Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
A full circle consists of 360°, so we can write the fraction of this arc as [tex]\frac{30}{360}[/tex], which can be simplified to [tex]\frac{1}{12}[/tex] by dividing the numerator and denominator by 30.
**This content involves simplifying fractions and knowledge on the angle sum of a circle which you may wish to revise. I'm always happy to help!
HELP i need help on part b
Wilson is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years.
Number of years 1 2 3
House 1 (value in dollars) 253,980 259,059.60 264,240.79
House 2 (value in dollars) 256,000 263,000 270,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)
Part C: Wilson wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points)
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.The HCF and LCM of two numbers x and 126 are 24 and 840 respectively. Find the value of x.
Answer:
x=160
Step-by-step explanation:
x×126=24×840
[tex]x=\frac{24 \times840}{126} =160[/tex]
HELP MEEE QUICK THIS MY LAST QUESTION!!!
Question 10 of 10
Is APQR- AXYZ? If so, name which similarity postulate or theorem applies.
80
Q
180°
P
5
R
х
10
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
Ο Ο
D. Cannot be determined
SUBMIT
Answer:
A. Similar - AA
Step-by-step explanation:
The given parameters of ΔPQR and ΔXYZ are;
In ΔPQR, we have; PQ = 3, PR = 5, and ∠PQR = 80°
In ΔXYZ, we have; XY = 6, XZ = 10, and ∠XYZ = 80°
In ΔPQR, by sine rule, we have;
3/(sin(∠PRQ)) = 5/(sin(80°))
sin(∠PRQ) = (3/5) × sin(80°)
∴ ∠PRQ = arc sin((3/5) × sin(80°))
In ΔXYZ, by sine rule, we have;
6/(sin(∠XZY)) = 10/(sin(80°))
sin(∠XZY) = (6/10) × sin(80°) = (3/5) × sin(80°)
∴ ∠XZY = arc sin((3/5) × sin(80°))
∠PRQ = ∠XZY by transitive property of equality
Therefore in ΔPQR and ΔXYZ, we have;
∠PRQ = ∠XZY and ∠PQR = ∠XYZ
Therefore, ΔPQR is similar to ΔXYZ by Angle Angle, AA, similarity postulate.
What is the correct expansion of (2x+3) (2x^2-5)
Answer:
4x^3 + 6x^2 -10x - 15
Step-by-step explanation:
* means multiply
4x^3 + 6x^2 -10x - 15
2x * 2x^2 = 4x^3
2x * -5 = 10x
3 * 2x^2 = 6x^2
3 * -5 = -15
Answer:
4x³ + 6x² - 10x - 15
Step-by-step explanation:
(2x+3) (2x²-5)
4x³ - 10x + 6x² - 15
4x³ + 6x² - 10x - 15
8
6471 sq. in.
25671 sq. in.
1,02471 sq. in.
Answer:
102471 sq .in the land answer Teri ma ki bosra
Answer:
=256 pi
Step-by-step explanation:
The surface area of a sphere is
SA = 4pi r^2
SA = 4 pi (8)^2
= 4 * pi *64
=256 pi
Mike was in charge of collecting contributions for the Food Bank. He received
contributions of:
$40, $80, $60, $40, and $100
Find the mean, median, and mode of the contributions.
What is mean: A mean is the simple mathematical average of a set of two or more numbers. To solve for it add all numbers together then divide by how many numbers are there. (Its best to put them in order)
$40 + $40 $60 + $80 + $100= $320/5= $64 is the mean
what is median: The median is the value separating the higher half of a data sample
40,40,60,80,100 (i like to cross it out so 40 and 100 cancle each other, another 40 and 80 cancel each other) now that you are left with only 1 number which is 60 that is the median.
What is Mode: the number that repeats the most
Mode is 40 because 40 repeats twice
I need help, I can’t figure out the answer
Answer:
Step-by-step explanation:
in negative exponents you should switch both numerator and denominator so for 2 raised to -1 you should switch the numerator and denominator and it will become 1/2 in which 2 is raised to power 1
you can do the same for the remining sums
so a is 1/2 in which 2 is raised to 6 so answer is 1/64
Polygon ABCD is rotated 90º counterclockwise about the origin to create polygon A′B′C′D′. Match each set of coordinates to the vertices of polygon A′B′C′D′.
Answer:.
Step-by-step explanation:
Circle w has a radius of 20 in and central right angle. VWX find the length of VX. Leave answer in terms of pi
The arc length is 10 Pi
(I don't know for sure, but its what I got)
QUICK PLEASE
42% of £719.24 Give your answer rounded to 2 DP.
Answer:
719.24 is the correct answer
find the shortest distance between the lines 3x+4y+10=0 and 3x+4y+20=0
Answer:
the lines are parallel they are 10 units apart
Step-by-step explanation:
The shortest distance between these two parallel lines is 2.5
Given equations:
3x + 4y + 10 = 0 ----- (1)
3x + 4y + 20 = 0 ---- (20)
To find:
the shortest distance between the two lines
The slope and y-intercept of the first equation is calculated as;
3x + 4y + 10 = 0
4y = -3x - 10
[tex]y = \frac{-3x}{4} - \frac{10}{4} \\\\y = \frac{-3x}{4} - \frac{5}{2}[/tex]
The slope = -³/₄ and the y-intercept = - ⁵/₂ = - 2.5
The slope and y-intercept of the second equation is calculated as;
3x + 4y + 20 = 0
4y = -3x - 20
[tex]y = \frac{-3x}{4} - \frac{20}{4} \\\\y = \frac{-3x}{4} - 5[/tex]
The slope = -³/₄ and the y-intercept = - 5
The two equations have the same slope = -³/₄
This shows that they are parallel with different y-intercepts
The shortest distance between the two lines is at their y-intercepts
The shortest distance between these two lines is calculated as;
[tex]distance = \sqrt{(-5 - (-2.5) )^2} \\\\distance = \sqrt{(-5+ 2.5)^2} \\\\distance = \sqrt{(-2.5)^2 } \\\\distance = \sqrt{6.25} \\\\distance = 2.5[/tex]
Thus, the shortest distance between these two parallel lines is 2.5
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If f(x) = k where k is a constant, and the
points (6, 1) and (8, 1) lie on the graph of y
= f(x), what is the value of f(0)?
Answer:
f(0) = 1Step-by-step explanation:
Since f(x) = k, is constant the value of k is same for any x.
From the given points we see:
f(6) = 1 and f(8) = 1It means k = 1 and the function is:
y = f(x) = 1The value of f(0) = 1
Una bañera en forma de trapecio tiene un area de 60 metro ademas se sabe que su base mayor es 3/2 mas grande que su base menor calcule la altura cuando la base menor es 18 metros
Respuesta:
3,2 metros
Explicación paso a paso:
Área del trapecio:
A = 1/2 (a + b) h
h = altura; ayb son las bases
Área, A = 60
Sea una base más pequeña = a = 18;
b = 18 + 3/2 = 19,5
La altura se puede calcular así;
60 = 1/2 (18 + 19,5) h
60 * 2 = 37,5 horas
120 = 37,5 h
h = 120 / 37,5
h = 3,2 metros
The circumference of a steering wheel of a car is 20 inches. What is the radius of
the steering wheel?
40 in.
20 in
100 in.
10 in.
The radius of the steering wheel is 10 inches.
What is a circle?A circle is the defined as a closed, two-dimensional curved shape in the geometry. Every point on the circle is equal distance from a certain point known as the centre of circle. A circle is a two-dimensional form that is measured in terms of radius.
What is the circumference of a circle?Circumference of a circle is defined as perimeter of circle is defined as the enclosing boundary of a curved geometrical figure called a circle. It is the product of π and its diameter.
Circumference (C) = π × d , where d is the diameter of a circle.
Given data as :
Circumference of a steering wheel of a car = 20π inches
Circumference(C) = 20π inches
Substitute the value of c in formula of Circumference :
20π = π × d [ diameter(d) = 2 radius(r) ]
20π = π × 2 r
Divided by 2π both the sides
10 = r
r = 10
r = 10 inches
Hence, the radius of the steering wheel is 10 inches.
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Question seems to be incomplete the correct question would be
The circumference of a steering wheel of a car is 20π inches. What is the radius of
the steering wheel?
Choose ALL terms like 5x?
92
No answer text provided.
-8.7
522
3
43
5
-5.0
Answer:
strange question...
I assume it is asking which ones can be expressed as "5x"
those are all the ones that are a multiple of 5
5, -5x , & 5x^2 satisfy that
Step-by-step explanation:
The terms that are like 5x are: -8x and 4x as they both have the variable x raised to the power of 1 (x).
Given are some algebraic terms 9x², -8x, 5x², 3, 4x, 5 and -5, out of these we need to choose the terms which are like 5x.
To determine the terms with properties similar to 5x, we need to look for terms that have the same variable (x) raised to the same power (1).
The terms that have similar properties to 5x are those with the variable x raised to the power of 1 (x) or simply x.
From the given terms:
9x² - This term has x raised to the power of 2, not 1.
-8x - This term has x raised to the power of 1 (x), similar to 5x.
5x² - This term has x raised to the power of 2, not 1.
3 - This is a constant term and does not have x.
4x - This term has x raised to the power of 1 (x), similar to 5x.
5 - This is a constant term and does not have x.
-5 - This is a constant term and does not have x.
Hence the terms that are like 5x are: -8x and 4x.
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PLEASE ANSWER ASAPPP
Answer:
the answer is 2035.75 cm³
Step-by-step explanation:
comment if you want explanation
could someone help me with this ASAP?
Answer:
just draw a circle that connects all of the 10's on the graph.
a circle is NOT a function
Step-by-step explanation:
A calculator requires a keystroke assembly and a logic circuit. Assume that 83% of the keystroke assemblies and 88% of the logic circuits are satisfactory. Assuming that defects in keystroke assemblies are independent of defects in logic circuits, find the probability that a finished calculator will be satisfactory. Group of answer choices
Answer:
0.7304
Step-by-step explanation:
According to the Question,
Given That, A calculator requires a keystroke assembly and a logic circuit. Assume that 83% of the keystroke assemblies and 88% of the logic circuits are satisfactory.We have,
P(keystroke satisfactory) =0.83 , P(logic satisfactory)= 0.88
Assuming that defects in keystroke assemblies are independent of defects in logic circuitsSince the events are independent. So, the probability that a finished calculator will be satisfactory
⇒ 0.83×0.88
⇒0.7304
i don’t know if i got the answer wrong but help!
Answer:
skew
Step-by-step explanation:
Perpendicular lines must intersect. In fact, they intersect forming right angles.
Lines AC and RC are not in the same plane and do not intersect.
They are called "skew lines."
Skew
Because they are in different plane and do not intersect and are not parallel
does anyone know how to solve this ?
Answer:
D) 144π sq. units
Step-by-step explanation:
The formula for finding the surface area of a sphere is 4π
Substitute 6 in for r. 4π = 144π
Answer:
144π sq. units
Step-by-step explanation:
The formula to determine the surface area of a sphere is: 4πr^2
But there’s no digit of pi given. Therefore we will use the formula but ignoring pi:
4πr^2
= 4r^2
= 4(6^2)
= 4(36)
= 144
Surface area is measured in square units.
Therefore the answer is 144π. The answer will be the true answer surface area once we know what π to use. For now, π will be just a variable next to 144 and will be later multiplied to it.
I hope you understand this! Hope I helped!
Arby's age is 6 years less than 7 times Anna's age. If Anna's age is x years, which expression best shows Arby's age?
A = x
B = 7x - 6
C = x - 1
D = 6x - 7
B = 7x - 6 is the correct answer.
4x^2+22x factor the polynomial
Answer:
2x(2x+11)
Step-by-step explanation:
4x^2 +22x
Factor out 2x
2x*2x +2x*11
2x(2x+11)
3/4 + 5/4 with explanation and steps....
Answer:
step 1
3/4+5/4
step 2
dinominator is same so we have to put 4
step 3
3+5/4
step 4
7/4
answer is 7/4
Answer:
2
Step-by-step explanation:
Given
[tex]\frac{3}{4}[/tex] + [tex]\frac{5}{4}[/tex]
Since the denominators are common, both 4 then add the numerators leaving the denominator
= [tex]\frac{3+5}{4}[/tex]
= [tex]\frac{8}{4}[/tex]
= 2
Find the solutions of the equation 3x = x4, rounded to two decimal places. (Enter your answers as a comma-separated list.)
Answer:[tex]-0.802; \ 1.517[/tex]
Step-by-step explanation:
Given
[tex]3^x=x^4[/tex]
Here, two functions are given that is [tex]y=3^x[/tex] and [tex]y=x^4[/tex]
Check for the intersection of the graph of two curves
From the graph, they cut at two different points i.e. [tex]x=-0.802\ \text{and}\ x=1.517[/tex]
Rest two roots are negative.
A bag of raisins contains 20 oz. If you want to give 25 people equal servings how many ounces should you
give each person? (It says leave your answer as a mixed number) I don’t understand how to do that.
Find the inverse of the function y = x2 – 12
Answer:
y=sqrt(x+12)
i hope this helped and have a nice day/night :)
expand the following:
a) 8(×-2y)
Answer:
8x-16y
Step-by-step explanation:
8*x-8*2y
8x-16y
Answer.
8x - 16y
Explained in the picture atteached:
Which of the following graphs represents the equation y=3x+2? A.Graph B. Graph B C. Graph C D. Graph D
The temperature is -3°C. As the day progresses, the temperature increases by 8°C, then drops by 6°C. Find the final temperature.
We know that the initial temperature is -3 then it rises to 8 and drops by 6 degrees then you just need to subtract six from 8 [tex]\displaystyle\ 8-6=2^\circ \\\\Answer: the\ secondary\ temperature \ will \ be equal \ to \ 2^\circ[/tex]
given the nth term of geometric expression is (as in the diagram)
a) state the value of k
b) the first term of progression
Step-by-step explanation:
a) k = 1
b) geometric progression formula:
Tn = ar^(n-1)
first term, a = 3/2
