The graph of g(x) = -|x + 2| + 4 is obtained after these following transformations from the parent function f(x) = |x|.
Reflection over the x-axis.Shift left of 2 units.Shift up of 4 units.Which transformations were used?The parent function in this problem is defined as follows:
f(x) = |x|.
The transformed function in this problem is defined as follows:
g(x) = -|x + 2| + 4
The transformations are listed and described as follows:
The multiplication by -1 represents a reflection of the parent function over the x-axis.The addition by 2 in the domain, that is, x -> x + 2, represents a shift right of two units of the parent function.The addition by 4 in the range, that is, y -> y + 4, represents a shift up of four units of the parent function.More can be learned about transformations at https://brainly.com/question/28792248
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The black graph is the graph of y = f(x).
Choose the equation for the red graph.
A. y - 1 = f(x)
B. = f(x)
C. y = f(x - 1)
D. y = f()
1
Answer:
It's A.
Step-by-step explanation:
If you subtract from y, the graph moves to the right. If you add, it moves to the left.
Find tα/2 for n = 18 and a 99% confidence interval.
The value of tα/2 of the t-test is 2.898
How to determine tα/2?A t-test is a statistical test that is used to compare the means of two groups. tα/2 refers to the t critical value from the t-distribution table that corresponds to α/2
Given: n = 18 and a 99% confidence interval
We have to find the critical t value for 99% confidence level and sample size of 18
Degrees of freedom = n - 1 = 17
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
In the t table (check the attached image), we have to check the value against the column 0.005 and for 17 degrees of freedom.
The value obtained from the table is 2.898
Therefore, tα/2 = 2.898
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Bucket a and bucket b have the same shade of blue paint. If white paint is added to bucket b, which bucket would have the darker shade of blue paint
Answer:
Bucket a would be a darker shade because the white makes bucket b lighter.
The mean age of 12 women in an office is 22 years old. The mean age of 3 men in an office is 24 years old. What is the mean age (nearest year) of all the people in the office?
The mean age (nearest year) of all the people in the office is 22.4.
How to find the mean age?Using this formula to find the mean age
Mean age = Sum of men and women age / Number of men and women
Let plug in the formula
Mean age = ( 12 women × 22 years old) + (3 men × 24 years old) / 12 women + 3 men
Mean age = 264 + 72 / 12 +3
Mean age = 336 /15
Mean age = 22.4
Therefore the mean age is 22.4.
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(-3y)^4 write the power as a product of powers
Answer: 81y^4
Step-by-step explanation:
expand then calculate, -3 to the power of 4+81 then 81 added to y ^4 81y^4 is your finally power.
integration of ∫x³+1/x³-x dx
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits \frac{x^3+1}{x^3-x} dx }} \end{gathered}$}[/tex]
We rewrite the integrand.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{x^3+1}{x^3+x}=1+\frac{1}{x-1}-\frac{1}{x} }} \end{gathered}$}[/tex]
We integrate terms by terms:
The integral of the constants have this constant multiplied by the variable of integration.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits 1 \ dx=x } } \end{gathered}$}[/tex]
That u = x -1. Then that du = dx and we put du.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\frac{1}{u} \ du }} \end{gathered}$}[/tex]
Integral 1/u is log(u). If you now substitute u further into:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{log(x-1) }} \end{gathered}$}[/tex]
The integral of the product of a function by a constant is the constant times the integral of this function:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\left(-\frac{1}{x}\right)dx=-\int\limits\frac{1}{x}dx }} \end{gathered}$}[/tex]
Integral 1/u is log(x). Therefore, the result is: -log(x).
The result is: x - log(x) + log(x - 1)
The graph of a quadratic function with vertex (4, 2) is
Find the range and the domain.
Write the range and domain using interval notation.
For the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
As given in the question,
For the given graph of quadratic function ,
Given graph represents the parabola.
Standard equation of the parabola with vertex ( h, k) is given by,
y = a ( x - h )² + k
Substitute the value ( h ,k ) = ( 4, 2 )
y = a ( x - 4 )² + 2
As it is a parabola in the first quadrant and faces in the upward direction,
Value of x tends to -∞ to ∞
Domain = ( -∞ , ∞ )
Minimum value of y coordinate is 2 and increases to ∞.
Range = ( 2, ∞ )
Therefore, for the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
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solve the system of linear inequalities by graphing
-2x+y greater than or equal to -3
y greater than 1/3x+ 2
The solution to the system of linear inequalities -2x + y ≥ -3 and y > 1/3x + 2 is (3, 3)
How to determine the solution to the system?In this case, the system of inequalities is given as
-2x + y ≥ -3
y > 1/3x + 2
Next, we plot the graph of the system of inequalities
In this case, the point of intersection of the inequalities represent the solution to the system
From the graph, the lines intersect at (3, -3)
Hence, the solution is (3, 3)
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if a 10800 cm^2 of material is available to make a box with a square base and an open top find the largest possible volume of the box
The largest possible volume of the box is 108000cm^3.
How can the largest possible volume of the box be found?The concept is the concept of
We can represent the length of the square box as x
we can also represent the surface of the box as S
we can represent the height of the square box as y
we can represent the volume as V= xy
Then since the top of the box is open and we can equate the material of the box is equal with surface area of box.
then S=[x^2 +2xy +2xy]
= x^2 +4xy
Then substitute the value of S we have
10800= x^2 +4xy
y= [10800-x^2/4x]
V=2700 * 1/4X^2
V=2700 * 1/4X^2
Then substitute the value of y into
V= xy
= x[10800-x^2/4x]
V= 2700x - 3/4X^2
Differentiate the volume to 0
=3x^2 = 2700
X^2 = 3600
X = 60 and Y = 30
V=2700 * 1/4X^2
V= 270(60) - 1/4* (60)^2 = 108000cm^3
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NO LINKS!! Please assist me with this problem Part 1m
Answer:
(x + 8)² + (y - 8)² = 64=======================
Given ConditionsTangent to x-axis,Tangent to y-axis,In the second quadrant,Radius is 8 units.SolutionEquation of circle:
(x - h)² + (y - k)² = r², where (h, k) is center and r - radiusThe center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.
So the coordinates of the center are:
x = - 8, y = 8The equation is:
(x - (-8))² + (y - 8)² = 8²(x + 8)² + (y - 8)² = 64Answer:
[tex](x+8)^2+(y-8)^2=64[/tex]
Step-by-step explanation:
Required conditions:
Tangent to both axes.Center in the second quadrant.Radius = 8 units.If the circle is tangent to both axes, its center will be the same distance from both axes. That distance is its radius.
If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).
Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.
If the radius is 8 units, then the center is (-8, 8).
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:
[tex]\implies (x-(-8))^2+(y-8)^2=8^2[/tex]
[tex]\implies (x+8)^2+(y-8)^2=64[/tex]
The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.
R(x) = 24x
C(x) = 17x + 161
We could finish this question by applying the linar programming concept.
The profit function for the business is P(x) = 7x - 161
The number of units must be produced for the business to break even is
To find the formula of profit function, we have to understand first that profit is the remaining of revenue after being reduced by costs. Hence we could write this equation:
Profit = Revenue - Costs
Profit = R(x) - C(x)
If we create a new function P(x) that represent profit function, hence we could rewrite the profit function into:
P(x) = R(x) - C(x) ... (i)
Based on the question, we have both revenue and costs formulas as stated below:
R(x) = 24x ... (ii)
C(x) = 17x + 161 ...(iii)
We could subtitute equations (ii) and (iii) into equation (i) to get the profit formula:
P(x) = R(x) - C(x)
P(x) = 24x - (17x+161)
P(x) = 7x - 161 ... (iv)
To get the units must be produced, we have to understand that Break Even is a condition where the revenue is exactly the same of its costs, or when the profit is 0 (zero). Hence we could write the equation:
P(x) = 0 ...(v) --> Break Even
Then we would subtitute the equation (iv) into equation (v) to find the units must be produced (x) to achieve the break even.
P(x) = 0
7x - 161 = 0
7x = 161
x = 23 ... (vi)
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Determine which set of side measurements could be used to form a right triangle.
5, 10, 30
2, 3, 4
square root of 26, square root of 34, 60
square root of 11, 7, square root of 60
Answer:
the 4th one
Step-by-step explanation:
because we determined by Pythagorean theorem (the square root of 11)2 + 7 the power of 2 =
(the square root of 60)2 .....square root cancelled by power of 2
11 + 49 = 60
60 = 60
Erica worked 14 hours last week and 20 hours this week. If she earns $9 per hour how much did she earn during these two weeks?
Answer: $306
Step-by-step explanation:
You can find the answer by multiplying 9 by each of the values.
14 * 9 = 126
20 * 9 = 180
Add these values together and you get 306 !
Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one
day. It is reasonable to assume that the population is approximately normal.
4.754 4.372 4.174 4.678 4.424 4.227
4.123 4.254 3.951 4.291 4.414
(a) Construct a 95% confidence interval for the mean rate. Round the answer to at least four decimal places.
A 95% confidence interval for the mean rate is < M
Using the confidence interval, a 95% confidence interval for the mean rate is (4.4206,4.2106).
In the given question, we have to construct a 95% confidence interval for the mean rate.
There is given interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day.
It is reasonable to assume that the population is approximately normal.
4.754, 4.375, 4.173, 4.678, 4.425, 4.227, 4.126, 4.250, 3.951, 4.197
We find the mean
Mean=4.754+4.375+4.173+4.678+4.425+4.227+4.126+4.250+3.951+4.197/10
Mean=43.156/10
Mean=4.3156
Standard Deviation(S)=√(x−mean)^2/n−1
S=√(4.754−4.3156)^2/10−1
S=√(0.4384)^2/9
S=√0.1922/9
S=√0.02136
S=0.1462
95%=0.95 confidence interval for z is
Z= [tex]z_{\alpha /2,dt}[/tex]
dt=n−1
dt=10−1
dt=9
[tex]\alpha[/tex] = 1−0.95=0.05
[tex]\alpha /2[/tex]=0.05/2=0.025
Z= [tex]z_{0.025,9}[/tex]
Z= 2.262
Confidence interval
CI=Mean±Z× s/√n
CI=4.3156±2.262× 0.1462/√10
CI=4.3156±2.262× 0.1462/3.1623
CI=4.3156±2.262×0.0462
CI=4.3156±0.105
CI=(4.3156+0.105),(4.3156−0.105)
CI=(4.4206,4.2106)
Hence, a 95% confidence interval for the mean rate is (4.4206,4.2106).
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solve by using substitution 2x-3y=-12 and x+y=9
i need help please, :))))))
Answer:
AAS
Step-by-step explanation:
Two angles and two sides are marked as congruent. Vertical angles are congruent, so the answer is AAS
A standard die is rolled. Find the probability that the number rolled is greater than 1. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Count on from 6. Write the number
that shows 2 more.
Using the addition, the number that shows 2 more count from 6 is 8.
In the given question we have to write the number that shows 2 more.
We have to start counting from 6.
To write the number that shows 2 more we add 2 in 6, then again add 2 in the result of add of 2 and 6 and so on.
Hence the number that shows 2 more starting from 6 is
6+2=8
So the number that shows 2 more is 8.
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Humberto walks 3 miles due north then turns around and walks 5 miles due south how far is Humberto from his starting point
Humberto's displacement is 2 miles due south far from his starting point.
How is the displacement completed?We understand that displacement is a vector quantity with both magnitude and direction, while distance is a scalar quantity with only magnitude.
Displacement, unlike distance, shows the direction and position of an object from its original base. This means that displacement refers to how far an object has traveled out of its original position with the direction included.
In other words, displacement shows the object's overall change in position and the direction of the new position from the former.
Starting point = 0
Distance covered toward the north = 3 miles
Distance covered toward the south = 5 miles
Displacement = 2 (0 - 3 + 5) miles
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Order these numbers from least to greatest.
2.8, 2.5081, 1.935, 2.58
2.8
<
2.5081
<
1.935
2.58
Answer:
Step-by-step explanation:
1.935<2.5081<2.58<2.8
∵1.9350<2.5081<2.5800<2.8000
Hey can someone please find the area of this shape? Thank you so much I’ll give brainly. Please explain
Answer:
44.63
Step-by-step explanation:
( The heart shape makes two half circles and a square )
1 ) The two half circles together make a whole, so we can first find the area of that circle!
2 ) We can see that the dynamiter is 5in. We can cut this in half to find the radius...
5 ÷ 2 = 2.5
3 ) The area of a circle is found with the equation ( A = πr2 ). We can plug in the radius ( 2.5 ) to find the area...
A = π( 2.5 )2 = 19.635in
4 ) Now that we know the area of the circle we can find the area of the square. To find this we can use the equation ( A = a2 ) where a represents the edge length in this case 5in.
A = ( 5 ) 2 = 25in
5 ) We can now add the area of the circle and the area of the square to get the area of the heart!
19.635 + 25 = 44.63
Hope this helps! :)
In Chase's grade, 162 students are enrolled in health and 38 students are not. What
percentage of the students in the school are enrolled in health?
Write your answer using a percent sign (%).
2 percentage of the students in the school are enrolled in health .
How do percentages work?
10%, a comparative figure denoting one hundredth of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.students are enrolled in health = 162
students are enrolled not in health = 38
162 + 38 = 200 Add
Total of 100 Students
then ,
200/100
= 2%
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A stadium has 51,000 seats. Seats sell for $28 in Section A, $16 in Section B, and $12 in Section C. The number of seats in Section A equals the total number of seats in sections B and C. Suppose the stadium takes in $1,078,400 from each sold-out event. How many seats does each section hold?
Answer:
A: 25,500
B: 14,600
C: 10,900
Step-by-step explanation:
This is what we know:
a = b + c
a + b + c = 51,000 Substitute in a for b + c
a + a = 51000 Combine like terms.
2a = 51000 Divide both sides by 2
a = 25,500
28a + 16b + 12c = 1078400 Substitute in 25.600 for a
28(25500) + 16b + 12c = 1078400
714000 + 16b + 12c = 1078400 Subtract 714000 from both sides
16b + 12 c = 364400
25500 +b + c = 51000 Subtract 25500 from both sides
b + c + = 25500 Multiply this equation all the way through by -12 and add it to the bold equation above it.
-12b -12c = -306000
16b + 12c = 364400
4b = 58400 divide both sides by 4
b = 14600
a + b + c = 51000 Plug in what we know
25500 + 14600 + c = 51000
40100 + c = 51000 Subtract 40100 from both sides
c = 10900
m∠7 = 100° . Find the measure of ∠5
The measures of angles 5 and 3 is 100 degrees.
How to find the measure of angles in intersecting lines?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles, linear angles etc.
Therefore,
m∠7 = m∠5 (corresponding angles)
corresponding angles are congruent.
Therefore,
m∠5 = 100 degrees
m∠3 = m∠7(alternate angles)
m∠3 = 100 degrees.
Alternate angles are congruent.
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Enter the repeating digit:
2/3 = 0.?
Answer:
6
the recurring digit is 6
ANS: 0.6
Consider f(x) = 3x² 30x - 72.
Find the x-intercept(s) and y-intercept of f(x).
The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72
Given,
In the question:
The function is given as :
Consider f(x) = 3x² 30x - 72.
To find the x-intercept(s) and y-intercept of f(x).
Now, According to the question:
f(x) = 3x²× 30x - 72.
f(x) = 90[tex]x^{3}[/tex] - 72
Solve the equation:
90[tex]x^{3}[/tex] = 72
Make the leading coefficient of the variable one
[tex]x^3 = 72/90\\[/tex]
Cross out the common factor
[tex]x^3[/tex] = 4/5
Take the n-th root on both sides:
x = [tex]\sqrt[3]{\frac{4}{5} }[/tex]
To find the y - intercept(s)
f(x) = 3x²× 30x - 72.
Set x = 0
f(0) = 3 × 0 × 30 × 0 - 72
f(0) = - 72
Hence, The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72
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A rental car company charges $53 per day to rent a car and $0.08 for every mile driven. Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend. Use the drop-down menu below to write an inequality representing dd, the total number of days Rashaad can rent the car while staying within his budget.
The inequality that can be used to represent the total number of days Rashaad can rent the car while staying within his budget is d ≤ 4 .
How to represent inequality?The rental car company charges $53 per day to rent a car and $0.08 for every mile driven.
Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend.
Therefore, the inequality to represent the total number of days Rashaad can rent the car can be represented as follows:
Therefore,
53d + 0.08(475) ≤ 250
53d + 38 ≤ 250
53d ≤ 250 - 38
53d ≤ 212
divide both sides of the inequality by 53
53d / 53 ≤ 212 / 53
d ≤ 4
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Question
An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.
Which proportion could be used to find the commission amount for sales totaling $15,000?
The commission amount for sales totaling $15,000 is $600.
How to calculate the value?From the information, the advertising sales representative has sales totaling $4500 and for these sales, the representative earns a commission of $360.
Therefore, the commission fraction will be:
= Commission / Sales
= 360 / 4500
= 1/25
Therefore, the commission on $15000 will be:
= 1/25 × $15000
= $600
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Answer:
(1) where y = 18 when x = 2.
What is the value of x when y = 36?
= 4
(2) when x is 4, y is 11.
What is the constant of proportionality for this relationship?
= 2.75
(3) What is 34% of 650?
=4.875
(4) 28 7
16 4
12 3
=1/4x
(5) Last month 288 people attended the monthly bingo night. This month 243 people attended bingo night.
= 15.6
(6) Over 6.8 months, a tree grew 7.48 inches.
=1.1
(7) A party-size bag of chips contains 15 ounces. This is 750% of the amount in the snack-size bag.
=2
(8) An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.
Which proportion could be used to find the commission amount for sales totaling $15,000?
=360/4500=x/15,000
(9) Brad's dinner bill, including a 16% tip, is $10.44.
= 9
(10) Do the values in the table represent a proportional relationship?
x 2 4 6 8
y 3.2 6.4 9.6 12.8
Select from the drop-down menu to correctly complete the statement.
response - correct
All of the y-values are a constant multiple of the corresponding x-values, so the relationship is proportional.
(11) Molly estimated the width of a poster to be 21 inches. The actual width is 26 inches.
=19.2
(12) Solve for x.
x−9= −5/24
=1 7/8
(13) Each 1/2 inch on a scale model represents an actual length of 1/6 of a yard.
=3
(14) Landon is buying a shirt priced at $19.99. The sales tax is 8.5%.
= 21.69
(15) A sprinter ran 100 meters in 15 seconds.
=400
(16) Two gears are connected and rotating at the same time. The smaller gear completes 3 2/3 rotations every time the larger gear completes 1/3 of a rotation.
=11
(17) Jasmine dumped her box of spare change and found out that she had saved 128 coins. She separated them and counted 48 dimes.
What percent of Jasmine's coins are dimes?
= 37.5
(18) A pair of boots costing $299 is marked down 45%.
= 164.45
(19) Figure 1 is dilated to get Figure 2.
What is the scale factor?
Enter your answer in simplest form in the box.
=5/8
(20) y=5/x Not proportional
y=5(−2x) Proportional
y=x/4 Proportional
y=6x+4 Not proportional
Step-by-step explanation:
Hey here u go i so tired lol completely POOPED God bless u have a great test
There are 1255 students in Sarah's high school. 40% of the students are taking Spanish. How many students are not taking spanish?
Which expression is equivalent to 8 ^ -3
The expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
First, let us understand the exponents or power:
A power, or index, is a little floating number that appears next to a number or letter.
It is denoted as a^m.
where a = base number
and m = power or index number.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
8^-3
We can solve as;
8^-3 = 8^(3 * -1) = (8^3) ^ -1 = 1 / 8^3 [since a⁻¹ = 1 / a]
So, 8^-3 = 1 / 8^3.
Thus, the expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
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