Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as service charges. Company B charges $8 per hour and an additional $40 as service charges.
Part A: Write an equation to represent each company's total charges for renting a truck for a certain number of hours. For both equations (one for Company A and one for Company B), define the variable used. (4 points)
Part B: Which company would charge less for renting a truck for 8 hours? Justify your answer. (3 points)
Part C: How much money is saved by using the services of Company A instead of Company B to rent a truck for 2 hours? (3 points)
If p-1 is a factor of p^4+p^2+p-k the value of k is
The value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]
How to determine the value of k?The expression is given as:
[tex]p^4+p^2+p-k[/tex]
The factor is given as:
p - 1
Set the factor to 0
p - 1 = 0
Add to both sides
p = 1
Substitute 1 for p in the expression and equate it to 0
[tex]1^4+1^2+1-k = 0[/tex]
Evaluate the exponents
1+1+1-k = 0
Evaluate the sum
3-k = 0
Add k to both sides
k = 3
Hence, the value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]
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How to simplify the expression 60/(-4)
Simplify the following expression: 2x − 6y + 3x2 + 7y − 14x. 3x2 + 12x + y 3x2 − 12x − y 3x2 − 12x + y 3x2 − 12x − 13y
The required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.
Given that,
To simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
= 2x − 6y + 3x² + 7y − 14x.
= 3x² + 2x -14x + 7y -6y
= 3x² -12x + y
Thus, the required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.
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Haley and Samuel can each make one gift box in two hours. Rachael takes three hours to make the gift box alone. If Haley, Samuel, and Rachael work together, how long will it take them to make one gift box?
It will take 40 minutes for them to make one gift box.
Combined ratesGiven that Haley and Samuel can each make one gift box in two hours, while Rachael takes three hours to make the gift box alone, to determine, if Haley, Samuel, and Rachael work together, how long will it take them to make one gift box, the following calculation must be performed, using combined rates:
1/2 + 1/2 + 1/3 = X3/6 + 3/6 + 2/6 = X8/6 = X6/6 = 1 hour8/6 = 40 minutesTherefore, it will take 40 minutes for them to make one gift box.
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Answer:It will take 40 minutes for them to make one gift box
Step-by-step explanation:
0.75 = log x raise each side of the equation as power
Two trains leave stations 252 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other travels at 100 miles per hour. How long will it take for the two trains to meet?
Final answer:
The time it takes for two trains traveling towards each other at speeds of 80 mph and 100 mph, and starting 252 miles apart, is found by dividing the distance by their combined relative speed. It takes them 1.4 hours or 1 hour and 24 minutes to meet.
Explanation:
To solve the problem of calculating the time it takes for two trains to meet, we need to understand the concept of relative speed in motion problems. When two objects move towards each other, their relative speed is the sum of their individual speeds. In this case, one train travels at 80 miles per hour and the other at 100 miles per hour, giving us a combined relative speed of 80 mph + 100 mph = 180 mph.
The distance between the two trains is 252 miles, and to find the time taken for the trains to meet, we divide the total distance by the relative speed:
Time = Distance / Relative Speed
Time = 252 miles / 180 mph
Time = 1.4 hours or 1 hour and 24 minutes for the two trains to meet.
Write an equation ten times the sum of half a number and 6 is 8.
A recipe for muffins calls for 3⁄5 of a cup of sugar and 4 cups of flour. If you want to make a bigger batch, using 5 cups of flour, how much sugar will you need?
Solve the equation for the letter L: A=LW
L = AW
L equals W over A
L = A − W
none of the above
Please help me :) Thanks!
Which is a unit rate ? 4 dollars to 3 cans 5 students to 2 teachers 6 hours and 1 book 3 miles 2 days
Answer:
6 hours to 1 book
Step-by-step explanation:
The restaurant bill you and your friend received was not itemized. You ordered 2 drink refills and the egg breakfast, for a total of $8.40. Your friend ordered 3 refills and the egg breakfast for $9.35.
(a) Write a system of equations for the situation. Use r for the amount charged for a refill and b for the amount charged for the egg breakfast.
(b) Graph the equations in the system.
(c) Use your graph to estimate how much each item cost.
Everett made 3/5 of the baskets he shot. Suppose he shot 60 baskets. How many did he make?
Module 04.03 Exponential Functions and Models: Essential Questions:
1) How do the properties of exponents apply to exponential functions?
2)How are key features of graphs and tables used to model relationships between two quantities?
3)How can the average rate of a change be identified for a function?
*PLEASE HELP! NEED TO KNOW THIS.*
Properties of exponents are used to simplify and manipulate exponential functions. In graphing, growth rate, intercept, and asymptotes model relationships. The average rate of change for a function is calculated based on changes in output divided by input changes over an interval.
Explanation:Understanding Exponential Functions and ModelsExponential functions are mathematical expressions where a constant base is raised to a variable exponent. The properties of exponents, such as product, quotient, and power rules, apply to these functions and are used to simplify and manipulate expressions.
When modeling relationships between two quantities using graphs and tables, key features like the growth rate, y-intercept, and asymptotes are important. The growth rate can be understood from the steepness of the graph or how quickly the y-values increase as x increases. The y-intercept represents the starting value of the quantity being modeled when x equals zero.
The average rate of change for a function is identified by calculating the change in the function's output values (y-values) divided by the change in the input values (x-values) over the interval of interest. For exponential functions, this rate of change is not constant, but increases or decreases at a rate proportional to the function's current value.
An example of exponential growth in a natural population might be the rapid increase in a bacteria population in an ideal lab condition, where it doubles every fixed amount of time. In contrast, a logistic growth pattern occurs when the growth rate decreases as the population reaches carrying capacity, such as the population of sheep in a field with limited grass for food.
Exploring the Exponential DistributionThe exponential distribution is typically used to model the time between events in a memoryless process, where the probability of an event occurring is the same at any moment. In an exponential distribution, outcomes are not equally likely as not all intervals of time are equally likely to occur before the next event. The mean (m), often referred to as the expected value, and the standard deviation can be derived from the rate parameter, which is the reciprocal of the mean.
Understanding how to manipulate a linear equation, as well as interpret and compute growth rates, is foundational in various applications including those in economics, biology, and environmental science. The ability to read and manipulate graphs is crucial for clearly presenting data and drawing accurate conclusions.
An architectural drawing lists the scale as 1/4 = 1. If a bedroom measures 3 1/2 by 5 1/4 on the drawing, how large is the bedroom
Answer:
The measure of the bedroom is 14 by 21
Step-by-step explanation:
This scale represents the every measure in the drawing is a 1/4 of the original measure, so to find the original measure you must multiply the measure you find in the drawing by 4.
So for the beadroom (3 1/2, 5 1/4), you multiply each one by 4
The real measures of the beadroom are:
(3 1/2 * 4, 5 1/4 * 4)
(14,21)
The measure of the bedroom is 14 by 21
how to write unit form for (2 tens 1 one) x 10
What is the area of a triangle that has a height of 4 feet and a base length of 9 feet? 18 feet2 36 feet2 144 feet2 324 feet2
18 feet is the answer hope this helps!!
Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}. What is A ∩ B? (2 points)
Select the factors of 6ab + 3ay − 2bx − xy.
A. (3a − x)(2b + y)
B. (3a − y)(2b + x)
C. (2a − x)(3b + y)
D. (2a − y)(3b + x)
I need the answer I don't get it ...and this is a really long test ..but so far I only need help on this one . thanks to whoever helps me and give correct answer
Answer:
The factors of given expression is (3a-x)(2b+y)
A is correct
Step-by-step explanation:
Given: [tex]6ab+3ay-2bx-xy[/tex]
We need to factor the given expression.
First we make two group
[tex]\Rightarrow (6ab+3ay)+(-2bx-xy)[/tex]
Factor each group
[tex]\Rightarrow 3a(2b+y)-x(2b+y)[/tex]
[tex]\Rightarrow (3a-x)(2b+y)[/tex]
So, we get two factor (3a-x) and (2b+y)
Hence, The factors of given expression is (3a-x)(2b+y)
11 POINTS GUYS PLZ
Answer 12 and 14
12) 10.77 + 2.09 + 0.75 = 13.61
13.61 x 1.07 = $14.56
total amount = $14.56
14) C shows the possible combinations
Find the value of X in the problem below. Geometry
(3x+10) +14x = 180
17x +10 = 180
17x=170
x = 170/17 = 10
x = 10
Which is an obtuse angle?
∠CAB
∠BAC
∠BCA
∠ABC
2. If you have budgeted 12% of your monthly income for groceries, how much can you spend on groceries if you earn $950 bi-weekly?
bi weekly means you get paid every 2 weeks ( 2 times a month)
950*2 = 1900 per month for pay
1900*0.12 = 228 a month for food
Answer:
if you earn $950 bi-weekly, you earn 2 x 950 = $1900 per month. If you have budgeted 12% of your monthly income for groceries you need to find 12% of $1900: (1900 / 100) x 12 = 228. Answer: you can spend $228 a month on groceries.
can someone help with this
A triangle has angles that measure 30, 60, 90. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle?
Which of the following best describes the expression 6(y + 3)?
1.)The product of two constant factors six and three plus a variable
2.)The sum of two constant factors six and three plus a variable
3.)The product of a constant factor of six and a factor with the sum of two terms
4.)The sum of a constant factor of three and a factor with the product of two terms
Answer: Hence, option '3' is correct.
Step-by-step explanation:
Since we have given that
[tex]6(y+3)[/tex]
This expression can be written in statement.
Here, we can see that there are two terms:
1) A constant factor of 6
2) Sum of two terms
So, according to options it can be written as :
The product of constant factor of 6 and a factor with the sum of two terms i.e. y and 3.
Hence, option '3' is correct.
If n = 8 and 16 • 2m = 4n – 8, then m = ?
Final answer:
The value of m is 0.75 when n = 8 and the equation 16 • 2m = 4n – 8 is satisfied, by performing simple algebraic operations to isolate and solve for m.
Explanation:
To find the value of m when n = 8 and 16 • 2m = 4n – 8, we first replace n with 8 in the second equation:
16 • 2m = 4(8) – 8
16 • 2m = 32 – 8
16 • 2m = 24
Now we divide both sides of the equation by 16 to isolate 2m:
2m = 24 / 16
2m = 1.5
Finally, to find m, we divide both sides of the equation by 2:
m = 1.5 / 2
m = 0.75
So the value of m that satisfies the given conditions is 0.75.
An angle measures 20° more than the measure of a complementary angle. What is the measure of each angle?
if O represents number of integers between 10,000 and 100,000 all of whose digits are odd, and E represents number of integers between 10,000 and 100,000 all of whose digits are even, what is the value of O - E?