Type the correct answer in each box. Use numerals instead of words.
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
Answers
The equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation of the parabola is y = 2 · x · (x - 4).
What is the equation of the parabola seen in a graph?
Herein we find a representation of a quadratic function on a Cartesian plane, whose formula in vertex form is presented below:
y - k = C · (x - h)²
Where:
(h, k) - Vertex of the parabola.C - Vertex constantBy direct inspection we find that the equation of the parabola has a vertex at (h, k) = (2, - 8) and the point (x, y) = (4, 0). Then, the vertex constant is:
C = (y - k) / (x - h)²
C = (0 + 8) / (4 - 2)²
C = 8 / 4
C = 2
Then, the equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation is determined by algebra:
y + 8 = 2 · (x - 2)²
y = 2 · (x - 2)² - 8
y = 2 · (x² - 4 · x + 4) - 8
y = 2 · x² - 8 · x + 8 - 8
y = 2 · x² - 8 · x
y = 2 · x · (x - 4)
The factored form of the equation of the parabola is y = 2 · x · (x - 4).
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Related Questions
25 points plus brainliest
Answers
Answer:
x = -7
Let the first integer be x.
Given the next two integers are consecutive, it would be: x+1, x+2
The problem states: "4 more than the smaller number plus twice the 3rd number is 7 less than the 2nd number."
Translating English to Algebra, you'll get:
(x + 4) + 2(x + 2) + 7 = x + 1
x + 4 + 2x + 4 + 7 = x + 1
3x + 15 = x + 1
2x = -14
x = -7
That would be the third option.
in a bowl containing 10 marbles, 5 are blue and 5 are pink. if 2 marbles are picked randomly, what is the probability that the 2 marbles will not both be pink?
Answers
Answer:from least to greatest:
1) g (x)
2) f (x)
3) h (x)
Step-by-step explanation:
Answer:
For f (x):
f (x) = (x + 3) ^ 2 - 2
For x = -1
f (-1) = (-1 + 3) ^ 2 - 2
f (-1) = (2) ^ 2 - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f (3) = (3 + 3) ^ 2 - 2
f (3) = (6) ^ 2 - 2
f (3) = 36 - 2
f (3) = 34
AVR = ((34) - (2)) / ((3) - (- 1))
AVR = 8
For g (x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g (x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2
For h (x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12
Step-by-step explanation:
What’s the answer to 4x(x+3) < -24
Answers
The answer to the inequality is expressed as x< 1 and x< -4
What are inequalities?Inequalities are mathematical expressions having both sides unequal or rather not equivalent to each other.
Given the inequality;
4x (x+3) < -24
First, expand the bracket
4x² + 12x < - 24
Let's turn to quadratic inequality
4x² + 12x - 24 < 0
Factorize further
4 ( x² + 3x - 4) < 0
4 ( x² + 4x - x - 4) < 0
4 ( x(x + 4) - 1 (x + 4) ) < 0
4(x - 1) ( x + 4) < 0
expand the bracket
4x - 4 < 0
x < 1
And
4x + 16 < 0
x < -4
Thus, the answer to the inequality is expressed as x< 1 and x< -4
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I’m not really sure what to do
Answers
Check out the attached photo
Determine the values of x in the equation x2 = 64.
x = ±32
x = 32
x = ±8
x = −8
Answers
Answer:
32 or +-8 depending on question
Step-by-step explanation:
If question is 2x = 64, then x= 32
If question is x^2 = 64, then x= +-8
Reorganize os termos
2x=64
Divida ambos os membros
Solução
x=32
Please help with problem 19
Algebra 1
Answers
The expression for r is n(4t-v) and the expression for the width is (P-2l)/2
Subject of formulaThis is a way of representing a variable with another variable.
Given the expression below:
r/n + t = 4v
Making r the subject
r/n = 4v - t
r =. n(4t-v)
Hence the expression for r is n(4t-v)
For the expression
P = 2l + 2w
P - 2l = 2w
2w = P - 2l
w = (P-2l)/2
Hence the expression for the width is (P-2l)/2
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How are postulates and theorems related?
Answers
Answer:
A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven
Step-by-step explanation:
Answer:
Theorems and postulates are statements of geometrical truth.
Explanation:
We create theorems based on postulates.
Postulates are the mathematical statements we assume to be true without any proof while theorems are mathematical statements we can or must prove as true.
--------------------
Hope this helps!
Have a great day and God bless! :)
The answersssssssssss
Answers
Answer:
pic 1 goes first second pic second slot
Step-by-step explanation:
what is the sum of 5x and 9x
Answers
Answer:
14x
Step-by-step explanation:
We just add the bases because they have the same variable terms, (they are like terms)
9 + 5 = 14
14x
For the function f(x) = -(x + 1)² + 4, identify the vertex, domain, and range.
Answers
Answer:
Vertex: (-1, 4)
Domain: All Real Numbers
Range: y < or equal to 4
Step-by-step explanation:
Vertex: Using my calculator, i determined the vertex. The vertex is the most bottom/top point of the parabola, depending on if it opens down or up.
Domain: All the answers have all real numbers so its obvious.
Range: the parabola opens down at (-1, 4), so all the numbers on the y axis below 4 fit in with the line
1. Jenny went bowling. She paid $2.75 to rent bowling shoes and she paid $4.25 for each game. If Jenny paid a total of $24, how many games did she bowl?
2. Mark and Gary had a basketball game Saturday. Mark had three times as many rebounds as Gary. If together they had 28 rebounds, how many rebounds did Gary have?
3. If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the width of the rectangle?
4. Mark and Gary had a basketball game Saturday. Mark had three times as many rebounds as Gary. If together they had 28 rebounds, how many rebounds did Mark have?
5. Tony spent a total of 140 minutes studying for his Algebra test. This total was 5 more than 3 times the amount of minutes he spent studying for his Biology test. How many minutes did Tony spend studying for his Biology test?
6. If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the length of the rectangle?
Group of answer choices
7. A transportation company charges a fee of $125 plus $50 per hour to rent a limousine. If John paid $425 for a limousine, for how many hours did he rent the limousine?
8. The sum of two numbers is 37. One of the numbers is 15 more than the other number. What are the two numbers?
9. Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra. How old is Pamela now?
10. Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra. How old is Debra now?
(Easy way to gain points)
Please show your work :)
Answers
Using equations, the solutions for the problems are given as follows:
1. She played 5 games.
2. Gary had 7 rebounds.
3. The width of the rectangle is of 38 inches.
4. Mark had 21 rebounds.
5. Tony spent 45 minutes studying for his Biology test.
6. The length of the rectangle is of 72 inches.
7. He rented the limousine for 6 hours.
8. The two numbers are 11 and 26.
9. Pamela is 8 years old.
10. Debra is 1 year old now.
What is the solution for item 1?The situation is modeled by the following linear function:
P(n) = 2.75 + 4.25n.
We have that P(n) = 24, hence we have to solve for n.
24 = 2.75 + 4.25n.
n = (24 - 2.75)/4.25
n = 5.
She played 5 games.
What is the solution for item 2?The situation is modeled by the following system of equations:
x = 3y.x + y = 28.Hence:
3y + y = 28
4y = 28
y = 7.
Gary had 7 rebounds.
What is the solution for item 3?Considering the equations for the perimeter of the triangle, and the situation described, we have that:
l = 2w - 4.2(l + w) = 220.Hence:
2(2w - 4 + w) = 220
2(3w - 4) = 220
3w - 4 = 110
3w = 114
w = 114/3
w = 38.
The width of the rectangle is of 38 inches.
What is the solution for item 4?Solution x for item 2, hence:
x = 3y = 3 x 7 = 21.
Mark had 21 rebounds.
What is the solution for item 5?This situation is modeled by the following equation:
3x + 5 = 140
3x = 135
x = 135/3
x = 45.
Tony spent 45 minutes studying for his Biology test.
What is the solution for item 6?This is the solution for l of item 3, hence:
l = 2w - 4 = 2 x 38 - 4 = 72.
The length of the rectangle is of 72 inches.
What is the solution for item 7?The situation is modeled by the following equation:
P(x) = 125 + 50x.
We have that P(x) = 425, hence we solve for x as follows:
425 = 125 + 50x
50x = 300
x = 300/50
x = 6.
He rented the limousine for 6 hours.
What is the solution for item 8?The situation is modeled by the following system:
x + y = 37.x = 15 + y.Hence:
15 + y + y = 37
2y = 22
y = 11.
x = 15 + 11 = 26.
The two numbers are 11 and 26.
What is the solution for item 9?The situation is modeled by the following system:
y = x - 7.x + 6 = 2(y + 6).Hence:
x + 6 = 2(x - 7 + 6)
x + 6 = 2(x - 1)
x + 6 = 2x - 2
x = 8.
Pamela is 8 years old.
What is the solution for item 10?This is the solution for y of the previous item, hence:
y = x - 7 = 8 - 7 = 1.
Debra is 1 year old now.
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In a class of 36 students for every four students who could only speak one language, five students could speak more than one language. How many students in the class can speak more than one language?
Answers
7 students in the class can speak more than one language.
Given that,
Total student = 36
For every four students who could only speak one language
For every five students who could only speak one language.
To determine how many students in the class can speak more than one language.
Since,
For every five students who could only speak one language,
= 36 / 5
quotient = 7 ; remainder = 1
Implies that, 7 students in the class can speak more than one language.
Thus, 7 students in the class can speak more than one language.
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For Brianna's lemonade recipe, 2 lemons are required to make 4 cups of lemonade. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answers
Using a proportional relationship, it is found that:
1 lemon is required for 2 cups.6 cups are required for 3 lemons.The graph for this relationship is given at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For this problem, we have that the variables are:
x: number of lemons.y: number of cups.Hence the proportional relationship between these two variables is given by:
y = 2x.
Then:
1 lemon is required for 2 cups. (y = 2, then x = 1).6 cups are required for 3 lemons. (x = 3, then y = 6).The linear graph of the relationship, considering the given points, is given at the end of the answer.
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A food manufacturer donates money to schools based on the number of
its product labels the school collects. The students at one school collected
2,100 product labels in three months. The number of labels collected in the
first two months was three times the number of labels collected in the thirc
month. How many product labels were collected in the third month?
Answers
The total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.
Let the number of labels collected in the first two months be 3 x.
We are given that the number of labels collected in the first two months was three times the number of labels collected in the third month.
So, the number of labels collected in the third month = 3 x / 3 = x
Now, we are also given that:
The total number of labels collected by the students at the school = 2100.
So, we get the equation as:
3 x + x = 2100
4 x = 2100
x = 2100 / 4
x = 525 labels.
Therefore, we get that, the total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.
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anna bought 8 tetras and 2 rainbow fish for her aquarium. the rainbow fish cost $6 more than the tetras. she paid a total of $37.
Answers
Answer-
The cost of one tetra is $2.5 and one rainbow fish is $8.5
Explanation
Let the cost one tetra be 'x';
Cost of rainbow fish = x + 6;
According to question;
8x + 2(x + 6) = 37;
10x = 25
x = $2.5;
the amount or equivalent paid or charged for something : price
The average cost of a university training has gone up dramatically.
the outlay or expenditure (as of attempt or sacrifice) made to acquire an item
He executed repute, but at the fee of dropping numerous buddies.
loss or penalty incurred specially in gaining some thing
the price of lives during war
three
costs plural : charges incurred in a judicial process
particularly : those given by the law or the courtroom to the triumphing party in opposition to the dropping birthday party
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Graph the line y=−15x on the coordinate plane.
Answers
Answer:
The graph is provided in the image
What is x if f(x) = -2
Answers
in that function x would be -2
Find the product of √6 x √12
pls help for brianlest
Answers
The product of √6 and √12 is option b 6√2.
Given,
Two square roots : √6 and √12
We have to find the product of these square roots:
That is,
√6 × √12
Multiplying square roots:
Multiply the two numbers as usual without considering the square root.After multiplying consider the square root of the product.It will be the product of the square roots.So here,
Multiply the numbers,
√6 × √12 = 6 × 12 = 72
Now consider the square root of 72
√72 = √36 × √2 = 6√2
That is, the product of the square roots √6 and √12 is 6√2
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4x1+6-9x3-6; answer 7
Add Brackets Or Parentheses to solve
Answers
Answer:
-23
Step-by-step explanation:
Remember Bedmas/Pedmas
P/B = Bractets or parentheses ( )
E = Exponents 3⁵
D = Division ÷
M = Multiply ×
A = Addition
S = Subtract
(4x1)+6-9x3-6
4+6-(9×3)-6
(4+6)-27-6
(10-27)-6
-17-6
-23
I WILL GIVE BRAINLIEST!!!
Please help me.
Translate all word problems into equations.
You only need to give equation+answer for number 7 and 9.
7. Between noon and midnight, the temperature
dropped 20°F. If the temperature was -8°F at
midnight, what was the temperature at noon?
8. If a strawberry pie is divided into 6 equal slices, each
slice has 240 calories. How many calories are in the
whole pie?
9. A chest was resting on the ocean floor 1000 ft below
the surface. It was lifted to the deck of a ship 8 ft
above the surface. How far was the chest lifted?
10. When all the kids who tried out for Little League
were divided into teams of 20 players, there were
exactly 8 teams. How many kids tried out?
Answers
Number 7:
-8=x-20
-8+20=x
12=x
Please help I’m struggling!!
Answers
Answer:
5
2
8
4
6
1
3
7
Step-by-step explanation:
set up the equation relating the new ratio of broth to solution to the new percentage of broth to solution. 25/60
Answers
The new percentage of broth to solution 25/60 is 41.67
Broth, also known as bouillon is a savory liquid made of water in which meat, fish or vegetables have been simmered for a short period of time .It can be eaten alone, but it is most commonly used to prepare other dishes, such as soups.
Commercially prepared liquid broths are available, typically chicken, beef, fish, and vegetable varieties. Dehydrated broth in the form of bouillon cubes were commercialized beginning in the early 20th century.
Broths have been used as a nutrition source for the sick in Great Britain since at least the early 1700s, such as for dysentery patients
Let,
60 represents the 100% of the broth to solution
25 represents the x percentage of the broth to solution
Now,
Solving for the 25 which represents the x percentage of the broth to solution.
25/100 = x/100*
25/60 = x/100*x
25(100) = 60x
x = 2500/60
x = 41.67
Therefore,
25 represents the 41.67 percentage of the broth to solution.
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Answer:
a) 25/60=x/100
Step-by-step explanation:
In the diagram, what is the ratio of patterned circles to plain circles?
Four arrays of circles are represented. First array has a plain circle. Second array has 4 patterned circles and 1 plain circle. Third array has 1 patterned circle and 4 plain circles. Fourth array has a plain circle.
Answers
The ratio of the patterned circles to plain circles is 6 : 7.
We are given the four arrays of the circles.
In the first array, we have only 1 plain circle.
In the second array, we have 4 patterned circles and 1 plain circle.
In the third array, we have 1 patterned circle and 4 plain circles.
In the fourth array, we have only 1 plain circle.
So, total patterned circles = 5 + 1
Total patterned circles = 6
Total plain circles = 1 + 1 + 4 + 1
Total plain circles = 7
Ratio of patterned circles to plain circles will be given as:
6 : 7
Therefore, we get that, ratio of the patterned circles to plain circles is 6 : 7.
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34. THOUGHT PROVOKING
A runner's times (in minutes) in the four races
he has completed are 25.5, 24.3, 24.8, and 23.5.
The runner plans to run at least two more races
and wants to have an average time of less
than 24 minutes. Write and solve an inequality
to show how the runner can achieve his goal.
Answers
Answer:
Step-by-step explanation: I'm not sure it's an interesting question I hope you figure it out soon(:
Answer: x<45.9?
Step-by-step explanation:
25.5+24.3+24.8+23.5=98.1
So (x+98.1)/6<24?
x<45.9?
Here are the first four terms of a quadratic sequence
3 10 21 36
Work out an expression for the nth term
Please please answers this question ill give u like and mark as brainlist
Answers
Answer:
2n² + n
Step-by-step explanation:
Given sequence:
3, 10, 21, 36, ...
Work out the first differences between terms:
[tex]3 \underset{+7}{\longrightarrow} 10 \underset{+11}{\longrightarrow} 21 \underset{+15}{\longrightarrow} 36[/tex]
As the first differences are not the same, work out the second differences.
[tex]7 \underset{+4}{\longrightarrow} 11 \underset{+4}{\longrightarrow} 15[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of n² is always half of the second difference. Therefore, as the second difference is 4, the coefficient of n² is 2.
To work out the nth term of the sequence, write out the numbers in the sequence 2n² and compare with the given sequence:
[tex]\begin{array}{|l|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4 \\\cline{1-5} 2n^2 & 2 & 8 & 18 & 32\\\cline{1-5} \sf Operation & +1 & +2& +3& +4\\\cline{1-5} \sf Sequence & 3 & 10 & 21 & 36\\\cline{1-5}\end{array}[/tex]
Therefore, we need to add n to 2n² to match the sequence.
Therefore, the nth term of this sequence is 2n² + n.
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After watching baking shows on T.V., Latrell signs up for a cake-decorating class. To practice
his new skills, he decorates a batch of cupcakes with sugar flowers. Latrell puts 4 sugar
flowers on each cupcake. In all, Latrell puts 32 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Latrell decorates?
Answers
assignment means participants have an equal chance of being in the control group or in the experimental group. blind double-blind random nonbiased
Answers
Random assignment means participants have an equal chance of being in the control group or in the experimental group.
Assignment refers to putting people into experimental or control group. In this, the Random assignment involves dividing the participants into two groups through randomization. That is, selection is on random. Tis method provides equal chance for the participants to be in the experimental or control group.
This kind of assignment will be unbiased and the participants in two groups does not differ in any way. So random assignment makes the experiment and control group equivalent. Also this makes the experimental study more accurate, acceptable and scientific too.
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find the equivalent fractionsss with large denominatorsss
Answers
Answer: 27/45
Step-by-step explanation:
[tex]\displaystyle\\\frac{3}{5} =\\\\\frac{3}{5}*1=\\\\ \frac{3}{5}*\frac{9}{9} =\\\\\frac{3*9}{5*9}= \\\\\frac{27}{45}[/tex]
m∠K=(6x+12)°. Find the measure of the complement of ∠K.
A. (102 + 6x)°
B. (112 + 6x)°
C. (67 − 6x)°
D. (78 − 6x)°
Answers
The measure of the complement of angle K is (78 - 6x)°. The correct option is D. (78 − 6x)°
Complement of an AngleFrom the question, we are to determine the complement of the given angle measure
From the given information, the measure of angle K (m ∠K) is (6x + 12)°
NOTE: If two angles are complementary, the measures of the angles sum up to 90°
Let the complement of angle K be angle L.
Thus,
∠K + ∠L = 90°
(6x + 12)° + ∠L = 90°
6x° + 12° + ∠L = 90°
∠L = 90° - 12° - 6x°
∠L = 78° - 6x°
∠L = (78 - 6x)°
Hence, the measure of the complement of angle K is (78 - 6x)°. The correct option is D. (78 − 6x)°
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Find the surface area of the figure.
6 in.
6 in.
6 in.
SA = [?]in.²
Hint: Area of Triangle = b•h
Answers
A 0.5 x 6 x 6
Answer is 18