Braden bought a piece of commercial real estate for $101,234. The value of the real estate appreciated at a constant rate per year. The table shows the value of the real estate after the first and second years: Year 1 2 Value (in dollars) $104,271. 02 $107,399. 15 Which function best represents the value of the real estate after t years? f(t) = 101,234(1. 03)t f(t) = 101,234(0. 03)t f(t) = 104,271. 02(1. 03)t f(t) = 104,271. 02(0. 03)t.
The function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]
The table is represented as:
Years - Values
1 - $104,271. 02
2 - $107,399. 15
Appreciation and depreciation are often represented using exponential function as follows:
[tex]f(x) = ab^x[/tex]
At year 1, we have:
[tex]104271. 02 = ab^1[/tex]
[tex]104271. 02 = ab[/tex]
At year 2, we have:
[tex]107399. 15 = ab^2[/tex]
Divide both equations
[tex]\frac{107399.15}{104271.02} = \frac{ab^2}{ab}[/tex]
[tex]1.03 = b[/tex]
Rewrite as:
[tex]b = 1.03[/tex]
He bought the real estate for $101,234.
So, we have:
[tex]a = 101234\\[/tex]
Substitute values for (a) and (b) in [tex]f(x) = ab^x[/tex]
[tex]f(x) = 101234(1.03)^x[/tex]
Replace x with t
[tex]f(t) = 101234(1.03)^t[/tex]
Hence. the function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]
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Compute the fare without tip: 4 passengers, 20 miles.
$57.50
$59.70
$56.40
$58.60
I had this question earlier, and if I remember correctly the answer was 56.40
PLEASE HELP TENTH GRADE GEOMETRY
Answer:
answer is 19............
if a/b-d=2c/b, find the value of c when a=3 b=4 and d=5
please explain your answer
Answer:
c= -17/2
Step-by-step explanation:
a/b-d=2c/b
3/4-5=2c/4
-17/4=2c/4
-17/4÷1/4=2c
-17/4×4=2c
2c=-17
c=-17/2
please give me the answer (click on file)
Answer:
x = 122
Step-by-step explanation:
PLEASE YOU GUYS I NEED REAL HELP !!!!!!
The population of a town is modeled by the equation P=3485e0.12t, where “P” represents the population as of the year 2000.
According to the model, what will the population of the town be in 2010?
In approximately what year will the population reach 50,000 people?
Must answer and show appropriate work for both questions here.
Part A: 11,571 people in 2010
Part B: approx. 22 years
Part A: 38,416 people in 2010
Part B: approx. 13 years
Part A: 11,571 people in 2010;
Part B: approx. 13 years
Part A: 38,416 people in 2010;
Part B: approx. 22 years
The amount of people in 2010 is 11571 and it would take approximately 22 years to reach 50000 people.
Let P represents the population as of the year(t) 2000. Given the equation:
[tex]P=3485e^{0.12t}[/tex]
In the year 2010 (t = 10 years), the population would be:
[tex]P=3485e^{0.12*10}=11571\ people[/tex]
For the population to reach 50000 people:
[tex]50000=3485e^{0.12t}\\\\t=22\ years[/tex]
The amount of people in 2010 is 11571 and it would take approximately 22 years to reach 50000 people.
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Write an equation for the graph.
Answer:
y = 3x + 2
Step-by-step explanation:
3 is the slope
2 is the y-intercept
Job bakes 48 cupcakes and 60 cookies. What is the biggest number of cupcakes and cookies that can be placed in boxes if these are of the same number?
pls answer it i really need it now
bonus big pts
if nonsense I'll report you
Answer:
12
Step-by-step explanation:
You need the GCF of 48 and 60
48 = 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
Both have 2 x 2 x 3, so the answer is 12
which one weighs more a watermelon that weighs 1.7 kilograms or a pumpkin that weighs 12 pounds?
Answer : pumpkin that is 12 pounds
Step - by - step explanation :
First, convert . . . what is 1.7 kilograms as pounds ? 3.74786 ( rounded is 4 pounds )
Second, compare . . . 4 < 12
Hope this helped ! :>
for each value c determine how many solutions the system has
Answer:
can we get a picture or something? we cant help unless we have more context
Step-by-step explanation:
The base of a triangle is V75 cm and its height is V12 cm. Find its area.
Answer:
450 cm area
Step-by-step explanation:
Formula 1/2*b*h
1/2*75*12cm
1/2*900
1*450cm
450 is area PLEASE MARK BRAINLIEST :))
geometry word problem:
The area of a square is four times the area of a triangle. If the base of the triangle and a side of the square are equal, what is the ratio of the height of the triangle to the side of the square?
(A) 1 : 4
(B) 1 : 2
(C) 2 : 1
(D) 3 : 2
(E) 2 : 3
The ratio of the height of the triangle to the side of the square (B) 1 : 2
What are the areas of triangle and square?The area of a triangle is (1/2)×base×height.
The area of a square is (side)².
Given, The area of a square is four times the area of a triangle.
∴ (side)² = 4{(1/2)×base×height}.
The base of the triangle and the side of the square are equal let this be 'a'.
∴ a² = 4(1/2)×a×height.
a = 2×height.
a = 2h.
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You roll a six sided die. You are given $8 if a 6 comes up, $2 if a 3, 4, 5 comes up, and
nothing otherwise. Find the expected value of the entries.
Expected Value Table for rolling a six-sided die
We want to get the expected value for the given experiment. We will see that the expected value is $2.33
For an experiment with outcomes {x₁, ..., xₙ} each one with probability {p₁, ..., pₙ} the expected value is defined as:
EV = x₁*p₁ + ... + xₙ*pₙ
Here we have 3 outcomes:
x₁ = winning $8x₂ = winning $2x₃ = winning $0.For x₁ we need to roll a 6, this is a probability of 1 out of 6, then:
p₁ = 1/6
For x₂ we need to roll a 3, 4, or 5 (3 out of 6), then:
p₂ = 3/6
For x₃ we need to roll a 1 or a 2 (2 out of 6) so the probability is:
p₃ = 2/6
Then the expected value is:
EV = $8*(1/6) + $2*(3/6) + $0*(2/6) = $2.33
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A company pays its employees $26 for every 4 hours of overtime worked in a day.
Mike works 9 hours of overtime and is paid $53.
Rachael works 8 hours of overtime and is paid $52.
Tom works 17 hours of overtime and is paid $442.
John works 16 hours of overtime and is paid $100.
Which employee receives an appropriate payment for the hours of overtime worked, according to the given unit ratio?
Answer:
John
Step-by-step explanation:
Please help me no links or bots please and thank you please actually help me with this please
Answer:
[tex]y=-1 \frac{2}{3}x+5[/tex]
Step-by-step explanation:
y=mx+b is slope-intercept form
m= slope
b= y-intercept (where the line on the graph touches the y=axis aka the line that goes vertically or up and down).
The photo you have attached is very blurry but i will do my best to read the numbers on the graph.
the y-intercept looks to be at 5
so we plug that in
y=mx+5
now let's get the slope.
pick two points you can easily see,
slope is change in y over the change in x --- which is simplified below
rise over run
y2-y1 divided by x2-x1
we can see the point (0,5) and the point (3,0)
(3,0) is going to be the x2 and y2 and the other point is the x and y 1s
0-5= -5
3-0= 3
-5/3
let's simplify that
we know three goes into five once, so that gives us one whole but it's still negative because our slope is negative.
-1 2/3
that is our slope
let's plug it in:
[tex]y=-1 \frac{2}{3}x+5[/tex]
that is our answer!
At Jared's school, he earns reward
points.
He has earned 350 points.
He wants to have at least 100 points left
at the end of year for prizes.
He wants to use 20 points each week
for Free-Sit Friday.
How many weeks can Jared have Free-
Sit Friday and still have at least 100
points at the end of the year?
Write the Inequality.
Answer:
ok so first take a way 100 from 350
250 then divide by 20
12
Hope This Helps!!!
What is the domain of the function?
Enter your answer in the box.
demos.
Answer: the x or the input of a function
Step-by-step explanation:
PLEASE HELP ME NOWWWWWWWWWW
Answer:
36 And 59
Step-by-step explanation:
Which term better describes the populations in the nations of Northern Europe?
1. homogeneous
2. heterogeneous
I need help again someone please help
G=45.89 gallons 46 gallons.
I hope this answers your question!
:)
how do you find the area of something
Answer:
multiply the length and the width of a rectangle or a square
Which graph is defined by the function given below?
y = (x-3)(x-3)
Answer: graph b
Step-by-step explanation:
Vertex: ( 3 ,0 )
Focus: ( 3 , 1 4 )
Axis of Symmetry: x = 3
Directrix: y = − 1 4
PLS HELP Jake has two dogs, Euclid and Pythagoras. Euclid is a smaller dog and Pythagoras is larger. Jake found that Pythagoras lost 13 pounds from January to June. If Pythagoras gains 1.2 times Euclid’s weight, Pythagoras’s weight would still be 1 4 pound less than he did in January. What is Euclid’s weight? (a) Write an equation that represents the scenario. Begin by defining your variable. (b) Solve the equation. Show your work. (c) What is Euclid’s weight? (d) Jake adopts a third dog, Riemann. Riemann weighs exactly twice what Euclid weighs. The combined weight of the three dogs is 1 60 2 pounds. What is Riemann’s weight, and what is Pythagoras’s weight? Show your work.
Answer: (weight = w)
This is a lot to answer but. (A) (13 x 1.2) - 14 = w
w = 1.6
Step-by-step explanation:
Draw a diagram of the archway modeled by the equation y = x^2 + 5x + 24. Fine and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis
Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25
The vertex of the parabola is at (-2.5, 17.75). And the y-intercept of the parabola is at (0, 24).
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation of the parabola is given as,
y = x² + 5x + 24
Convert the equation into a vertex form, then we have
y = x² + 5x + 25/4 - 25/4 + 24
y = (x + 5/2)² + 71/4
y = (x + 2.5)² + 17.75
The vertex of the parabola is at (-2.5, 17.75). The y-intercept of the parabola is given as,
y = (0)² + 5(0) + 24
y = 24
The y-intercept of the parabola is at (0, 24).
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Lincoln middle school had a canned food drive. The 6th grader brought in 5.75
So the Lincoln middle school will have +5.75 pounds or ounces of ffod
nth term of 5,8,13,20,29
Answer:
nth term = 4 + n^2
Step-by-step explanation:
Sorry if the answer is long but I'm hoping my explanation can help.
In order to understand the issue, we should try to find the pattern between the terms given.
The terms given were 5, 8, 13, 20 and 29.
Between the first term and second term, the difference is 3.
Between the second and third term, the difference is 5.
The pattern goes on and we find out that the difference between the (n-1)th term and the nth term is
2n - 1.
Hence, we can determine the pattern of the numbers is
nth term = (n-1) term + 2n - 1
We can use this to find term 0 (before term 1) by plugging in the values for term 1
5 = 0th term + 2 (1) - 1
5 = 0th term + 1
Hence the 0th term = 4
If we expand on the summation,
We can find the nth term
nth term = 4 + 2 (1) - 1 + 2(2) - 1 + ... + 2(n-1) - 1 + 2n - 1
As we can see, the number 1 has been subtracted n times (excluding the -1 in 2(n-1)). Hence, we can split combine all of the subtracted ones into -n.
We can rewrite it as
nth term = 4 + 2 (1) + 2(2) + ... + 2(n-1) + 2n - n
Now, we will move 4 and n to one side.
nth term = 4 - n + 2 (1) + 2(2) + ... + 2(n-1) + 2n
We can factorize 2 out from every term to the right of -n. This would give out
nth term = 4 - n + 2 (1 + 2 + ... + (n-1) + n)
The term (1 + 2 + ... + (n-1) + n) can actually be rewritten by using the triangular formula.
The triangular formula is stated such that
Tn = (n*(n+1))/2
This heavily simplifies the equation into
nth term = 4 - n + 2 [(n*(n+1))/2]
This equation becomes
nth term = 4 - n + n^2 + n.
Now, we can finally simplify into the final equation
nth term = 4 + n^2
I NEED HELP ASP AHH
I need help on number 5 and 8
This is for geometry
number 5 and 8 are rhe blank ones
#5:
Let's first start by solving for x. The two angles with x's in them form a linear pair, or are supplementary angles, meaning that they add up to 180 degrees.
(4x + 23) + (9x - 38) = 180
13x - 15 = 180
13x = 195
x = 15
Now that we have x, we can solve for y. Alternate interior angles are congruent.
(4x + 23) = (21y - 1)
4(15) + 23 = 21y - 1
60 + 23 = 21y - 1
83 = 21y - 1
84 = 21y
y = 4
#8:
Let's first start by solving for x. The two angles with x's in them are corresponding angles, meaning that they are congruent.
10x = 13x - 33
-3x = -33
x = 11
Now that we have x, let's figure out how we can find y. Looking at the angle with a value of 10x, we can find its supplement. That supplement then, is a corresponding angle with the 5y angle, meaning that they are congruent.
Supplement = 180 - 10x
Supplement = 180 - 10(11)
Supplement = 180 - 110
Supplement = 70
Supplement = 5y
70 = 5y
y = 14
Hope this helps! :)
- #5 -
y = 4
[] First we need to solve for x, these are on a straight line so we can set them equal to 180 degrees and solve because they are supplement angles:
4x + 23 + 9x - 38 = 180
13x - 15 = 180
13x = 195
x = 15
[] Now we will plug-in and solve for one of them
9x - 38
9(15) - 38
135 - 38 = 97
[] Last, the y angle and the angle we just solved for can be added together and set equal to 180 because they are supplement angles:
97 + 21y - 1 = 180
96 + 21y = 180
21y = 84
y = 4
- #8 -
y = 14
[] First we need to solve for x, these are corresponding angles so we can set them equal to each other:
13x - 33 = 10x
-33 = -3x
11 = x
[] Plug-in and solve for one of them
10x = 10(11) = 110
[] Last, the line is 180 degrees so we can add them together, set it equal to 180, and solve
110 + 5y = 180
5y = 70
14
- See attached for where I am pulling numbers from -
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Write an expression that represents the perimeter of the figure below. Write your answer in simplified form. P=??
The perimeter of the figure in simplified form is expressed as: P = 2p + 2q + 2r + 4s
How to find the Perimeter of a FigureTo find the perimeter of any figure, add all the side lengths of the figure together.
Thus, the given side lengths of the figure are:
p, p, q, q, r, r, s, s, s, and s.
To find the perimeter add them together.
Perimeter of the figure = p + p + q + q + r + r + s + s + s + s
Perimeter = 2p + 2q + 2r + 4s
Therefore, the perimeter of the figure in simplified form is expressed as: P = 2p + 2q + 2r + 4s
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Select all the ordered pairs that are solutions to the equation 2x+y=−12
(−10, 8)
(−9, −6)
(−8, −2)
(0, −12)
(4, −20)
Answer:
(-10,8)(0,12)(4,-20)
Step-by-step explanation:
You just have to insert the points into the equation and then solve.
Ex: 2(4)-20=-12- True
a cylinder has a radius of 3 feet and a height of 2.1 feet. what is the approximate volume of the cylinder? use 3.14 for pi. 12.6 ftł 59.3 ftł 237.5 ftł 8550.2 ftł
Answer:
59.3ft³
Step-by-step explanation:
The formula for the volume of a cylinder is V= πr²h, where r is radius and h height.
So in our case, we have r= 3ft and h=2.1 ft and π≅3.14
So from the formula for the volume of a cylinder, we get 3.14*3²*2.1 = 59.3 ft³
The volume of the cylinder is about 59.3 ft³