The graphs below have the same shape. What is the equation of the blue
graph?
f(x) = x²
g(x) = ?
A. g(x) = (x - 3)2 + 1
B. g(x) = (x + 3)2 + 1
C. g(x) = (x - 3)2 - 1
O D. g(x) = (x + 3)2 - 1
The correct answer is A. g(x)=(x-3)^2+1
The equation of the blue graph is g(x) = (x - 3)² + 1.
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Since the graphs of f(x) and g(x) intersect at (1.5, 2.5), we can substitute these values into the equations and solve for the constant term:
f(1.5) = g(1.5)
1.5² = g(1.5)
2.25 = g(1.5)
Therefore, we know that the vertex of g(x) is (1.5, 2.25).
Also, since the graphs have the same shape, we know that the vertex of g(x) is obtained by shifting the vertex of f(x) horizontally by the same amount, which is 3 units to the right.
So, the equation of the blue graph can be obtained by replacing x with (x-3) in the equation of the green graph:
g(x) = (x - 3)² + 1
Expanding this equation, we get:
g(x) = x² - 6x + 9 + 1
g(x) = x² - 6x + 10
g(x) = x² - 2 x 3x + 9 + 1
g(x) = (x - 3)² + 1
Therefore,
The equation of the blue graph is g(x) = (x - 3)² + 1.
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Write the equation of the line fully simplified slope-intercept form.
Answer:
y = 1/3x - 1
Step-by-step explanation:
Decide which estimate is closer to the actual answer. Explain your reasoning as store bought 25lb of produce if store spent $110.90 about how much does the produce cost per pound in dollars? 0.04,0.4,4,40 (b) a 6 pack of juice boxes contains 54.6 oz of juice in total about how many ounces of juice does each juice box contain ? 0.9,9,90,900 (c) in 20 L of air there is about 0.42 L of carbon dioxide about how many liters of carbon dioxide are there in 1 L of air 0.02,0.2,2,20
In the first week of January, there are 49 dogs and 28 cats in an animal shelter. Throughout the month, the ratio of dogs to cats remains the same. In the last week of January, there are 20 cats in the shelter. How many dogs are there?
Answer:
35 dogs
Step-by-step explanation:
Given
[tex]49\ dogs: 28\ cats[/tex]
Required
Determine the number of dogs for 20 cats
Represent the required number of dogs as a ratio of number of cats
[tex]x : 20\ cats[/tex]
So, we have:
[tex]49\ dogs: 28\ cats[/tex]
[tex]x : 20\ cats[/tex]
Since, the ratio is the same throughout, we have:
[tex]x : 20\ cats[/tex] = [tex]49\ dogs: 28\ cats[/tex]
Convert ratio to fraction
[tex]\frac{x}{20} = \frac{49}{28}[/tex]
[tex]\frac{x}{20} = \frac{7}{4}[/tex]
Multiply through by 20
[tex]x = \frac{7}{4} * 20[/tex]
[tex]x = 7 * 5[/tex]
[tex]x = 35[/tex]
Maggie made the following quilt from 64 square pieces of fabric. 7.52 ft What is the side length of each square piece of fabric? Enter your answer in the box. feet
Answer:
Step-by-step explanation:
Maggie made the following quilt from 64 square pieces of fabric, what is the side length of each square piece
Which expression is equivalent to 4.4.4.4.4.4.4.4?
Answer:
your answer is D
Step-by-step explanation:
hope this helps
HELP ME IF YOU KNOW ;((
Answer:
1.5
Step-by-step explanation:
Your answer is 1.5 have a good day
What is the correct answer to “2+5*4-8÷⅘=?
Answer:
no it is not c it is b
Step-by-step explanation:
2+(5×4)-(8×5/4)
2+20-40/4
22-10
12
The correct option is B, which is 12.
Given to us:
[tex]2+5\times4-8 \div (\frac{4}{5})[/tex]
To solve such questions, we use BODMAS Rule which helps us decide the order of the operations to solve the mathematical problems.
B - Brackets
O - Order/Power
D - Division
M - Multiplication
A - Addition
S - Subtraction
Therefore, In equation [tex]2+5\times4-8 \div (\frac{4}{5})[/tex] ;
1. solve brackets first,
[tex]2+5\times4-8 \div (0.8)[/tex]
2. solve Division,
[tex]2+5\times4-10[/tex]
3. Solving Multiplication,
[tex]2+20-10[/tex]
4. Solving Addition,
[tex]22-10[/tex]
5. Solving Subtraction,
12.
Hence, the correct option is B, which is 12.
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Please help!
Which equation has a constant of proportionality equal to 1?
Choose 1 answer:
A. Y= 10/11x
B. Y = 7/8x
C. Y= 3/15x
D. Y=x
Answer:
[tex]\huge\boxed{\sf D.}[/tex]
Step-by-step explanation:
If
Y is directly proportional to x
Then
Y ∝ x
Changing proportionality to equality
Y = k x
If k = 1 , then
Y = x
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
it's D
Step-by-step explanation:
Khan Academy
i need big help because this is due today
Answer:
Step-by-step explanation:
x | y
30 | 6
60 | 12
90 | 18
120 | 24
If the slope is 3 what does it represent using this table
Answer:
The table represents a linear function.
The graph of linear function y = 3x is attached below.
Step-by-step explanation:
Given the table
Number of Hours 1 3 5
Number of Tents 3 9 15
Given that the slope is 3.
Finding the slope between (1, 3) and (3, 9)
Slope = (y₂-y₁) / (x₂-x₁)
= [9-3] / [3-1]
= 6 / 2
= 3
Finding the slope between (3, 9) and (5, 15)
Slope = (y₂-y₁) / (x₂-x₁)
= [15-9] / [5-3]
= 6 / 2
= 3
As the value of slope remains constant i.e. slope = m = 3.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 3 and the point (1, 3)
[tex]y - 3 = 3 (x-1)[/tex]
[tex]y-3 = 3x-3[/tex]
[tex]y = 3x-3+3[/tex]
[tex]y = 3x[/tex]
Comparing with the slope-intercept form of a linear function of line
y = mx+b where m is the slope and b is the y-intercept
slope = 3 and y-intercept b = 0
Therefore, the table represents a linear function.
The graph of linear function y = 3x is attached below.
A company has determined that its maximum profit occurs when it sells 10,000units per month. For every 1,000 units more or less than 10,000 units that thecompany sells, its profit decreases by $5,000. Which of the following equationscan be used to find the number of units, q, in thousands, for which the profitdecreases $35,000 from the maximum?
A. 10 |q−35| =5
B. 5 |q−10| =35
C. 35 |q−10| =5
D. 5 |q−35| =10
Answer:
B. 5 |q−10| =35
Step-by-step explanation:
Solution:
let's try to understand the problem clearly.
In this question, we asked to calculate the number units which that company produces so that it's profit is decreased from the maximum profit.
We know that, for 10000 units = company will get maximum profit.
Any value less than or greater than 10000 units will decrease the profit.
and we also know that,
For every 1000 units profit is decreased by $5000.
So if maximum profit is at 10000 units,
Then at 9000 units = it will have profit decreased by 5000 from the maximum
if q = 11000 then profit = Maximum - 5000
But we are asked to calculate the profit decrease of $35000 from the maximum.
it means we need 5000 decreased by 7 times = 10000 + 7000 = 17000 units
So, if company produces 17000 units,
profit will be decreased by 5(7000) = 35000
Finally,
B. is the only equation which satisfies this condition.
B. 5 (q-10) = 35
(q-10) = 7
q = 10 + 7 = 17
q = 17000 units
Hence, for 17000 units, company's profit will decrease $35000 from the maximum profit.
Someone help me please
Please friend I do not know
James bought a new digital camera for $175.00. He pays a sale ax of 7.2%. What was the total of the camera
Answer:
187.6 i think
Step-by-step explanation:
Answer:
$187.60
Step-by-step explanation:
Find 7.2% of the price to figure out the sales tax:
7.2% * 175 / 100% = $12.60
Add the sales tax to the original price:
$12.60 + $175.00 = $187.60
Joe and Susan are both 40 years old and hope to have enough money saved to retire by the time they're 65. They deposit $6,000 each
year into an account that pays 4% interest compounded annually. Use this information to complete the table.
Formula to Use
Account Balance in 20 years
Total Interest Earned
present value of an annuity
future value of a lump sum
future value of an annuity
$99,875
$112,253
$149,875
$249,875
$286,363
Answer:
Formula: Future value of annuity
In 20 years: $249,875
Total Interest: $99,875
Step-by-step explanation:
Use the formula for future value:
FV =
P = $6,000
r = 0.04
n = 1
t = 25
FV =
FV = $249,875
To find the total interest earned, first find the total value of the deposit payments:
$6,000 annual payments for 25 years = 6,000 • 25
= $150,000
(I copied that explanation from somewhere else so its a little messed up. I just couldn't explain it properly. Hope this helps!)
Account balance In 20 years is $249,875 and total interest earned is $99,875.
What is the future value?The FV formula assumes a constant rate of growth and a single up-front payment left untouched for the duration of the investment. The FV calculation can be done one of two ways, depending on the type of interest being earned.
We have,
P = $6,000
r = 0.04
n = 1
t = 25
We know the formula for future value
FV= PV [tex](1 + r)^{n}[/tex].
where:
P=Investment amount
R=Interest rate
T=Number of years
According to the question
FV=$6,000×(1+0.04
FV = $249,875
To find the total interest earned, first find the total value of the deposit payments:$6,000 annual payments for 25 years = 6,000 × 25= $150,000
Total interest earned = FV - annually payment for 25 year = $249,875 - $150,000 = $99,875
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5. Evaluate the following expression - 12(-3) + 7
Answer:
43
Step-by-step explanation:
Rosie sells her laptop to John and makes a 15% profit. John then sells the laptop to
Michael for £391. John makes a 15% loss. How much did John pay for the laptop?
Answer:
John pay:449.65
Step-by-step explanation:
(391×15)÷100=58,65
391+58,65=449,65
Write the equation of a line in Point-Slope form that has a slope of -2/3 and
passes through the point (-1,3).
Answer:
The equation of a line in Point-Slope form is y -3=[tex]-\frac{2}{3}[/tex] *(x+1)
Step-by-step explanation:
Linear equations can take various forms, such as the point-slope formula. This formula gives the slope of a line and the coordinates of a point on it. The point-slope form of a linear equation is written as:
y - y1= m*(x-x1)
In this equation, m is the slope and (x1, y1) are the coordinates of the point.
In this case, you know that the line has a slope of [tex]-\frac{2}{3}[/tex] and passes through the point (-1,3). This is, m=[tex]-\frac{2}{3}[/tex] and (x1;y1)=(-1;3). Replacing:
y -3=[tex]-\frac{2}{3}[/tex] *(x-(-1))
This is:
y -3=[tex]-\frac{2}{3}[/tex] *(x+1)
The equation of a line in Point-Slope form is y -3=[tex]-\frac{2}{3}[/tex] *(x+1)
Please help i put max points for u!!
Marley used 7 cups of water to make 4 loaves of French bread. What equation can be used to model the total cups of water needed y for making x loaves of French bread? Write the equation in the forn y = kx. How many cups of water do you need for 6 loaves of French Bread? Express your answer as a fraction in simplest form.
Answer:
Equation: y = [tex]\frac{7}{4}[/tex] x
21/2 cups of water
Step-by-step explanation:
Plug in 7 as y and 4 as x
7 = 4k
Find k
k = 7/4
Then plug k into th equation
y = 7/4 x
For the second part of the question:
Plug in x which is 6 into the bolded equation.
y = (7/4)(6) = 42/4 = 21/2 (simplified form)
21/2 cups of water
You go out to eat at the Outback Steakhouse. Your meal, drink and desert cost $38.56. You are
going to leave the waitress at 15% tip. How much money will you leave the waiter and what is
the total cost of the meal?
I
Answer:
44.34
Step-by-step explanation:
[tex]15 \div 100 \times 38.56 = [/tex]
[tex] = 5.78[/tex]
[tex]38.56 + 5.78 = 44.34[/tex]
Combine like terms to simplify: H + g + h + g - g
Answer:
2h + g
Step-by-step explanation:
Helpppppppp pleaseeeee
Answer:
B and C; 0.5 and 4.5
Write the ratio of height of the building to the number of floors. Then, find the unit rate, and explain what it means in this situation. Fill in the correct answers to complete the sentences.
The ratio of height of the building to the number of floors is nothing. The unit rate is nothing. This means that each floor of the building is nothing ft high.
Answer:
I love a building that's nothing feet high
Step-by-step explanation:
Can that building be my new home?
Write the equation in exponential form.
Log3 1/9=-2
O 3=9-2
O 1/9=3^-2
O 9=3^2
O 3=3^1
Answer:
a
Step-by-step explanation:
Answer: The correct answer is B. 1/9=3^-2
Step-by-step explanation:
Tim flips a weighted coin 6 times and gets 2 tails. What is the experimental probability that the next flip will come up tails?
Answer:
1/3
Step-by-step explanation:
bc 2/6 reduces to 1/3
Arianna has $0.70 worth of nickels and dimes. She has 4 more dimes than nickels. By
following the steps below, determine the number of nickels, x, and the number of
dimes, y, that Arianna has.
Determine three ways to have 4 more dimes than nickels:
Who can solve this for me?
Answer:
x=2 and y=6
Step-by-step explanation:
thee isn't any other way im sorry but there isn't here is a list:
1 nickel = $0.05 and 5 dimes =$0.50 = $0.55
2 nickels = $0.10 and 6 dimes = $0.60 = $0.70
3 nickels = $0.15 and 7 dimes = $0.75 = $0.85
4 nickels = $0.20 and 8 dimes = $0.80 = $1.00
5 nickels equal $0.25 and 9 dimes equals $0.90 = $1.15
so as you can see the more you add the higher the number gets and if its any lower it won't be enough sorry if you really needed that last part
A school cafeteria has 30 boxes of Wheaty Squares cereal and 20 boxes of Mighty O's
cereal. Each box has the same number of ounces of cereal. Write an expression to
represent the total ounces of cereal. Then simplify it to create an equivalent expression.
Answer:
50e=t
Step-by-step explanation:
Wheaty Squares = w
Mighty O's = m
ounces in each box = e
total ounces of cereal = t
w+m=30+20=50
may run 6 miles in 54 minutes how long will it take her to run 10 miles
Answer:
It would take her 90 minutes to run 10 miles.
Step-by-step explanation:
First you should divide 54 by 6 and you'll get 9. So it takes her 9 minutes to run 10 miles (which is physically impossible). You multiply 9 times 10 and get 90.
please help asap!! no trolls
Answer:
Cannot prove as congruent
Step-by-step explanation:
AAA cannot be used to prove whether a triangle is congruent. Only SSS, SAS, ASA, and AAS can be used.
What is the slope of a line that is perpendicular to 5 x – 2 y = 1 ?
Answer:
The slope is 5/2