The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282
Answers
V (t)=V0 (1+r)^t
V (t) ?
V0 225000
R 0.035
T 8 years
V (8)=225,000×(1+0.035)^(8)
V (8)=296,282
The value of the house in 8 years. (D) ≈ $296,282
How to predict the value?The given parameters are:
Initial value, a = $225,000
Rate, r = 3.5%
The scenario is an illustration of an exponential growth function.
So, we have:
V(x) = a * (1 + r)^x
Substitute known values
V(x) = 225000 * (1 + 3.5%)^x
This gives
V(x) = 225000 * (1.035)^x
Next, we plot the graph of V(x)
See attachment
From the attached graph
V(x) = $296,282
Read more about exponential functions at:
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Related Questions
Can you square both sides of an inequality
Answers
Squaring both sides of an inequality can be valid if you know both sides are non-negative, but it can introduce extraneous solutions. Therefore, it's important to check any solutions against the original inequality to ensure their validity, especially in cases involving negative numbers or functions with restricted domains.
When you're working with inequalities, you have to be careful when performing operations like squaring both sides. Unlike equalities, where multiplication or division by the same number on both sides does not change equality, with inequalities, the effect can be more complex due to the direction of the inequality sign and the possibility of dealing with negative numbers.
For instance, squaring both sides of an inequality is not always a valid operation because if one or both sides of the inequality are negative, squaring could lead to incorrect results. When you square a negative number, it becomes positive, which could potentially reverse the inequality's direction. However, if you know that both sides of the inequality are non-negative, then squaring both sides is permissible. This concept is similar to solving quadratic constraints without introducing square roots, using identities like |(1 + ix)²|² = ([1 + ix|²)².
To avoid introducing solutions that were not there originally (extraneous solutions), it is important to check the solutions obtained after squaring against the original inequality. An example where squaring both sides might be questioned is when solving trigonometric inequalities, where a common mistake is to square both sides without considering the domain of the original function.
(07.05 MC)
An equation is shown below:
4x + 2(x – 3) = 4x + 2x – 11
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points
Answers
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
6x - 6x = -11 + 6
0 = -5...incorrect......this has no solution...0 solutions
one property used was the distributive property :2(x - 3) = 2x - 6
Answer:
-6 = -11
Distributive Property
Step-by-step explanation:
A.
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
-6 = -11
since -6 is not equal to -11, so there's no solution
B. Distributive property
A line passes through (2, –1) and (8, 4).Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.
Answers
Hello : let
A(2,-1) B(8,4)
the slope is : (YB - YA)/(XB -XA)
(4+1)/(8-2) = 5/6
y+1 = (5/6)x -5/3
6y+6 = 5x -10
the equation in standard form is : 5x-6y = 16
Answer: Equation of line in point slope form,
[tex]y + 1 = 5 ( x - 2 )[/tex]
And, Equation of line in standard form,
[tex]5 x - 6 y = 16[/tex]
Step-by-step explanation:
Since, If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] ,
Then the equation of line,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Here [tex]x_1 = 2[/tex], [tex]y_1=-1[/tex], [tex]x_2=8[/tex] and [tex]y_2=4[/tex]
Thus, the equation of the given line,
[tex]y-(-1)=\frac{4-(-1)}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{4+1}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{5}{6} (x-2)[/tex] -----(1)
⇒ [tex]6(y+1)= 5(x-2)[/tex]
⇒ 6 y + 6 = 5 x - 10
⇒ 6 = 5x - 6y - 10 ( By subtracting by on both sides )
⇒ 6 + 10 = 5x - 6y ( By adding 10 on both sides )
⇒ 16 = 5x - 6y
⇒ 5 x - 6 y = 16 ------(2)
Since, in slope for of a line is, [tex]y-y_1= m (x-x_1)[/tex]
Thus, equation (1) shows the in slope form of the line.
And, standard form of the line is ax + by = c where a, b and c are the integers.
Thus, equation (2) shows the standard form of the given line.
SOMEBODY HELP ME WITH THESE PLEASE! I really need the help like NOW PLS!
Answers
[tex]f(n) = 2n^2 - 5n[/tex]
then [tex]g(n) +f(n) = (n-4) + (2n^2 - 5n)[/tex]
[tex]= n - 4 + 2n^2 - 5n[/tex]
[tex]= 2n^2 -5n + n - 4[/tex]
[tex]= 2n^2 - 4n -4[/tex]
95. [tex]f(n) = -n+3[/tex]
[tex]g(n) = n^3 + 3n[/tex]
Then [tex]f(n) . g(n) = (-n+3) . (n^3 + 3n)[/tex]
[tex]= -n^4 + 3n^3 - 3n^2 + 9n [/tex]
97. [tex]f(x) = 3x+1[/tex]
[tex]g(x) = 2x[/tex]
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
[tex]f(g(x)) = 3*(2x) + 1[/tex]
[tex]= 6x + 1[/tex]
99. [tex]f(n) = n - 3[/tex]
[tex]g(n) = 2n^2 - 3n[/tex]
[tex]g(-7) = 2*(-7)^2 - 3 * (-7) = 2* 49 + 21 = 98 + 21 = 119[/tex]
[tex]f(g(-7)) = 119 - 3 = 116[/tex]
Answer:
97.
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
99.
Step-by-step explanation:
traveling at 65 miles per hour how many minutes rounded to the nearest whole number does it takes to drive 125 miles from san digit to malibu
Answers
divide total miles by speed
125/65 = 1.923 hours
there are 60 minutes per hour
multiply 1.923*60 = 115.384 minutes
rounded off to nearest whole number = 115 minutes
I don't get it I got a different answer then these
Answers
So you multiply the first fraction of both numerator and denominator by 3, and the second by 2:
3(g-2) / 18 - 2(g+3) / 18 = (3g - 6 - 2g - 6) / 18 = (g-12)/18
= ---------------------
18
3g - 6 -2g - 6
= ---------------------
18
g - 12
= -----------
18
this is what i got
A video game club charges a fixed annual membership fee of $18 and $3 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $20 the next year?
Answers
f(x)=mx+b, where m=slope and b=y-intercept so in terms of n, games rented, the cost, f(n) is:
f(n)=3n+18
Answer:
The correct answer is f(n)=3n+38
Step-by-step explanation:
Put in y=mx+b form, so y= f(n), $3 is fee per video game rented and n is the number of video games rented, b is ($18 fixed fee for this year +$20 fee for next year). So, f(n)=3n+38.
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is ____ cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be _____ times the original volume.
options for the first blank are: 20.22, 35.08, 50.07, or 100.11
options for the second blank are: 2, 4, 6 or 8
Answers
The total volume of the flask will be 50.06 [tex]\rm inches ^3[/tex] and if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
Given :
Flask can be modeled as a combination of a sphere and a cylinder.
The volume of Sphere is given by the:
[tex]V_s = \dfrac{4}{3}\pi r^3[/tex]
Given - diameter of sphere = 4.5 inches. Therefore, radius is 2.25 inches.
Now, the volume of sphere of radius 2.25 inches will be:
[tex]V_s = \dfrac{4}{3}\times \pi\times (2.25)^3[/tex]
[tex]\rm V_s = 47.71\; inches^3[/tex]
The volume of Cylinder is given by the:
[tex]V_c = \pi r^2h[/tex]
Given - diameter of cylinder = 1 inches then radius is 0.5 inches and height is 3 inches.
Now, the volume of cylinder of radius 0.5 inches and height 3 inches will be:
[tex]V_c = \pi\times (0.5)^2 \times 3[/tex]
[tex]\rm V_c = 2.35\; inches^3[/tex]
Therefore the total volume of the flask will be = 47.71 + 2.35 = 50.06 [tex]\rm inches ^3[/tex].
Now, if both the sphere and the cylinder are dilated by a scale factor of 2 than:
Radius of sphere = [tex]2.25\times 2[/tex] = 4.5 inches
Radius of cylinder = [tex]0.5\times 2[/tex] = 1 inch
Height of cylinder = [tex]3\times 2[/tex] = 6 inches
Now, the volume of sphere when radius is 4.5 inches will be:
[tex]V_s' = \dfrac{4}{3}\times \pi \times (4.5)^3[/tex]
[tex]\rm V_s' = 381.70\; inches ^3[/tex]
And the volume of cylinder when radius is 1 inch and height is 6 inches will be:
[tex]V_c' = \pi \times (1)^2\times 6[/tex]
[tex]\rm V_c'=18.85\;inches^3[/tex]
Therefore the total volume of the flask after dilation by a scale factor of 2 will be = 381.70 + 18.85 = 400.55 [tex]\rm inches ^3[/tex].
Now, divide volume with dilation by theorginal volume of the flask.
[tex]\dfrac{400.55}{50.06}=8[/tex]
Therefore, if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
For more information, refer the link given below:
https://brainly.com/question/15861918
A rectangular garden has length twice as great as its width. A second rectangular garden has the same width as the first garden and length that is 4 meters greater than the length of the first garden. The second garden has area of 70 square meters. What is the width of the two gardens?
Answers
this the picture for my question
Answers
Use the given graph to determine the limit, if it exists. A
Find limit as x approaches three from the left of f of x..
Answers
(25 Points)Enter numbers to write 4.23×10^3 in standard notation.
Answers
So the answer will be 4230
let n be the first 3 of consecutive even integers. what is the sum of those integers?
Answers
even integers are 2 apart
so the 3 integers are n,n+2,n+4
the sum is n+n+2+n+4=3n+6
the sum is 3n+6
Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.
Part A: Find (f + g)(x). Show your work. (3 points)
Part B: Find (f ⋅ g)(x). Show your work. (3 points)
Part C: Find f[g(x)]. Show your work. (4 points)
Answers
(f+g)(x)=f(x)+g(x)
(f+g)(x)=4x-5+3x+9
(f+g)(x)=7x+4
B:
(f•g)(x)=f(x)•g(x)
(f•g)(x)=(4x-5)(3x+9)
(f•g)(x)=12x^2-15x+36x-45
(f•g)(x)=12x^2+21x-45
C:
(f○g)(x)=f(g(x))
(f○g)(x)=4(3x+9)-5
(f○g)(x)=12x+36-5
(f○g)(x)=12x+31
Line BC has an equation of a line y = 2x + 3, and line EF has an equation of a line y = negative one over 2 x + 4. These two equations represent
Answers
Answer:
Perpendicular lines.
Step-by-step explanation:
We have been given that line BC has an equation of a line [tex]y=2x+3[/tex] and line EF has an equation of a line [tex]y=-\frac{1}{2}x+4[/tex]. We are asked to determine what these both equations represent.
We know that slope of two perpendicular lines is negative reciprocal of each other. This means the product of slope of both lines is equal to [tex]-1[/tex].
Let us find the product of slopes of both lines.
[tex]2\times \frac{-1}{2}[/tex]
Upon cancelling 2 with 2 we will get,
[tex]=-1[/tex]
Therefore, the given two equations represent equations of two perpendicular lines.
A rectangle is 42 square feet. what percent of the area of the rectangle is a square with side lengths of 6 feet?
Answers
area = L x w
42 = 6 x w
w=42/6 = 7
rectangle is 6 x 7
square would be 6 x 6 = 36 square feet
36/42 = 0.857 = 85.7% ( Round answer if needed)
(Solve for r) 0.5r − 3.8 = 5.66
Answers
0.5r = 5.66 + 3.8
0.5r = 9.46...divide both sides by 0.5
r = 9.46 / 0.5
r = 18.92 <==
0.5r = 9.46
r = 9.46 ÷ 0.5
r = 18.92
r = 18/23/25
What are the roots of the function y = 4x2 + 2x – 30? To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of .
Next, factor the trinomial completely. The equation becomes .
Use the zero product property and set each factor equal to zero and solve. The roots of the function are .
Answers
factor out the GCF:
2(2x² + x - 15) = 0
factor the trinomial completely:
2x² + x - 15 = 0
2x² + 6x - 5x - 15 = 0
2x(x + 3) - 5(x + 3) = 0
(2x - 5)(x + 3) = 0
use the zero product property and set each factor equal to zero and solve:
2x - 5 = 0 or x + 3 = 0
2x = 5 x = -3
x = 2.5
The roots of the function are x=-3, x=2.5
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
Roots of a quadratic equationThe given quadratic equation is:
[tex]y=4x^2+2x-30[/tex]
Set y = 0
[tex]4x^2+2x-30=0[/tex]
Factor the trinomial completely
[tex]4x^2-10x+12x-30=0\\\\2x(2x-5)+6(2x-5)=0\\\\(2x-5)(2x+6)=0[/tex]
Set each factor to zero and solve
2x - 5 = 0
2x = 5
x = 5/2
2x + 6 = 0
2x = -6
x = -6/2
x = -3
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
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what is the period of the sinusoid given by y=-4sin( [tex] \frac{2π}{3} [/tex] x) ?
Answers
[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ [/tex]
[tex]\bf \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]
with that template in mind, let's see
[tex]\bf \begin{array}{llll} y=&-4sin(&\frac{2\pi }{3}x)\\ &A&B \end{array}\qquad period\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{2\pi }{3}}\implies \cfrac{\frac{2\pi }{1}}{\frac{2\pi }{3}} \\\\\\ \cfrac{2\pi }{1}\cdot \cfrac{3}{2\pi }\implies 3[/tex]
Answer:
The answer is 3 for A P E X
Step-by-step explanation:
The sum of four consecutive whole numbers is 54, what are the four numbers
Answers
The sum of the four numbers is 54, therefore
x + (x+1) + (x+2) + (x+3) = 54
4x + 6 = 54
4x = 54 - 6 = 48
x = 12
Answer:
The four numbers are 12, 13, 14, and 15
Use complete sentences to describe the range of the sine function.
Answers
Given the sine function f(x)=sinx,
This function is the function which calculates the sine of the values of x.
According to the definition of the sine of an angle x in the unit circle,
[tex]-1 \leq sinx \leq 1[/tex],
so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.
This means that the values that the sine function takes are any values between -1 and 1, inclusive.
This determines the Range of the sine function.
So the Range of the sine function is [-1, 1]
What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?
Answers
both equal y so
2x-5=-x+1
3x-5=1
3x=6
x=2
sub back
y=2x-5
y=2(2)-5
y=4-5
y=-1
intersection is (2,-1)
paralell to a line is having same slope
y=mx+b, m is slope
given
y=1/2x+4
slope is 1/2
so
y=1/2x+b
find b
given the point (2,-1) that it must pass through
(x,y) so x=2 and y=-1
-1=1/2(2)+b
-1=1+b
-2=b
the equation is y=1/2x-2
y = -x + 1
2x - 5 = -x + 1
2x + x = 1 + 5
3x = 6
x = 6/3
x = 2
y = -x + 1
y = -2 + 1
y = -1
solution is (2,-1)...point of intersection between the 2 lines given.
y = 1/2x + 4....slope here is 1/2. A parallel line will have the same slope.
y = mx + b
slope(m) = 1/2
(2,-1)...x = 2 and y = -1
sub and find b
-1 = 1/2(2) + b
-1 = 1 + b
-1 -1 = b
-2 = b
so ur parallel equation is : y = 1/2x - 2 <==
Two 6-sided dice are rolled. what is the probability the sum of the two numbers on the die will be 4?
Answers
3/6 or 1/2 if only addition
5-1=4. 6-2=4.
2/6 or 1/3 if only subtraction
if both 5/6
Answer:
[tex]\frac{1}{12}[/tex].
Step-by-step explanation:
Given : Two 6-sided dice are rolled.
To find : what is the probability the sum of the two numbers on the die will be 4.
Solution : We have given
Two 6-sided dice are rolled.
Dice have number { 1,2,3,4,5,6} { 1,2,3,4,5,6} .
[tex]Probability =\frac{outcome\ happn}{total\ outcome}[/tex].
sum of the two numbers on the die will be 4.
Case (1) : first dice rolled 3 and second dice rolled 1.
{3,1}
3 +1 = 4 .
Case (2) : first dice rolled 1 and second dice rolled 3 .
{1,3}
1 + 3 = 4 .
Case (3) : first dice rolled 2 and second dice rolled 2.
{2,2}
2 + 2 = 4.
Then there are 3 possible outcomes where the sum of the two dice is equal to 4.
The number of total possible outcomes = 36.
[tex]Probability =\frac{3}{36}[/tex].
[tex]Probability =\frac{1}{12}[/tex].
Probability of getting sum of two dice is [tex]\frac{1}{12}[/tex].
Therefore, [tex]\frac{1}{12}[/tex].
A giraffe can run 40 meters per second what is its speed in miles per hour
Answers
60 seconds in 1 minute,
60 minutes in 1 hr,
1000 meters in 1 km,
and 1.609 km in 1 mile
[tex]\bf \cfrac{40\underline{m}}{\underline{s}}\cdot \cfrac{60\underline{s}}{\underline{min}}\cdot \cfrac{60\underline{min}}{hr}\cdot \cfrac{\underline{km}}{1000\underline{m}}\cdot \cfrac{mi}{1.609\underline{km}}\implies \cfrac{40\cdot 60\cdot 60\cdot mi}{hr\cdot 1000\cdot 1.609} \\\\\\ \cfrac{144000mi}{1609hr}\approx 89.496581\frac{mi}{hr}[/tex]
Write an equation for the line that is parallel to the given line and that passes through the given point.
y = 1/2 – 8; (–6, –17)
A.) y = 2x – 14
B.) y = 1/5x + 5/2
C.) y = -2x + 14
D.) y = 1/2x – 14
Answers
How could the relationship of the data be classified?
scatter plot with points loosely scattered going down to the right
A positive correlation
A causation
A negative correlation
No correlation
Answers
Answer: A negative correlation
Step-by-step explanation:
If the points in the scatter plot scattered going down to the right, it shows that there are inverse relationship between the quantities.
With the increase of one quantity or variable there is decrease in the other quantity or variable.
Therefore, if in the scatter plot with points loosely scattered going down to the right , then the relationship of the data be classified as a negative correlation.
The sum of two rational numbers will always be
Answers
A) side-side-side triangle similarity postulate
B) angle-angle triangle similarity postulate
C) angle-side-angle triangle similarity postulate
D) hypotenuse-lag triangle similarity postulate
Answers
For similarity you only have to know that 2 corresponding angles are equal.
system of equations with different slopes and different y-intercepts have one solution.
A. Always
B. Sometimes
C. Never
I think it is A but I am not sure and it is impossible for system of equations with different slopes and different y-intercepts to be parallel or infinite.
Answers
A. Always
Also
If two equations have different slopes but equivalent y-intercepts, they will have one solution and that will be the point where the y-intercept is. If two equations have different slopes and different y-intercepts, then there will be one solution where those two lines meet. If two equations have the same slope but different y-intercepts, the lines will be parallel, and there is no possible intersection point. And if two equations have equal slopes and equal y-intercepts, these lines will have an infinite amount of solutions, because if the equations are one the same line, every single point on that line is a solution to the system.
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Jean has 5 different colors of markers: red, blue, green, orange, and purple. Two colors are used to make a sign. How many different combinations are possible? List them.
Answers
Jean has 5 different colors which means that n=5 and 2 colors are used to make a sign, which means r=2.
The number of combinations can be calculated with the formula:
C=n!/((n-r)!r!)
C=5!/(5-2)!*2!
C=5*4*3!/3!*2*1
C=20/2=10
The possible combinations are:
1.red blue
2.red green
3.red orange
4.red purple
5. blue green
6. blue orange
7. blue purple
8. green orange
9. green purple
10. orange purple