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
Jenifer is the high scorer on his basketball team. He made 36 free throws out of 50 free throws attempted. What was his percentage of free throw shots made?
Answers
Answer:
72%
Step-by-step explanation:
36/50 = 0.72
0.72 x 100 = 72%
Ya'll how do I graph this? I haven't graphed anything in 3 years
Use a coordinate plane to plot these points and connect them to make a quadrilateral. Then construct a similar quadrilateral (A’B’C’D’) on the same coordinate plane. You may use a ruler and protractor if necessary.
A (-2,3), B (1, 5), C (3, -1), (-1, 3)
Answers
There you go! Hope this helps! :)
(X-1)squared
Expand and simplify
Answers
Answer:
Step-by-step explanation:
(a - b)² = a² -2ab + b²
Here, a = x and b = 1
(x -1)² = x² - 2 * x *1 + 1²
= x² - 2x + 1
[tex]\sf \longmapsto \:( x + 1) {}^{2} [/tex]
[tex]\sf \longmapsto(x+1)(x+1)[/tex]
[tex]\sf \longmapsto(x)(x)+(x)(1)+(1)(x)+(1)(1)[/tex]
[tex]\sf \longmapsto \: x {}^{2} +x+x+1[/tex]
[tex]\sf \longmapsto \: x {}^{2} +2x+1[/tex]
[tex] \boxed{ \boxed{ \red {\sf x {}^{2} +2x+1}}}[/tex]
in figure below, lines r and s are parallel. If the m<1=47° , find:
Answers
Answer:
<3 = 47 degrees
<4 = 133 degrees
<5 = 47 degrees
<6 = 133 degrees
<7 = 47 degrees
<8 = 133 degrees
Angles 1 = 3 = 5 = 7 (vertical angles
Step-by-step explanation:
If your getting paid 5$ every week how long will it takes you to get 10,000$?
Answers
10,000 divided by 5 = 2,000
the problem solving plan indentify step to organize your information which of the following answers choices are included in the steps to organize your information?
A) organize the problem and find the question
B) solve the problem and change your strategy if necessary
C) write the facts, organize your thoughts and define your strategy
D) organize the step and underline the question
Answers
that's the answer Just look at the picture's
ashtons containor of water holds 80 milliliters. nelsons container holds 9/16 of that amont. how many milliniters of water do the two containors hokd together
Answers
Answer: Neither
Step-by-step explanation: Technically the containers hold no water at all as they hold only the bottles in which the water is actually contained. So the answer I suppose is 'Neither'.
help with my math plz
Answers
Answer:
Step-by-step explanation:
The side is S= 5 cm , and the area is A= S² = 5²= 25
If the side would be doubled will be S= 5*2 = 10 cm, and the area A= 10²=100
Compare the area of S=5 to area of S=10 , 100 = 4*25
Conclusion:
If we double the side the area is 4 times greater.
this graph shows how much lisa earns babysitting compared with thge number of hours she works
Answers
Answer:
For every hour she earns 12$
Step-by-step explanation:
If your question looks like the picture, then the answer above is the right answer. If it's not, oh well, show the picture next time!
sorry here is the question!! please help and Thank you!!
Answers
Answer:
B. 4
Step-by-step explanation:
[tex] \dfrac{\sqrt{32}}{\sqrt{2}} = [/tex]
[tex] = \dfrac{\sqrt{16 \times 2}}{\sqrt{2}} [/tex]
[tex] = \dfrac{\sqrt{16} \times \sqrt{2}}{\sqrt{2}} [/tex]
[tex] = \dfrac{4\sqrt{2}}{\sqrt{2}} [/tex]
[tex] = 4[/tex]
Please help I've never been more confused
Answers
Step-by-step explanation:
2.
Two pairs of corresponding angles
i. angle C angle D
ii. angle G angle F
Two pairs of alternate angles
i. angle B angle D
ii. angle H angle F
Two pairs of interior angles
i. angle C angle H
ii. angle D angle E
Identify the indicated sum for the geometric series.
S, for 3 - 6 + 12 – 24 + .....
Answers
Answer:
Here,
3
,
(
−
6
)
,
12
,
(
−
24
)
,
...
is the geometric sequn.
w
h
e
r
e
,
1
s
t
t
e
r
m
=
a
1
=
3
and
common ratio
r
=
−
6
3
=
12
−
6
=
−
24
12
=
−
2
and
S
9
=
?
⇒
n
=
9
We know that,
The sum of first n term of Geometric series is :
S
n
=
a
1
(
r
n
−
1
)
r
−
1
Putting ,
a
1
=
3
,
r
=
−
2
and
n
=
9
S
9
=
3
[
(
−
2
)
9
−
1
]
(
−
2
)
−
1
∴
S
9
=
3
[
−
512
−
1
]
−
3
⇒
S
9
=
3
(
−
513
)
−
3
⇒
S
9
=
513
Step-by-step explanation:
Answer:
Step-by-step explanation:
c.r. r=-6/3=-2
[tex]S_{n}=3\frac{(-2)^n-1}{-2-1} =-(-2)^n+1\\let~n\rightarrow \infty\\then S_{\infty} \rightarrow \infty~or~ -\infty[/tex]
At the movie theatre, child admission is $6.50 and adult admission is $9.60. On Monday, 129 tickets were sold for a total sales of $1071.00. How many adult tickets were sold that day?
Answers
1071/129 = 8.30
75 adult tickets + 54 child’s tickets = $1071 so 75 adult tickets were sold that day
Jeriel decides to research the relationship between the length in inches and the weight of a certain species of catfish. He measures the length and weight of a number of specimens he catches, then throws back into the water. After plotting all his data, he draws a line of best fit. Based on the line of best fit, how much would you predict a catfish with a length of 33 inches would weigh?
Answers
A catfish with a length of 33 inches would weigh 30 pounds.
Linear equationA linear equation is in the form of:
y = mx + b
where y,x are variables, m is the rate of change and b is the y intercept.
Let y represent the catfish weight with x inches length
From the line of best, it passes through (20, 4) and (23, 10), hence:
y - 4 = [(10 - 4)/(23 - 20)](x - 20)
y = 2x - 36
For a length of 33 inches:
y = 2(33) - 36 = 30 pounds
A catfish with a length of 33 inches would weigh 30 pounds.
Find out more on Linear equation at: https://brainly.com/question/14323743
Show that dividing a number by 5 1/2 gives the same answer as multiplying the number by 2/11 plz help!!!
Answers
Answer:
plz explain so i can help am i mutiplying the 2 numbers or...?
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
[tex]\frac{x}{5 \frac{1}{2} } \\\\ \frac{11}{11/2} \\\\11. \frac{2}{11}\\\\=2[/tex]
also,
[tex]x . \frac{2}{11} \\\\11 .\frac{2}{11} [x=11]\\\\=2\\[/tex]
Which is the correct quotient with a letter as the remainder?
Answers
Answer:
A
Step-by-step explanation:
876 divided by 43 = 20
and the remainder is 16
in the case of other options, the quotients are correct but the remainders are wrong.
Therefore, A is the option with both correct quotient and remainder.
Jamie and Raul both work at the Pizza House. Together, they work a total of 15 hours per week. Raul works 3 more than twice the hours as Jamie. How many hours does Jamie work per week?
Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
List the facts phrase by phrase.
Total = 15 hours
Let Raul's hours = x
Let Jamie's hours = y
Total = x + y = 15
x = 3 + 2y
From total, find x
x+ y = 15 Subtract y from both sides.
x = 15 - y Put the value for x in x = 3+ 2y
3 + 2y = 15 - y Subtract 3 from both sides
2y = 15 - 3-y Combine
2y = 12 - y Add y to both sides.
2y + y = 12 Combine
3y = 12
y = 12 / 3
y = 4
Jamie worked 4 hours
Raul worked 11
The length of a rectangle is 20cm longer than its width.
The area of the rectangle is 1000cm?
Find the width and length of the rectangle.
Give your answers in surd form.
Answers
[tex]\text{Width} ~= w ~ cm \\\\ \text{Length}~,l = (20+ w) ~ cm \\\\\text{Area of rectangle} = 1000 cm^2\\\\\\\text{Now,}\\\\l \cdot w = 1000\\\\\implies (20 + w) w= 1000\\\\\implies w^2 +20w -1000=0\\\\\\\implies w = \dfrac{-20 \pm \sqrt{20^2 - 4 \cdot 1 \cdot (-1000)}}{2 \cdot 1}\\\\\\\implies w = \dfrac{-20 \pm \sqrt{4400}}{2}= \dfrac{-20\pm 20\sqrt{11}}2 = -10 \pm 10\sqrt{11}\\\\\text{Width cannot be negative so,} \\\\w= -10+10\sqrt{11}=10\left(\sqrt{11} - 1 \right) ~ cm\\\\[/tex]
[tex]\text{And length,}[/tex]
[tex]l= 20+ 10\left(\sqrt{11} - 1} \right) = 20 + 10\sqrt{11} - 10 = 10 + 10\sqrt{11} = 10 \left(1+ \sqrt{11} \right)~ cm[/tex]
Match the Vocab Word to the definition.
Remember, you are allowed to use your notes to help you!
Question 1 options:
Multiply a sum by multiplying each addend separately and then adding the products.
∙a(b + c) = ab + ac
∙k(m – n) = km - kn
Part of an expression that is added or subtracted.
∙These can be a single number or a variable, or
numbers and variables multiplied together.
A letter or symbol that represents a value.
It's a number on its own, it has a fixed value.
The number in front of a variable.
1.
Distributive Property
2.
Term
3.
Variable
4.
Constant
5.
Coefficient
Answers
Term, Part of an expression that is added or subtracted. These can be a single number, variable, or numbers and variables multiplied together.
Variable, A letter or symbol that represents a value.
Constant, It’s a number kn it’s own, but it has a fixed value.
Coefficient, the number in front of a variable.
Hope this helped!!
write the value of (2+root3)(2-root3)
Answers
Answer: 1
Step-by-step explanation: use foil and get 4-3.
Jack and Jill, trying to do math and chill, when they ran into a problem. They can't agree on what the answers should be, so now it's up to you to solve them.
In class, Jack thought as Jill she sought solve an absolute value... she removed the sign from her negative nine and said "the problem should be just about through".
But Jack he said, "no Jill you misread, the negative is on the outside". Still Jill didn't budge, so you be the judge, does this mean that the teacher lied?
Here's the problem Jack and Jill are trying to solve: -|9| = ?Jack thinks the answer is -9, because the negative is outside the absolute value signs. Jill thinks the answer is 9, because the teacher said absolute value is always positive.
Who is right and why? Explain your steps using sentences.
Answers
Answer:
-9
Step-by-step explanation:
the teacher was right
A pool company is creating an image for a client that has the look of a 3-D image for a family pool and a similar dog pool. Find the value of a in the drawing below:
Answers
Answer:
a = 21
Step-by-step explanation:
Based on the information given, we can calculate that
WZ x 3 = a
so...
7 x 3 = 21
Hope that helped!! :)
Answer:
I think it is 21 since the relationship between 4 and 12 4 * 3 is equal to 12 so I did the same for each side but angles don't change so 7*3=21
helppppppppppp i hv 5 mins
Answers
Answer: 342.5 miles
Step-by-step explanation:
Distance = Speed x Time
Speed(mph) Time(hr) Distance(miles)
55 x 3.5 = 192.5
60 x 2.4 = 150
Total Distance (miles) = 342.5 miles
Plzzz help me plzzzzzz
Answers
Answer:
Circumference of a circle = pi * diameter
[tex]219.8=3.14*d[/tex]
[tex]d=\frac{219.8}{3.14}[/tex]
[tex]d=70[/tex]
Radius = half of diameter
[tex]r=\frac{1}{2} d[/tex]
[tex]r=\frac{1}{2}*70[/tex]
[tex]r=35[/tex]
Area of circle = [tex]\pi r^2[/tex], where r is the radius:
[tex]a=3.14*35^2[/tex]
[tex]a=3846.5[/tex]
If they ran around the track 3 times, they would cover the circumference three times.
[tex]219.8*3=659.4[/tex]
Convert to centimetres:
[tex]659.4*100=65940[/tex]
How do you write 7460 in standard form?
Answers
Answer:
7460
Step-by-step explanation:
To write a linear expression in standard form, rearrange the terms in alphabetical order.
7460
Answer:
a = 7.46
7.46 x 103
103 = 1,000 x 7.46 = 7,460
here your answer
hope it helps you
100 POINTS
Given Point P(3,4), what is the resulting point after the following transformations?
Translate 3 up and 2 left
Rotation 180° around origin
Reflection over y-axis
Answers
Answer:
(1, -7)
Step-by-step explanation:
P(3,4)
3 up ---> y = 4 + 3 = 7
2 left ----> x = 3 - 2 = 1
new point (1, 7)
after 180 rotation around origin
point is (-1, -7)
now reflection over y-axis
(1, -7)
Answer:
[tex](1,-7)[/tex]
Step-by-step explanation:
Refer to the image below
0(-7) helppppppppppppppppppppp
Answers
Answer:
0
Step-by-step explanation:
anything multuplied by 0 is 0
multiply (2x+3) (-x -2)
Answers
Answer:
[tex]-2x^{2} -7x-6[/tex]
Step-by-step explanation:
(2x + 3) (-x - 2)
distribute first term, to the second term:
2x(-x) + 2x(-2) + 3(-x) + 3(-2)
multiply:
[tex](-2x^{2})[/tex] + (-4x) + (-3x) + (-6)
[tex]-2x^{2} -4x-3x-6[/tex]
combine the like terms:
[tex]-2x^{2}[/tex] - 4x - 3x - 6
-7x
[tex]-2x^{2}[/tex] - 7x - 6
final answer :
[tex]-2x^{2}[/tex] - 7x - 6
hope this helped !!
mark me brainliest :D
A line passes through the point (-6,9) and has a slope of 3/2. Write an equation in slope-intercept form for this line.
Answers
Answer:
y=3/2x+18
Step-by-step explanation:
Hi there!
We are given a point (-6,9) and a slope of 3/2
We want to write the equation of this line in slope-intercept form
Slope-intercept form is written as y=mx+b, where m is the slope and b is the y intercept
Since we already know the slope of the line as 3/2, we can substitute it as m into the equation:
y=3/2x+b
Now let's find b
Since the equation of the line passes through (-6,9), we can use it to help solve for b
Substitute -6 as x and 9 as y:
9=3/2(-6)+b
Multiply
9=-9+b
Add 9 to both sides
18=b
Substitute 18 as b into the equation.
y=3/2x+18
Hope this helps!
Write a two paragraph summary of what you are learning in your current math class.
Answers
Answer:
what are you even learning?
Answer:
what is your topic in math class..?