Given:
Vertex of a quadratic function is at (3,-10).
The quadratic function passes through the point (0,8).
To find:
The equation of the quadratic function.
Solution:
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where, (h,k) is vertex and a is a constant.
Vertex of a quadratic function is at (3,-10). So, [tex]h=3,k=-10[/tex].
[tex]y=a(x-3)^2+(-10)[/tex]
[tex]y=a(x-3)^2-10[/tex] ...(ii)
The quadratic function passes through the point (0,8).
Putting [tex]x=0,y=8[/tex] in (ii), we get
[tex]8=a(0-3)^2-10[/tex]
[tex]8+10=a(-3)^2[/tex]
[tex]18=9a[/tex]
Divide both sides by 9.
[tex]2=a[/tex]
Putting [tex]a=2[/tex] in (ii), we get
[tex]y=2(x-3)^2-10[/tex]
Therefore, the correct option is J.
I will Mark the brainliest pls help
Answer:
Bella do you know the distance formula? that's the "tool" you need for these questions. :) Answers are bolded below :)
Step-by-step explanation:
dist = sqrt[ x2-x1)^2 +(y2-y1)^2]
Robins house is at Point P1 = (-9,10) in the form (x1,y1)
Sarah's house is at Point P2=(3,5) in the form (x2,y2)
dist from Robin's to Sarah's is
dist_RS = sqrt[ (3-(-9))^2 +(5-10)^2]
dist_RS = sqrt[ (3+9)^2 + (-5)^2]
dist_RS = sqrt[ 12^2 + 25 ]
dist_RS = sqrt [ 144+25]
dist_RS = sqrt [ 169]
dist_RS = 13
distance from Robin's to Jada's
where Jada's house is at Point P3 =(-3,2) in the form (x3,y3) (we can think of this as P2 in the form (x2,y2) in our formula)
dist_R J= sqrt [ (-3-(-9))^2 + (2-10)^2 ]
dist_R J= sqrt [ (-3+9)^2 + (-8)^2 ]
dist_R J= sqrt [ (6)^2 + 64 ]
dist_R J= sqrt [ 36 + 64]
dist_R J= sqrt [ 100 ]
dist_R J= 10
distance to Madison's house
where Madison's house is at Point P4 = (-1,-5) in the form (x2,y2)
dist_RM = sqrt [ (-1-(-9))^2 + (-5-10)^2 ]
dist_RM = sqrt [ (-1+9)^2 + (-15)^2 ]
dist_RM = sqrt [8^2 + 225 ]
dist_RM = sqrt [ 64 + 225 ]
dist_RM = sqrt [289 ]
dist_RM = 17
Jada's house is 10 , Madison's is 17 so it's 7 miles farther to Madison's than to Jada's
I NEED HELP LIKE ASAP I NEED TO PASS THIS CLASS >:PILL GIVE 20 POINTS
Answer: (-2,4) to (2,-2)
go up 1 from the origin
then 2 to left since it’s -2
3 up since it’s 3
go up 1 from the origin
then 2 right since it’s 2
3 down since it’s -3
a. Find the value of x from given figure
There were 8,454 pencils that were produced in the factory. When inspecting the pencils they noticed that 1,789 pencils were cracked. How many pencils were they able to use
Answer: They were able to use 665 pencils
Step-by-step explanation: You would simply do 8,454 - 1,789=665
Give Brainliest please :)
DaJuan has a photo that is 4 inches in width by 6 inches in length that
he wants to enlarge for his mother's birthday. The width of the enlarged
photo is 10.5 inches. What is the length of the enlarged photo?
please help if u can! thx
Answer:3x-x+2=4
Step-by-step explanation: source: (Too much work) srry
The mass of an adult North Pacific right whale is about 70,000 kg, or 7 x 104
kg.
The mass of a male African elephant is about 7000 kg, or 7 x 103 kg.
About how many times more massive is the right whale than the African
elephant?
PLZZZZ HELP 20 points
what happens between the sun, moon, and Earth during the 4 phases of the moon?
Answer:
theres like 8 phases of the moon
Step-by-step explanation:
i will need the answer for this
Answer:
Hello! r would equal 0.4. To do this, first subtract 4 from both sides. So (10r+4-4=8-4). You are then left with 10r=4. So then you divide both sides by 10. 10r/10=4/10. So you are left with 0.4. r=0.4
Step-by-step explanation:
A rectangle has a perimeter of 60 inches and a length of 22 inches. What is the width of the rectangle?
Answer:
8in
Step-by-step explanation:
I hope this helps. have a great dsy
Answer:
perimeter of a rectangle = 2( l+b )
perimeter = 60 inches
length = 22 inches
∴ width =
2 ( 22 + b ) = 60
22 + b = 60/2 = 30
22 + b = 30
b = 30 - 22 = 8 inches
∴ width = 8 inches
hope this answer helps you..
please mark as brainliest .. thank you!
What is the area of B
If there is no more informations, then:
A = ¹/₃(6 + x)The diameter of a circle is 6 feet find its area to the nearest 10th
Answer:
The area of the circle is 113.0 ft²
Step-by-step explanation:
To solve this problem we need to use the area formula of a circle:
a = area
r = radius = 6ft
π = 3.14
a = π * r²
we replace with the known values
a = π * (6ft)²
a = π * 36ft²
a = 113.04ft²
The area of the circle is 113.04ft²
round to the nearest tenth
a = 113.04ft² = 113.0 ft²
You pick a card at random. 4 5 6 6 7 8 9 )) What is P(prime)? Write your answer as a fraction or whole number.
The probability of getting prime number is 2/7.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Outcome = 4, 5, 6, 6, 7, 8, 9.
Number of outcome = 7.
a) The prime numbers from the outcome are 5 and 7.
So, the probability of getting prime number
= 2/7
Hence, the probability is 2/7.
Learn more about Probability here:
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Toby has made 298 goals out of 347 goals attempted.
About what percent of his attempts were successful?
Answer:
Convert fraction (ratio) 298 / 347 Answer: 85.878962536023% so round it up to 86%
Step-by-step explanation:
took the test
What is the area in square meters of the trapezoid below
Given:
Bases of the trapezoid are 5.2 m and 14.6 m.
The height of the trapezoid is 7 m.
To find:
The area of the trapezoid.
Solution:
The area of a trapezoid is:
[tex]A=\dfrac{a+b}{2}\times h[/tex]
Where, a,b are bases and h is the height of the trapezoid.
Putting [tex]a=5.2,b=14.6,h=7[/tex] in the above formula, we get
[tex]A=\dfrac{5.2+14.6}{2}\times 7[/tex]
[tex]A=\dfrac{19.8}{2}\times 7[/tex]
[tex]A=9.9\times 7[/tex]
[tex]A=69.3[/tex]
Therefore, the area of the trapezoid is 69.3 square meters.
2/9 divided by 6/27 fill the box with a fraction that makes the equation true
Answer:
1
Step-by-step explanation:
2 /9÷ 6/ 27=1
Find the area of each composite figure.
Round to the nearest TENTH if necessary.
Mrs. Braden has 7 1/2 yards of string. She needs to cut them into strips that are 1 1/2 feet in length. How many 1 1/2 feet strips of string can she cut from her 7 1/3 yards?
helppppppppppp me plz ;)
Answer:
1/4 x 20
Step-by-step explanation:
Half of 12 is 6, a third of 18 is 6, a sixth of 36 is 6, but a fourth of 20 is only 5. So it does not belong.
What are the solutions to the equation (10−x)(3x−9)=0?
Answer:
10−x)(3x−9)=0
−3x2+39x−90=0
−3(x−3)(x−10)=0
x=3 or x=10
The solutions to the equation (10 - x)(3x - 9) = 0 are x = 10 and x = 3.
Given that the equation (10 - x)(3x - 9) = 0
The factors will have the form (ax + b)(cx + d), where a, b, c, and d are constants.
To find values for a, b, c, and d such that (ax + b)(cx + d) is equal to 0
To determine the solutions of (ax + b)(cx + d), equate each term to zero and solve for x which gives the solutions.
The two solutions of (ax + b)(cx + d) are -b/a and -c/d.
To find the solutions to the equation (10 - x)(3x - 9) = 0, set each factor equal to zero and solve for x.
Setting (10 - x) = 0 gives:
10 - x = 0
To isolate x, subtract 10 from both sides of the equation:
10 - x - 10 = 0 - 10
Simplifying gives:
-x = -10
Multiplying both sides by -1 to solve for x:
(-1)(-x) = (-1)(-10)
x = 10
So, one solution is x = 10.
Now, setting (3x - 9) = 0, gives:
3x - 9 = 0
To isolate x, we add 9 to both sides of the equation:
3x - 9 + 9 = 0 + 9
Simplifying gives:
3x = 9
Dividing both sides by 3 to solve for x:
(1/3)(3x) = (1/3)(9)
x = 3
Therefore, the second solution is x = 3.
The solutions to the equation (10 - x)(3x - 9) = 0 are x = 10 and x = 3.
Learn more about solving quadratic equations and factoring, click here:
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how do I find the volume?
Answer:
Width x length
Step-by-step explanation:
Find the width or how wide it is
Then find the length or how long it is
multiply those
please help
Mofor and Shanice are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Mofor sold 12 small boxes of oranges and 3 large boxes of oranges for a total of $96. Shanice sold 6 small boxes of oranges and 6 large boxes of oranges for a total of $84. Find the cost each of one small box of oranges and one large box of oranges.
Answer:
$6 = cost of small box
$8 = cost of large box
Step-by-step explanation:
Let s = cost of small box
l = cost of large box
(1) 12s + 3l = 96 (2) 6s + 6l = 84
Multiply by -2 -24s - 6l = -192
-18s = - 108
s = $6 = cost of small box
12(6) + 3l = 96
72 + 3l = 96
3l = 24
l = $8 = cost of large box
The size and shape of a figure will stay the same after a translation is performed.
o True
o False
Answer: true
Step-by-step explanation:
True, because translation means just to move a figure, not to change a shapes's size, width, height, or any other property of the shape.
9. Plot A(8,-4), B(3, -4), C(7, 1), and D(7.-3) in a coordinate plane.
Then determine whether AB and CD are congruent.
Answer:
Just put it into Geogebra Classic. It's an app that really helps with this kinda stuff
8. This model of the backboard of a basketball goal is made of a semicircle. Use the ruler provided to measure the dimensions of the model to the nearest half inch. Which measurement is closest to the area of the model of the backboard in square inches? Use 3 for π.
It is c i did it oh khan
(pls branliest)
Can someone please help me
p.s. round to the nearest tenths
Answer:
Apothem:
radius is the same length as the base/length of each side of the hexagon.
r = 8
use pythagorean theorem to calculate the apothem
[tex]4^2+a^2=8^2\\\\16+a^2=64\\\\a^2=48\\\\a= 6.928[/tex]
≈ 6.9
Area
[tex]A = \frac{3\sqrt{3} }{2} *a^2\\\\=\frac{3\sqrt{3} }{2}(6.928)^2\\\\=124.7[/tex]
What was an effect of the Second Punic War?
ФCarthage remained a major trading center.
ФRome gained control over Sicily and Greece.
ФRome maintained control of Egypt and Spain.
ФCarthage became a major military rival to Rome.
please answer ASAP!!!!! I'm on a times unit test on edge please help ASAP!!!!!
Answer:
ithink its a or c
Step-by-step explanation:
not sure but dang what grade u in??
Will give brainliest if your answer is correct.
Answer:
B
Step-by-step explanation:
One hour would cost $30 and every hour after is $5 more so B is the correct answer.
Help plz need answers less than 10 minutes
Answer:
the answer wouldbe 8585434930.123
Step-by-step explanation:
A house has increased in value by 35% since it was purchased. If the current value is 648,000, what was the value when it was purchased?
Answer:
Purchase rate of the house is $480000.
Step-by-step explanation:
Let the purchase rate of the house = $p
Current value of the house = $648000
If the current rate of the house has increased by 35% of the purchase rate,
Current rate = Purchase rate + 35% of the purchase rate
648000 = p + (35% of p)
648000 = p + [tex]p\times \frac{35}{100}[/tex]
648000 = p + 0.35p
648000 = (1.35)p
p = [tex]\frac{648000}{1.35}[/tex]
p = $480000
Therefore, purchase rate of the house is $480000.
Find the area of each sector. Use exact answers
Answer:
B) 54π in²
Step-by-step explanation:
area of full circle = πr² = 81π in²
area of 4π/3 segment = (81)(4π/3)/2π = 54π in²