Question
The value of a computer y, depreciates, or decreases as time passes. A computer was purchased for $3200 in 2018. In
2020 the computer was worth $2000. Assume the relationship between number of years after 2018 x, and value of
computer, y is linear.
Answers
The value of the computer decreases by $800 per year.
A linear equation is given by:
y = mx + b
where y, x are variables, m is the rate of change, b is the initial vale of y (y intercept).
Let y represent the cost of the computer and x represent the years after 2018.
A computer was purchased for $3200 in 2018. It is represented by the point (0, 3200). Also, in 2020 the computer was worth $2000, it is represented by the point (2, 2000). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3200=\frac{2000-3200}{2-0}(x-0)\\\\y-3200=-800x\\\\y=-800x+3200[/tex]
Therefore the value of the computer decreases by $800 per year.
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A linear relationship will always decrease or increase at a constant and uniform rate.
The linear equation is [tex]\mathbf{y = -600x +3200}[/tex]The estimated value in 2022 is $800The estimated value in 2024 is -$400, and it does not make sensePart 1
(a) The linear equation
In 2018, the value is $3200
In 2020, the value is $2000
Let the number of years since 2018 be x, and the value be y
So, we have the following representation
[tex]\mathbf{(x,y) = (0,3200) (2,2000)}[/tex]
Start by calculating the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{2000 - 3200}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{- 1200}{2}}[/tex]
Divide
[tex]\mathbf{m = - 600}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x -x_1) +y_1}[/tex]
So, we have:
[tex]\mathbf{y = -600(x -0) +3200}[/tex]
[tex]\mathbf{y = -600x +3200}[/tex]
Hence, the linear equation is [tex]\mathbf{y = -600x +3200}[/tex]
(b) The estimated value in 2022
In 2022, x = 4
So, we substitute 4 for x in the linear equation
[tex]\mathbf{y = -600x +3200}[/tex]
[tex]\mathbf{y = -600 \times 4 +3200}[/tex]
[tex]\mathbf{y = 800}[/tex]
Hence, the value in 2022 is $800
Part 2
The estimated value in 2024
In 2024, x = 6
So, we substitute 6 for x in the linear equation
[tex]\mathbf{y = -600x +3200}[/tex]
[tex]\mathbf{y = -600 \times 6 +3200}[/tex]
[tex]\mathbf{y = -400}[/tex]
Hence, the value in 2024 is -$400
This value does not make sense, because the value cannot be negative
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Related Questions
What is the slope of the line that passes through the points (-9, 2) and
(1, 27)? Write your answer in simplest form.
Answers
Answer:
5/2
Step-by-step explanation:
Y(2)-Y(1)/ X(2)-X(1)
(27-2)/(1-(-9)
25/10
simplified=5/2
pls help!!
Dominick buys a package of soup mix that is 1.38 ounces. How many ounces are 6 packages of soup mix?
Answers
Answer:
8.28
Step-by-step explanation:
this is the answer because
.08*6= .48
.3*6= 1.8
1*6=6
.48+1.8 = 2.28
6+2.28=8.28
Ron is 25 years old and is retiring at the age of 65. When he retires, he will need a monthly income of $4,123 for 20 years. If Ron contributes 10% of his monthly income to a 401(k) paying 5.5% compounded monthly, will he reach his goal for retirement given that his monthly income is 3,142.23? If he does not make his goal then state by what amount he will need to supplement his income. Round all answers to the nearest cent.a.Ron will meet his monthly goal of exactly $4,123 for retirement.b.Ron will meet his monthly goal of $4,123 for retirement with an excess of $125.34.c.Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.d.Ron will not make his monthly goal of $4,123 and will need $450.61 to supplement his monthly income when he retires.
Answers
Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.
What is Compound interest?Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.
Given monthly income of Ron is $3,142.23
Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.
Total amount he contribute in 40 years paying 5.5% compounded monthly is given by
interest rate(r) = 0.055/12
time period = 40 years = 480 months
Principal amount = $314.223
Future value = [tex]P(\frac{(1+r)^{n}-1 }{r} )[/tex]
Substitute, we get,
= 3142.23 [tex].10(\frac{(1+\frac{0.055)^{12.40}-1) }{12} }{\frac{0.055}{12} }[/tex]
Thus, future value is $547074.681009.
After retirement his monthly income when he has $547074.681009 amount.
P = (A.i/2)/(1-(1+i/12)⁻ⁿ)
Putting values, we get,
P = (547074.68×0.55/12)/1-(1+0.055/12)⁻²⁴⁰
P = $3763.25
He will receive a monthly income of $3763.25.
But given he will need a monthly income of $4,123 for 20 years, which is not met by Ron.
So, the amount he needs to supplement his monthly income when he retires by (4123-3763.25)= $359.74
Hence, Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.
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The answer for this lol thanks
Answers
Answer:
x times (x+1).
If it's wrong, then I'm an idiot.
Step-by-step explanation:
The sun of 3 less than 5 times a number and the number increased by 9 is 24. What is the number?
Answers
Answer:
the answer is 3
Step-by-step explanation:
5 x - 3 + x + 9 =24
6X + 6 = 24
6X =18
×=3
Which function has the smallest y-intercept?
1) f(x) = 5x
2) x + 3y = 12
3) the line that has a slope of 2 and passes through (-1,3)
Answers
Answer:
y=2x+1
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was 2. So you can right away fill in the equation for a line somewhat to read:
y=2x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(1,3). When x of the line is 1, y of the line must be 3.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: b is what we want, the 2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (1,3).
So, why not plug in for x the number 1 and for y the number 3? This will allow us to solve for b for the particular line that passes through the point you gave!.
(1,3). y=mx+b or 3=2 × 1+b, or solving for b: b=3-(2)(1). b=1.
The equation of the line that passes through the point (1,3) with a slope of 2
is
y=2x+1
What are the coefficient terms and Constants of 10x + 5 + 3x + 1
Answers
Answer:
The Coefficients in this expression are 10 and 3, while the constants are 5 and 1.
Step-by-step explanation:
Coefficients = The number that is in front of the variable.
Constant = Any number without a variable.
(Variables are the letters that you may find in an equation or function.)
Hope this helps you :)
Answer:
The coefficient are 10 and 3
The constants are 5 and 1
Step-by-step explanation:
A coefficient is the number in front of any known term.
A constant is a number by itself.
So the coefficient are 10 and 3
The constants are 5 and 1
Genny's monthly salary was $2000in November. In December she received a 20% raise. In January, what was Genny's monthly salary?
Answers
Answer:400
Step-by-step explanation:
10%= 200
x2=400
Ophelia has 5 flower less than Daisy. Together they have 20 flowers. How many flowers have each of them?
Answers
I tried
Mackenzi is buying school supplies. She needs to buy 30 writing utensils so that she doesn't run out during the year
but only has $20.90 saved up. If pencils are $0.35 and pens are $0.95 at the school store, how many of each could
she get if she spent all of her savings?
х
Answer the following questions. Round your answers to the nearest whole numbers.
How many pencils can she buy?
How many can she buy?
*Help ASAP please!*
Answers
She can buy 16 pens and 16 pencils.
Let B be the basis of P3 consisting of the Hermite polynomials in Exercise 21, and let p.t / D 7 ! 12t ! 8t 2 C 12t 3. Find the coordinate vector of p relative to B.
Answers
To calculate the relative vector of B we have to:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
The coordenates of:
[tex]p(t)= 12t^3-8t^2-12t+7[/tex], with respect to B satisfy:
[tex]C_1(1)+C_2(2t)+C_3(-2+4t^2)+C_4(-12t+8t^3)= 7-12t-8t^2+12t^3[/tex]
Equating coefficients of like powers of t produces the system of equation:
[tex]\left \{ {C_1-2C_3=7} \atop {2C_2-12C_4=-12} \right. \\\left \{ {{4C_3=-8} \atop {8C_4=12}} \right.[/tex]
After solving this system, we have to:
[tex]C_1=3\\C_2= 3\\C_3= -2\\C_4= \frac{3}{2}[/tex]
And the result is:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
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HELP PLEASE!!! WILL GIVE BRAINLIEST
Answers
Answer:
See below for answer
Step-by-step explanation:
Domain is the x-value in the ordered pair
Range is the y- value in the ordered pair
1. D = {3, 2, 1, 0} R = {-5, -4, -3, -2}
2. D = {-2, 0, 2, 4} R = {1, 2, 4, 6}
3. D = {10, 8, 6, 4} R = {-1, 2, 5, 8}
4. D = {-5, -3, -1, 1} R = {-5, -3, -1, 1}
5. D = {-4, -1, 2, 3} R = {4, 0, 4, 6}
The rectangle PQRS is dilated by a scale factor of 34 first, and then reflected across the y-axis to form rectangle P'Q'R'S'.
What are the coordinates of the transformed rectangle P'Q'R'S'?
A.
P'(−1.25,−1.25), Q'(−5.25,−1.25), R'(−5.25,−3.25), S'(−1.25,−3.25)
B.
P'(−1.5,1.5), Q'(−4.5,1.5), R'(−4.5,3), S'(1.5,−3)
C.
P'(1.5,−1.5), Q'(4.5,−1.5), R'(4.5,−3), S'(1.5,−3)
D.
P'(−1.5,−1.5), Q'(−4.5,−1.5), R'(−4.5,−3), S'(−1.5,−3)
Answers
Answer:
The answer should be A.
Step-by-step explanation:
I'm strictly only going off the coordinates you gave relying on the information displayed by the question. Also, the coordinates are backwards, anyways if -5.25 portrays Q and R, it should be the correct answer. (This is simply an estimate, not a guaranteed answer because there is no graph presented.)
100 POINTS IF U GET THIS RIGHT!
Answers
Answer:
9/8Step-by-step explanation:
Slope- intercept form:
y = mx + b, where m is the slopeThe line given:
y = 9/8x + 1/8This includes the slope, which is:
m = 9/8Option A: 40 trash bags for $6.29 Option B: 24 trash bags for $3.89
Which is the better option. Explain step by step-by-step.
Answers
Step by step:
I divided 40/6.29 and got about 6.3.
I divided 24/3.89 and got about 6.1.
Which is less, 6.3 or 6.1?
If you said 6.1 you are correct, so option B has a less cost, making it a better option.
in spring 2017, data was collected from a random selection of sta 2023 students. one of the questions asked how many hours they had worked in the past 24 hours. for the 39 randomly selected upperclassmen, the sample mean was 0.61 and sample standard deviation was 2.32. for the 35 randomly selected underclassmen, the sample mean was 1.40 and the sample standard deviation was 2.65. what is the point estimate of the difference in the population mean volunteered between underclassmen and upperclassmen?
Answers
Step-by-step explanation:
Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. n=
PLEASE I NEED HELP
The figure shows a quarter circle and an equilateral triangle. What is the area of the shaded part? Give your answer to 3 significant figures. (Take π = 3.14.)
Answers
Answer:
14.0
Step-by-step explanation:
First, find the area of the whole circle using the equation pi * r^2.
pi * (7^2) = 49pi
Then, to only get the area of a quarter of the circle, divide this number by 4.
49pi/4 = 38.485
Then, to get only the shaded region, you have to find the area of the triangle and subtract it from the area of the quarter circle. The area of the triangle is found using 1/2 * b * h.
1/2 * (7*7) = 24.5
Then subtract that number from the previous one.
38.485 - 24.5 = 13.985
You need to round this to 3 significant figures, so it would be 14.0.
Hope this helps
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
C. y + 3 = f(x)
d. y - 3 = f(x)
Answers
Answer:
C
Step-by-step explanation:
When
f(x+3) would indicate a Shift 3 units to the left
f(x-3) indicates a Shift 3 units to the right
y+3=f(x) indicates a Shift 3 units up
y-3=f(x) indicates a Shift 3 units down
Because the graph is shifted 3 units up, it would be y+3=f(x), which is option C
What is 3.50 rounded to the nearest whole ounce?
Answers
Answer:
4.00
Step-by-step explanation:
because it is rounding to the whole number
Answer
if 3.50 refers to ounces, it would round to 4.
Step-by-step explanation:
What are the places in decimals called.
Answers
Answer: the tenths place
Step-by-step explanation:
A boat can travel 16 Kilometers per hour in still water. The boat travels 15 kilometers down a river and then 15 kilometers up stream. The entire trip takes 5.5 hours. Which equation describes the current, c, of the river?
a)
[tex] \frac{16}{15 + c} + \frac{16}{15 - c} = 5.5 [/tex]
b)
[tex] \frac{5.5}{16 + c} + \frac{5.5}{16 - c} = 15 [/tex]
c)
[tex] \frac{5.5}{15 + c} + \frac{5.5}{15 - c} = 16 [/tex]
d)
[tex] \frac{15}{16 + c} + \frac{15}{16 - c} = 5.5[/tex]
Answers
Answer:
d)
Step-by-step explanation:
the sites of the boat alone is 16 km/h.
downstream and upstream the effective speed is then influenced plus and minus by the current.
the distance traveled is 15km.
as speed = distance/time
then distance / speed = distance / (distance/time) = time
and we know the time it takes : 5.5 hours.
so, only answer d uses the right values in the "right places".
Simplify 7-2 + 2(4 divide 1/2)
Answers
Answer:
21
Step-by-step explanation:
5 + 16 = 21
Answer:
21
Step-by-step explanation:
hope it helps
A network of roads connects locations T, O, W, N, and S. How many different routes are there to travel from T to W along the given roads (line segments) without retracing any part of the route or going to any town more than once per route?
Answers
Answer:
9 routes
Step-by-step explanation:
every time you make a route, you can make a symmetrical route on the other side.
Answer:
9
Step-by-step explanation:
What is an equation of the line that passes through the points (6, 2)and (-6, -8)
Answers
Answer:
Step-by-step explanation:
(-8 - 2)/(-6 - 6)= -10/-12= 5/6
y - 2 = 5/6(x - 6)
y - 2 = 5/6x - 5
y = 5/6x - 3
The hanger image below represents a balanced equation.
27
V
Find the value of v that makes the equation true.
U =
I need the answer
Answers
Answer:
2x =3
The hanger image given in the figure represents balanced equation.
Then we have to write an equation to represent the image.
In balanced form left side = right side
x + x = 1 + 1 + 1
2x = 3
The value v is 9.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that is a structure showing a balanced hanger we need to find the value,
So we can say since the hanger is balanced therefore the weight both sides will be equal,
Therefore,
v + v + v = 27
3v = 27
v = 27
Hence the value v is 9.
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1/8 x 5/6 as a fraction in simplest form
Answers
Answer:
5/48Step-by-step explanation:
1/8 x 5/6 as a fraction in simplest form
1/8 * 5/6 =
5/48
The fraction in simplest form is 5/48.
Given that are two fractions 1/8 and 5/6, we need to find the product of the fractions,
To multiply fractions, we multiply the numerators together and the denominators together.
In this case, we have 1/8 multiplied by 5/6.
1/8 x 5/6 = (1 x 5) / (8 x 6)
Multiplying the numerators (1 x 5) gives us 5, and multiplying the denominators (8 x 6) gives us 48.
Therefore, 1/8 x 5/6 simplifies to 5/48.
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I NEED HELP THIS HW IS DUE TODAY
Answers
b) -6x^3y
c) 6x^2y^2
d) -7y
2.
a) 2a
b) -7b
c) -12
3a. (d) 10x^2
3b. (d) -3x^2
n/4 = -11
what does the N =
Answers
Answer:
N = -44
Step-by-step explanation:
have a great day! :)
Answer:
n=44
Step-by-step explanation:
n/4=11/1
crossmultiply
n=4×11=44
7th grade math please help
Answers
Answer:
11.8
Step-by-step explanation:
brainlest
6.
3. Use the clues to determine
the number
I have 36 hundreds, 34 tens, and
7 ones. What number am I?
Answers
The number is 3947
It should be noted that 36 hundreds will be equal to:
= 36 × 100
= 3600
It should be noted that 34 tens will be:
= 34 × 10
= 340
7 ones will be:
= 7 × 1
= 7.
Therefore, the sum will be:
= 3600 + 340 + 7 = 3947
Answer:
3947
Step-by-step explanation: