G( x )= a(x^2)+bx+cConvert it to vertex form (also known as standard form) by putting the values for a,h and k into the correct boxes.G(x)=a(x-h)^2+kIdentify the vertex(x,y)General form: G( x )=-7 x^2+-9 x +-4 Vertex form: G( x )= Answer for part 1 and coordinate 1 (x- Answer for part 1 and coordinate 2 )^2 +Answer for part 1 and coordinate 3Vertex: (Answer for part 2 and coordinate 1,Answer for part 2 and coordinate 2)
Answers
The vertex form of G(x) is
\(G(x)=-7(x-\frac{9}{2})^2-\frac{583}{4}\)\(\text{Vertex}=(\frac{9}{2},-\frac{583}{4})\)STEP - BY - STEP EXPLANATION
What to find?
Vertex form of the given equation.
Given:
G(x) = - 7x² + -9x + -4
We can re-write the above as:
G(x) = -7x² - 9x - 4
To write the above in a vertes form, we wil follow the steps below:
Step 1
Insert a parenthesis before x² and after 9x.
G(x) = -7(x²-9x) - 4
Step 2
Add/subtract the square half of the co-efficient of x.
That is; half square of -9 = (-9/2)² = 81/4
So that we have:
G(x) = -7(x² - 9x + 81/4) -7(81/4) - 4
Step 3
Simplify
\(\begin{gathered} G(x)=-7(x^2-9x+\frac{81}{4})-7(\frac{81}{4})-4 \\ \\ =-7(x^2-9x+\frac{81}{4})-\frac{567}{4}-4 \\ \\ =-7(x^2-9x+\frac{81}{4})-\frac{567-16}{4} \\ \\ =-7(x^2-9x+\frac{81}{4})-\frac{583}{4} \end{gathered}\)Step 4
Factorize the expression in the parenthesis.
\(G(x)=-7(x-\frac{9}{2})^2-\frac{583}{4}\)Hence, the vertex form is G(x) = -7(x- 9/2)² + -583/4
The vertex
Given the general formula y=a(x-h)² + + k
The vertex is (h, k).
Comparring the general form to our answer in step 4. Observe that h=9/2 and k=-583/4
Therefore, the vertex is ( 9/2 , -583/4)
Related Questions
The Unit Circle
In a unit circle, the sine of the angle is represented by the vertical leg of the triangle. What is represented by the horizontal leg of the triangle?
a. cosecant of the angle
b. tangent of the angle
c. cosine of the angle
d. cotangent of the angle
Please select the best answer from the choices provided
Answers
Answer:
c. cosine of the angle
Step-by-step explanation:
Cos = adj/hyp
in unit circle
cos = x/1
cos = x
x is the horizontal leg
Answer:
C. Cosine of the angle
Step-by-step explanation:
I calculated it logically
evaluate 10 + 8÷4 - 12
Answers
Answer:
0
Step-by-step explanation:
evaluate 10 + (8÷4) - 12
Answer:
0
Step-by-step explanation:
First of all we need to divide then add then only subtract
Solve the equation. Please help
Answers
\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)
Step 1: Add 3/4 on both sides
We get
2y/3 = 1/12+3/4
We add fractions by calculating a common denominator, adjusting the numerators accordingly and adding them. See this in action below:
12 and 4 have a common multiple in 12 which will be our common denominator. Now, 1/12 does not need to be adjusted, but 3/4 becomes 3*3 / 3*4 = 9/12.
In total 1/12 + 9/12 = 10/12
So, we have 2y/3 = 10/12
Now we multiply both sides by 3, so that the 3 will cancel out the 3 in the denominator on the left side:
2y =30/12
Now we just need to divide by 2 and get the solution:
y = 15/12 = 3*5 / 3*4 = 5/4
Therefore the final answer is A:
The solution set is {5/4}
EXER 1. Evaluate the following (a) 28-{15 (3+2)
Answers
The value of the expression 28 - {15 (3+2)} is -47.
To evaluate the expression 28 - {15 (3+2)}, we need to follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's break down the expression step by step:
First, we solve the expression inside the parentheses:
3 + 2 = 5
Now, we substitute the result back into the original expression:
28 - {15 * 5}
Next, we perform the multiplication:
15 * 5 = 75
Now, we substitute the result back into the expression:
28 - 75
Finally, we perform the subtraction:
28 - 75 = -47
Therefore, the value of the expression 28 - {15 (3+2)} is -47.
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A real estate office manages an apartment complex with 40 units. When the rent is $780 per month, all 40 units are occupied. However, when the rent is $824, the average number of occupied units drops to 36. Assume that the relationship between the monthly rent p and the demand x is linear. (Note: the term demand refers to the number of occupied units.)(a) Write a linear equation giving the demand x in terms of the rent p.x (p) = (b) Use a graphing utility to graph the demand equation and use the trace feature to predict the number of units occupied if the rent is raised to $835.units(c) Predict the number of units occupied if the rent is lowered to $802. Verify graphically.units
Answers
a) A linear equation giving the demand x is x = -4/44 (p) + 820.
b) The number of units occupied if the rent is raised to $835 is 36.125 units.
c) To predict the number of units occupied if the rent is lowered to $802 is 38 units.
For a, The linear equation for demand x in terms of rent p is given by x = m(p) + b, where m is the slope of the demand function and b is the y-intercept. Using the information given in the problem, we can write two linear equations based on the known values of x and p:
x = 40, p = 780
x = 36, p = 824
Solving for m and b, we have:
m = (-4) / (824 - 780) = -4/44
b = 40 - m * 780 = 40 + 4 * 195 = 40 + 780 = 820
Thus, the demand equation is x = -4/44 (p) + 820.
For b, To predict the number of units occupied if the rent is raised to $835, we can substitute this value into the demand equation:
x = -4/44 (835) + 820 = 36.125 units
For c, To predict the number of units occupied if the rent is lowered to $802, we can again substitute this value into the demand equation:
x = -4/44 (802) + 820 = 38 units.
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If 5 is increased to 9, the increase is what percentage of the original number
Answers
Answer: It's a 80% increase
Step-by-step explanation:
h(n)=2/n -2 solve inverse function
Answers
Answer:
2/n+2
Step-by-step explanation:
A group of 70 people is going on a boat tour. If each boat holds 26 people, how many people will be on the last boat?
Answers
Answer:
18
Step-by-step explanation:
Suppose Nancy has 15 sorts of colors black, red, and of wschure black and were
What is the probability
randomly selected stw be blue
Answers
Answer:
Hi there here is the answer!
Step-by-step explanation:
Out of the 3 main chioces there is a total of 15!
so, it would be a probability of 5/15. or 1/3 / 1:3
A grocer can buy strawberries for $1.38 per pound.
1. How much would they pay to buy 25 lbs of strawberries?
Answers
Answer:
$34.5
Step-by-step explanation:
1.38 * 25 = 34.5
Answer:
The answer is $34.5.
Step-by-step explanation:
$1.38 x 25 = $34.5.
Suppose that, as reported by the Centers for Disease Control, about 18% of high school students smoke tobacco. You randomly select 120 high school students to survey them on their attitudes toward scenes of smoking in the movies. a) What's the expected number of smokers? b) What's the standard deviation of the number of smokers?
Answers
a) the expected number of smokers is 21.6, and
b) the standard deviation of the number of smokers is approximately 4.21.
a) To find the expected number of smokers, you need to multiply the probability of a student being a smoker (18% or
0.18) by the number of students surveyed (120). So, the expected number of smokers is:
Expected number of smokers = 0.18 × 120 = 21.6
b) To find the standard deviation of the number of smokers, you can use the formula for the standard deviation of a
binomial distribution, which is:
Standard deviation = √(n × p × (1 - p))
where n is the number of students surveyed, p is the probability of a student being a smoker, and (1 - p) is the
probability of a student not being a smoker. Plug in the values:
Standard deviation = √(120 × 0.18 × (1 - 0.18)) = √(120 × 0.18 × 0.82) ≈ 4.21
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In 2016, a school started its own aquarium with x fish. In 2019, there were x3 fish in the same aquarium. There were 512 fish in 2019. How many fish were there in 2016? Show your work.
Answers
Answer:
Step-by-step explanation:
We are given that in 2016, the aquarium had x fish, and in 2019, there were x3 fish. We also know that in 2019, there were 512 fish. So we can set up the equation:
x3 = 512
To solve for x, we need to take the cube root of both sides of the equation:
x = ∛512
Using a calculator or simplifying by prime factorization, we can find that:
512 = 2^9
So,
∛512 = ∛2^9 = 2^3 = 8
Therefore, there were 8 fish in the aquarium in 2016.
Answer:
Let's use algebra to solve the problem. We can start by using the information given to set up an equation relating the number of fish in 2016 (x) to the number of fish in 2019 (x3):
x3 = 512
To solve for x, we can isolate x by dividing both sides of the equation by 3:
x = 512/3
x = 170.67 (rounded to two decimal places)
Therefore, there were approximately 170.67 fish in the aquarium in 2016. However, since we cannot have a fraction of a fish, we can round up to the nearest whole number to get the final answer:
x ≈ 171
So there were 171 fish in the aquarium in 2016.
Step-by-step explanation:
Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answers
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.
In figure below points T,R,X,Y and Z
Answers
Answer:
a
Step-by-step explanation:
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
Answers
The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
m represents the slope.c represents the y-intercept.x and y are the data points.What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Based on the information provided regarding the equations and graphs, the y-intercept are as follows:
The y-intercept of y = 4x + 5 is equal to 5.The y-intercept of this graph with point (0, 4) is 4.Read more on y-intercept here: brainly.com/question/19576596
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ILL MARK AS BRAINLIEST!! PLEASE HELP FAST!!
Answers
Answer:
neither
Step-by-step explanation:
Solve: –3x – 7 < 11
Α) α
X > -2
B
2 <
2
С
x < -2
D
2 > -6
Answers
Answer:
Step-by-step explanation:
Here you go mate
Step 1
-3x-7<11 Equation/Question
Step 2
-3x-7<11 Simplify
-3x-7<11
Step 3
-3x-7<11 Add
-3x<18
Step 4
-3x<18 Divide by 3
answer
x>-6
Hope this helps
PLEASE PLEASE PLEASE HELP!
use the distributive property to express the sum 24 + 30 with a common factor multiplied by a sum of two whole numbers with no common factor
Answers
Answer:
6(4+5)
Step-by-step explanation:
I can't figure it out it keeps telling me it's wrong
Answers
The answer of the given question based on to determine the constant of proportionality equation for the given table is, the correct answer is (a) y = 1/4x.
What is Constant of proportionality?The constant of proportionality, also known as the proportionality constant, is a value that relates two variables that are directly proportional to each other.
When two variables, x and y, are directly proportional to each other, it means that as x increases or decreases, y also increases or decreases in proportion to x. This relationship can be expressed mathematically as:y = kx
where k is the constant of proportionality that relates the two variables.
The value of the constant of proportionality is found by dividing any value of y by the corresponding value of x for a given set of data. In other words, k is the ratio of y to x for any pair of corresponding values of the two variables.
To determine the constant of proportionality equation for the given table, we can check the ratio of y to x for each pair of corresponding values:
y/x = 2/8 = 1/4
y/x = 3/12 = 1/4
y/x = 5/20 = 1/4
y/x = 6/24 = 1/4
Since the ratio of y to x is the same for all pairs of corresponding values, we can conclude that the equation is proportional and the constant of proportionality is 1/4.
Therefore, the equation that represents the given table is:
y = 1/4x
So, the correct answer is (a) y = 1/4x.
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What is the meaning of "\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\)"?
![What is the meaning of "[tex] \mathbb{N}=\bigcap \left \{X:X inductive \right \}[/tex]"?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/MNBWazTJH6rrqRMGv9XGZlF09a3XoahD.png)
Answers
The meaning of \(\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\) is that the set of natural numbers is the intersection of all inductive sets.
What does the set show ?The set of natural numbers is inductive because it satisfies both of these conditions. The set is non-empty because it contains the number 1. And if x is a natural number, then x+1 is also a natural number.
In other words, a set is inductive if it satisfies the following two conditions:
The set is non-empty.If x is an element of the set, then x+1 is also an element of the set.The concept of an inductive set is important in mathematics because it allows us to define the set of natural numbers.
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What is -20/2(7 2/3)
Answers
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
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Do the ratios 3 4 and 7 8 form a proportion?
no
Answers
No, the ratios are not proportional because they are not equivalent.
We are given a table which has the values of the "x" column and the corresponding "y" column.The values in the "x" column are 3 and 7.The values in the "y" column are 4 and 8.The ratio of the first corresponding values in each column is 3/4 = 0.75.The ratio of the second corresponding values in each column is 7/8 = 0.875.The ratios for all the corresponding values in the table are not equivalent.Hence, they are not proportional because the ratios are not equivalent to a single value.To learn more about ratio, visit :
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Help me with this plz
Answers
Answer:
Take the square root of both sides
A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
12
Blue
17
Green 17
Yellow 12
Purple 17
If the spinner is spun 500 more times, about how many times would you expect to
land on blue? Round your answer to the nearest whole number,
Answers
(3×10 – 4)(2×1010) whats the scientific notion
Answers
The result of the multiplication in scientific notation is given by:
\(6 \times 10^{6}\)
What is scientific notation?A number in scientific notation is given by:
\(a \times 10^b\)
With the base being \(a \in [1, 10)\).
When we multiply two numbers in scientific notation, we multiply the bases and add the exponents.
For this problem, the numbers are given by:
\(3 \times 10^{-4}, 2 \times 10^{10}\)
The result of the multiplication is given by:
\(3 \times 10^{-4} \times 2 \times 10^{10} = 6 \times 10^{-4 + 10} = 6 \times 10^{6}\)
The result of the multiplication in scientific notation is given by:
\(6 \times 10^{6}\)
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In the figure below, please awnser the question
Answers
Answer:
76
Step-by-step explanation:
Angle bisectors split angles into two. So, angle BAD must be twice of BAC.
Substituting, we get 38*2=76
how does the NBA draft work?
Answers
The NBA draft is an important event for teams to improve their roster and build for the future.
Explaining the NBA draftThe NBA draft is an annual event where the teams in the National Basketball Association (NBA) select new players to join their team.
The order in which the teams select players is determined by a lottery, with the worst-performing teams from the previous season having a higher chance of getting a higher draft pick.
The draft consists of two rounds, with each team having one pick per round.
Teams can also trade their draft picks with other teams before or during the draft. The selected players are then signed to a contract and can begin playing for their new team in the upcoming NBA season.
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if 2/5 of my money =60 what is 1/5 of my money
Answers
Answer:
1/5 of your money is = 30
Step-by-step explanation:
2/5 of your money is equal to 60, so if you divide 60 by 2 you will get 30, which is 1/5 of your money. A way to check if it is right is by multiplying 30 by 5, which is 150, and divide it by 5, to see if it matches (150 : 5 = 30).
hope this helps!
answer:30
explanation:
2/5×X=60
X=150
means your money is 150
so 1/5 of your money is 1/5×150=30
3/5 * 5/7 / 3/14 - 2/5
Answers
Answer:
3/5*5/7*14/3-2/5
8/5...
FINANCE Yetunde is purchasing a refrigerator, which costs $950. The store has a finance option: pay 10% now, and pay the remaining balance
in one year, with a 5% annual simple interest rate applied to the remaining balance.
How much will she pay up front if she uses the finance option? $
How much interest will she pay at the end of one year? $
What is the total cost of the refrigerator after using the one-year finance option? $
What is the total cost of the refrigerator if she pays the balance and interest at 6 months? $
S
Answers
1. The amount that Yetunde will pay upfront if she uses the finance option is $95.
2. The interest she will pay at the end of one year is $42.75.
3. The total refrigerator cost after using the one-year finance option is $992.75.
4. The total cost of the refrigerator if she pays the balance and interest at 6 months is $971.375.
What is a finance charge?A finance charge is the interest cost added to the amount borrowed or used for credit purchases.
Cost of the refrigerator = $950
Finance Option: Initial deposit = 10% = $95 ($950 x 10%)
Balance to be financed = $855 ($950 - $95)
Simple Interest rate = 5%
Simple interest amount = $42.75 ($855 x 5%)
The total cost with finance option is $992.75 ($950 + $42.75)
Simple interest amount at 6 months = $21.375 ($42.75/2)
The total cost at 6 months = $971.375 ($950 + $21.375)
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