac {2\: -\:0}{0\: +\:4}}[/tex]
[tex]\LARGE\mathsf{m = \frac {2}{4}\:=\:\frac{1}{2}}[/tex]
Therefore, the slope of the line is ½.
If the confidence interval and hypothesis test both used the same data, how did they come up with different standard errors
Answers
Confidence intervals and hypothesis testing share the characteristic that they are both inferential techniques
Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution.
What is confidence interval?
Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. It is possible that occasionally, when the hypothesis produces a non-significant result, the confidence interval will exclude the value specified under the null hypothesis because the standard error used to calculate the confidence interval is different from the standard error used in hypothesis testing.
We use the standard error of the mean to show the degree of uncertainty surrounding the estimation of the mean measurement. Most helpful for calculating a confidence interval is the standard error.
Hence , Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution.
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What is the slope in other words the answer
Answers
Answer:
gradient
Step-by-step explanation:
gradient is the same as steepness and slopes r steep so its gradient
can somebody tell me if these answers are correct?
Answers
I would handle b) like this: 8.50:12~0,7
1,55-0.7=$0,85
each chicken coop can hold 8 chickens what's the maximum of chickens that can fit in 7 Coops?
Answers
Answer:
56
Step-by-step explanation:
each can fit 8 chickens so that means that 7 coops can fit 56 chickens
8×7=56
Find the value of x.
Answers
Answer:
x = 69
Step-by-step explanation:
2x - 3 = 135
2x = 135 + 3
2x = 138
2x/2 = 138/2
x = 69
What is the value of a if 5a = 1/125
(It’s not 1/625)
Please answer!!
Answers
Answer:
a = -3.
Step-by-step explanation:
5^a = 1/125
5^3 = 125
so 5^-3 = 1/125
Answer:
a = -3
Step-by-step explanation:
5^a = 1/125
Rewriting 1/125 as 1/5^3 = 5^-3
5^a = 5^-3
a = -3
Not sure on this. (Im really bad at math)
Answers
Answer:
13. C
14. B
Step-by-step explanation:
yeah-ya........... right?
If the chance of rolling a 3 on a dice is 1/6, what is the chance of not rolling a
3?
Answers
Answer:
5/6
Step-by-step explanation:
Assuming we are using a standard 6-sided die, we can say that there are 6 numbers on the die. 1, 2, 3, 4, 5, and 6. The chance of rolling any number, including 3, is 1/6
The change of not rolling a 3 would be 5/6, because there are 5 other numbers besides 3
Coordinate plane .........
Answers
Answer:
The answer is the blue dot
Step-by-step explanation:
You should remember that the x goes first in (x,y).
a
Russ worked a total of 135 hours during the month of July. He earned $3,600.
Russ earned $25 per hour each weekday that he worked. He earned $40 per hour
each Saturday that he worked. How many hours did he work on the weekend?
Answers
Answer:
3375
Step-by-step explanation:
what is 3x-4y= -24 answer
Answers
Answer:
The answer will be ( [tex]x=\frac{-24+4y}{3}[/tex] )
whats 5 x 2x x 2y?? im doing hw and im confused
Answers
Because
5 x 2x = 10x
10x x 2y = 20xy
Over the summer, Jarrod did online tutoring with kids. He was paid a total of $342.30 for 42 hours of tutoring. What was his hourly rate of pay?
Answers
Answer:
His hourly rate is $8.15.
Step-by-step explanation:
The hourly rate is how much he earns in one hour. We know how much he earns in 42 hours ($342.3).
So what we need to do is to divide that amount ($342.3) by 42.
And we get $8.15.
Solve the quadratic by factoring.
4x^2 – 2x – 3 = 2x
PLS HELP ASAP!!!
Answers
Answer: X = -(1/2) AND X = (3/2)
Step-by-step explanation:
4x^2 – 2x – 3 = 2x
4x^2 – 4x – 3 = 0
(2x+1)(2x-3) = 0
1. (2x+1) = 0
2x = -1
X = -(1/2)
2. (2x-3) = 0
2X = 3
X = (3/2)
The total length of 5 belts and 3 shoe laces is 4.2 m. The total length of 3 shoe laces is equal to the length of 2 belts
a) Find the length of a belt
b) Find the total length of 7 belts and 2 shoe laces
Answers
Answer:
a= 0.84m
b= 7m
i tried my best but im not sure of the answer
Step-by-step explanation:
5x+3y=4.2
2x=3y
x = 4.2-3y/5
2*(4.2-3y/5) = 3y
=1.68/3 = 0.56
y=0.56
2x = 3*0.56
x = 0.84
a) The length of one belt (b) is 0.6 meters, or 60 centimeters.
b) The total length of 7 belts and 2 shoe laces is: 5 meters.
Let the length of one belt be "b" meters, and the length of one shoe lace be "s" meters.
a) Find the length of a belt:
According to the given information, the total length of 5 belts and 3 shoe laces is 4.2 meters. We can express this information as an equation:
5b + 3s = 4.2
b) Find the total length of 7 belts and 2 shoe laces:
The total length of 3 shoe laces is equal to the length of 2 belts. We can express this information as another equation:
3s = 2b
Now, we can use these two equations to solve for the values of "b" and "s."
Step 1: Solve the second equation for "s":
3s = 2b
Divide both sides by 3:
s = (2/3)b
Step 2: Substitute the value of "s" from the second equation into the first equation:
5b + 3((2/3)b) = 4.2
5b + 2b = 4.2
7b = 4.2
Step 3: Solve for "b":
b = 4.2 / 7
b = 0.6
Now that we have the value of "b," we can find the value of "s" using the second equation:
s = (2/3)b
s = (2/3) * 0.6
s = 0.4
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John's father spent 2 hours and 55 minutes working on his truck if it was 4:55 when he stopped what time did he start
Answers
Answer:
2
Step-by-step explanation:
4-2=2
55-55=0
so:
2:00
pls help will mark as brainlist
Answers
Step-by-step explanation:
total angle= 360°.
sides = 360/36 = 10 (decagon).
total angle= 360°
sides = 360/120 = 3(triangle).
hope this helps you to.
The new location for a park needs to be exactly 5 miles from the school. When plotted on the coordinate plane, the school is located at (3, 3).
Use the Pythagorean theorem to determine two possible locations on the coordinate plane for the park.
Answers
Answer:
the answer is -1, 0 and 6, -1
Step-by-step explanation:
-1, 0 and 6, -1
(Hope this helps can I pls have brainlist (crown)☺️)
HELP ME please please please
Answers
Answer:
d.
took the test
Step-by-step explanation:
What is the value of a? Enter the answer in the box.
Answers
Answer:
a = 25°
Step-by-step explanation:
60° and 3a - 15° are congruent because they are corresponding.
60 = 3a - 15
75 = 3a
a = 25°
-Chetan K
Please help quickly please
Answers
Answer
169
Step-by-step explanation:
[tex](5x10^3)x(9x10^7)[/tex]
Answers
Answer:
Step-by-step explanation:
[tex](5x10^{3})x(9x10^{7})=5*9*x^{1+1+1}*10^{3+7}\\\\=45x^{3}*10^{10}[/tex]
I don’t know what way the line goes
Answers
Answer:
line goes from bottom left to top right or as we would call it positive. now the +5 is your y intercept so start at 5 and go up one over 2 right because that is your slope
What is the slope-intercept form of the linear equation 2x - 8y = 32?
(Don't forget to simplify fractions if possible)
Answers
Answer:
y = 1/4x + 4
Step-by-step explanation:
2x - 8y = 32
-2x -2x
-8y = -2x + 32
divide everything by -8
so that y becomes positive
answer : Y = 1/4x + 4
The slope-intercept form of the linear equation 2x - 8y = 32 is y = (1/4)x - 4.
Given is an equation of a line 2x - 8y = 32, we need to convert it into slope-intercept form of the linear equation.
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To convert the equation 2x - 8y = 32 into slope-intercept form, we need to isolate y on one side of the equation.
Let's rearrange the given equation to solve for y:
2x - 8y = 32
Subtract 2x from both sides:
-8y = -2x + 32
Divide both sides by -8:
y = (2/8)x - 4
Simplifying further, we get:
y = (1/4)x - 4
So, the slope-intercept form of the linear equation 2x - 8y = 32 is y = (1/4)x - 4.
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