Answers
The answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
a)
We know that the two point -slope form of a line is given by :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
where : m is slope and represented by
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
As per the questions hint is that two points that is (-2 , 11) and (1 , -4).
These points can be represented by :
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (0 , 294000)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (7 , 288400)
So : the slope will be :
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{288400-294000}{7 - 0}[/tex]
m = -5600 / 7
m = -800
So , the point -slope form of line will be :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
y - 294000 = -800 ( x - 0)
y - 294000 = - 800 x
or
y = -800x + 294000
So , the average price of a new home (y) is given by a linear equation which is :
y = -800x + 294000
b)
As per the question y is the average price of a new home in year x and is given by :
y = -800x + 294000
It is given that x = 0 meant year 2004. So , for year 2014 value of x will be x =10.
Substituting this value to get the value of y or average price of a new home in year 2014 , we get :
y = -800x + 294000
y = - 800 × 10 + 294000
y = -8000 + 294000
or
y = $ 286000
Therefore , the answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
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Related Questions
In this example, the rapper wants to divide a recipe in half to make a cake for 5 people instead of 10. Explain why he multiplies the first ingredient, ⅔ of a cup sugar, by ½.
Answers
Answer:1 889 - 1927 = 1889 - 1927 =9
Step-by-step explanation:
The value of y is directly proportional to the value of x.If y=12 when x=9, what is the value of x when y=80
Answers
Step 1:
Write the formula connecting y and x.
[tex]\begin{gathered} y\text{ }\propto\text{ x} \\ y\text{ = kx} \\ k\text{ = }\frac{y}{x} \end{gathered}[/tex]Step 2:
Find the value of k when y = 12 and x = 9
[tex]\begin{gathered} k\text{ = }\frac{y}{x}\text{ = }\frac{12}{9}\text{ = }\frac{4}{3} \\ \text{Therefore} \\ y\text{ = }\frac{4}{3}x \end{gathered}[/tex]Step 3
You can find x when y = 80.
[tex]\begin{gathered} \text{Frpm y = }\frac{4}{3} \\ \text{When y = 80} \\ 80\text{ = }\frac{4x}{3} \\ \text{Cross multiply} \\ 4x\text{ = 80}\times3 \\ 4x\text{ = 240 Divide both sides of the equation by 4} \\ x\text{ = }\frac{240}{4} \\ x\text{ = 60} \end{gathered}[/tex]Final answer
x = 60
ALGEBRA - 30 POINTS
In a volatile housing market, the overall value of a home can be modeled by V(x) = 210x2 – 4400x + 125000, where V represents the value of the home and x represents each year after 2020. Find the vertex and interpret what the vertex of this function means in terms of the value of the home. Show the work you completed to determine the vertex.
Answers
Answer: the vertex is 157x4
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Students in Mrs. McGee's third grade class are working on times tables, and they demonstrate mastery by passing tests. Rebecca has passed 12 tests so far. Her classmate, Marie, has passed 3 tests of them. From now on, Rebecca plans to take and pass 2 tests per week. Meanwhile, Marie plans to do 5 per week. At some point, Rebecca will catch up to Marie. How long will it take? How many tests will each child have passed? In weeks, the children will each have passed tests.
Answers
Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the unknown terms
Let x represents the number of weeks
Let y represents the total number of test passed
STEP 2: Interpret the statements
For Rebecca
[tex]y=2x+12[/tex]For Marie
[tex]y=5x+3[/tex]STEP 2: Find the number of weeks they will pass the same amount of test.
This means that y will be equal to y
[tex]\begin{gathered} y=y \\ 2x+12=5x+3 \\ 2x-5x=3-12 \\ -3x=-9 \\ x=\frac{-9}{-3}=3\text{ weeks} \end{gathered}[/tex]Hence, they will both pass the same number of tests in 3 weeks
STEP 3: Find the amount of tests passed
For Rebecca
[tex]\begin{gathered} 2x+12 \\ x=3 \\ y=2(3)+12=6+12=18 \end{gathered}[/tex]For Marie
[tex]\begin{gathered} y=5x+3 \\ x=3 \\ y=5(3)+3=15+3=18 \end{gathered}[/tex]Both will pass 18 tests in 3 weeks
ANSWER:
In 3 weeks, the children will each have passed 18 tests.
Is 4 over 14 simplified and is 15 over 20 simplified and is 21 over 35 simplified
Answers
Solution
For this case we have the following:
[tex]\frac{4}{14}=\frac{2}{7}[/tex]Then the answer is:
2/7
(Score for Question 1: of 3 points) 1 1. Mahala is standing and fishing on a dock that is 2 - feet above the surface of the water in the pond. Her baited hook is 1.5 feet below the surface of the water. The surface of the water is represented by the 4 rational number 0. Use the number line to graph the distance the dock, point D. is above the water and the hook, point H, is below the water. Make sure you label each point appropriately. Answer: 3 2 -1 0 1 2 3
Answers
graphing the distance of the dock, point D. is above the water and the hook, point H, is below the water.
See the diagram below :
Point D , is above the water =highlited in yellow.
Point H, the hook, is below the water = shown by colour green.
The ratio of 8 books to 20 books isA) 2:5B) 5:2C) 4:5D) 5:4
Answers
the ratio of 8 books to 20 books is:
[tex]8\colon20[/tex]now we can divide by the same number so:
[tex]\begin{gathered} \frac{8}{2}\colon\frac{20}{2} \\ \frac{4}{2}\colon\frac{10}{2} \\ 2\colon5 \end{gathered}[/tex]SO is option A)
After 4 months of a new nutrition program rashid has lost 16% of his original weight he lost 36lb what was rashids original weight?
Answers
Rashids original weight based on the information illustrated is 225lb.
What was the original weight?From the information given, after the nutrition program rashid has lost 16% of his original weight he lost 36lb.
Let the original weight be given as x.
Therefore, 16% × x = 36
0.16x = 36
Divide through by 0.16
0.16x / 0.16 = 36 / 16
x = 36/0.16
x = 225lb
The weight is 225lb.
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what is the midpoint of the segment that would be created between points L and N on the graph
Answers
Given:
The figure KLMN on graph.
Required:
what is the midpoint of the segment that would be created between points L and N .
Explanation:
We know the mid point formula
[tex]LN=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]We have L(-2, 3) and N(6, 3)
and
[tex]\begin{gathered} LN=(\frac{-2+6}{2},\frac{3+3}{2}) \\ =(\frac{4}{2},\frac{6}{2}) \\ =(2,3) \end{gathered}[/tex]Answer:
Midpoint is (2,3).
fractions and geometry studying for a win test workeys
Answers
Given that the pharmacist can fill 250 prescriptions in 40 hours.
Consider the following,
[tex]\begin{gathered} 1\text{ hour}=60\text{ minutes} \\ 40\text{ hour}=40\times60=2400\text{ minutes} \end{gathered}[/tex]So it can be understood that the pharmacist can fill 250 prescriptions in 2400 minutes.
Then the time taken to fill 1 prescription is calculated as,
[tex]\begin{gathered} 250\text{ prescriptions}\equiv2400\text{ minutes} \\ \Rightarrow1\text{ prescription}\equiv\frac{2400}{250}=9.6\text{ minutes} \end{gathered}[/tex]Thus, it will take 9.6 minutes to fill 1 prescription.
Therefore, option (E) is the correct choice.
Determine the x-intercept from the given Coordinate Pairs. * {(-1,8), (0.6). (5:5).(3,0). 1.5.-17)} O r= 3 b = 6 x = ? = -2
Answers
The x interception is when y = 0
the fouth point is (3,0), in that point y is 0 and x is 3
So the x interception is at x = 3
The answer is the first option x = 3
In the year 2003, a person bought a new car for $12500. For each consecutive year after that, the value of the car depreciated by 7%. How much would the car be worth in the year 2005, to the nearest hundred dollars?
Answers
Answer + Explanation:
13500x0.07 = 945
945 x 2 = 1890
13500 - 1890 = 11610
To the nearest hundred dollars: 11,600
ANSWER: 11,600
can you help me to answer 2736×2
Answers
Answer
[tex]\begin{gathered} 2\text{ 7 3 6} \\ \times\text{ 2} \\ =5\text{ 4 7 2} \end{gathered}[/tex]2 7 3 6
x 2
------------------
5
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 2". Find P(A). Outcome Probability 1 0.2 2 0.1 3 0.3 4 0.03 5 0.03 6 0.04 7 0.06 0.14 8 0.03 9 0.07 10
Answers
Solution
From the info given the numbers divisible by 2 are:
2,4,6,8,10
And the respective probabilities are:
P(2)= 0.1
P(4) =0.03
P(6)= 0.04
P(8) = 0,14
P(10)= 0.07
And addinf all the values we got:
P(A)= 0.1+0.03+ 0.04+ 0.14 +0.07= 0.38
solve for y 10x+8y=4
Answers
Solve the equation.
[tex]\begin{gathered} 10x+8y=4 \\ 8y=-10x+4 \\ y=-\frac{10}{8}x+\frac{4}{8} \\ =-\frac{5}{4}x+\frac{1}{2} \end{gathered}[/tex]So y = -5/4 x +1/2.
Find the values of x and y
Answers
Check the picture below.
[tex]13y=20x+3y\implies 10y=20x\implies y=\cfrac{20x}{10}\implies y=2x \\\\[-0.35em] ~\dotfill\\\\ 13y+(8x+y)=180\implies 14y+8x=180\implies \stackrel{\textit{substituting}}{14(\underset{y}{2x})+8x=180} \\\\\\ 28x+8x=180\implies 36x=180\implies x=\cfrac{180}{36}\implies \boxed{x=5}~\hfill \boxed{\stackrel{y = 2(5)}{y = 10}}[/tex]
in the rhombus shown below AC and BD are 6 and 4in respectively determine the area of the figure in square inches
Answers
The area of a rhombus is computed as follows:
A = p*q*1/2
where p and q are the diagonals of the rhombus.
In this case:
A = AC*BD*1/2
A = 6*4*1/2
A = 12 square inches
hi i need help as i try with old answer and its wrong
Answers
SOLUTION
The exercise has no question
Salim sells fax machines that come in Standard and Enhanced models. The Standard model sells for $325 and the Enhanced model sells for $385. If Salim sold a total of 45 units and took in $15,525, how many of the Enhanced model did he sell?
Answers
Could I get help with this problem I have in algebra?
Answers
Answer
Explanation
Cost of a lower deck ticket = 42 dollars
Cost of an upper deck ticket = 75%
I need help on this one! Please and thank you!
Answers
Given:
[tex]\cos \theta\text{ =- }\frac{1}{8}[/tex]Solving for the angle measure:
[tex]\begin{gathered} \theta\text{ = }\cos ^{-1}(-\frac{1}{8}) \\ =\text{ }97.181 \end{gathered}[/tex]Hence, we can find the exact value of sin theta:
[tex]\begin{gathered} But\text{ }\theta\text{ is in the third quadrant.} \\ \sin (97.181\text{ -180) = sin(-82.8190}) \\ =\text{ -0.992} \end{gathered}[/tex]Hence, the exact value of sin theta is -0.992
Solve using the fractions 5/8 and 1 2/7
Answers
107/56 is the solution of fractions .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.The given fractions are 5/8 and 1 2/7.
We need to find the sum of given fractions.
Now, we can write 1 2/7 as 9/7.
So, 5/8 + 9/7
Here, LCM of 8 and 7 is 56
Then, 35/56 + 72/56
=(35+72)/56
=107/56
Therefore, the sum of the two given fractions is 107/56.
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at a batting cage, each set of baseballs the machine pictures cost $2.50 which inequality represents n, the number of sets of baseballs machine will pitch for no more than $15. 00?
Answers
We have that each set of baseballs cost $2.50, and for the inequality, notice that we cannot spend more than $15. Since each set cost 2.50, then the inequality to represent this situation is:
[tex]5.50n\le15[/tex]Find the area of this circle. Use3.14 for i.7 AtThe area of the circle is aboutfta.(Round to the nearest hundredth as needed.)
Answers
153.86 ft²
Explanation:[tex]\text{Area of a circle = }\pi r^{2}[/tex][tex]\begin{gathered} r\text{ = radius = 7 ft} \\ \pi\text{ = 3.14} \\ In\text{serting into the formula:} \\ \text{Area of the circle = 3.14 }\times7^2 \end{gathered}[/tex][tex]\text{Area of the circle = 153.86 ft}^2[/tex]To the nearest hundredth, Area of the circle = 153.86 ft²
On the first day a man did 3/8 of a job on the next day he completed another 2/5of the job what fraction the job was left undone?
Answers
Step-by-step explanation:
3/8+2/5
L.C.M=40
15+16/40=31/40
1/1-31/40
40-31/40
9/40
The price of a local newspaper increases from 80p to £1.
Find the percentage increase
Answers
Answer:
25%Step-by-step explanation:
The price of a local newspaper increases from 80p to £1.
Find the percentage increase
increase = Increase ÷ Original Number × 100
increase = 1 : 0.8 x 100
increase = 125
so the percentage increase is
125 - 100 =
25%
Is the following relation a function? Justify your answer.
y
X
6
-1.
4
2
-1
3
O No, because there is an input value with more than one output value
O No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value
Answers
No, because there is an input values with more than one output value is the following relation a function.
Based on the given function is,
x y
6 2
-1 -1
4 3
What is the Function :A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
So,
We can write,
One input value has more than output values.
In this function we have,
-1 is mapped to both -2 and -1
In this case,
-1 input value is mapped to both output values of -2 and -1.
Therefore,
No, because there is an input values with more than one output value is the following relation a function.
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Drag each tile to the correct box Arrange the cylinders in order from least volume to greatest volume. agindur math a diameter of 28 un and a test of 18 units acide with a radius of 13 units and a height of 17 units a cyinder with a diameter of 30 pts and a hught of 14 units onder with a radius of 12 units and a hot 20 units
Answers
Answer:
Explanation:
The volume of a cylinder is given by
[tex]V=\pi r^2h[/tex]Now, to correct the order of the cylinders from least to greatest, we have to calculate the volume of each.
(a). A cylinder with a diameter of 28 units and a height of 18 units.
Diameter is 2 times radius; therefore, r = 14 and the volume is
[tex]V=\pi(14)^2\times18[/tex][tex]V=3529\pi[/tex](b). A cylinder with a radius of 13 units and a height of 17 units.
The volume is
[tex]V=\pi(13)^2\cdot17[/tex][tex]V=2873\pi[/tex](c). A cylinder with a diameter of 30 units and a height of 14 units.
The radius is 15 units; therefore, the volume is
[tex]V=\pi(15)^2\cdot14[/tex][tex]V=3150\pi[/tex](d). A cylinder with a radius of 12 units and a height of 20 units.
The volume is
[tex]V=\pi(12)^2\cdot20[/tex][tex]V=2880\pi[/tex]Hence, from least volume to greatest volume the order is
[tex](b)<(d)<(c)<(a)[/tex]Adalyn uses 1/5 cup of blue paint for every 2/5 cup of red paint to make purple paint. Enter the number of cups of blue paint Adalyn uses for 1 cup of red paint.
Answers
Given that;
Adalyn uses 1/5 cup of blue paint for every 2/5 cup of red paint to make purple paint.
[tex]\frac{1}{5}\text{ cups of blue paint }\rightarrow\frac{2}{5}\text{ cups of red paint}[/tex]For 1 cup of red paint, the amount of blue paints Adalyn will use is;
[tex]\frac{1}{5}\text{ cups of blue paint }\rightarrow\frac{2}{5}\text{ cups of red paint}[/tex]A wire of length 22cm is bent in the shape of a circle . find the area of the circle. if the same wire is recent in the form of a square, find it's area which figure encloses more area
Answers
The circle is found to have the more area as compered to the square.
What is termed as the perimeter?A perimeter is a loop that encompasses, encircles, or outlines a two-dimensional shape or length. The circumference of a circle or perhaps an ellipse is its perimeter.For the given question;
The length of the wire is given as 22 cm.
The wire is bent in the circle.
Then, the perimeter of the circle is 22 cm.
Perimeter = 2πr = 22 cm.
Where, π = 3.14 and r is the radius of the circle.
2πr = 22 cm.
r = 11/π 11/3.14
The area of the circle is found as;
Area = πr²
Put the values.
Area = 3.14(11/3.14)²
Area = 38.53 cm².
For the square.
Perimeter = 4 side
22 = 4 side
side = 22/4 = 11/2 = 5.5
Area of square = side²
Area of square = 5.5²
Area of square = 30.25 cm².
Thus, the circle is found to have the more area as compered to the square.
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