Two plumbers charge an initial fee and an hourly rate.
The equation y = 100 + 30x models plumber A's fee, where y is the total charge, in dollars, and x is the number of
hours worked
The table shown represents plumber B's total charge for different numbers of hours.
Plumber B
Hours Total Charges ($)
1
105
2.
160
3
215
2.
Part A: Which plumber charges more money per hour? Explain how you know.
Part B: Which plumber charges a higher initial fee? Explain how you know.
Part C: Which plumber charges less money for working 5 hours? Show your work to justify your answer.
Answers
Answer:
A) Plumber B charges 55 dollars per hour (105=50+55(1)) because for 1 hour the total is 105, meaning that 105 is y and 1 is x. 50+55=105
B) Plumber A charges more because he charges 100 dollars vs Plumber B's 50 dollars.
C) Plumber A: 250=100+30(5) Plumber B: 325=50+55(5)
Plumber A charges less money for working 5 hours.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that,
Two plumbers charge an initial fee and an hourly rate.
The equation y=100+30x -----(I) models plumber A's fee, where y is the total charge, in dollars, and x is the number of hours worked.
Part A:
From the table, we have (1, 105) and (2, 160)
Now, m=(160-105)/(2-1)
= 55
Substitute m=55 and (x, y)=(1, 105) in y=mx+c, we get
105=55(1)+c
c=60
Substitute m=55 and c=60 in y=mx+c, we get
y=55x+60 -----(II)
By comparing (I) and (II), we can conclude that plumber B charges more hourly fee.
Part B: By comparing (I) and (II), we can conclude that plumber A charges more initial fee.
Part C: Substitute x=5 in y=100+30x, we get
y=$250
Substitute x=5 in y=55(5)+60, we get
y=$335
Plumber A charges less money for working 5 hours.
Therefore, plumber A charges more initial fee.
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Related Questions
what is the slope of the line in the graph?
Answers
Randy owns 120 baseball cards, and Phil owns 95 baseball cards. The number of baseball cards Davis owns is equal to 5 times the difference between Randy's number of cards and Phil's. How many cards does Davis own?
A. 25 cards
B. 30 cards
C. 125 cards
D. 150 cards
Answers
Answer:
125
Step-by-step explanation:
First you want to find out the difference between Randy and Phil:
120 - 95 = 25
Then, multiply that by five:
25 × 5 = 125
Hope this helps
Answer:
Davis owns 125 cards
Step-by-step explanation:
120 - 90 = 25 x 5 = 125
What is the area of this figure?
10 cm
7 cm
6 cm
17 cm
10 cm
4cm
Answers
Answer:
285,600
Step-by-step explanation:
I calculated it I am pretty sure I am correct
Answer:
110
Step-by-step explanation:
I split the shape into smaller pieces and got 10 for the width and 7 height I multiplied them and got an area of 70 for the first shape. For the second I got the width of 4 and length of 10 multiply them and you'll get 40. Last add them and you get 110 cm.
Cherie accepted a job through an employment agency. The job pays $1,100 a week. The agency charges 30% of her first 4 weeks pay. Find the amount she owes the agency
Answers
Cherie owes the employment agency amount of $1,320.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
To determine the amount Cherie owes the agency, we need to calculate 30% of her first 4 weeks of pay.
Since she earns $1,100 a week, the total pay for 4 weeks is $1,100 × 4 = $4,400.
Now that we have the total pay for 4 weeks, we can calculate 30% of that amount by multiplying $4,400 by 0.30.
So, 30% of her first 4 weeks' pay is $4,400 × 0.30 = $1,320.
Therefore, she owes the employment agency $1,320.
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Gavin is saving up to buy a new phone. He already has $100 and can save an additional $7 per week using money from his after school job. How much total money would Gavin have after 10 weeks of saving? Also, write an expression that represents the amount of money Gavin would have saved in w weeks.
Answers
The total money would Gavin have after 10 weeks of savings is $ 170 and the required expression is 100 + 7w
Mathematical expression:
A mathematical expression is a combination of numbers, symbols, and operators that represents a mathematical relationship or calculation. It is written in a way that follows specific rules of mathematical notation, such as using parentheses to indicate the order of operations.
Here we have
Gavin is saving up to buy a new phone.
He already has $100 and can save an additional $7 per week using money from his after-school job
Let us assume that he worked for 'w' weeks
The amount earned for 'w' weeks = 100 + 7w
Hence, the required expression is 100 + 7w
The total amount saved in 10 weeks = 100 + 7(10) = $ 170
Therefore,
The total money would Gavin have after 10 weeks of savings is $ 170 and the required expression is 100 + 7w
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A building is 360 feet tall. On a scale drawing, 1/4 inch = 10 feet. What is the height of the building in the scale drawing?
Answers
Answer:
the answer is 9 inches
360/10=36
36*.25 =9
what is 4 × 10^2 in scientific notation?
Answers
Answer:
104 = 10 × 10 × 10 × 10 = 10,000
Step-by-step explanation:
In words: 104 could be called "10 to the fourth power", "10 to the power 4" or "10 to the 4"
A mirror is 24 inches high and 28 inches wide. The center of the mirror will hang 514 feet from the floor on a wall that is 8 feet high.
What will be the distance from the top of the mirror to the ceiling once the mirror is hung on the wall?
A
[tex]1\frac{3}{4}[/tex] feet
B
[tex]2\frac{3}{4}[/tex] feet
C
[tex]5\frac{1}{4}[/tex] feet
D
8 feet
Answers
Answer:
A is the answer
Step-by-step explanation:
I think
WILL MARK BRAINLIST!!! only for correct answer
NEED CORRECT ANSWER ASAPPP
Answers
Answer:
B
Step-by-step explanation:
The answer is B because the slope is [tex]\frac{4}{1}[/tex] and there is no y- intercept
Answer:
A.
Step-by-step explanation:
It starts from 32 on the y-axis and goes up 4 times on x-axis.
When is the slope intercept form only y= mx and not y = mx+b?
Answers
Answer:
No Y-Intercept
Step-by-step explanation:
The only way for a slope to never have B within itself, is when Slope intercept form has no value for B or the Y intercept.
A triangle has a base of two to the third power units and a height of chicken fourth power units what is the area of the triangle
Answers
What is the value of the expression (0.4)2
Answers
Comparing Methods to solving systems.
x -y =-2
7x +2y =-5
Solve it by graphing method
Answers
Answer:
[tex]x = - 1 \\ y = 1[/tex]
Step-by-step explanation:
[tex]x - y = - 2 [/tex]
[tex]x = y - 2[/tex]
[tex]7x + 2y = - 5[/tex]
[tex]7(y - 2) + 2y = - 5 \\ [/tex]
[tex]7y - 14 + 2y = - 5[/tex]
[tex]9y = 14 - 5[/tex]
[tex]9y = 9[/tex]
[tex]y = \frac{9}{9} = 1[/tex]
[tex]x = y - 2 = 1 - 2 = - 1[/tex]
Michael earns $900 per month, plus 5% commission on all his sales over $750. what is the minimum amount of sales Michael must have to earn at least $3500 in a month?
Answers
Answer:
The minimum amount of sales Michael must have to earn at least $2500 in a month is $ 32000
Explanation: The minimum amount of sales Michael must have to earn at least $2500 in a month is $ 32000
Solution:
The expression to Michael earnings is:
Where,
b is the base salary, which is $ 900 in this sum
c is the commission rate
Given that commission rate is 5%
Michael must have to earn at least $2500 in a month
Here, at least means, "greater than or equal to" 2500
The inequality is framed as:
base salary + 5 % on sales 2500
Solve the inequality
Therefore minimum amount of sales Michael must have to earn at least $2500 in a month is $ 32000
Find the slope of the graph
Answers
On the first day, you pay $5 for 2 boxes of popcorn.
The next day you pay $7.50 for 3 boxes. Are the ratios
equivalant.
Answers
Answer:
10 5
Step-by-step explanation:
Answer: Yes
Step-by-step explanation:
First find the unit rate by find the cost per box.
To find the cost per post you will divide the cost by the number of boxes.
5/ 2 = 2.5
7.50/ 3 = 2.5
2.5 is indeed equal to 2.5 so they are equivalent.
can u pls help me with this question
Answers
Answer:
A
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
A is the variable.
10+x=21 ?
What’s the answer
Answers
Answer:
x=11
Step-by-step explanation:
first you flip the X and the 10, then subtract the 10 on both sides and you should be left with x=11
help me plzz will mark brainliest
Answers
Answer:
[tex]x=7,\\y=6[/tex]
Step-by-step explanation:
The segment [tex]UV[/tex]consists of [tex]UZ[/tex] and [tex]VZ[/tex]. Therefore, we can write the following equation:
[tex]3y-5+2y+2=27,\\5y-3=27,\\5y=30,\\y=\fbox{$6$}[/tex].
Since [tex]UV[/tex] bisects [tex]TW[/tex], [tex]TZ\cong WZ[/tex].
Therefore,
[tex]3x+3=3y+6,\\3x+3=3(6)+6,\\3x+3=18+6,\\3x+3=24,\\3x=21,\\x=\fbox{$7$}[/tex]
A bag contains 49 coins consisting of quarters and dimes. There are 2.5 times as many quarters as there are dimes in the bag. Write a system of equations that models this situation. How many dimes are in the bag?
pls write step by step so that I can understand :)
Answers
Answer:
Dimes = 35
Quarters = 14
Step-by-step explanation:
Let
quarters = q
Dimes = d
Total coins = 49
There are 2.5 times as many quarters as there are dimes in the bag
Dimes = 2.5q
Quarters + Dimes = Total
q + 2.5q = 49
3.5q = 49
q = 49/3.5
q = 14
d = 2.5q
= 2.5 * 14
= 35
d = 35
Therefore,
Dimes = 35
Quarters = 14
Answer:
The system of equations that models this equation area:
d + q = 49
q = 2.5d
I need help -5 + g = -2 step by step so I can learn
Answers
Answer:
Step-by-step explanation:
if you need to find g,
add 5 on both sides
g=-2+5
g=3
I
Write an equation of the line passing through the point (2, 3) and
PERPENDICULAR to the line y = -2x + 2.
Answers
Answer:
y= 1/2 x +7
the slope is 1/2 since hwne it's perpendicular, it's reciprocal and the sign also changes
Step-by-step explanation:
3= -4 +b
b= 7
Is this relation a function? justify your answer
Check image
A
B
C
D
Answers
Answer: No C
Step-by-step explanation:
The x values of the coordinates cannot repeat.
Using a straight line test, a straight line can be drawn vertically on the x axis point of 4.
Julien is baking cookies with his mother.
The recipe calls for:
1 ½ cups of flour
2 ⅔ cups of oatmeal
3 ¼ cups of chocolate chips
1 cup of sugar
½ cup of brown sugar
The only measuring cups that Julien can find are ⅛ cup and ⅓ cup. How will he make the cookies?
Answers
Answer:
well quite easily just doing the math
Step-by-step explanation:
Ta -Da
1 1/2 cups of flour = 12/8 cups of flour
2 2/3 cups of oatmeal = 2 2/3 cups of oatmeal
1 cup sugar = 3/3 or 8/8 cups of sugar
1/2 cup of brown sugar = 4/8 cups of brown sugar
Find the probability of this event. Enter each answer as a fraction in simplest form, as a decimal, and as a percent.
You draw one card at random from a shuffled deck of 52 playing cards. The deck has four 13−card suits (diamonds, hearts, clubs, spades).
The card is a diamond or a heart.
The probability expressed as a fraction is:
The probability expressed as a decimal is:
.
The probability expressed as a percent is:
Find the probability of this event. Enter each answer as a fraction in simplest form, as a decimal, and as a percent.
2. You draw one card at random from a shuffled deck of 52 playing cards. The deck has four 13−card suits (diamonds, hearts, clubs, spades).
The card is a diamond or a heart.
The probability expressed as a fraction is:
The probability expressed as a decimal is:
.
The probability expressed as a percent is:
Answers
Answer:
There we go!!!
How many solutions does the system have?
x = -6y + 3
5x + 30y = 15
one solution
two solutions
infinitely many solutions
no solution
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
we have: x+6y= 3
5x+30y=15
where a1/a2 = b1/b2 = c1/c2 (1/5 = 6/30 = 3/15)
Thus, the system has infinitely many solutions.
another approach:
convert to slope-intercept form
y= -1/6x + 1/2
y= -1/6x + 1/2
thus, the system has infinitely many solutions.
(explain: if two lines have a same slope (-1/6), they can be either parallel or coincided. But in this case, they also have a same y-intercept so they must be the latter case)
does anyone know how to do this? If so can you please help me?!
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If (1/4)^2-y, =1 find the value of y
Answers
1/16 - y = 1
Then you subtract 1/16 on both sides
-y = 1 - 1/16
Then subtract 1/16 from 1
-y = 15/16
Then divide by -1 to make y positive
answer —-> y = -15/16
44 laps in 7 days = ____ laps in 14 days
Answers
Answer:88
Step-by-step explanation:
Answer:
88?
Step-by-step explanation:
Find the solution between - x - 3y = 6 and the equation of the line shown on the graph below.
Answers
Answer:
They are the same line.
Step-by-step explanation:
y = -1/3x - 2
-x - 3y = 6
First, we need both lines to follow the equation of y = mx + b so that we can graph them. We already have one equation in that form (the one from the graph given), so we can ignore that for now.
Next, we need to solve -x - 3y = 6. Let's first move the x to the other side of the equal sign.
-3y = x + 6
Now, since we have a similar equation to what we need, we just need to divide the y by the given number in front (or -3). But that also means that we must divide the other side by the same amount (or each variable).
-3y = x + 6. -> y = -1/3x - 2
So, your final equation for -x - 3y = 6 should be;
y = -1/3x -2
Bringing down the other equation, we get:
y = -1/3x - 2 and y = -1/3x - 2
Making both equal to each other (they cancel each other out).
Hope this helps!
(And sorry that this is a long explanation)
