The rule for the function g(x) is:
g(x) = 1.15*(x^2 - 3x -16)
How to write a rule for the function g?
First we know that the function f(x) is f(x) = x^2 - 7x
And we know that h(x) is a translation of 6 units down and 2 units to the left of f(x), then:
h(x) = f(x + 2) - 6
Now we know that g(x) is 115% of h(x), then we can write:
g(x) = 1.15*h(x)
Replacing h(x) by the rule above we get:
g(x) = 1.15*(f(x + 2) - 6)
Replacing the actual function there:
g(x) = 1.15*( (x + 2)^2 - 7*(x + 2) - 6)
g(x) = 1.15*( x^2 + 4x + 4 - 7x - 14 - 6)
g(x) = 1.15*(x^2 - 3x -16)
This is the rule for function g(x).
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Reply and I’ll do your work for you for a week
Answer:
Graph the solution to this inequality on the number line.
0.3(x − 4) > -0.3
Step-by-step explanation:
A rental car agency charges $180 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $382.50?
Answer:
810
Step-by-step explanation:
382.50-180= 202.5
202.5 / 0.25= 810
Hope this helps!
Answer:
810 miles
Step-by-step explanation:
$180 a week is the fixed cost so we subtract this first.
($382.50 - $180 = $202.50)
The number left is the amount of dollars charged per mile.
So if we divide this number by $0.25, we get how many miles travelled.
($202.50 ÷ $0.25 = 810 miles)
how do you solve this
a truck driver drove 119 miles in 3 1/4 hours. how many miles did he drive per hour
The truck driver drive 36.61 miles per hour .
The unit method is a method of finding the value of one unit and then finding the value of the required number of units. For simplicity, always write what you calculate on the right and what you know on the left.The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.It is given that a truck driver drove 119 miles in 3 1/4 hours .
On simplifying the time , we get
[tex]3\frac{1}{4} =\frac{3\times4+1}{4}\\\\ 3\frac{1}{4} =\frac{13}{4}[/tex]
which means that truck driver drove 119 miles in [tex]\frac{13}{4}[/tex] hours .
Using unitary method , we get
[tex]\frac{13}{4}[/tex] hours is taken by driver to complete = 119 miles
1 hour is taken by driver to complete [tex]=\frac{119\times4}{13} \\[/tex]
[tex]=36.61 \ miles[/tex]
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Use a decimal number to fill in the blank. a 16 input mux has _____ select lines.
Use a decimal number to fill in the blank. a 16 input mux has 4 select lines.
What is a decimal number?
A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities. For instance, there is one complete pizza and a half of another pizza in the photograph.How do you write decimal numbers?
To write a decimal in word form, follow these steps:
Write the whole number part.Write "and" for the decimal point.Write the decimal part the same way you would write a whole number.Write the. place value. of the last digit.Learn more about decimal numbers
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Find each angle measure in the figure.
A triangle with angles labeled 4 y degrees, 20 degrees, and left-parenthesis y minus 10 right-parenthesis degrees.
The angle measures are $20\degree$,
°, and
\left(y-10\right)
°.
Question 2
Use the equation to justify your answer.
$20+\left(y-10\right)+4y=$
$y=$
Based on the triangle sum theorem:
20° + (y - 10)° + 4y° = 180
y = 34
What is the Triangle Sum Theorem?The triangle sum theorem states that if we add up all the three interior angles in a triangle, the sum we would get would be equal to 180 degrees.
Given the following are interior angles of a triangle:
4y°(y - 10)°20°Based on the triangle sum theorem, we have the following equation:
20° + (y - 10)° + 4y° = 180
Solve for y
20 + y - 10 + 4y = 180
10 + 5y = 180
5y = 180 - 10
5y = 170
5y/5 = 170/5
y = 34
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Solve for x.
Your answer must be simplified.
X/3>-33
The simplified equation of the X/3 ≥-33 is will be X ≥ -99.
Define Equation simplification:Solving a math problem is another way of saying simplifying an expression. When you simplify an expression, you are attempting to write it in the most straightforward manner feasible. Finally, no more adding, subtracting, multiplying, or dividing should be required.
What is meant by simplification?To make anything simpler or simpler to reduce it to the fundamentals. to reduce in scope or complexity: to streamline management procedures.
Solving:Given = X/3>-33
This can be written as:
X/3 ≥-33
X ≥ -33 * 3
X ≥ -99
The simplified equation of the X/3 ≥-33 is will be X ≥ -99.
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Find the slope of the line. (-4,-1) (4,-3)
Answer:
Step-by-step explanation:
Ans:
−
0.6
Mrs Atkins makes 3 withdrawals of $25. What is the change in her account? Please help me
Her change in account is x - 75 dollars.
How to find her change in account?She makes 3 withdrawals of $25.
Her change in account can be calculated as follows:
Therefore, let's find her change in her account,
Let us say she had x dollars in her account.
She withdraws 25 dollars on three occasions.
Therefore,
total withdrawer = 25 × 3
total withdrawer = 75 dollars
Therefore,
Her change in account = x - 75
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Answer:
Step-by-step explanation:
1. 25x3
2.75
Simplify
(3y)^2 x y^-1
Answer:
9y
Step-by-step explanation:
[tex]\bullet\; \tt{(3y)^2} = 3^2y^2 = 9y^2}[/tex]
[tex]\bullet\; \tt y^{-1} = \dfrac{1}{y}\\\\\bullet\;(3y)^2 \times y^{-1} = 9y^2 \times \dfrac{1}{y } = \dfrac{9y^2}{y}\\\\\\bullet \tt \dfrac{y^2}{y} = y\\\\\tt \bullet \dfrac{9y^2}{y} = 9y[/tex]
a designer builds a model of a canoe. the finished model is exactly the same shape as the original, but smaller. the scale factor is . (a) find the ratio of the surface area of the model to the surface area of the original. (b) find the ratio of the height of the model to the height of the original. (c) find the ratio of the volume of the model to the volume of the original.
Model is same shape as original with scale factor 2:9.
Ratio of
a. Surface area of model and original is 4:81.
b. Height of model and original is 2:9.
c. Volume of model and original is 8:243.
As given,
Scale factor (a: b)=2:9
Ratio of model and original for
a. Surface area =a²: b²
=4:81
b. Height=a :b
=2:9
c. Volume=a³ :b³
=8:243
Therefore, model is same shape as original with scale factor 2:9.
Ratio of model and original for
a. Surface area is 4:81.
b. Height is 2:9.
c. Volume is 8:243.
The complete question is :
A designer builds a model of a canoe. the finished model is exactly the same shape as the original, but smaller. the scale factor is 2:9.
(a) find the ratio of the surface area of the model to the surface area of the original. (b) find the ratio of the height of the model to the height of the original. (c) find the ratio of the volume of the model to the volume of the original.
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what is 34-/5=
please help me with this question and i don't know the answer to this
Answer:
34-5=29
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
hope it helps and have a nice day! :)
Communicate and Justify:
Tau says that the
sum of -1 3/4 and 2 1/2 is the same as the difference
between 2 1/2 and 1 3/4. Is Tau correct? Explain why
or why not.
Tau is correct, the sum between -(1 ³/₄) and (2 ¹/₂) is equal to the difference between (2 ¹/₂) and (1 ³/₄)
Is Tau correct?
Remember that the sum between a number A and a negative number -B is written as:
A + (-B)
And that is equal to the difference between A and B.
A - B
In this case, Tau says that the sum between:
-(1 ³/₄) and (2 ¹/₂)
Is written as:
(2 ¹/₂) + (-(1 ³/₄) )
(2 ¹/₂) - (1 ³/₄)
And, using the above property, we conclude that this is equal to the difference between (2 ¹/₂) and (1 ³/₄)
So Tau is correct.
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if they are given 2 days to work how many scarves could alexandra make if she spent the whole time knitting scarves?
Alexandra could make 24 scarves if she spent the whole time knitting, by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Now,
Refer to the image attached for the values and information.
According to the timeline for Alexandra's production options, if she knits 0 sweaters every day, In one day, 12 scarves were knit. This suggests that if Alexandra knitted scarves all day for two days, by unitary method, she could finish 24 scarves.Hence, Alexandra could make 24 scarves if she spent the whole time knitting, by unitary method.
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Please help will mark brainliest
Answer:135
Step-by-step explanation:6075/45=135 hope this helps
Answer:
135
Step-by-step explanation:
Let x be the number of sessions.
Create an equation.
45x=6075
Divide 45 from both sides.
x=135
135 practice sessions.
Hope this helps! :)
Determine f –1(x) if f of x is equal to the quantity x plus 2 end quantity over the quantity x minus 3 end quantity where x ≠ 3.
f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 2 end quantity
b
f inverse of x is equal to the quantity x minus 2 end quantity over the quantity x plus 3 end quantity
c
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 3 times x plus 2 end quantity
d
f inverse of x is equal to the quantity 3 times x plus 2 end quantity over the quantity x minus 1 end quantity
The inverse function of f(x) = (x + 2)/(x - 3) is given as follows:
[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]
How to obtain the inverse function?The function in this problem is defined as follows:
f(x) = (x + 2)/(x - 3).
Using the notation y = f(x), it is given as follows:
y = (x + 2)/(x - 3).
To obtain the inverse, the first step is exchanging the variables x and y, as follows:
x = (y + 2)/(y - 3).
Now the variable y must be isolated to obtain the inverse function, as follows:
xy - 3x = y + 2
xy - y = 3x + 2
y(x - 1) = 3x + 2
y = (3x + 2)/(x - 1).
Hence the inverse function is given by:
[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]
Meaning that the fourth option is correct.
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rewrite: [tex]15\frac{1}{6}[/tex] as a decimal. Round to the nearest thousandths.
Answer:
[tex]15 \frac{1}{6}=15.167\:\:\sf(nearest\:thousandth)[/tex]
Step-by-step explanation:
[tex]15 \frac{1}{6}=15+\dfrac{1}{6}[/tex]
Convert ¹/₆ into a decimal by using long division:
[tex]\large \begin{array}{r}0.1\:6\:6\phantom{..}\\6{\overline{\smash{\big)}\,1. 0 \:0\: 0\: \phantom{.}}}\\{-~\phantom{(}\underline{0.6\:0\phantom{-)}}\\0.4\:0\:\:\phantom{))}\\-~\phantom{()}\underline{0.3\:6\:\:\phantom{))}}\\0.0\:4\:0\:\:\phantom{}\\-~\phantom{()}\underline{0.0\:3\:6\:\:\phantom{}}\\0.0\:0\:4\:\:\phantom{}\\\end{array}[/tex]
Therefore, ¹/₆ = 0.166666.....
[tex]\begin{aligned}\implies 15 \frac{1}{6} & =15+\dfrac{1}{6}\\\\& = 15 + 0.166666...\\\\& = 15.166666...\\\\& = 15.167\:\:\sf(nearest\:thousandth)\end{aligned}[/tex]
A ribbon is 4m long.how many pieces each 30cm long can be cut from the ribbon
Answer: 13 pieces
Step-by-step explanation:
4 m * 100 cm/1 m=
4 * 100/1=
4*100=400 cm.
400/30=
(10+390)/30=
10/30 + 390/30=
1/3 + 13 ==> 13 pieces
Work Shown:
1 meter = 100 cm
4 meters = 400 cm
400/30 = 13.33 approximately
That rounds down to 13
You'll have 400-13*30 = 400-390 = 10 cm of ribbon leftover.
Mae raised $80 by selling boxes of cookies. Let
b represent the number of boxes of cookies sold.
Each box cost $2.50. Which equation should be
used to determine how many boxes of cookies
Mae sold?
A. 2.50+ b = 80
C. b÷ 2.50 = 80
B. b-2.50 = 80
D. 2.50b = 80
Answer: D
Step-by-step explanation: 2.50xb=80 b= 32 boxes
What is the missing factor in this factor tree?
Answer:
15
Step-by-step explanation:
30 ÷ 2 = 15
to check, 15 × 2 = 30
charlotte denning earns both $13/hour and $26 for every sale she completes. during the most recent week, she worked 47 hours and made a total of 71 sales.
simplify 9 +(-2)^3
A. 3
B. 1
C.17
Answer:
B
Step-by-step explanation:
9+(−2)^3
=9+ −8
=1
Answer:
b is your answer
4x-2y=6 for y in terms of x
The inequality -15 <-6 is given. Perform the given operation, then write a true
inequality to match the result.
Subtract 12 from both sides of the inequality.
The result of the operation is -27 < -18 and the result is true
How to perform the operation on the inequality expression?The inequality expression is given as:
-15 < -6
The operation on the inequality expression is given as:
Subtract 12 from both sides of the inequality.
So, we start by subtracting 12 from both sides of the above inequality
This is represented as
-15 - 12 < -6 - 12
Evaluate the difference
So, we have
-27 < -18
The above inequality is true because -27 is less than -18
Hence, the result of the operation is -27 < -18 and the result is true
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giving branliestb: The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July?
2 feet
28 feet
14 feet
16 feet
The difference between depths in January and July is equal to: D. 16 feet.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols
How to determine the difference between depths?In order to determine the difference between depths, we would calculate the magnitude of the depth for each of the month.
For January, we have:
January depth = 20 - 6
January depth = 14 feet.
For July, we have:
July depth = 20 - 22
July depth = -2 feet.
Now, we can calculate the difference between depths in January and July:
Difference = 14 - (-2)
Difference = 14 + 2
Difference = 16 feet.
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A website begins its first week with 3 subscribers. The number of subscribers each week is listed in the table. Write an expression to model the number of subscribers at the website each week. Use your expression to determine the number of subscribers in week 24.
There are _____
subscribers in week 24.
Answer:
72
Step-by-step explanation:
This is clearly multiplication so all you have to do is multiply 24 x 3 and your answer is There are 72 subscribers in week 24
Geometric mean of 4 and 64
Answer: 16
Step-by-step explanation:
Let's say x=Geometric mean.
4*64=x*x
x*x=256
x^2=256
x=16
Find the quotient: (-y5 - 9y) = y
The quotient of the equation (-y5 - 9y) = y
= 0What is Quotient?The term "quotient" is used frequently in mathematics, and it may also refer to a fraction or a ratio as well as the integer portion of a division (in the case of Euclidean division)[2] (in the case of proper division). In the Euclidean division sense, and in the proper division sense, the quotient is "6 with a remainder of 2" when 20 (the dividend) is divided by 3 (the divisor). A quotient in the second meaning is only the proportion of a dividend to its divisor.
According to the given value,
-y*5-9y=y
Mutiply
-5y-9y=y
Combine like terms
-14y=y
Rearrange the terms
-14y -y= O
Combine the terms
-15y =O
divide on both sides
y=o
Hence , the Quotient is 0.
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solve the equation show your solution x plus 12 equals 7
Answer:
-5+12=7
Step-by-step explanation:
7-12=-5
Answer:
-5
Step-by-step explanation:
x + 12 = 7
x + 12 - 12 = 7 - 12
x = -5
Alessa had 50 in her account. she then received four $-25 charges to her account. what is the new balance of her account
The new balance in her account will be $150.
We have Alessa.
We have to find the new balance of her account after receiving four $-25 charges.
What is Account ?Account is referred here as a bank account used for the purpose of saving money by the people.
According to the question -
Initial money in Alessa's account = $50
Total money received = $25 x 4 = $100
Therefore, the new balance in her account will be -
$50 + $25 x 4 = $150
Hence, the new balance in her account will be $150.
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