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.
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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.
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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.If f(x) = 2x2 + 1, what is f(x) when x = 3?
Answer:
18
Step-by-step explanation:
f(x)=2x(2+1)
f(3)=2(3)(2+1)
=6(2+1)
=12+6
=18
A fruit punch mixture is made of Orange juice, Pineapple juice, and Cranberry juice in a 3:5:7 ratio. How much of each juice type do you need for a 375 ml mixture?
Answer: a good amount
Step-by-step explanation:
because if you just get a table spoon for all flavour mixtures then wala they are all the same amount -__-------------i is not smart at all srry
What is the simplified value of the expression below?
1/3 divided by 2/3
0
1/3
1/2
1
Answer:
option C : 1/2
Step-by-step explanation:
[tex]\frac{1}{3} \div \frac{2}{3} \\\\\frac{\frac{1}{3}}{\frac{2}{3}}\\\\\frac{1}{3} \times \frac{3}{2} \\\\\frac{1}{2}[/tex]
Regan earns $1380 per month out of which he saves $1140 per month. What is the ratio (in the lowest form) of Regan's income to his savings? $$
Answer:
23:19
Step-by-step explanation:
This questions is looking for this ratio:
income:savings
Regan's income is $1,380 per month.
Regan's savings is $1,140 per month.
Substitue those numbers in our original ratio, and you'll get this:
1380:1140
However, this question wants the lowest form of the ratio.
To do that, you can find the GCF (greatest common factor) and divide both number's by it, or you can just randomly divide them by small numbers you know both of them are divisible by.
I'm going to use the 2nd method because it's usually quicker for big numbers like these:
1380/10 = 138
1140/10 = 114
138/2 = 69
114/2 = 57
69/3 = 29
57/3 = 19
29 and 19 are prime numbers, so you can't divide them anymore. This is how we know we've reached the lowest terms of these numbers.
So the answer is 29:19
Hope this helps (●'◡'●)
Answer: 23:19
Step-by-step explanation: 1380 and 1140 LCM is 60. 1380/6 = 23 and 1140/6= 19
Therefore, the answer is 23:19
In a group of 26 pupils, 3 play the flute only.
5 play the piano only.
7 play neither instrument.
How many pupils play both instruments?
Here is a Venn diagram:
what is the value of x? (3x-14)°=180° [4(x-9)]°=180°
Answer:
3x-14=180
3x=194
x= 64 2/3
4(x-9)=180
4x-36=180
4x=216
x=54
Hope This Helps!!!
Step-by-step explanation:
(3x-14)°=180°
3x-14=180
3x=180+14
3x=194
x=64.6
[4(x-9)]°=180°
4x-36=180
4x=180+36
4x=216
x=54
Evaluate the expression.
32 + 6 x 22-42 - 23
Answer:
25
Step-by-step explanation:
You need to simplify
.
.
.
.
................... :)
Answer:
D
Step-by-step explanation:
9+24-16+8= 25
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answer:
(1/3) r2 =(1/3) r +14
1/6 divided by 83 r + 14
97r
i think...
I hope this helps you!
XoXo Mashayla
Step-by-step explanation:
What is the answer to this question
Answer:
26 m is the answer to the question
Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
Answer:
its the 2nd
Step-by-step explanation:
The graph showing common region to both inequalities represents the solution coordinates that satisfy both inequalities.
What is inequality in mathematics?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given are the following inequalities -
x – 4y < 4
y < x + 1
We have the following inequalities -
x – 4y < 4
y < x + 1
Inequality [1]
x - 4y < 4
x - 4 < 4y
4y > x - 4
y > x/4 - 1
Inequality [2]
y < x + 1
Refer to the graph attached. The common region to both inequalities represents the solution.
Therefore, the graph showing common region to both inequalities represents the solution coordinates that satisfy both inequalities.
To solve more questions on inequalities, visit the link below-
brainly.com/question/26434651
#SPJ2
can someone help me with this?
Answer:
-64 is the 26th number
it's an arithmetic sequence because the difference between the number is constant : -3
they are all -3 in difference
Step-by-step explanation:
an = a1 + (n-1)d
an = the nᵗʰ term in the sequence
a1=the first term in the sequence
d=the common difference between terms
-64 = 11 + (n - 1)-3
-64=11 -3n+3
-78 = -3n
n = 26
Find angle m
A. 69
B. 23
C. 46
D. 167
Answer:
a
Step-by-step explanation:
∠DAF - ∠CFA=∠DFC
118-49 =69
The sum of a father's and his son's age is 60. Eight years ago, the father's age was 3 times that of his son. How old is each of them?
Answer:
Father=41
Son=19
Step-by-step explanation:
Father=f
Son=s
f+s=60
Eight years ago would mean that 16 is subtracted from 60 since there is both of them
3s+s=4s
4s=44
s=11
11+8=19
33+8=41
find the next four terms of the sequence 5, 4, 9, 13, 22
Hello,
It is the Fibonacci 's suit.
[tex]u_1=5\\u_2=4\\u_3=u_1+u_2=5+4=9\\u_4=u_2+u_3=4+9=13\\u_5=u_3+u_4=9+13=22\\u_6=13+22=35\\u_7=22+35=57\\u_8=35+57=92\\u_9=57+92=149\\\\\\\boxed{u_{n+2}=u_{n}+u_{n+1}}\\[/tex]
What is the y-intercept of the line y = -3x + 7?
O A. -7
O B. 3
O C. 3
O D. 7
Answer:
Answer would be
D: 7
50 pts pls help
What is the range of the function shown on the graph above?
Answer:
[0, 7]Step-by-step explanation:
The range is the set of y-values.
The graphed function has its range between 0 and 7, both inclusive.
So the range is:
y ∈ [0, 7]Find the constant of proportionality if y is
proportional to x.
A. 25
B. 21
C. 26
D. 28
HELPPP!!!!!!
Solve the system of equations.
5x – 4y = -10
y = 2 x – 5
x =
y =
Answer:
6x2+3y2=12,x+y=2,2x-y=-1x+y=4,x-y=2
Step-by-step explanation:
I just know.
Answer:
Step-by-step explanation:
5x – 4y = -10
y = 2 x – 5
Rearrage the equation:
5x – 4y = -10 (1)
-2 x +y = 5. (2)
pluging variable y equation2 in 1
5x - 4•(2x-5) = -10
-3x = -30
Solve equation [1] for the variable x
3x = 30
x = 10
x = 10
y = 2x-5
Use the x value to solve for y
y = 2(10)-5 = 15
x= 10
y= 15
Rewrite the equation 8x + 6x2 - 7= in standard form and identify a, b, and c.
Select one:
a. a =5,b= 8.c = -7
b.a=6,6= 8,0 = 1
ca=5,b=8,0= 7
da= 8,b= 6.c = -7
40
Answer:
a = 6
b = 8
c = -7
Step-by-step explanation:
In standard form, we have ;
y = ax^2 + bx + c
Here, we have;
6x^2 + 8x - 7
a is the coefficient of x^2 which is 6 in this case
b is the coefficient of x which is 8
c is the last number which is -7
So we have;
a = 6
b = 8
c = -7
The length of a rectangle is 7 ft less than three times the width, and the area of the rectangle is . Find the dimensions of the rectangle.
Answer:
See explanation
Step-by-step explanation:
the length of a rectangle is 7 feet less than three times it’s width. if the area of the rectangle is 180 ft, find the dimensions of the rectangle.
Width = x
Length = 3x - 7
Area of a rectangle = length × width
180 = (3x - 7) * x
180 = 3x² - 7x
3x² - 7x - 180 = 0
Using quadratic formula
a = 3
b = -7
c = -180
x = -b ± √b² - 4ac / 2a
x = -(-7) ± √(-7)² - 4(3)(-180) / 2(3)
x = 7 ± √49 - (-2160) / 6
= 7 ± √49 + 2160 / 6
x = 7 ± √2209/6
= 7 ± 47 / 6
= (7 + 47)/6 or ( 7 - 47)/6
= 54/6 or -40/6
x = 9 or -6.67
x cannot be negative
Therefore,
x = 9 ft
Width = x = 9 ft
Length = 3x - 7
=3(9) - 7
= 27 - 7
= 20 ft
What is the slope of the line? What is the y-intercept of the line? y = 2x + 5
Slope intercept form of a line is, y = mx + c where m is the slope and c is constant.
Judging the given equation y = 2x + 5
Slope (m) of the line is 2,
y-intercept of the line,
y = 2x + 5
y = 2×0 + 5
y = 5
Answered by GAUTHMATH
Answer:
m = 2
y intercept = 5
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = 2x +5[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = 2 [/tex]
[tex]\implies y - intercept= 5[/tex]
Evaluate the expression 2
2^5 = 32
Hope this helps! :)
Answer:
32
Step-by-step explanation:
[tex]2^{5}[/tex]
= 2 × 2 × 2 × 2 × 2
= 4 × 4 × 2
= 16 × 2
= 32
Quadrilateral A B C D is shown. All sides are congruent. Angle C is a right angle.
Which statements are true regarding quadrilateral ABCD? Check all that apply.
ABCD has congruent diagonals.
ABCD is a rhombus.
ABCD is not a rectangle.
ABCD is not a parallelogram.
ABCD has four congruent angles.
Answer:
The first one and last one
Step-by-step explanation:
Answer:
1,2,5
Step-by-step explanation:
got it right on edge
which of the following functions is graphed below?
Answer:
d number on is the wright answer
hope it may help you
Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women
Answer:
The number of ways is 26,400 ways
Step-by-step explanation:
Given;
total number of men, M = 10
total number of women, W = 12
number of committees to be formed = 6
If there must be equal gender, then it must consist of 3 men and 3 women.
[tex]The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways[/tex]
Therefore, the number of ways is 26,400 ways
The cost of having a window fixed is $175 plus $30 per hour of labor. Using h for the number of hours of labor, write an expression that represents the total cost.
Answer:
175 + 30h
Step-by-step explanation:
Hope this helps
Answer:
total cost = 175+30h
Step-by-step explanation:
Total cost = fixed cost + cost per hour * hours
total cost = 175+30h where h is the number of hours
Find the greatest number such that; x360y is divisible by 24
WILL GIVE BRAINIEST, NEED ANSWER ASAP
Answer:
93600
Step-by-step explanation:
24=3*2*2*2
y=0,8
1) x3600, then x=9,6,3
2)x3608, then x=1,4,7
9 is the largest so the final answer is 93600
If 4/3 . sin42⁰ = x then 4/3 . cos48⁰ = ?
Step-by-step explanation:
If 4/3 . sin42⁰ = x then 4/3 . cos48⁰ = ?
so it's that
On Monday, a localamburger shop said a combined total of 225 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number
of hamburgers sold. How many hamburgers were sold on Monday?
hamburgers
х
?
Answer:
h = hamburgers sold
2h - 72 = 578
2h = 650
2 2
h = 325
There were 72 fewer cheeseburgers sold than hamburgers. That means cheeseburgers = 325 - 72
325 - 72 = 253
253 = cheeseburgers
325 = hamburgers
253 + 325 = 578
Hamburgers = 325
Hope this helps :)
Find the area
Help me please
Answer:
143
Step-by-step explanation:
to find the area we multiply half of the sum of the bases with height
(18+8)/2*11 = 143
