The graph shows g(x), which is a translation of f(x)=x^2. Write the function for g(x)
Answers
The function after the transformation of f(x) is g(x) = (x - 2)^2
How to determine the transformation of the graph?The equation of the graph is given as
f(x) = x^2
The above equation a parent equation of a quadratic equation
Using the graph as a guide, we can see that
The function f(x) is translated to the right by 2 units to get g(x)
This means that
g(x) = f(x - 2)
So, we have
g(x) = (x - 2)^2
Hence, the equation of g(x) is g(x) = (x - 2)^2
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Related Questions
PLEASE HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x = 14
Step-by-step explanation:
First step is to set the opposite sites equal to each other (they are congruent)
13 = 2y + 1
and
x = y + 8
Now solve for y in terms of x so you can substitute it in the other equation
x - 8 = y
Plug into equation
13 = 2(x-8) + 1
13 = 2x - 16 + 1 distribute
13 = 2x - 15 simplify
28 = 2x add 15 to both sides
x = 14
I hope this helps
You have a plate of 40 cookies. Ten have chocolate chips and 15 have pecans. Of the cookies mentioned in the preceding sentence, two have both chocolate chips and pecans. You select a cookie at random. What is the probability that your cookie has chocolate chips or pecans ?
Answers
Answer:
see below
Step-by-step explanation:
23 out of the 40 have cc or pecans
23/40
Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
Answers
A table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
In this question, we have been given some table that shows functions.
A 2-column table consists of six rows. The first column is labeled x (input values). The second column is labeled f(x) (output values)
We need to find a function which is increasing only over the interval (–2, 1), and nowhere else.
We can observe that for a second table, the first column x with entries negative 3, negative 2, negative 1, 0, 1, 2 and the second column with entries negative 2, negative 4, negative 1, 1, 4, 3 function f(x) is increasing only over the interval (–2, 1), and nowhere else.
Therefore, a table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
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A package of 6 pairs of insulated socks costs 49.74 $. What is the unit price of the pairs of socks ?
Answers
The pairs of insulated socks has a unit rate of $7.99
How to determine the unit rate?From the question, the given parameters are
Number of pairs of insulated socks = 6Cost of the insulated socks = $47.94The above parameters can be represented as the following points
(x, y) = (6, 47.94)
The unit rate of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have the following equation
k = 47.94/6
Evaluate the quotient
So, we have
k = 7.99
Hence, the unit rate is $7.99
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a box contains 6 red, 8 green, 10 blue, 12 yellow and 15 white balls. what is the minimum number of balls we have to choose randomly from the box to ensure that we get 9 balls of same color?
Answers
The minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.
Given that a box contains 6 red, 8 green, 10 blue, 12 yellow, and 15 white balls.
As the question says that the minimum number of balls chosen must ensure that we get 9 balls of the same color, so we must consider the balls of those colors which are more than 9 in number.
Here, 10 blue, 12 yellow, and 15 white balls are considered as they are more than 9.
By applying the Pigeon principle,
we can get.,
9 blue + 9 yellow + 9 white – 3 + 1 = 25
As we are picking randomly so we can get all the red and green balls before the above 25 balls.
Therefore we add the balls 6 red + 8 green + 25 = 39
Hence, the minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.
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There were three questions on the test
each question was worth 5 marks
Each Question was marked right or wrong(no part marks).
30% of the students got all 3 questions correct
40% of the students got exactly 2 question correct
25% of the students got exactly 1 question correct
5% of the students got no questions correct
Determine The overall clas average(mean)
Answers
Answer:
9.75 marks
Step-by-step explanation:
30% of the students got 15 marks (3 questions)
40% of the students got 10 marks (2 questions)
25% of the students got 5 marks (1 question)
5% of the students got 0 marks (0 questions)
0.3(15)+0.4(10)+0.25(5)+0.05(0)/1
the one as denominator represents all students that took the test
4.5+4+1.25+0
9.75
the class average is 9.75
what is the total area of the shaded sections of trapezoid?
Answers
The shaded sections of the trapezoid are triangles.
We know how to find the area of triangles
A = 1/2 bh
Lets start with the left triangle
The bases is 1.1 inches and the height is 3.8 inches
A left triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
The right triangle has the same dimensions
A right triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
Add the two triangles together
2.09+2.09 = 4.18 in^2
The area of the shaded region is 4.18 in^2
Can someone please give me the solution for x (−2)exponent2 = 4(−2).
Answers
Answer:
Step-by-step explanation:
Exponent calculator helps you find the result of any base raised to a positive or negative exponent.
Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. What was her change? Write one other combination of coins Susan could use with her $10 bill to get only bills.
Answers
The change left when Susan buys lotion for $2.33 and gives the bill is $8.
How to calculate the value?Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. The total amount will be:
= $10 + (3 × 0.1) + (3 × 0.01)
= $10.33
The change left will be:
= Total amount - Cost of lotion
= $10.33 = $2.33
= $8
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Find the domain of the function.
1-
X
O all real numbers such that x ≥ -7 and x ≤ 0
O all real numbers except x > -7 and x ≤ 0
O all real numbers except x = -7 and x = 0
O only x = -7 and x = 0
O all real numbers
g(x) =
=
Need Help?
4
x+7
Read It
Answers
The domain of the given function is all real numbers expect x> -7 and x ≥ 0.
What is domain?The entire range of independent variable values is the domain of a function.
According to this definition, it means:
The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.
Keep these things in mind when locating the domain:
A fraction's denominator (bottom) cannot be 0.
In this section, the integer following a square root symbol must be positive.
Given,
g(x) = 1/x- 4/x+7
Applying the definition of rational function that denominator is non zero
x ≠ 0 and x+7 ≠ 0
solving the inequality,
x ≠ 0 and x ≠ -7
Combining the values,
x < -7 or -7 < x< 0 or x> 0.
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A principle of $300 was deposited in a savings account that pays 3.5 interest compoundedyearly. Find the balance after 5 years. Your answer should be numerical only.
Answers
Explanation:
The balance after t years can be calculated using the following equation:
[tex]A=P(1+r)^t[/tex]Where P is the principal amount and r is the rate of interest per year.
So, replacing P by $300, r by 3.5%, and t by 5, we get:
[tex]\begin{gathered} A=300(1+0.035)^5 \\ A=300(1.1877) \\ A=356.3059 \end{gathered}[/tex]So, the balance after 5 years is $356,3059
Answer: $356.3059
Dave earned $637 last week. He worked 35 hours and earned the same amount rach hour. How much was he paid per hour?
Answers
which expression is equivalent to 3/4-2/5
15/20-8/20
8/9-6/9
3/20-2/20
3/9-2/9
Answers
The expression that can be considered as been equivalent to 3/4-2/5 is 15/20-8/20.
How can the equivalent expression be gotten?The equivalent expression be gotten by finding the values of the given answer one after the other, from the given option, we can see that the value of the difference in the given expression is 0.35, then the value option A is also 0.35 which implies that the option A as well as the given expression have the same value.
It should be noted that the option A can as well be simplified as still get the vale of the given option.
Therefore, option A is correct.
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Consider a car with a cash price of $4,000, offered on the installment plan for $146 per month for 36 months.
Calculate (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the car for its cash price.
Use commas and decimal points in your answers when appropriate. Round to two decimal places if necessary
Answers
The total installment price is 34 and the carrying charges is 34
A sort of contract or arrangement known as an installment loan involves a loan that must be returned over period with a predetermined number of periodic instalments; typically, at least two each payment is required.
The expense related to keeping a financial instrument for a set length of time is known as a carrying charge. This issue is caused by the additional cost of purchasing the bicycle on an instalment plan. This is the additional amount (total) you will pay over cash price since you choose to use an instalment plan.a) Total charge of the Installment price = 146 × 30 = $5256
b) The carrying charges = $5256 - $4000 = $1256
c) Number of months needed to save money = $4000 ÷ 36 = 111.11..
Therefore 11.11 months or 12 months is needed to save money to buy the car.
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Factor 8y^2+18. Please show work!!!
Answers
Answer:
2*(4y² + 9)
Step-by-step explanation:
Factorize the expression:8y² = 2 * 2 * 2 * y²
18 = 2 * 3 * 3
GCF = 2
8y² + 18 = 2* 4y² + 2*9
= 2*(4y² + 9)
7 3/4 divided by 1/3
Answers
Answer:
23.25 or 23 1/4
Step-by-step explanation:
keep change flip
7 3/4 = 31/4
31/4 x 3/1
31 x 3=93
4 x 1 =4
93/4 simplifies to 23 1/4 or 23.25
From problems 1-4 state whether or not the equation is a quadratic equation
1. y = x^(2) + 3x - 15
2. y = 6x^(5) - 0.7 x (pi symbol)
3. y = 9x
4. y = (-4/3)x^(2)
(Chapter 61 in Big Fat Notebook Algebra)
Answers
Answer:
1. Quadratic
2. Not quadratic
3. Not quadratic
4. Quadratic
Step-by-step explanation:
A quadratic equation will have a degree of 2. The degree is the highest power of the x term in the equation.
Therefore a quadratic equation will be of the form
y = ax² + bx + c,
where a, b and c are constants
a ≠ 0 but either b or c or both can be 0
In Triangle ABC, AB= 6cm, AC= 8cm, and BC= 12cm.
Angle ACB= 26.4
Calculate the area of triangle ABC
Answers
The area of the triangle is 18 cm.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In Triangle ABC,
AB= 6cm
AC= 8cm
BC= 12cm.
Angle ACB= 26.4
The area of a triangle is given as:
Area = 1/2 x base x height
From the figure below,
Base = BC = 12
D is the midpoint of BC.
BC = BD + DC
DC = 12/2 = 6
Height = Tan 26.4
Tan 26.4 = AD / DC = AD / 6
0.50 = AD / 6
AD = 0.50 x 6
AD = 3
Now,
Area of the triangle ABC:
= 1/2 x base x height
= 1/2 x 12 x 3
= 18 cm
Thus,
The area of the triangle is 18 cm.
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7
John is less than half his mother's age, though the sum of their ages is greater than
sixty. John was born on his mother's twenty-sixth birthday.
By expressing these facts as two inequalities and one equation, find the range of
possible ages for John.
Answers
Answer:
Step-by-step explanation:
ans is 7
A) Justin bought 27 pounds of sugar for $11. How many pounds of sugar did he get per dollat? Pounds per dollars mearest hundredth. B) A color printer prints 20 pages in 7 minutes. How many minutes does it take per page? Minutes per page nearest hundredth.
Answers
A)
[tex]\begin{gathered} \frac{27\text{ pounds }}{11\text{ dollars}}=\text{ } \\ 2.45\text{ pounds per dollar } \end{gathered}[/tex]b)
[tex]\begin{gathered} \frac{20\text{ pages}}{7\text{ minutes}}= \\ 2.86\text{ pages per minutes} \\ \\ Then: \\ If\text{ 2.86 pages are printed in 1 minute, how many minutes does it take for 1 page?} \\ \frac{1\text{ page \lparen1 minute\rparen}}{2.86\text{ pages}}=\text{ } \\ 0.35\text{ minutes takes to print 1 page. } \end{gathered}[/tex]
Please help me
:) thank you
Answers
Answer:
11 degrees
Step-by-step explanation:
Answer: 28 degrees
Step-by-step explanation: Set the two equations equal to each other, and solve. X equals 4 and then you plug that into 7x. 7x4 is 28.
7y+2=11y-3please help me answer
Answers
Equation
[tex]\begin{gathered} 7y+2=11y-3 \\ 11y-7y=2+3 \\ 4y=5 \\ y=\frac{5}{4} \\ \end{gathered}[/tex]Steps
1. Group the variables and constants on each side of the equality
2. Operate the variables and operate the constants.
3. Divide both parts by 4 to clear y
The answer would be y = 5/4
Write the equation of a line parallel to the line shown that has a y-intercept of (0, -6):
Answers
The required equations of the line are as follows;
(y + 6) = 1(x - 0); Point-slope form.y = x - 6; Slope-intercept form.x - y = 6; Standard form.Which equations represent the equation of the line on different forms?The line shown in the task content has a slope of 1 as it has a unit rate of change and also, the y-intercept of the graph shown is at the point; (0, 1).
On this note, it follows from line graphs that parallel lines have equal slopes. Hence, the required line would have the same slope, m = 1 too.
The equations are therefore as follows;
In point slope form; (y - y1) = m (x - x1). Hence we have; (y + 6) = 1(x - 0).In slope-intercept form; y = mx + c. Hence we have; y = x - 6.And finally, in standard form; ax + by = c. Hence, we have; x - y = 6.Read more on equations of a line;
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root 18 times root 2
[tex] \sqrt{18} \times \sqrt{2} [/tex]
Answers
2 and 9> 3 and 3
3 square root of 2 x square root of 2
3x2=6
Answer=6
The graphs of f (x) = x3 + x2 – 6x and g(x) = ex + 2 – 1 have which of the following features in common?
Rational function f of x increases from the left in quadrant 3 passing through the point negative 2 comma 0 and going to a local maximum and then decreasing through the point 0 comma 0 to a local minimum and then increasing through the point 3 comma 0 to the right and the exponential function g of x increases from the left in quadrant 3 asymptotic to the line y equals negative 1 and passes through the points negative 2 comma 0 and increases through the point 0 comma 6 to the right
x-intercept
y-intercept
End behavior
Range
Answers
The end behavior of the graphs of the functions f(x) and g(x) are common.
Consider the two functions,
f(x) = x³ + x² - 6x and g(x) = [tex]e^{x+2}[/tex] - 1
Now,
y = x³ + x² - 6x
The x-intercept will be:
0 = x³ + x² - 6x
x( x² + x - 6 ) = 0
x( x - 2 )( x + 3 ) = 0
So, x = 0, 2, - 3
Hence, the x-intercepts are ( 0, 0 ), ( 2, 0 ), and ( - 3, 0 ).
The y-intercept will be:
y = x³ + x² - 6x
y = (0)³ + (0)² - 6(0)
y = 0
Hence, the y-intercept is ( 0, 0 ).
The range of the function f(x) = x³ + x² - 6x is ( - ∞, ∞ ).
Using the degree 3 and the leading coefficient 1 of the function f(x) the end behavior of the function will be:
Falls to the left and rises to the right.
For the function,
y = g(x) = [tex]e^{x+2}[/tex] - 1
The x-intercept will be:
y = [tex]e^{x+2}[/tex] - 1
0 = [tex]e^{x+2}[/tex] - 1
[tex]e^{x+2}[/tex] = 1
[tex]e^{x+2}[/tex] = e⁰
x + 2 = 0
x = - 2
Hence, the x intercept is ( - 2, 0 ).
The y-intercept will be:
y = g(x) = [tex]e^{x+2}[/tex] - 1
y = e² - 1
Hence, the y-intercept will be ( 0, e² - 1 ).
The range of the function g(x) is ( - 1, ∞ ).
The end behavior of the function g(x) constantly rises to the right in the positive y-axis.
Hence, the functions f(x) and g(x) have the end behavior in common.
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Does anyone know how to do this? I keep getting stuck on it. Look at this graph. What is the equation of the line in slope-intercept form?
Answers
Answer: 4/1
Step-by-step explanation: You go on the y-axis up to 6 then you count up until you get to 10 then you go over 1 so the equation would be 4/1
The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n+29.99, where n is the number of different colors in the design. Write a simplified expression that represents the cost of 15 sweatshirts.
Answers
Answer:
3.5n + 29.99 × 15
Step-by-step explanation:
Since it is an expression there are no equals, and since we do not know how many colors there are in the design we leave the variable.
A factory produces widgets and zurls. The combined number of
widgets and zurls made each day cannot be more than 12. The
maximum number of widgets the factory can produce in a day is
4.
Select each ordered pair that represents an allowable
combination of widgets and zurls produced in one day.
(4,5)
(11,1)
(3,9)
(4,12)
Answers
(4,5) and (4,12) are this pair is allowable to the maximum number of widgets the factory can produce in a day is 4, so x ≤ 4 .
(11,1) and (3,9) are this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12, so x + y ≤ 12.
Let us assume the number of widgets = x
Let us assume the number of zurls = y
According to question,
The combined number of widgets and zurls made each day cannot be more than 12.
That means,
x + y ≤ 12 (Equation-1)
The maximum number of widgets the factory can produce in a day is 4.
That means,
x ≤ 4 (Equation-2)
So,
We can write each pair has,
(4,5)
x = 4,
y = 5
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 5 ≤ 12 ; 4 ≤ 4
9 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
(11,1)
x = 11,
y = 1
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
11 + 1 ≤ 12 ; 11 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(3,9)
x = 3,
y = 9
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
3 + 9 ≤ 12 ; 3 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(4,12)
x = 4,
y = 12
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 12 ≤ 12 ; 4 ≤ 4
16 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
Therefore,
(4,5) and (4,12) are this pair is allowable to the maximum number of widgets the factory can produce in a day is 4, so x ≤ 4 .
(11,1) and (3,9) are this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12, so x + y ≤ 12.
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The maximum number of widgets the factory can create in a day is 4, therefore x 4. (4,5) and (4,12) are this pair is permissible.
The total number of widgets and zurls produced each day is limited to 12, therefore (11,1) and (3,9) are acceptable. Therefore, x + y 12.
Let's assume there are x widgets.
Assume that y is equal to the number of zurls.
According to the inquiry,
There can never be more than 12 widgets and zurls produced each day.
That implies,
x + y ≤ 12 (Equation-1)
The maximum number of widgets the factory can produce in a day is 4.
That means,
x ≤ 4 (Equation-2)
So,
We can write each pair has,
(4,5)
x = 4,
y = 5
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 5 ≤ 12 ; 4 ≤ 4
9 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
(11,1)
x = 11,
y = 1
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
11 + 1 ≤ 12 ; 11 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(3,9)
x = 3,
y = 9
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
3 + 9 ≤ 12 ; 3 ≤ 4
12 ≤ 12
Therefore, this pair is permitted as long as the total number of widgets and zurls produced each day does not exceed 12.
The factory can only manufacture a maximum of 4 widgets per day, so this combination is not permitted.
(4,12)
x = 4,
y = 12
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 12 ≤ 12 ; 4 ≤ 4
16 ≤ 12
Because the maximum daily production of widgets and zurls is limited to 12, this pair is not permitted.
The factory can only make a maximum of 4 widgets every day, hence this pair is permitted.
Therefore,
The maximum number of widgets the factory can create in a day is 4, therefore x 4. (4,5) and (4,12) are this pair is permissible.
The total number of widgets and zurls produced each day is limited to 12, therefore (11,1) and (3,9) are acceptable. Therefore, x + y 12.
Which graphs are correct?
Answers
Question 11
The slope is 7/2 (so the line is increasing), and the y-intercept is 3.
Answer is A.Question 12
The slope is -8/3 (so the line is decreasing), and the y-intercept is -5.
Answer is D.Please answer the question in the picture
Answers
A loan of $50,000 is taken out for six years at 9% interest compounded annually. If the loan is paid off in full at the end of that time period, $50433 must be returned.
What is Compound interest?Compound interest is calculated by multiplying the initial loan amount, or principal, by one plus the annual interest rate multiplied by the number of compound periods multiplied by one. Compound interest is when you earn interest on both your savings and your interest earnings. When you compound interest, you add the interest you've earned back into your principal balance, which earns you even more interest, compounding your returns. Assume you have $1,000 in a savings account earning 5% interest per year. You'd earn $50 in year one, giving you a new balance of $1,050. Compound interest occurs when interest earned on savings begins to earn interest on itself.
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