If the composite functions f(g(x)) and g(f(x)) equal x then the function g is the __________ function of ff.
Sue receives a base salary of $90 weekly plus a 12% commission on all sales. sue had $3,000 in sales this week. how much did she make total?
Her gross pay was the amount of $450 for last week.
What is the commission?The commission is determined by the product of the commission rate and the total sales.
Commission = Commission rate x Total sales
As per the question, we have data :
Commission rate = 12 %
Total sales = $3,000
The base salary = $90
We know that,
Commission = Commission rate x Total sales
= 12% x $3,000
= 0.12 x $3,000
= $360
The total pay is then the base salary increased by the commission:
Total pay = base salary + Commission
Total pay = $90+ $360
Total pay = $450
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The cruise control function on Georgina's car should keep the speed of the car within 3 miles per hour of the set speed. The set speed is 55 miles per hour. Write a compound inequality to show the leaves that are within each range. Then graph the solutions.
Answer:
Given,
Set speed of car = 55,
∵ The speed of the car within 3 miles per hour of the set speed.
So, the maximum speed of car = 55 + 3,
And, the minimum speed of car = 55 - 3
Let x shows the current speed of car,
x ≤ 55 + 3 or x ≥ 55 - 3
x - 55 ≤ 3 or x - 55 ≥ - 3
x - 55 ≤ 3 or -(x-55) ≤ 3
⇒ | x-55 | ≤ 3
Which is the required compound inequality,
Now, 55 - 3 ≤ x ≤ 55 + 3
52 ≤ x ≤ 58
⇒ [52, 58]
Which is the solution of the above compound inequality.
Also, the graph is shown below.
Jenny has been saving quarters in a piggy bank since she was born. She currently has 192 quarters in her piggy bank. She wants to save $75 to buy a new Ipod, so she decides to add 2 quarters every day. She sets up and solves the equation shown. What does her solution mean?
y = 192(.25) + .25x
75 = 192(.25) + .25x
27 = .25x
x = 108
Question 1 options:
She needs to save an additional $108.
She needs to save 216 more quarters.
She needs to save for 108 more days.
She needs to save an additional 108 quarters.
What is767,074 rounded to the nearest hundred thousand
Subtract (enter answer is standard form)
(-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)
Which graph represents the inequality? (has picture)
2x-3y≤6
Multiply
8y^4(2y^4-3y^3+5y)
Solve for x
0=7x^2+x+5
Harold and Helen both spend 3 hours reading a novel. Helen reads 30 more pages than Harold. Helen reads at least 40 pages in 1 hour, but no more than 70 pages in 1 hour.
Which statement correctly describes the range of pages Harold reads?
Harold reads more than 90 pages, but less than 180 pages.
Harold reads at least 90 pages, but no more than 180 pages.
Harold reads more than 150 pages, but less than 240 pages.
Harold reads at least 150 pages, but no more than 240 pages.
PB&P sells peanut butter and pickle sandwiches. The Standard special sells for $2 and the Deluxe special sells for $4.50. When all related business expenses are included, the Standard special costs $0.50 to prepare and the Deluxe special costs $1.25 to prepare.
Last Monday, PB&P sold at least $200 worth of Standard and Deluxe peanut butter and pickle sandwich specials and its expenses were no more than $100. At least 30 Standard special were sold.
Let x be the number of Standard Specials sold last Monday and y be the number of Deluxe specials sold last Monday.
Which ordered pairs representing a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation?
Select each correct answer.
(30,68)(30,68)
(80,40.5)(80,40.5)
(60,70)(60,70)
(40,60)(40,60)
(50.5,40)
Effie is selling candles to raise money for new soccer league equipment. A small candle sells for $8 and a large candle sells for $12. The number of large candles Effie sells must be greater than or equal to 2 times the number of small candles she sells. She has at most 48 candles to sell.
The number of small candles sold is represented by x and the number of large candles sold is represented by y.
What is the maximum revenue she can make?
$448
$512
$576
$588
What is the product of 4−5i and 2+3i?
Enter your answer, in standard form, in the box.
Answer:
Part 1) [tex]-3x^4+3x^3+8x^2-2x-5[/tex]
Part 2) The graph in the attached figure
Part 3) [tex]16y^8-24y^7+40y^5[/tex]
Part 4) [tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex] and [tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]
Part 5) Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page
Part 6) [tex](30,68)[/tex], [tex](40,60)[/tex]
Part 7) [tex]\$576[/tex]
Part 8) [tex]23 + 2i[/tex]
Step-by-step explanation:
The complete answers in the attached figure because is too long
Part 1) Subtract (enter answer is standard form)
we have
[tex](-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)[/tex]
Eliminate parenthesis
[tex]-2x^4-2x^3+8x^2+2-x^4+5x^3-2x-7[/tex]
Combine like terms
[tex](-2x^4-x^4)+(-2x^3+5x^3)+8x^2-2x+(2-7)[/tex]
[tex]-3x^4+3x^3+8x^2-2x-5[/tex] ------> standard form
Part 2) Which graph represents the inequality?
we have
[tex]2x-3y\leq 6[/tex]
Rewrite the inequality ------> [tex]3y\geq2x-6[/tex]
the solution is the shaded area above the solid line
the equation of the line is equal to [tex]3y=2x-6[/tex]
the slope of the line is positive
the y-intercept of the line is the point [tex](0,-2)[/tex] ---> value of y when the value of x is equal to zero
the x-intercept of the line is the point [tex](3,0)[/tex] ---> value of x when the value of y is equal to zero
The solution in the attached figure
Part 3) Multiply
we have
[tex]8y^4(2y^4-3y^3+5y)\\=( 8y^4*2y^4)-(8y^4*3y^3)+(8y^4*5y)\\=16y^8-24y^7+40y^5[/tex]
Part 4) Solve for x
we have
[tex]0=7x^2+x+5[/tex]
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]7x^2+x+5=0[/tex]
so
[tex]a=7\\b=1\\c=5[/tex]
substitute in the formula
[tex]x=\frac{-1(+/-)\sqrt{1^{2}-4(7)(5)}} {2(7)}[/tex]
[tex]x=\frac{-1(+/-)\sqrt{-139}} {14}[/tex]
remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{-1(+/-)\sqrt{139}i} {14}[/tex]
[tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex]
[tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]
Part 5) Harold and Helen both spend [tex]3[/tex] hours reading a novel. Helen reads [tex]30[/tex] more pages than Harold. Helen reads at least [tex]40[/tex] pages in [tex]1[/tex] hour, but no more than [tex]70[/tex]pages in [tex]1[/tex] hour.
Which statement correctly describes the range of pages Harold reads?
Let
x------> the number of pages that Harold read
y------> the number of pages that Helen read
we know that
[tex]y=30+x[/tex] -----> equation A
[tex]y\geq 40\ pages[/tex] ------> in one hour
so
in three hours -------> [tex]y\geq 120\ pages[/tex] ------> inequality B
[tex]y\leq 70\ pages[/tex] ------> in one hour
so
in three hours ------->[tex]y\leq 210\ pages[/tex] ------> inequality C
Substitute equation A in the inequality B
[tex]x+30\geq 120\ pages[/tex] ------> [tex]x\geq 90\ pages[/tex]
Substitute equation A in the inequality C
[tex]x+30\leq 210\ pages[/tex] ------> [tex]x\leq 180\ pages[/tex]
therefore
Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page
Part 6) Let
x------> the number of Standard Specials sold last Monday
y------> the number of Deluxe specials sold last Monday
we know that
[tex]2x+4y\geq 200[/tex] -----> inequality A
[tex]0.50x+1.25y\leq100[/tex] -----> inequality B
[tex]x\geq30[/tex] -----> inequality C
Remember that
If a ordered pair representing a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation
then
the ordered pair must satisfy all restrictions
Verify
A) [tex](30,68)[/tex]
Substitute the value of x and y in each inequality
Inequality A
[tex]2(30)+4(68)\geq 200[/tex]
[tex]332\geq 200[/tex] ------> is true
Inequality B
[tex]0.50(30)+1.25(68)\leq100[/tex]
[tex]100\leq100[/tex] -----> is true
Inequality C
[tex]30\geq30[/tex] -----> is true
The ordered pair [tex](30,68)[/tex] represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation
B) [tex](80,40.5)[/tex]
The value of [tex]y=40.5[/tex] not make sense in the context of the situation, because is not a whole number
C) [tex](60,70)[/tex]
Substitute the value of x and y in each inequality
Inequality A
[tex]2(60)+4(70)\geq 200[/tex]
[tex]400 \geq 200[/tex] ------> is true
Inequality B
[tex]0.50(60)+1.25(70)\leq100[/tex]
[tex]117.5\leq100[/tex] -----> is not true
therefore
the ordered pair [tex](60,70)[/tex] is not a solution
D) [tex](40,60)[/tex]
Substitute the value of x and y in each inequality
Inequality A
[tex]2(40)+4(60)\geq 200[/tex]
[tex]320\geq 200[/tex] ------> is true
Inequality B
[tex]0.50(40)+1.25(60)\leq100[/tex]
[tex]95\leq100[/tex] -----> is true
Inequality C
[tex]40\geq30[/tex] -----> is true
The ordered pair[tex](40,60)[/tex] represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation
E) [tex](50.5,40)[/tex]
The value of [tex]x=50.5[/tex] not make sense in the context of the situation, because is not a whole number
Twice a number is added to the number and the answer is 90. find the number
the perimeter of a square picture frame is 48 inches. one side length of the frame is 30.48 centimeters. how many centimeters are in an inch?
The answer is 2.54 centimeters but i need help with my work
Laura drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 8 hours. when laura drove home, there was no traffic and the trip only took 6 hours. if her average rate was 16 miles per hour faster on the trip home, how far away does laura live from the mountains
To find the distance Laura lives from the mountains, calculate her average speed when driving to the mountains and use the time taken during the trip. With the given speeds and travel times, the distance can be determined using a simple equation.
Explanation:To find the distance Laura lives from the mountains:
Let x be Laura's average speed when driving to the mountains.Since Laura drove 16 mph faster on the way home, her speed returning was x+16 mph.Distance to mountains = x * 8 (hours) and distance from mountains = (x+16) * 6 (hours).Set up the equation: x * 8 = (x+16) * 6 to solve for x.Once x is found, the distance Laura lives from the mountains can be calculated as x * 8.
I've never even seen a box and whiskers plot before!! Should be pretty straight forward though. Thanks!
If two lines are perpendicular describe the relationship between their slopes
The graphs below have the same shape. The equation of the blue graph is f(x) = 2x. Which of these is the equation of the red graph, g(x)?
The functions f(x)=x² and g(s)=s² are essentially the same function with different variable notations. The f(x)=2x graph is linear, and the red graph g(x) with the same shape would also be linear, involving a transformation that retains the proportional relationship between x and y.
Explanation:Based on the provided information, the equation of f(x) is given as f(x) = x². If the blue graph represents this function, and we are looking for the red graph equation g(x), which has the same shape, we need to understand the transformation involved.
Regarding the equations provided in the examples, functions f and g are both defined as taking an input, squaring it, and outputting the result. Although they use different variable names (x for f and s for g), they are effectively the same function. When you have a transformation such as f(x-2), the graph of the function shifts to the right without changing its shape. Similarly, if the red graph were g(x) = 2x, the transformation applied would be to double the output, stretching the graph vertically relative to f(x).
Since the blue graph equation is given as f(x) = 2x and the red graph has the same shape, it means the red graph, g(x), also has a linear relation with a proportional transformation applied. Common linear transformations include multiplying by a scalar to scale the graph or adding/subtracting a number to shift the graph along the x-axis or y-axis.
Claire made 1⁄2 pound of trail mix. If she puts 1⁄4 pound of trail mix into each bag, how many bags are filled?
-3x+2y=-10, -2x+y=-6 solve by substitution
Need help finishing problem 27.
Evaluate the function for x = m/4
f(x) = 8x^2 - 4x
A. 2m^2 - m
B. m^2 - m
C. m^2/2 - 4m
D. m^2/2 - m
Final answer:
To evaluate the function for x = m/4, substitute m/4 for x in the function[tex]f(x) = 8x^2 - 4x[/tex]and simplify to get the result [tex]m^2/2 - m.[/tex]
Explanation:
To evaluate the function [tex]f(x) = 8x^2 - 4x[/tex] for x = m/4, we substitute m/4 for x in the function and simplify.
Substitute x with m/4:
[tex]f(m/4) = 8(m/4)^2 - 4(m/4)[/tex]
Simplify the equation:
[tex]f(m/4) = 8(m^2/16) - m[/tex]
[tex]f(m/4) = (8/16)m^2 - m[/tex]
[tex]f(m/4) = m^2/2 - m[/tex]
Therefore, the correct answer is D. [tex]m^2/2 - m.[/tex]
Write the polynomial in standard form. identify the degree and leading coefficient of the polynomial. then classify the polynomial by the number of terms
The Standard Form: -w¹² + 4w¹¹,
Degree: 12 degree
Leading Coefficient: -1
What is polynomial?Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given equation
4w¹¹ - w¹²
Standard form of polynomial,
List the exponents in decreasing order of importance.
-w¹² + 4w¹¹
Degree of polynomial,
The degree, or the exponent in the first term, if it is in standard form, is the biggest exponent.
degree is 12.
Leading coefficient,
the first term's standard form coefficient Before the w in the first phrase, there is and understood 1.
for equation coefficient is -1,
Hence degree = 12, and leading coefficient is -1.
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The complete Question is
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial.
Then classify the polynomial by the number of terms.
4w11 - w12
standard form
degree
leading coefficient.
Which expression represents the phrase, "one third the sum of 12 and a number"?
Let
x--------> the number
we know that
1) the phrase, "the sum of 12 and a number"
represent the expression --------> [tex](12+x)[/tex]
and
2) the complete phrase, "one third the sum of 12 and a number"
represent the expression --------> [tex]\frac{1}{3}(12+x)[/tex]
therefore
the answer is
[tex]\frac{1}{3}(12+x)[/tex]
Jana is thinking of a number. If she divides her number by 12 and then multiplies the quotient by 8, the result is 520. What number is Jana thinking of?
Find the value of x in the triangle
if you live in Dallas then you live in Texas what is the biconditional of this
The biconditional of the statement 'If you live in Dallas then you live in Texas' is 'You live in Dallas if and only if you live in Texas'. This means that living in Dallas is both necessary and sufficient for living in Texas.
Explanation:The biconditional of the statement 'If you live in Dallas then you live in Texas' would be 'You live in Dallas if and only if you live in Texas'. In other words, living in Dallas is both necessary and sufficient for living in Texas. This means that if one condition is true, then the other must also be true. Similarly, if one condition is false, then the other must also be false. A biconditional statement essentially equates the truth of two conditions.
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How do I solve a liner equation in the form a(x-b)=cx? I have no idea plz help
4 pieces of wood each 11 and a half inches long are required to build a cabinet. If all four pieces are cut from one board and 1 inch is allowed for waste in cutting each piece, how long should the board be?
what is the area of a circular mirror with a radius of 10 cm?
Final answer:
The area of a circular mirror with a radius of 10 cm is calculated using the formula πr², which results in an area of 314.16 cm².
Explanation:
The area of a circular mirror can be calculated using the formula πr², where π (pi) is approximately 3.1416 and r is the radius of the circle. Given the radius of the circular mirror as 10 cm, we can substitute this value into the formula to find the area.
Area = π × (10 cm)²
A = 3.1416 × 100 cm²
A = 314.16 cm²
Therefore, the area of the circular mirror is 314.16 cm².
Three sides of a fence and an existing wall form a rectangular enclosure. the total length of fence used for three sides is 240 ft. write the area function in terms of one variable, then find the domain of that function
Solve the literal equation 2a-b=8b-4a for a
Amy leaves a rest stop at 2 PM traveling west, at 45 miles per hour. Sarah leaves 2 hours later, also traveling west, but at 55 miles per hour. At what time will Sarah catch up with Amy?
55(t-2) =45t
55t-110 = 45t
-110 = -10t
t = 11 hours
2 pm plus 11 hours = 1 am
Answer: mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? ... If the range and IQR are small, the values are clustering around some central value.
Step-by-step explanation:
Suppose that you have he option to buy an item with either cash or credit. Under which condition would you use credit?
Answer:
If you want to build a good credit history
Step-by-step explanation:
Buying something in order to build a good credit history does not benefit in the short run such as any financial or non-financial benefit.
However, when need arises to make request for a large sum of loan in the long run (such as buying house, purchasing vehicle or capital for investing in business) from the financial institution or any other credit providers, then the good credit history would be winning key factor for obtaining the loan.
How many n's are there in an atom of p-33?
Solve 2x - 5 = 2x + 4x - 12 plz :)