Answer
Number of years 1 2 3
House 1 (value in dollars) 249,000 253,980 259,059.60
House 2 (value in dollars) 249,000 256,000 263,000
House 1: exponential function
House 2: linear function
House 1: f(x) = 249,000 * (1.02)^(x-1)
→ f(3) = 249,000 * (1.02)³⁻¹ = 249,000 * (1.02)² = 259,059.60
House 2: f(x) = 249,000 + 7,000(x-1)
→ f(3) = 249,000 + 7,000(3-1) = 249,000 + 7,000(2) = 249,000 + 14,000 = 263,000
House 1:
f(45) = 249,000 * (1.02)⁴⁵⁻¹ = 249,000 * (1.02)⁴⁴ = 249,000 * 2.39 = 595,110
House 2:
f(45) = 249,000 + 7,000(45-1) = 249,000 + 7,000(44) = 249,000 + 308,000 = 557,000
House 1 will have a greater value than House 2 after 45 years.
Step-by-step explanation:
Hope this helps, if not let me know and I will fix it.
Part A
The value for house 1 follows an exponential growth function since the value is increasing by 2% each year. This is because we multiply each value by 1.02 to get the next year's value.
249,000*1.02 = 253,980253,980*1.02 = 259,059.60259,059.60*1.02 = 264,240.792 = 264,240.79In contrast, house 2's value increases by the same amount each year (7000 per year)
249,000 + 7,000 = 256,000256,000 + 7,000 = 263,000263,000 + 7,000 = 270,000This fixed amount it increases directly leads to house 2 having linear growth.
-----------
Summary:House 1 = exponential functionHouse 2 = linear function=================================================
Part B
The equation for house 1's value is y = 249000(1.02)^x
This is in the form y = ab^x, where a = 249000 is the starting value and b = 1.02 is the growth rate factor.
We can think of 1.02 as 1+0.02 to represent the 2% growth.
In other words, 1.02 = 1+r solves to r = 0.02 = 2%
-----------
The equation for the second home's value is y = 7000x+249000
The slope m = 7000 tells us how the value is going up per year.
The y intercept b = 249000 is the original home value (when x = 0).
-----------
Summary:Equation for home 1 is f(x) = 249000(1.02)^xEquation for home 2 is f(x) = 7000x+249000=================================================
Part C
Let's plug x = 45 into each equation mentioned in part B
For home 1, we have
f(x) = 249000(1.02)^x
f(45) = 249000(1.02)^45
f(45) = 607,025.697
f(45) = 607,025.70
So that's the value of home 1 after 45 years of constant 2% growth per year
For the second home, we have,
f(x) = 7000x+249000
f(45) = 7000*45+249000
f(45) = 564,000
So there is a significant difference. This difference is 607,025.70 - 564,000 = 43,025.70 dollars.
-----------
Summary:Home 1's value = $607,025.70Home 2's value = $564,000This is a difference of $43,025.70 which is fairly significant. It's better to go with home 1.PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The ___________ of a set of numbers tells how much a value would be if the values were spread evenly among every number in the data set.
A. mode
B. range
C. mean
D. median
4x + 7 + 4
I need helppp pls
Answer:
4x+11
Step-by-step explanation:
you have to add the like terms,in this case the like terms are 7 and 4.4x isn't a like term cause it has a variable.
so you just have to add 7+4
4x+11
I hope this helps
Step-by-step explanation:
hope this may help you tq
The cost of a pen is three times and Rs 4 more than the cost of a pencil. If three pencils and two pens cost Rs 71, find the cost of each item.
Answer:
1.
= Here,
cost of pen = 3+4 ( x ) = 7x
costs of two pen = 7x
cost of three pencils = 71 - 7x = 64x
cost of 1 pencil = 64/3
= 21.333334
c
Simplify x + (7+14x)
Answer:
15x + 7
Step-by-step explanation:
x + (7 + 14x)
x + 7 + 14x
15x + 7
Answer:
15x + 7
Step-by-step explanation:
Remove parenthesis:
x + 7 + 14x
Combine like terms:
14x + x = 15x
Add the seven:
15x + 7
Hope this helped.
A student said that since -9 is less than 4, then |-9| is less than |4|. Is the student correct? Explain why or why not.
Answer:
No.
Step-by-step explanation:
They are not correct because the "| |" signs mean absolute value. What ever is inside the signs must be positive. So -9 becomes 9 and 9 is greater than 4. So, the student is not correct.
Help pls ?? I really don’t know what to do
Answer:
The answer is "C" f(x)= x+ 4 and g(x)= x^3 - 1
Step-by-step explanation:
all you have to do is replace the x in "G" with the "F" function
F(x) = x+4 and G(x) = x^3-1
===========================================================
Explanation:
Let's try choice A to see if it works or not
G(x) = (x+4)^3
G( F(x) ) = ( F(x)+4 ) ^3 .... replace every x with F(x)
G( F(x) ) = ( x-1+4 ) ^3 .... plug in F(x) = x-1
G( F(x) ) = (x+3)^3
This isn't the same as (x+4)^3 - 1. You can confirm this with a graph or a table of values. We cross choice A off the list.
------------
Let's try choice B
G(x) = x+4
G( F(x) ) = F(x)+4
G( F(x) ) = x^3-1 + 4
G( F(x) ) = x^3 + 3
Similar to choice A, this isn't the same as (x+4)^3-1. We can cross this off the list as well.
--------------
Now choice C
G(x) = x^3 - 1
G( F(x) ) = ( F(x) )^3 - 1
G( F(x) ) = (x+4)^3 - 1
We found the final answer.
Simplify xy-5x+y^2xy−5x+y 2 if x = -3 and y = 5.
The simplification of the expression [tex]xy-5x+y^2xy-5x+y ^2[/tex] gives - 335.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
[tex]xy-5x+y^2xy-5x+y ^2[/tex]
Substitute x = -3 and y = 5.
[tex]-3\times 5-5\times -3+5^2\times -3\times 5-5\times -3+5 ^2[/tex]
= -15 + 15 - 375 + 15 + 25
= -335
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please help me solve this exercise.!!
find the value of tanx if sinx+cosx=1/5 and 0<x<π.
=============================================================
Explanation:
Let's square both sides and do a bit of algebra to get the following.
[tex]\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\[/tex]
Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25
This then means tan(2x) = sin(2x)/cos(2x) = 24/7.
From here, you'll use this trig identity
[tex]\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\[/tex]
which is the same as solving
[tex]\tan(2x) = \frac{2w}{1-w^2}\\\\[/tex]
where w = tan(x)
Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4
So either tan(x) = -4/3 or tan(x) = 3/4.
If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.
Since tan(x) < 0 in this case, we go for tan(x) = -4/3
On what sum of money will the compound interest for 2 years at 8% p.a. will be ₹7448?
Answer:
Rs.6420
Step-by-step explanation:
we know that A=P(1+r/100)
7488=P(1+8/100)2
7488*10000/108*108=P
P=Rs.6420
Answer:
Principal=Rs.45000 ; And Amount=Rs.52488.
Step-by-step explanation:
For finding Principal i used the formula:[ x(1+8/100)^2-x] =C.I ( where x = P)
And for Amount : Sum of principal and interest.
Hope so, you liked my solution.
1. Paulina wants to find the width, AB, of a river. She walks along the edge of the river 200 ft and marks point C. Then she walks 60 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown. (a) Can Paulina conclude that ΔABC and ΔEDC are similar? Why or why not? (b) Suppose DE = 40 ft. Calculate the width of the river, AB. Show all your work and round answer to the nearest tenth. Answer
Answer:
Step-by-step explanation:
a). In ΔABC and ΔEDC,
Since, AB and DE are parallel and AE is a transversal,
Therefore, ∠CAB ≅ ∠CED [Alternate interior angles]
m∠D = m∠B = 90°
ΔABC ~ ΔEDC [By AA property of similarity of two triangles]
b). Therefore, by the property of similar triangles,
"Corresponding sides of two similar triangles are proportional"
[tex]\frac{DC}{BC}= \frac{DE}{AB}[/tex]
[tex]\frac{60}{200}=\frac{40}{AB}[/tex]
AB = [tex]\frac{40\times 200}{60}[/tex]
= 133.33
≈ 133.3 ft
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that:
She plans to drive 400 miles.
She has at most $210 to spend.
Use the drop-down menu below to write an inequality representing dd, the total number of days Claire can rent the car while staying within her budget.
The required inequality that expresses the given condition is 36 + 29x ≤ 210.
Given that,
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that she plans to drive 400 miles. she has at most $210 to spend.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of days be x,
Total cost to drive 400 miles = 400(0.09) = $36.
According to the question,
36 + 29x ≤ 210
Thus, the required inequality that expresses the given condition is 36 + 29x ≤ 210.
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The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 49 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon. Construct a 89% confidence interval for the mean gas mileage for this car model.
Answer:
The answer is "(27.030,29.770)"
Step-by-step explanation:
[tex](\bar{x}) = 28.4[/tex]
[tex](n)= 49[/tex]
[tex](\sigma) = 6[/tex]
[tex](CI) = \bar{x}\pm z^*_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}[/tex]
[tex]z^*_{\frac{\alpha}{2}}\ for \ 89\%\ confidence = 1.598 \\\\\text{Using z table }\\\\ NORM.S.INV(1-\frac{(1-0.89)}{2})[/tex]
[tex]CI = 28.4 \pm 1.598 \times \frac{6}{\sqrt{49}}=(27.030,29.770)[/tex]
How high up the wall can a 12-foot ladder reach if its base is 4 feet from the wall? Round your answer to the nearest tenth of a foot if necessary.
Answer:
11.3 feet
Step-by-step explanation:
let x= answer
x²+4²=12²
x²=128
x=11.3137085
which rounds to
11.3
Answer:
≈ 11.3 ft.
Step-by-step explanation:
In order to solve this, we must use some trigonometry, in this case, SOH-CAH-TOA. If you don't know what it is, here's a quick explanation:
- SOH: Sin(θ) = Opposite / Hypotenuse
- CAH: Cos(θ) = Adjacent / Hypotenuse
- TOA: Tan(θ) = Opposite / Adjacent
(Remember, SOH-CAH-TOA can ONLY be used for right triangles. If the problem does not clearly show a right triangle, meaning that there's no box in the corner, you cannot use it)
When using SOH-CAH-TOA, we first must choose an angle, either the top one or the bottom one. We can't use the right angle as, well, you just can't :). First, we have to find the bottom angle, so circle it. Literally, just circle the angle, you'll thank me later. I'll explain why we don't solve the top angle later on.
After that, we just do some labeling on the sides of the triangle. First, label the shortest side that forms the circled angle, which is the floor (4 ft), as the Adjacent side. Then label the longest side of the triangle, which is the ladder (12 ft), as the Hypotenuse. Finally, label the side that doesn't form the circled angle as the Opposite side. This is why the circling comes in handy :)
Then, out of SOH, CAH, and TOA, we choose the one that has the sides that forms the circled angle. In this case, it's CAH, or cosine, as the adjacent and hypotenuse form the circled angle.
Next, we write out the formula and solve:
Cos(m∠Circled Angle) = Adjacent/Hypotenuse
Cos(m∠Circled Angle) = 4/12
Cos(m∠Circled Angle) x Cos^-1 = 1/3 x Cos^-1
m∠Circled Angle ≈ 70.5288 (Rounding to the nearest ten-thousandth)
Note: Pay attention to the 3rd line. 'Cos^-1' is basically the equivalent of '÷ Cos'.
The reason why we did the bottom angle first is because you cannot have two unknown variables when solving for one of them. That would've been the case if we did choose the top angle as we wouldn't know the measure of the wall nor the angle. Now that we have solved the bottom angle, we can move onto solving the length of the wall.
Looking at SOH-CAH-TOA, we can either use sine or tangent as we have the measures for both the adjacent and hypotenuse. I'll use sine cause why not? Anyways, let's move on!
Just like last time, we write out the formula and solve:
Sin(m∠Circled Angle) = Opposite/Hypotenuse
Sin(70.5288) = Opposite/12
0.9428 = Opposite/12
0.9428 x 12 = Opposite/12 x 12
11.3137 ≈ Opposite (Wall)
Wall ≈ 11.3 ft. (Rounding to the nearest tenth, as asked to do so by the problem)
Note: Be careful with SOH-CAH-TOA because I've messed up multiple times with my calculator while typing out my explanation, so just make sure you go over it several times before submitting your answer when solving trig problems :). But I'm confident with my answer, so just submit it without hesitation as I've already double-checked my work.
Someone please help me!!!
Answer:
<2 = 75°
<3 = 75°
Step-by-step explanation:
<2 = <6
2x+15 = 45+x
or, 2x-x = 45-15
or, x = 30
so, <2 = 30×2+15 = 75
<6 = 45+30 = 75
Answered by GAUTHMATH
Please apply the properties of rational exponents to simplify expressions with radical or rational exponents. Explain the steps so that I understand because this is for my notes. Thank you for your time, the properties and problems to apply them to will be below.
Step-by-step explanation:
Product property
If the bases are the same, you don't multiple them. However, if they are the same, you do multiple for example : (2³ * 2¹ = 2⁴.when the bases are the same) (2³ * 3¹ =6⁴. When the bases are not the sameWe add the index.Quotient property
Same here, if the bases are the same, they stay the way they wereWe subtract the indexPower property
Here we multiple the index because of the bracket for example : (9²)²= 9⁴Negetive exponent property
When ever the index has a negative sign its convected to a fraction, for instance : 9¯² = 1 /9²Note, when it turns to a fraction th index becomes positiveHelp! ASAP. The question is in the attachment below
Answer:
Step-by-step explanation:
The most obvious answer is the line y = 1.
three less than twice the square of a number is 47.
Answer:
5
Step-by-step explanation:
[tex]5^{2}[/tex] = 25
25 * 2 = 50
50 - 3 = 47
Hope that this helps!
Answer:
Step-by-step explanation:
let the number be x
Square of a number: x²
Twice the square of a number = 2*x² = 2x²
Three less than twice the square of a number = 2x² - 3
2x² - 3 = 47 {Add 3 to both sides}
2x² = 47 + 3
2x² = 50 {Divide both sides by 2}
x² = 50/2
x² = 25 Take square root
x = √25
x = 5
You are driving 2760 miles across the country. During the first 3 days of your trip, you drive 1380 miles. If you continue to drive at the same rate each day, how many days will the entire trip take? Show your work and circle your answer.
The entire trip will take 6 days.
(Encircle this answer, as said on the directions)
Step-by-step explanation:
We know that the first three days of the trip, we traveled 1380 miles.
Find the UNIT RATE of MILES PER day:
1380/3 = 460
Unit rate = 460 miles per day
If we were to drive at this (460 mi per day) rate EACH day and the whole journey takes 2760 miles across the country.
FInd the NUMBER of DAYS of the ENTIRE TRIP:
2760/460 = 6
It will take us 6 days to drive to the destination.
A rectangle has side lengths 2x + 3 and 5x - 2.
Write an expression without brackets for the area of the rectangle
Answer:
10x² + 11x - 6
Step-by-step explanation:
The area (A) is the product of the sides, that is
A = (2x + 3)(5x - 2) ← expand using FOIL
= 10x² - 4x + 15x - 6 ← collect like terms
= 10x² + 11x - 6
Can you please help me!!!!!
Một ôtô đi từ A đến B với vận tốc 60km/h và đi từ B về A với vận tốc 45km/h. Thời gian cả đi và về hết 7giờ. Tính quãng đường AB
Please explain in english
Answer:
Đáp án: 180km
Step-by-step explanation:
Giải thích các bước giải:
Gọi quãng đường AB là x (km)
(x > 0)
Thời gian ô tô đi từ A -> B là x/60 (h)
Thời gian ô tô đi từ B -> A là x/45 (h)
Vì thời gian cả đi và về hết 7h
=> x/60 + x/45 = 7
=> x = 180 (TM)
Vậy quãng đường AB là 180 km
Help pls will give brainliest
Answer:
195.06
Step-by-step explanation:
area of circle = πr^2 = π8^2 = 64π
area of triangle = 1/2 x 4 x 3 = 6
area of shape = 64π-6 = 195.061929 = 195.06
Which Venn Diagram is NOT correct?
Can anyone help me with this question?
x^{2} + 7x -144
quadratic equations
Answer:
?
Step-by-step explanation:
Brainly challenge.
Determining the Domain and Range from a Graph
Determine the domain and range of the given function.
The domain is
ty
4
The range is
2
-4
-2
4
Into
Answer:
Domain is all real numbers, and range is all numbers greater than or equal to -2. If thee was anything you didn't understand let me know.
Step-by-step explanation:
The domain is what x values work, or it may be better to say the horizontal axis. is there any number you cannot use? if you cannot tell, this is a parabola, like x^2. Is there any number you cannot plug into x^2. The answer is no, the domain for all parabolic functions is all real numbers.
The range you really want to look at visually here. Range is y values you can get, or values on the vertical axis. I would also compare it to x^2 again. You should know you can make it as high as you want, here is the same. but at -2, there is no point below that. so the range is -2 and up
The other options are just specific numbers. you can disprove those by choosing a number not on their lists. For the domain literally any other number. For range any number not on the list greater than -2
The volume of the triangular prism is 54 cubic units.
What is the value of x?
O 3
O 5
7
09
3x
Answer:
3
Step-by-step explanation:
The value of x is 3 if the volume of the triangular prism is 54 cubic units.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that volume of the triangular prism is 54 cubic units.
We have to find the value of x
The volume of the prism with triangular base is 54 unit³.
The base is a triangle with,
base = 4 units
height = x units
height of the prism = 3x
V= 6x²
54= 6x²
Divide both sides by 6
x² = 9
x=3
Hence, the value of x is 3 if the volume of the triangular prism is 54 cubic units.
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not sure how to solve
Find the equations of line in y = mx + b form...
a) Passes through the points (7, 9) and (2, -2)
Answer:
y = 11/5x - 32/5
Step-by-step explanation:
y2 - y1 / x2 - x1
-2 - 9 / 2 - 7
-11 / -5
= 11/5
y = 11/5x + b
-2 = 11/5(2) + b
-2 = 22/5 + b
-32/5 = b
Plot the following of point on coordinate axis A1 (3,3), and A2 (-3,2) A3(-2,-3)and A4 (-3,-2)A5 (0-4) and
A6 (-2,0) A7 (4,0) and 0(0,0)please help me to do this homework please
Answer:
Graph is attached below with coordinated points of (3,3), (-3,2), (-2,-3), (-3,-2), (0, -4), (-2,0), (4,0), and (0,0)
Step-by-step explanation:
I need help please Brainly fam
Answer:
The third one
Step-by-step explanation:
Just took the quiz
