The table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of years.
Answers
Answer:
i) y = 25x + 500
ii) y = 30x + 400
iii) The washing machines would cost the same amount after 20 years of use
iv) Standard machine
Step-by-step explanation:
i)
We are to determine a straight line equation that models the cost of High-Efficiency washing machine over the years;
The first step step is to determine the slope of the line,
( change in y) / ( change in x ) = (550 - 525) / ( 2 - 1) = 25
The equation is slope-intercept form will be;
y = 25x + c
Where y is the cost of the High-Efficiency washing machine and x the number of years. To determine the y-intercept, c, we use any pair of points given in the data table;
when x = 1, y = 525
525 = 25(1) + c
c = 500
Therefore;
y = 25x + 500
ii)
The straight line equation that models the cost of Standard washing machine over the years;
Slope = (460 - 430) / (2 - 1) = 30
The equation is slope-intercept form will be;
y = 30x + c
when x = 1, y = 430
430 = 30(1) + c
c = 400
Therefore;
y = 30x + 400
Where y is the cost of the standard washing machine and x the number of years.
iii)
Given the cost functions for both machines over the number of years, we simply equate the two equations and determine the value of x when both machines would cost the same amount;
We have the cost functions;
y = 25x + 500
y = 30x + 400
Equating the two and solving for x;
25x + 500 = 30x + 400
500 - 400 = 30x - 25x
100 = 5x
x = 20
Therefore, the washing machines would cost the same amount after 20 years of use.
iv)
In order to determine which machine would be the more practical purchase if kept for 9 years we use the cost functions obtained in i) and ii)
The cost function of the High-Efficiency washing machine is;
y = 25x + 500
To determine the cost, we solve for y given x = 9
y = 25(9) + 500
y = 725
The cost function of the Standard washing machine is;
y = 30x + 400
We solve for y given x = 9
y = 30(9) + 400
y = 670
Comparing the two values obtained, the cost for the Standard washing machine is more practical.
1) y=25x+500
2) y=30x+400
3) 20
4) standard machine
Related Questions
3n-7/6=2n+5/3 n=what
Answers
[tex]\frac{3n-7}{6}=\frac{2n+5}{3}[/tex] Multiply 3 and 6 on both sides to get rid of the fraction (or cross multiply)
[tex]\frac{3n-7}{6}(3)=\frac{2n+5}{3} (3)[/tex]
[tex]\frac{3n-7}{6}(3)(6)=(2n+5)(6)[/tex]
3(3n - 7) = 6(2n + 5) Distribute/multiply 3 into 3n-7, and 6 into 2n+5
(3)3n - (3)7 = (6)2n + (6)5
9n - 21 = 12n + 30 Subtract 9n on both sides
-21 = 3n + 30 Subtract 30 on both sides
-51 = 3n Divide 3 on both sides
-17 = n
Answer:
n = 17/6 = 2.833
Step-by-step explanation:
Step by step solution :
Step 1 :
5
Simplify —
3
Equation at the end of step 1 :
7 5
(3n - —) - (2n + —) = 0
6 3
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
2n 2n • 3
2n = —— = ——————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2n • 3 + 5 6n + 5
—————————— = ——————
3 3
Equation at the end of step 2 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 3 :
7
Simplify —
6
Equation at the end of step 3 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 6 as the denominator :
3n 3n • 6
3n = —— = ——————
1 6
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
3n • 6 - (7) 18n - 7
———————————— = ———————
6 6
Equation at the end of step 4 :
(18n - 7) (6n + 5)
————————— - ———————— = 0
6 3
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
3 1 1 1
Product of all
Prime Factors 6 3 6
Least Common Multiple:
6
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (18n-7)
—————————————————— = ———————
L.C.M 6
R. Mult. • R. Num. (6n+5) • 2
—————————————————— = ——————————
L.C.M 6
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(18n-7) - ((6n+5) • 2) 6n - 17
—————————————————————— = ———————
6 6
Equation at the end of step 5 :
6n - 17
——————— = 0
6
Step 6 :
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
6n-17
————— • 6 = 0 • 6
6
Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
6n-17 = 0
Solving a Single Variable Equation :
6.2 Solve : 6n-17 = 0
Add 17 to both sides of the equation :
6n = 17
Divide both sides of the equation by 6:
n = 17/6 = 2.833
One solution was found :
n = 17/6 = 2.833
what are the next three terms in the sequence -1, 9, 19, 29
Answers
39. each term is ten more than the term before it :)
Answer:
39, 49, 59
Step-by-step explanation:
Note the difference between consecutive terms
9 - (- 1) = 9 + 1 = 10
19 - 9 = 10
29 - 9 = 10
The difference is a constant + 10
To obtain the next term in the sequence add 10 to the previous term
29 + 10 = 39
39 + 10 = 49
49 + 10 = 59
The next 3 terms are 39, 49, 59
What is the total number of different 6-letter arrangements that can be formed using the letters in the word QUASAR?
Answers
There are 720 different 6-letter arrangements that can be formed using the letters in the word QUASAR, calculated by 6 factorial (6!).
Explanation:The question asks for the total number of different 6-letter arrangements that can be formed using the letters in the word QUASAR. This is a problem of permutations where all the letters are distinct. To find the number of different permutations of the letters in QUASAR, we multiply the number of choices available at each position. There are 6 choices for the first letter, 5 for the second, and so on, until 1 choice for the last letter.
Therefore, the permutations are calculated as 6 × 5 × 4 × 3 × 2 × 1, which is equal to 6! (6 factorial).
The calculation of 6! is as follows:
6 × 5 × 4 × 3 × 2 × 1 = 720.So, there are 720 different 6-letter arrangements that can be formed from the word QUASAR.
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1 and 1/3 mineus 3/4
Answers
Answer:
7/12
Step-by-step explanation:
1 1/3 - 3/4
= 4/3 - 3/4
= 16/12 - 9/12
= 7/12
Answer:
[tex]1\frac{1}{3}-\frac{3}{4}=\frac{7}{12}[/tex]
change [tex]1\frac{1}{3}[/tex] into [tex]\frac{4}{3}[/tex]
[tex]=\frac{4}{3}-\frac{3}{4}[/tex]
get like denominators:
12
[tex]\frac{16}{12}-\frac{9}{12}[/tex]
16 - 9 = 7
Hope this helps and have a great day!!!
Line AB contains (0,4) and (1,6). Line CD contains points (2,10) and (-1,4). Lines AB and CD are
A) parallel, because the slopes are the same
B) perpendicular, because the slopes are the same
C) parallel, because the product of the slopes is -1
D) perpendicular, because the product of the slopes is -1
Answers
Answer: parallel because the slopes are the same
Step-by-step explanation:
Eric sells shirts. It costs him $100 to buy all the shirts and $10, total, to print designs on them. Eric sells each shirt for $4. So far he has sold 20 shirts. He uses the equation y = 4x − 110 to calculate his profit. In the equation y = 4x − 110, which is the constant term?
A) y
B) 4
C) x
D) −110
Answers
Answer:
D) -110
Step-by-step explanation:
x and y are variables, and any number that is in front of a variable (multiplication) is called a coefficient. 4 is the coefficient. x can be substituted. A constant is a number that does not change. -110 is the constant.
A birdhouse has a shadow that is 12 feet long.
Jin is 5 feet tall, and he is standing next to the birdhouse.
Jin has a shadow that is 3 feet long.
Use this information to complete the statement about the birdhouse.
Math item stem image
CLEAR CHECK
The height of the birdhouse is
feet.
Answers
Answer:
20
Step-by-step explanation:
Set up ratios
for the shadows- 12:3, or 4:1
then height=4*5, or 20
Answer:20 feet
Step-by-step explanation:
5/3 = x/12
Use butterfly method.
3x = 60
x = 20
The price of a bag of bagels rose from $2.80 in January to $3.50 in April. What was the percent increase of the price of a bag of bagels
Answers
Answer:
25%
Step-by-step explanation:
% increase = (3.50 - 2.80)/(2.80) x 100
= 25% increase
The required percent increase of the price of a bag of bagels from $2.80 to $3.50 is 25%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To find the percent increase of the price of a bag of bagels, we can use the formula,
percent increase = [(new value - old value) / old value] x 100%
In this case, the old value is $2.80 and the new value is $3.50. Substituting these values into the formula, we get:
percent increase = [(3.50 - 2.80) / 2.80] x 100%
percent increase = (0.70 / 2.80) x 100%
percent increase = 0.25 x 100%
percent increase = 25%
Therefore, the percent increase in the price of a bag of bagels from $2.80 to $3.50 is 25%.
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You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a system with the same solution? 3x + 3y = 4 18x − 9y = 12 A) multiply the first equation by 6 and subtract the second equation B) multiply the first equation by −6 and add the second equation C) multiply 3x by 6 in the first equation and subtract the second equation D) add 2 times the first equation and −1/3 times the second equation Eliminate
Answers
C would be the correct answer. You caanot multiply just one part of an equation, you must multiply the whole thing. All of the other steps follow this rule, so C is an incorrect step, and is therefore the correct choice.
Hope this helps!
Answer:
C) Multiply 3x by 6 in the first equation and subtract the second equation.
Step-by-step explanation:
We have been given a system of equations.[tex]3x+3y = 4[/tex] and [tex]18x-9y = 12[/tex]. We are asked to choose the "incorrect" step that will make "not" produce a system with the same solution.
Let us see our give choices one by one.
A) multiply the first equation by 6 and subtract the second equation.
When we will multiply 1st equation by 6, the coefficient of x would be 18. When we will subtract 2nd equation the both x's will cancel out. Therefore, option A is correct.
B) multiply the first equation by −6 and add the second equation.
When we will multiply 1st equation by -6, the coefficient of x would be -18. When we will add 1st equation to 2nd equation the both x's will cancel out. Therefore, option B is correct as well.
C) Multiply 3x by 6 in the first equation and subtract the second equation.
We need to remember that we cannot multiply only one term of equation by some quantity as it will make the whole equation false, therefore, option C is incorrect.
What is the value of x? Round to the nearest tenth. Please Help
Answers
Answer:
x = 6.5 cmStep-by-step explanation:
The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm[/tex]
Substitute:
[tex]x^2+20.2^2=(14.7+x)^2[/tex] use (a + b)² = a² + 2ab + b²
[tex]x^2+408.04=14.7^2+(2)(14.7)(x)+x^2[/tex] subtract x² from both sides
[tex]408.04=216.09+29.4x[/tex] subtract 216.09 from both sides
[tex]191.95=29.4x[/tex] divide both sides by 29.4
[tex]x\approx6.5\ cm[/tex]
Find the median of the set of data.
23 18 67 32 54 41 70 11 56 33 41 58
35
56
42
41
Answers
41 there are 12 numbers take middle
Hi
The answer is 41
11 18 23 32 33 =41= 54 56 58 67 70
Answer:
42
Step-by-step explanation:
23+18+67+32+54+41+70+11+56+33+41+58=504
(There's 12 sets of numbers)
504/12=42
Solve three and four and nothing more ok
Answers
Answer:
4=2/3 . 7/9=14/21
4/5. /5/6=20/30=2/5
Step-by-step explanation:
3.
Franco deposits $3600.00 in a savings account. The account pays an annual interest rate of 4%. He makes no other deposits or withdrawals. After 3 months, the interest is calculated. How much simple interest did his money earn?
36.00
38.00
35.47
37.00
Answers
Answer:
His money earned $36 after 3 months
Step-by-step explanation:
* Lets revise the rules of simple interest
- Simple Interest Equation (Principal + Interest)
A = P(1 + rt)
- Where:
• A = Total amount (principal + interest) future amount
• P = Principal Amount
• I = Interest Amount
• r = Rate of Interest per year in decimal; r = R/100
• t = Time Period involved
* To calculate the interest I use the formula
I = P × r × t
* Lets solve the problem
- The rate is annual
- The interest calculated after 3 months
∴ I = P × R/100 × t/12
∵ P = $3600.00
∵ R = 4%
∵ t = 3 month
∴ I = 3600.00 × 4/100 × 3/12 = $36
* His money earned $36 after 3 months
What percent is represented by the shaded area
Answers
Answer:
the answer is 25%
Step-by-step explanation:
100% : 4 =25
What is the solution to the system of equations?
Answers
Answer:
There are infinitely many solutions. It is the same line.
Step-by-step explanation:
If you start by multiplying the first equation by 2 to get rid of the fractions, you get -x + y = -2. If you solve it for y, you get y = x - 2. The second equation can be solved for y also, giving you y = x - 2. That means they are the same line and the solution to this situation is infinitely many solutions because all the points on one line are identical to the points on the other line because they are the same line.
HELP ME WITH THIS MATH PROBLEM FOR 17 POINTS!!
Maureen deposited $19,000 at 11 percent interest compounded annually. What was the total interest earned at n = 8 years?
Answers
Answer:
%88 i believe
Step-by-step explanation:
hope this helps!
Answer: $43786.22 (Round)
Step-by-step explanation: Use this formula: A= P(1+r/n)^nt
We are trying to find A in this problem.
Plug it in:
A= 19,000(1+0.11/1)^(1)(8)
Helllllppppppp!! Can i have an explanation of this?
Answers
Okay so if the regular price of the shirt is 100% as $25 and you have a 30% discount you are still paying 70% (100-30=70) so 70% as a decimal is .70 and $25 x .70 is $17.50. Therefore the shirt is $17.50 after the discount.
Alright so, what it’s basically asking for is 70% of 25. This is the price of the shirt after you’ve accounted for the 30% discount
Then you would multiply 25 by .70, giving you $17.50
Hope this helps!
Given z1 = -3
[tex] \sqrt{3} [/tex]
+ 3i and z2 = 6cos150° + 6isin150°, use complete sentences to explain why z1 = z2. Explain the steps of your work for full credit.
Answers
Answer:
See explanation
Step-by-step explanation:
The given complex number are:
[tex]z_1=-3\sqrt{3}+3i[/tex]
and
[tex]z_2=6\cos 150\degree+6i\sin 150\degree[/tex]
When we rewrite [tex]z_1=-3\sqrt{3}+3i[/tex] in complex form, we obtain;
[tex]z_1=r(\cos \theta+i\sin \theta)[/tex]
where
[tex]r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6[/tex]
and
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]
[tex]\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree[/tex]
Hence,
[tex]z_1=6(\cos 150\degree+i\sin 150\degree)[/tex]
[tex]z_1=6\cos 150\degree+6i\sin 150\degree[/tex]
Hence
[tex]z_1=z_2[/tex]
a group of musicians wants to sell a total of 1,000 tickets for 20 concerts suppose they sell the same number of tickets for each concert how many tickets with they sell for each concert?
Answers
Answer:
50 tickts
Step-by-step explanation:
We want to spread 1,000 tickets equally over 20 concerts. This calls for division
1000/20=50
50 tickets are sold each concert
The high school field hockey team needs to buy new practice uniforms. The company the team is ordering from charges $250.00 for a one time print layout fee and then $28.00 for each uniform. What is the maximum number of uniforms the team can buy and stay within its budget of $550.00?
Answers
Answer:
10 uniforms
Step-by-step explanation:
You will start by subtracting 250 from 550 to get 300. You will then divide 300 by 28 to get the total number of uniforms. You will get the answer 10.7, but because we are dealing with uniforms, we will remove the decimal and just use 10.
Find the solution to the system of equations. You can use the interactive graph below to find the solution.
{21x + 7y = 42
{-5x + 5y = 10
X =
Y =
Answers
X=1 and
Y=3
Look at the image attached to see what I did
X = 1
Y = 3
Hope this helps!
Explain what type of function is the best model for the data set and justify your choice. Help???????
Answers
Answer:
The function is linear
Step-by-step explanation:
* Lets check from the table the type of the function
- At first check if it is linear or not
- The points are:
(165 , 198) , (168 , 201.6) , (170 , 204) , (172 , 206.4) , (175 , 210)
* Find the slope for each two points if the value of the slop is
constant, then the function will be linear
∵ The slop = (y2 - y1)/(x2 - x1)
∴ m1 = (201.6 - 198)/(168 - 165) = 1.2
∴ m2 = (204 - 201.6)/(170 - 168) = 1.2
∴ m3 = (206.4 - 204)/(172 - 170) = 1.2
∴ m4 = (210 - 206.4)/(175 - 172) = 1.2
∵ m1 = m2 = m3 = m4
# Note: You can use any to points to find the slope you will
have the same value
∴ The graph of the points is a line with slope 1.2
* The function is linear
Answer:
A linear function is the best model.
The ratio of y to x for the ordered pairs is constant, so the relationship is a direct variation. A direct variation is a type of linear function.
When the data set is plotted, it forms a line.
Step-by-step explanation:
10. Marcia drew a scatter plot comparing the number of people who bought tickets to the school play and
the amount of money raised by the event. She graphed the ordered pairs (number of tickets, money
raised) for each date of the play. Which of the three scatter plots below most likely represents the data?
Answers
Answer:
C- graph III
Step-by-step explanation:
The only graph showing a positive trend. If your selling tickets, you'll have an increased profit.
HELPPPP ME PLSSSS!!!!!
Answers
Answer:
I believe the answer would be C.
Step-by-step explanation:
First, simply look at the roots of each answer choice. A rational number is any number that can be written as a fraction.
In the first option choice [A.], the square root of 8 is 2.8284.... a long decimal that continues for a whi;e. So, it can't be written as a fraction.
In the second option choice [B.], the square root of 24 is 4.8989.... another long decimal that continues for a while. So, it can't be written as a fraction.
In the third option choice [C.], the square root of 81 is 9. 9 can be written as a fraction [for example 27/3] So it's the correct answer.
In the last option choice [D.], the square root of 2 is 1.4142.... another long decimal that continues for a while. So, it can't be written as a fraction.
This is why C. is the right answer! I hope this helps!!!
VARIABLE ON BOTH SIDES. PLEASE HELP! 40 PTS
2x + 4 = 3 (x-2) + 2 show your work
Answers
2x+4= 3x-6+2
2x+4=3x-4
2x-3x+4=3x-3x-4
-x+4=-4
-x+4-4= -4-4
-x=-8
Need to multiply by -1 for x to be positive and also for -8
-1(-x)= -1(-8)
x=8
Answer:
Step-by-step explanation:
2x+4=3(x-2)
2x+4=3x-6
+6 -2x
10 = 1x
1 = 1x
10= x
what is the volume of the sphere? round to the nearest cubic unit.
diameter: 16cm
a)268cm
b)2145cm
c)17, 157cm
d)536cm
Answers
Volume of a sphere:
(4/3)(pi)r^3
.
radius (r) is half the diameter or 8 inches.
(4/3)(3.14)8^3
2144 cubic inches
The volume of the sphere would be 2144 cubic inches
What is the Volume of a sphere?A sphere is a three-dimensional shape analouge of a circle.
The Volume of a sphere = 4/3πr^3
We are given that the diameter of the sphere as 16 cm.
Since radius (r) is half the diameter or 8 inches.
Volume of a sphere:
= 4/3πr^3
= (4/3)(3.14)8^3
2144 cubic inches
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Solve for x. (X+10)(x+10)=0
Answers
Answer:
use foil method-first inside outside last
Step-by-step explanation:
Answer:
X = -10
Step-by-step explanation:
Adding negative ten and ten results in zero, and zero multiplied by anything is, of course, still zero.
(-10 + 10) * (-10 + 10) = 0
0 * 0 = 0
X=-10
Because (x+10)(x+10)=0
So it becomes (x+10)^2=0
And therefore x=-10
an elevator in a hotel moves at 20 feet per second. leaving form the ground floor, its height in feet after t second is given by the formula h(t)=20t. a bolt comes loose in the elevator shaft above, and its height in feet after falling for t second is given by h(t)=-16t^2+200. at what time and at what height does the bolt hit the elevator?
Answers
After 3 seconds and at 60 feet, the bolt hit the elevator if the height in feet after t second is given by the formula h(t)=20t.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
When the bolt hit the elevator, they would be at the same height.
∴ 16t²+200 = 20t
16t² -20t + 200 = 0
It is a quadratic equation:
a = 16, b = -20, and c = 200 plug this values in the formula.
After calculating, we will get:
t = -4.2 or t = 3
Time cannot be negative.
So t = 3 seconds
And height h(3) = 20(3) = 60 feet
Thus, after 3 seconds and at 60 feet, the bolt hit the elevator if the height in feet after t second is given by the formula h(t)=20t.
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which of the following is an equivalent expression?
Answers
just open the bracket and do algebra. the answer should be C
The range of the graphed function is
Answers
Answer:
C
Step-by-step explanation:
plato gang
Answer:
B
Step-by-step explanation:
The range of the function are the corresponding values of y for the given points
x = 1,3 → y = 5
x = 4 → y = 2
x = 6 → y = - 2
The range of the graphed function is { - 2, 2, 5 } → B