The equation of a line perpendicular to y = x that passes through the point (8,2) is y = -x + 10
How to find the equation of the perpendicular line?The equation of the line is given as
y = x
Rewrite the equation as
y = x
A linear equation is represented as
y = mx + c
Where
Slope = m
So, we have
m = 1
The slopes of perpendicular lines are opposite reciprocals
This means that
m2 = -1/m1
So, we have
m = -1/1
Evaluate
m = -1
The equation of the perpendicular line is then calculated as
y = m(x - x1) + y1
Where
(x1, y1) = (8, 2)
This gives
y = -1(x - 8) + 2
Evaluate
y = -x + 8 + 2
Evaluate the sum and the difference
y = -x + 10
So, the equation of a line perpendicular to y = x that passes through the point (8,2) is y = -x + 10
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f(t) = 10.72(0.9t + 10)0.3 (0 ≤ t ≤ 20)
where t is measured in years, with t = 0 corresponding to the year 2000.† At what rate was the percentage of Americans age 55 and older changing at the beginning of 2008? (Round your answer to four decimal places.)
____ % per year
At what rate was the percentage of Americans age 55 and older changing in 2017? (Round your answer to four decimal places.)
____% per year
What was the percentage of the population of Americans age 55 and older in 2017? (See Note on page 168. Round your answer to two decimal places.)
____%
a) The rate % at the beginning of 2008 rounded off to four decimal places will be 25.1682 % per year.
b) The rate % at the beginning of 2017 rounded off to four decimal places will be 28.2573 % per year .
c) The rate % at the beginning of 2017 rounded off to two decimal places will be 28.26% per year.
What is a function ?
A function is a relationship between inputs and outputs where each input has precisely one output and the output can be linked to its input.
It is given that , a function which represents rate % is f(t) = 10.72 × [tex](0.9t + 10)^{0.3}[/tex]. Also , t = 0 corresponding to the year 2000.
The rate % of Americans age 55 and older changing at the beginning of 2008 i.e., t = 8 , rounded off to four decimal places will be :
So : f(t) = 10.72 × [tex](0.9* 8 + 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](7.2+ 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](17.2)^{0.3}[/tex]
f(t) = 10.72 × 2.347
f(t) = 25.1682 % per year
The rate % of Americans age 55 and older changing at the beginning of 2017 i.e., t = 17 , rounded off to four decimal places will be :
f(t) = 10.72 × [tex](0.9* 17 + 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](15.3 + 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](25.3)^{0.3}[/tex]
f(t) = 10.72 × 2.6359
f(t) = 28.2573 % per year
The rate % of Americans age 55 and older changing at the beginning of 2017 rounded off to two decimal places will be :
f(t) = 28.26% per year
Therefore , the answers are :
a) The rate % at the beginning of 2008 rounded off to four decimal places will be 25.1682 % per year.
b) The rate % at the beginning of 2017 rounded off to four decimal places will be 28.2573 % per year .
c) The rate % at the beginning of 2017 rounded off to two decimal places will be 28.26% per year.
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For each polynomial function, rewrite the polynomial in standard form. Then state its degree and constant term.
a. f(x) = (x + 1)(x+3)(x-4)
b. g(x) = 3(x + 1)(x+3)(x-4)
a. The stand form is f(x) = x^3 - 13x - 12
degree = 3
constant term = - 12
b. The stand form is g(x) = 3 x^3 - 39x - 36
degree = 3
constant term = - 36
Given data
f(x) = (x + 1)(x+3)(x-4)
g(x) = 3(x + 1)(x+3)(x-4)
How to find the standard form of the polynomialsfor f(x) = (x + 1)(x+3)(x-4) we have
f(x) = (x + 1)(x+3)(x-4)
f(x) = ( x + 1 ) ( x^2 - 4x + 3x - 12 )
f(x) = (x + 1) ( x^2 - x - 12 )
f(x) = x^3 - x^2 - 12x + x^2 - x - 12
f(x) = x^3 - 13x - 12
degree = 3
constant term = -12
g(x) = 3(x + 1)(x+3)(x-4)
g(x) = 3(x + 1) ( x^2 - 4x + 3x - 12 )
g(x) = 3(x + 1) ( x^2 - x - 12 )
g(x) = 3 ( x^3 - x^2 - 12x + x^2 - x - 12 )
g(x) = 3 ( x^3 - 13x - 12 )
g(x) = 3 x^3 - 39x - 36
degree = 3
constant term = - 36
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what is the following ratio using two other notations. 3:8
Answer:
3 to 83/8Step-by-step explanation:
You want to see two other ways to write the ratio 3:8.
RatiosA ratio is a way of saying that some number of one thing is always associated with some (often different) number of another thing. The two things may or may not be measured with the same units, and may or may not refer to parts of the same object.
Here, we're concerned with how we write a ratio. One way is shown in the problem statement:
3 : 8 . . . . . . . . using a colon
Two other ways to write the same ratio are ...
3 to 8 . . . . . . using the word "to"
3/8 . . . . . . . . using a fraction bar
__
Additional comment
A ratio is in "simplest form" if the numbers involved are mutually prime (have no common factors).
Sometimes an extended ratio is useful for specifying the relationship between more than two measures, for example, 3 : 8 : 5.
write ____ as a single power of 3
Answer:
[tex]3^{16/5}[/tex]
Step-by-step explanation:
[tex]3^3 \times \sqrt[5]{3} \\ \\ =3^3 \times 3^{1/5} \\ \\ =3^{16/5}[/tex]
The party is at 3 pm in only 12 minutes the party starts. what time is it right now?
well, let's say is 3pm, now, let's take away 10 minutes, that means 2:50pm, now let's take away another 2 minutes, that's 2:48pm.
(xy^4)^3 simplify simplify simplify
Answer:
[tex]x^3y^{12}[/tex]
Step-by-step explanation:
[tex]\left(xy^4\right)^3\\\left(xy^4\right)^3=x^3\left(y^4\right)^3\\=x^3\left(y^4\right)^3\\=(y^4)^3\\=(y)^{4\times 3}\\= y^{12}\\= x^3y^{12}[/tex]
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{By using the \textbf{Exponent Property}, we can simplify this.}[/tex]
[tex]\textsf{This is what it states:}[/tex]
[tex]\sf{(x^m)^n=x^{(m*n)}}[/tex]
[tex]\textsf{Multiply:}[/tex]
[tex]\sf{(xy^4)^3=x^3y^{3*4}=x^3y^{12}}[/tex]
[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star[/tex]
Two boxes are shown below. What is the combined volume? Show your work
Check the picture below.
The solution is, the combined volume of the boxes is 180 unit cube.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
from the given diagram, we get,
there is two boxes in the diagram.
now, we have to find the combined volume.
here, we get,
the boxes are cuboids.
we know that,
Volume of cuboid = length * width * height
V = l*w*h
here, we get, from the figure,
for 1st box, l = 3, w = 5 , h = 8
so, V = 3 * 5 * 8 = 120
and, for 2nd box, l = 4, w = 5, h = 3
so, V = 4*5*3 = 60
we get, the combined volume 120 + 60 = 180
Hence, The solution is, the combined volume of the boxes is 180 unit cube.
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Mrs. Burke’s geography class has 106 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collect yesterday’s work.
Mrs. Burke’s Geography Class
Academic Year Geography Majors Non-Geography Majors
Freshmen 15 14
Sophomores 11 16
Juniors 13 11
Seniors 14 12
Step 2 of 2 : What is the probability that she selects a senior, given that she chooses a non-geography major? Enter a fraction or round your answer to 4 decimal places, if necessary.
Probability is the measure of the likelihood that an event will occur in a Random Experiment. The probability of selecting a senior from non geography is 0.1132
What is probability?Probability is the measure of the likelihood that an event will occur in a Random Experiment
Given
Geography Majors Non Geography Majors
Freshmen 15 14
Sophomores 11 16
Juniors 13 11
Seniors 14 12
The total number of students are 106
The number of seniors in non geography is 12
So probability of selecting one senior from 106 is 12/106
Probability(senior of non geography)=12/106=0.1132
Therefore required probability is 0.1132.
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Given the function P(n)=3n^4+30n^3+63n^2
its P -intercept is
its n -intercepts are
The P-intercept of the function P(x) is 0.
The n -intercepts of the function are n = 0, -3 and -7
How to find the intercepts of a function?
We are given the function;
P(n) = 3n⁴ + 30n³ + 63n²
Now, the P intercept of the function P(n) will occur when n = 0. Thus;
P(0) = 3(0)⁴ + 30(0)³ + 63(0)²
P(0) = 0
Thus, the P intercept of the function P(x) is 0.
Now, the n-intercept will be the roots of the given function P(x). Thus;
3n⁴ + 30n³ + 63n² = 0
n²(3n² + 30n + 63) = 0
Thus;
n² = 0 or 3n² + 30n + 63 = 0
Using quadratic equation calculator we have;
n = 0, -3 and -7
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2.28times10^9 3times10^8
What is the area, in squared feet, of a rectangle whose length is three times its
width which is 4 feet?
A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
Based on the number of people employed in education and health service industries in 2009, the number of new jobs that will be gained between 1/2009 and 1/2016 is b. 2,826,800 people.
How many jobs will be gained?The number of total jobs in 2016 can be found as:
= Number of jobs in education and health service industries x (1 + rate of increase)
= 19,200,000 x (1 + 14.8%)
= 19,200,000 x 1.148
= 22,041,600 people
The number of new jobs are:
= 22,041,600 people - 19,200,000
= 2,841,600 people
= 2,826,800 people approximate
Graph and options for the question are:
Education and Health Services - All Employees, 2000-2009 A line graph titled Education and Health Services, All Employees, 2000 to 2009, where the x-axis shows years and the y-axis shows all employees, in thousands. Line starts at 15,000 on January 2000, and increases gradually to 16,000 on January 2002, 17,200 on January 2005, 18,100 on January 2007, and 19,200 on January 2009.
a. 21,926,800
b. 2,826,800
c. 16,273,200
d. 1,790,600
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Answer:
b on edge
Step-by-step explanation:
$7.99 by 16.2 ounces
Answer:
.49 if you're dividing them.
Step-by-step explanation:
Find the next two terms of the sequence:
5, 15, 45, 135, 405, 1215
The next two terms of the sequence are blank and blank
Answer:
3645, 10935
Step-by-step explanation:
1215*3 = 3645
3645*3= 10935
What is the mapping rule you use to reflect a figure across the y-axis?
in terms of height.
9 Modelling The inside of a saucepan has diameter 20 cm and height 13 cm.
The manufacturer claims that the pan has a capacity of 4 litres.
Is the claim correct?
Explain your answer.
Step-by-step explanation:
this is practically a cylinder.
the volume of a cylinder is
ground area × height = pi×r² × height.
r being the radius (half of the diameter).
so, we have here
V = pi×10² × 13 = pi × 100 × 13 = 1300pi =
= 4,084.07045... cm³
1 liter = the content of a cube with 10 cm side length.
10×10×10 cm³ = 1000 cm³ = 1 liter.
the pan has a volume of 4,084.07045... cm³, so, yes, it has the capacity of 4 liters as 4×1000 cm³ (and a little bit extra).
2x-2(5x-3)=4x-6
Solve for X
Step-by-step explanation:
2x-10x+6=4x-6
2x-10x-4x=-6-6
-12x=-12
x=1
Suppose you go shopping for a new futon bed for your room. The model you really like happens to be on sale for $200. It's original price is $500. What percent of the original price will you save if you purchase it?
Round your percentage to one decimal place.
Do not include
%
sign with your answer.
60 percent of the original price is saved if the futon bed is purchased.
The percent of the original price that will be saved can be calculated as followsThe original price of the futon bed is $500
The new price is $200
The first step is to calculate the price change
Price change= 500-200
= 300
The amount saved can be calculated as follows
300/500 × 100
= 0.6 × 100
= 60
Hence 60 percent of the original price which is $500 will be saved
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trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes
When the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes, the time when they will stop at same time is 18 minutes.
How to illustrate the information?From the information, the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes.
Therefore, the time when will they stop at same time will be the lowest common multiple for 9 and 6. This is 18. Therefore, 18 minutes is the appropriate answer.
Therefore, the the time when they will stop at same time is 18 minutes.
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Trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes. When will they stop at same time?
Shoreside Bikes is a bike rental company that charges tourists by the hour as
shown in the table. Use the table to fill in the missing representations.
Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 32 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 176 square feet of carpeting. What dimensions should the rug have?
The rug will have dimension of 8ft. wide and 22ft. long.
Dimensions of room :
Wide (w) = 18 ft.
Long (l) = 32 ft.
Area of the room = l × w
= 32 × 18 = 576 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft.
Then the dimensions of the rug will be = (18- 2x)ft. × (32- 2x)ft.
Area of the rug = (18 - 2x) × (32 - 2x) ft²
176 = (18 - 2x) × (32 - 2x)
176 = 576 - 36x - 64x + 4x²
4x² - 100x + 400 = 0 ( Divide the equation by 4 )
x² - 25x + 100 = 0
x² - 20x - 5x + 100 = 0
x(x - 20) -5(x - 20) = 0
(x - 20) (x - 5) = 0
x = 20, 5
If we take 20 as x then it will become a negative number when we will substract it from dimensions of the rug.
Therefore, The width of the rug will be 5 ft.
Thus, The Dimension of the rug = (18- 2x)ft. × (32- 2x)ft.
= (18 - 10) × (32 - 10)
= 8ft. × 22ft.
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Find the total cost to the nearest cent.
$20 haircut; 10% tip
Answer:
$22.00
What is a tip in sales?A tip in sales is an added monetary contribution to the worker responsible for your bill. Tips are usually in percentage form and represent a portion of the total before you add a tip.
To find a tip in sales, convert the percentage to a decimal and then add 1 to that decimal. Finally, multiply the total by this sum.
SolveTo solve, first convert the percentage into a decimal by dividing by 100.
[tex]\displaystyle \frac{10}{100}[/tex]
[tex]0.1[/tex]
Then, add 1 to this quotient.
[tex]1+0.1 =1.1[/tex]
Finally, multiply the total ($20) by this sum.
[tex]20\times 1.1[/tex]
[tex]22[/tex]
Therefore, the total cost is $22.00.
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The total cost to the nearest cent is $22.00 when haircut is $20 and tip is 10%.
To find the total cost, we need to add the cost of the haircut and the tip amount.
Given:
Haircut cost = $20
Tip percentage = 10%
First, calculate the tip amount:
Tip = (10/100) × Haircut cost
Tip = (10/100) × $20
Tip = $2
Add the haircut cost and the tip amount to find the total cost:
Total cost = Haircut cost + Tip
Total cost = $20 + $2
Total cost = $22
Therefore, the total cost to the nearest cent is $22.00.
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8:50+ 7 hours and 35 minutes
Answer:
4:25 I think
Step-by-step explanation:
just added them all up I don't know if that's what you needed yho
Answer:
15:85 or 4:25
Step-by-step explanation:
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how do i simplify 4² X 4 ^4 / 4^3
Answer:
4³
Step-by-step explanation:
using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
then
4² × [tex]4^{4}[/tex] / 4³
= [tex]4^{(2+4)}[/tex] / 4³
= [tex]4^{6}[/tex] / 4³
= [tex]4^{(6-3)}[/tex]
= 4³
When you subtract a constant from y=x2 what happens to the graph? Eg y = x2 - 2
When you subtract a constant from y = x², the following happens to the graph: C. graph moves DOWN.
What is a graph?
A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any quadratic function is parabolic because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive.
In conclusion, when a constant is subtracted from y = x², we can reasonably infer and logically deduce that the graph moves down as shown in the image attached below.
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Complete Question:
When you subtract a constant from y = x² what happens to the graph? Eg y = x² - 2
answer choices
Graph moves UP
Graph moves to the RIGHT
Graph moves DOWN
Graph moves to the LEFT
Explain why you use addition to
check subtraction.
Answer: The reason that you would use addition to check subtraction is because it is the easiest, fastest, and most reliable way to check your subtraction problem.
Step-by-step explanation:
for example. you do something like: 42 - 19 = 23
you just add 19 and 23. if you get 42 then that means your answer if correct.
hope it helps
Find the greatest common factor: 9ab2, 108ab3
The greatest common factor of 9ab², 108ab³ is 9ab².
What is the greatest common factor?The factor of a number is the number that divides a number evenly; without any remainders. The factors of a number can either be positive or negative. For example, a factor of 10 is 2. This is because 10 divided by 2 is 5. 2 divides 10 evenly.
The greatest common factor is the highest factor that is common to two or more numbers. The highest common factor of 10 and 20 is 10. This is because it is the greatest common factor that is common to both numbers.
Factors of 9ab², 108ab³ = 3ab², 9ab²
The greatest common factor = 9ab²
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pls help me with this:(. What is 532 divided by 46. Can you help?
Answer: 11.5652174
.
Hello I'm Ash I'm here to help you! <3
Answer:
11 Remainder 26
Step-by-step explanation:
The number 532 is called the numerator or dividend, and the number 46 is called the denominator or divisor.the quotient and remainder of 532 divided by 46 = 11 R 26The quotient of 532÷ 46 equals 11; the remainder (“ the number left over”) is 26.I hope this Helps!
Answered by:AshTheNeko <3
Jack is 29 of age he weighs 81kg he works out in a hot day what is the amount of water he will need to drink
Answer:
8 gallons
Step-by-step explanation:
9 (8 + 4) using pemdas
Answer:
108
Step-by-step explanation:
9(8 plus 4)
Simply do 8 plus 4 = 12 then 12x9=108