Find the area of the shape shown below. 7 3
Answers
To find the area of the figure you can divide the figure into to smaller shapes
calculate the area of each of the smaller figures.
for the square
[tex]\begin{gathered} A=s\cdot s \\ A=3\cdot3 \\ A=9 \end{gathered}[/tex]For the triangle the base is the difference between the longest side which is 7 and the side on the square which is 3
[tex]7-3=4[/tex]find the area of the triangle
[tex]A=b\cdot\frac{h}{2}[/tex][tex]\begin{gathered} A=4\cdot\frac{3}{2} \\ A=\frac{12}{2} \\ A=6 \end{gathered}[/tex]Add both areas to find the area of the figure
[tex]\begin{gathered} A_T=9+6 \\ A_T=15 \end{gathered}[/tex]
Related Questions
I need help on 2 please Directions: Find the value of x. Round each answer to the nearest tenth.
Answers
The angle indicated is a right angle, so the triangle is a right triangle.
Thus, we can apply the Pythagora's Theorem:
[tex]a^2+b^2=c^2[/tex]Where c is the hypotenuse, the angle opposite to the right angle, and a and b are the legs.
x is the hypotenuse in this case, so:
[tex]\begin{gathered} 22^2+27^2=x^2 \\ x^2=484+729 \\ x^2=1213 \\ x=\sqrt[]{1213} \\ x=34.8281\ldots\approx34.8 \end{gathered}[/tex]A square ABCD has the vertices A(n,n), B(n,-n), C(-n,-n), and D(-n,n). Which vertex is in Quadrant II?Answers:A.CB.DC.BD.A
Answers
Given:
A square ABCD has the vertices A(n,n), B(n,-n), C(-n,-n), and D(-n,n).
In quadrant II, the cordinates of the x have negative sign and coordinates of y axis have poistive sign.
Thus, the vertex is in Quadrant II is D(-n,n).
Find all possible rational roots of f(x)=4x^3-13x^2+9x+2
Answers
Polynomial
[tex]f(x)=4x^3+13x^2+9x+2[/tex]Find the area of the figure. (Sides meet at right angles.) Check 7 yd 5 yd 3 yd 3 yd 13 yd 3 yd 5 yd 7 yd yd²
Answers
Given:
The figure with sides measurements.
Required:
Find area of the figure.
Explanation:
First we will draw figure
In figure, we can see that all figure ABIJ, CDHI and EFGH are rectangles.
So, we need area of rectangle formula. That is
[tex]A=length\times width[/tex]So, area of given figure
[tex]\begin{gathered} A=\text{ Area of ABIJ +Are of CDHI + Area of EFGH} \\ ABIJ=EFGH \\ So, \\ A=2\times(ABIJ)+CDHI \\ A=2\times(7\times5)+(4\times3) \\ A=70+12 \\ A=82yd^2 \end{gathered}[/tex]A) Find the simple interest amount earned for $5500 at 6.5% for 5 months. b)What is the total value of the investment?
Answers
The simple interest I on an amount P invested at an interest rate R %, for a period of time T per annum is evaluated as
[tex]I\text{ = }P\times R\times T[/tex]A) The interest earned at $5500 at 6.5% for 5 months is thus evaluated as
[tex]\begin{gathered} P\text{ = 5500} \\ R\text{ = 6.5\% = }\frac{6.5}{100} \\ T\text{ = 5 months = }\frac{5}{12}\text{ year} \\ thus, \\ I\text{ = }5500\times\frac{6.5}{100}\times\frac{5}{12} \\ \Rightarrow I\text{ = \$ 148.958} \end{gathered}[/tex]thus, the interest earned for $5500 at 6.5% for 5 months is $ 148.985.
B) Total value of the investment.
The total value of the investment is the sum of the interest earned and the initial amount invested.
Thus,
[tex]\begin{gathered} Total\text{ value of investment = interest earned + amount invested} \\ A\text{ = I + P} \\ A\text{ = 148.985 + 5500} \\ \Rightarrow A\text{ = \$ 5648.985} \end{gathered}[/tex]Hence, the total value of the investment is $ 5648.985.
Hi, can you help me to find (Ir possible) the complement andsupplement of the angle of exercise
Answers
The angle is given 24 degree.
To determine the complement angle ,
[tex]90^{\circ}-24^{\circ}=66^{\circ}[/tex]To determine the supplement angle ,
[tex]180^{\circ}-24^{\circ}=156^{\circ}[/tex]A Ferris wheel has a radius of 12 meters and takes 16 seconds to complete one full revolution. The seat you are riding in, takes 4 seconds to reach the top which is 28 meters above the ground. Write a sine or cosine equation for the height of your seat above the ground as a function of time.
Answers
EXPLANATION
Given that the wheel has a radius of 12 meters and it takes 16 seconds to complete one full revolution, if we call t to the time in seconds and since the top of the wheel is 28 meters above the ground, the bottom is 4 meters above the ground.
Now, we need to consider that the equation that applies is the following:
[tex]height=16-12\cos \theta[/tex]As theta is the angle between the radius from the center of the wheel to the bottom and the rider's coordinate, we need to represent the angle as a function of the time. We have that it takes 16 second to complete one full revolution, this means that the wheel rotates 360 degrees in 16 seconds. Now, we can use the angular velocity: w= 360/16 = 22.5 degrees/s
Then, we need to represent the angular velocity in radians, as 360 degrees is 2π radians, the obtained angular velocity would be: w = 2π/16 = π/8 rad/s
Hence the appropiate equation as a function of the time would be as follows:
[tex]h=16-12\cdot\cos (\frac{\pi t}{8})[/tex]
Select the correct answer.378Convert4 to rectangular form.OA.Y = -1OB.y = 1O C.y =O D.O E.I = -1
Answers
The Solution.
Assuming the radius is 1.
[tex]x=\cos (\frac{3\pi}{4})=-\sin (\frac{3\pi}{4})[/tex]Therefore,
[tex]\begin{gathered} x=-y \\ or \\ y=-x \end{gathered}[/tex]So, the correct answer is option D
The rabbit population in a certain area is 200% of last year's population. There are 1100 rabbits this year. How many were there last year?
Answers
As per the given percentage, the population of rabbits in the area is 2200 in last year.
Percentage:
Percentage refers the ratio or the fraction that is multiplied and divided by 100. And it will be represented by the symbol "%".
Given,
The rabbit population in a certain area is 200% of last year's population. There are 1100 rabbits this year.
Now, we need to find the population of rabbit in last year.
Let us consider x be the total number of rabbit in last year.
We know that the rabbit in the current year is 110.
And we also know that, there are 200% of rabbits in last year.
So, we have to write it in the following expression,
200% of 1100 = x
so, the value of x is,
x = 200/100 x 1100
x = 2200
Therefore, there are 2200 rabbits in last year.
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The figure on the left is a trapezoidal prism. The figure on the right represents its base. Find the volume of this prism. 13 ft 10 ft 10 ft 2 ft 13 ft 12 ft 13 ft 20 ft 13 ft 5 ft 10 ft 5 ft The area of the trapezoidal base is 8 ft2, the height is ft. Therefore, the volume is IN
Answers
volume of the trapezoidal prism is
[tex]V=A_b\times h[/tex]then, area of the trapezoidal base
[tex]\begin{gathered} A_b=\frac{1}{2}(b1+b2)h \\ A_b=\frac{1}{2}(10+20)\times12 \\ A_b=\frac{1}{2}(30)\times12 \\ A_b=\frac{360}{2}=180 \end{gathered}[/tex]area of the trapezoidal base = 180 ft^2
height = 2ft
so, the volume is:
[tex]\begin{gathered} V=180\times2 \\ V=360 \end{gathered}[/tex]volume = 360 ft^3
The dot plot shows the hourly pay rate for ten employees at best books bookstore.
Answers
We will have the following:
The strongest case he can make is the mean hourly rate since Levi's current pay rate is well bellow the average hourly pay rate.
Emily reads 22 pages per hour. In all, how many hours of reading will Emily have to do this week in order to have read a total of 44 pages?
Answers
Answer:
The number of hours of reading it will take Emily to read a total of 44 pages is;
[tex]2\text{ hours}[/tex]Explanation:
Given that Emily reads 22 pages per hour.
Her rate of reading is;
[tex]r=22\text{ pages/hour}[/tex]The amount of time she needs to read 44 pages will be the number of pages divided by the rate;
[tex]\begin{gathered} t=\frac{\text{number of pages}}{\text{rate}}=\frac{44}{22}\text{hour} \\ t=2\text{ hours} \end{gathered}[/tex]Therefore, the number of hours of reading it will take Emily to read a total of 44 pages is;
[tex]2\text{ hours}[/tex]Find the area of a shaded region shown below, which was formed by cutting an isosceles trapezoid out of the top half of a rectangle. The width of the rectangle is 32 in, the height of the rectangle in 24 in. The leg of the isosceles trapezoid is 15 in.
Answers
Step 1: Redraw the diagram and label it.
From the figure, the hypotenuse of triangles A and B is 15 in and the height is 12 in. We can apply the Pythagoras theorem to find the base.
Let base of the triangle A and B be the adjacent.
Opposite = 12
Adjacent = ?
Hypotenuse = 15
[tex]\begin{gathered} Next,\text{ apply the Pythagoras theorem to find the adjacent.} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ 12^2+Adj^2=15^2 \\ 144+Adj^2\text{ = 225} \\ \text{Collect like terms.} \\ \text{Adj}^2\text{ = 225 - 144} \\ \text{Adj}^2\text{ = 81} \\ F\text{ ind the square root of both sides.} \\ \sqrt[]{Adj^2\text{ }}=\text{ }\sqrt[]{81} \\ \text{Adj = 9 in} \end{gathered}[/tex]The area of the shaded region = Area of A + Area of B + Area of C
[tex]\begin{gathered} \text{Area of A = }\frac{Base\text{ x Heigth}}{2} \\ \text{Base = 9} \\ \text{Height = 1}2 \\ \text{Area of A = }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ =54in^2 \\ \text{Area of B = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ \text{= 54 in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of rectangle C = Length }\times\text{ Breadth} \\ Lenght\text{ = 32} \\ \text{Breadth = 12} \\ \text{Area of C = 32 x 12} \\ =384in^2 \end{gathered}[/tex]Therefore,
Area of the shaded region = 54 + 54 + 384 = 492 inches square
Final answer
Area of the shaded region = 492 inches square
Meri invests 15000 into an account the interest is compounded monthly for 17 years. The account balance will be 87,219.93 at the end of 17 years. What is the annual interest rate?
Answers
Annual interest rate will be 11.95% or 12% approx.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
P = principal
i = nominal annual interest rate in percentage terms
n = number of compounding periods
formula for compound interest is [tex]P [(1 + i)^n - 1][/tex]
According to the question
P=15000
i = ?
compound interest = 87,219.93
n=17 years
Therefore
[tex]87219.93=15000 [(1 + i)^1^7 - 1][/tex]
[tex]\frac{87219.93}{15000} = [(1 + i)^1^7 - 1][/tex]
[tex]6.814662 = (1+i)^1^7[/tex]
[tex](6.814662)^\frac{1}{17} = (1+i)[/tex]
i =1.1195-1
i =0.1195
i.e. 11.95%
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When asked to find f ( g ( x ) ), what should you do? plug f (x) into g (x)plug g (x) into f (x)multiply f (x) by g (x)none of the above
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From the given question,
f(g(x)) means,
Plug g(x) into f(x)
Hence, the correct option is B
graphing a parabola of the form y=ax squared 2
Answers
The graph of the parabola given by the equation:
[tex]y=\frac{1}{4}x^2[/tex]has a vertex when y=0 which happens iff
[tex]\begin{gathered} \frac{1}{4}x^2=0 \\ x^2=0 \\ x=0 \end{gathered}[/tex]Therefore the graph is:
The vertex has coordinates (0,0). Now, two points to the left of the vertex that are on the parabola have coordinates (-2,1) and (-4,4). Two points that are to the right of the parabola have coordinates
I need help with this question Subtraction:3+(-4) = ?
Answers
Given:
We have to use subtraction
[tex]3+(-4)[/tex]To find: Solve the above expression?
Explanation:
Here we use the subtraction operation to solve the given expression.
We know the operator property,
[tex]\begin{gathered} (+)(-)=(-) \\ (-)(-)=(+) \\ (+)(+)=(+) \\ (-)(+)=(-) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} =3+(-4_) \\ \\ =3-4 \\ \\ =-1 \end{gathered}[/tex]Thus, 3+(-4) = -1.
Answer: 3+(-4) = -1.
Find x, where a=14 degrees and b=22 degrees. Find the measure of each angle of the polygon. Shown below.
Answers
To answer this question, we need to remember that the sum of the interior angles of a quadrilateral is equal to 360º (in fact, we can divide a quadrilateral into two triangles, and the sum of interior angles of a triangle is equal to 180º).
Then, we have that a = 14º and b = 22º, then we can state the next equation:
[tex](2x+14^{\circ})+(3x+22^{\circ})+2x+x=360^{\circ}[/tex]And now, we can solve the equation for x as follows:
1. Add the like terms as follows:
[tex](2x+3x+2x+x)+14^{\circ}+22^{\circ}=360^{\circ}[/tex][tex]8x+36^{\circ}=360^{\circ}[/tex]2. Subtract 36º from both sides of the equation:
[tex]8x+36^{\circ}-36^{\circ}=360^{\circ}-36^{\circ}\Rightarrow8x=324^{\circ}[/tex]3. Divide both sides by 8 as follows:
[tex]\frac{8x}{8}=\frac{324^{\circ}}{8}\Rightarrow x=40.5^{\circ}[/tex]Therefore, the value for x = 40.5º
Then, we can find the values for the measure of angle A as follows:
[tex]m\angle A=2(40.5^{\circ})+14^{\circ}=95^{\circ}[/tex]The measure of angle B is
[tex]m\angle B=3(40.5^{\circ}_{})+22^{\circ}=143.5^{\circ}[/tex]The measure of angle C is
[tex]m\angle C=x^{\circ}=40.5^{\circ}[/tex]The measure of angle D is
[tex]m\angle D=2(40.5^{\circ})=81^{\circ}[/tex]Find the slope and y-intercept of the line shown below.10-8-6-co +4-2--10-8-64-2-2- 2 4 6 8 10~ 60--4-X-6--8--10-
Answers
Looking at the graph
we have a horizontal line
the equation is
y=-5
The slope of a horizontal line is equal to zero
so
m=0
The y-intercept is the point (0,-5)
therefore
b=-5
The answer is
m=0b=-5Remember that
y=mx+b
substitute
m=0
b=-5
y=(0)(x)-5
y=-5
An adult elephant drinks about 225 liters of water each day. Is the number ofdays the water supply lasts proportional to the numberof liters of water the elephant drinks?Is it proportional
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An elephant drinks 225 liters of water per day, then in 2 days it drinks 2*225 = 450 liters, in 3 days it drinks 3*225 = 675 liters.
time (days) | 1 | 2 | 3
water (L) | 225 | 450 | 675
If an elephant drinks more water per day, the number of days the water supply lasts decrease. Then these two variables are inversely proportional.
hello can you help me with this trigonometry question read carefully of how it has to be answered
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Area of a circle = πr²
Replacing with radius = 8.4 in:
Area of a circle = π(8.4)²
Area of a circle = 221.6708 in²
This area corresponds to 2π radians. To find the area corresponding to 2.37 radians, we can use the next proportion:
[tex]\frac{2\pi\text{ rad}}{2.37\text{ rad}}=\frac{221.6708^{}}{x^{}}\text{ }[/tex]Solving for x:
[tex]\begin{gathered} 2\pi\cdot x=221.6708\cdot2.37 \\ x=\frac{525.359796}{2\pi} \\ x=83.6136\text{ sq. in} \end{gathered}[/tex]Find (3/5x+3/4)−(1/3x−1/8)
Answers
The answer is [tex]\frac{32x+105}{120}[/tex].
The area of mathematics known as algebra is used to represent situations or problems using mathematical expressions. In algebra, we combine integers with variables like x, y, and z.
A fraction is a number that is a component of a whole. In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.
The given equation is an algebraic fraction having variables in the numerator. This equation is written as,
[tex]\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)[/tex]
First combine, x with the nearby fraction,
[tex]\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}+\frac{3}{4}\right)-\left(\frac{x}{3}-\frac{1}{8}\right)\\&=\frac{3x}{5}+\frac{3}{4}-\frac{x}{3}+\frac{1}{8}\end{aligned}[/tex]
Now, group the fraction with a common denominator,
[tex]\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}-\frac{x}{3}\right)+\left(\frac{3}{4}+\frac{1}{8}\right)\\&=\left(\frac{3x\cdot3}{15}-\frac{x\cdot5}{15}\right)+\left(\frac{3\cdot2}{8}+\frac{1}{8}\right)\\&=\left(\frac{9x-5x}{15}\right)+\left(\frac{6+1}{8}\right)\\&=\frac{4x}{15}+\frac{7}{8}\\&=\frac{32x+105}{120}\end{aligned}[/tex]
Therefore, the final answer is [tex]\frac{32x+105}{120}[/tex].
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1277 concert tickets were sold for a total of $16,267. If students paid $11 and nonstudents paid $17, how manystudent tickets were sold?
Answers
Hello there. To solve this question, we'll have to remember some properties about system of equations.
Given that 1277 concert tickets were sold, for a total of $16,267, knowing that students paid $11 and non-students paid $17, we have to determine how many students tickets were sold.
Let's start labeling the variables we have. Say x is the number of tickets sold for students, while y is the number of tickets sold for non-students.
The total number of tickets sold can be found by adding how many students and non-students tickets were sold, i.e.
[tex]x+y=1277[/tex]To find the total amount collected, we have to multiply the number of each ticket sold by its respective fee, adding everything as follows:
[tex]11\cdot x+17\cdot y=16267[/tex]With this, we have the following system of equations:
[tex]\begin{cases}x+y=1277 \\ 11x+17y=16267\end{cases}[/tex]We can solve it using the elimination method. It consists in multiplying any of the equations by a factor (usually the easier equation) that when added to the other equation, one of the variables are cancelled out.
In this case, multiply the first equation by a factor of (-11)
[tex]\begin{cases}-11x-11y=-14047 \\ 11x+17y=16267\end{cases}[/tex]Add the two equations
[tex]\begin{gathered} -11x-11y+11x+17y=-14047+16267 \\ 6y=2220 \end{gathered}[/tex]Divide both sides by a factor of 6
[tex]y=370[/tex]Now we plug it back into the first equation in order to solve for x (i. e the number of tickets sold for students)
[tex]\begin{gathered} x+y=1277 \\ x+370=1277 \\ x=1277-370 \\ x=907 \end{gathered}[/tex]This is how many tickets were sold to students.
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. the premium antifreeze solution contains 90% pure antifreeze. the company want to obtain 180 gallons of a muxture that contains 45% pure antifreeze how many and how many gallons of the premium antifreeze solution must be mixed
Answers
Answer:
Both should be 90 gallons
Explanation:
Let the gallons of pure water used = x gallons
Since the company want to obtain 180 gallons of a mixture, the gallons of 90% pure antifreeze needed = (180-x) gallons
We therefore have that:
90% of (180-x) gallons = 45% of 180 gallons
[tex]\begin{gathered} 0.9(180-x)=0.45\times180 \\ 162-0.9x=81 \\ 0.9x=162-81 \\ 0.9x=81 \\ x=\frac{81}{0.9} \\ x=90 \end{gathered}[/tex]• The number of gallons of pure water used = 90 gallons
• The number of gallons of premium antifreeze solution
= 180-90
= 90 gallons.
A rectangular garden is 15 feet wide. If its area is 1050ft², what is the length of the garden?
Answers
The width is w=15 ft.
The area is A=1050 sq ft.
The length of the garden is,
[tex]\begin{gathered} L=\frac{A}{w} \\ =\frac{1050ft^2}{15ft} \\ =70ft \end{gathered}[/tex]Thus, the length of the garden is 70 ft.
Solve the system by the method of your choice. Identify inconsistent systems and systems with dependent equations, using set notation to express solution sets
Answers
The given system of equations is
[tex]\begin{gathered} y=3x+5\rightarrow(1) \\ 5x-2y=-7\rightarrow(2) \end{gathered}[/tex]Substitute y in equation (2) by equation (1)
[tex]5x-2(3x+5)=-7[/tex]Simplify the left side
[tex]\begin{gathered} 5x-2(3x)-2(5)=-7 \\ 5x-6x-10=-7 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (5x-6x)-10=-7 \\ -x-10=-7 \end{gathered}[/tex]Add 10 to both sides
[tex]\begin{gathered} -x-10+10=-7+10 \\ -x=3 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-x}{-1}=\frac{3}{-1} \\ x=-3 \end{gathered}[/tex]Substitute x in equation (1) by -3 to find y
[tex]\begin{gathered} y=3(-3)+5 \\ y=-9+5 \\ y=-4 \end{gathered}[/tex]The solution of the system of equations is {(-3, -4)}
Since the system has only one solution then it is an independent consistent system.
arina runs up 4 flights and runs down 4 flights of stairs does this situation repreasent additive inverses explain . A. Yes; The numbers combine to eight B. Yes; The numbers are combine to zero C. No;The numbers are both represented by the same integer. D. No; The numbers cannot be added together.
Answers
B. Yes; The numbers are combine to zero
is additive inverses because the sum is 0
[tex]\begin{gathered} 4+(-4) \\ =0 \end{gathered}[/tex]Determine the domain and range of the quadratic function. f(x)=−2(x+8)^2−4
Answers
Since the given is a polynomial with a degree of 2, there are no restrictions to its domain. The domain therefore is
[tex]\text{Domain: }(-\infty,\infty)[/tex]The given function is in the vertex form
[tex]\begin{gathered} f(x)=a(x-h)^2+k \\ \text{where} \\ (h,k)\text{ is the vertex} \end{gathered}[/tex]By inspection, we determine that the vertex of the function is at (-8,-4), and since a = -2, then the parabola opens up downwards. This implied that its output peaks at y = -4, and the graph continues towards negative infinity.
We can conclude therefore that the range is
[tex]\text{Range: }(-\infty,-4\rbrack[/tex]So the question is A local theater sells admission tickets for $9.00 on Thursday nights, where n is the number of customers M(n) the amount of money the theater takes What is the domain of M( n ) in this context
Answers
We have the function M(n):
M( n ) = 9 · n
which describes the amount of money the theater takes.
Since the domain of a function refers to the values n can take and n is the number of costumers
In this particular case we do not have a restriction of the number of costumers. Then n can take the following values:
n = 0, 1 , 2, 3, ...
Domain: all non- negative integers
If the maximum capacity of the theater is 100 costumers then
n = 0, 1, 2, 3, ..., 100
Therefore its domain would correspond to
Domain: all non- negative integers less than or equal to 100
Write an exponential equation using y = a(b)^x“ thatrepresents the growth or decay of the situation.A house was purchased for $370,000. The house has anannual appreciation rate of 3%. Please write a let statementand an equation that represents the house's value over time.
Answers
Let:
PV = Initial value = 370000
r = appreciation rate = 3% = 0.03
x = time
the equation will be given by
[tex]\begin{gathered} y=PV(1+r)^x \\ so\colon \\ y=370000(1+0.03)^x \\ y=370000(1.03)^x \end{gathered}[/tex]