One leg of a right triangle is twice as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg.
The length of the Hypotenuse is, [tex]\sqrt{5}x[/tex] units.
What is Pythagoras Theorem?
The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
Let the one leg of a right triangle is twice as long as the other.
Suppose the shorter leg is x.
So the longer leg is 2x.
Let, the hypotenuse is h.
By Pythagoras Theorem,
[tex]x^2 + (2x)^2 = h^2\\x^2 + 4x^2 = h^2\\5x^2 = h^2\\h = \sqrt{5} x[/tex]
Hence, the hypotenuse as a function of the length of the shorter leg, is [tex]\sqrt{5}x[/tex] units.
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The population of a city is increasing at a steady rate of 2.4% per annum.
The current population is 528 000.
What is the expected population in 4 years?
Give your answer to the nearest thousand.
The expected population of a city in 4 years is 581,000.
What is defined as the rate of population growth?The average annual rate of change in population size for a specific ethnicity, country, or region over a given time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and also the total population in that year.Current population (P) = 528 000.
Rate of growth (r) = 2.4%
Time t = 4 years
Expected population (A) = ?
The formula used is-
A = P(1 + r/100)∧t
Put the values.
A = 528 000(1 + 2.4/100)∧4
A = 528 000 x (1.042)∧4
A = 581,000
Thus, the expected population of a city in 4 years is 581,000.
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HELP PLEASE HELP PLEASE ADD WORK!! PLEASE HELP NEED IT NOW
The high temperature in Northville one day was 16°F. The low temperature on the same day was –11°F. What was the difference between the high and low temperatures for that day?
Answer: The answer should be a 27-degree difference
Step-by-step explanation:
If you add -11 and 11 you get 0 then add 16. 11+16 is 27 so a 27-degree difference!!!
The weight of one serving of trail mix is 2. 5 ounces. How many servings are there in 22. 5 ounces of trail mix?.
9 servings are there in 22.5 ounces of trail mix.
Given:
The weight of one serving of trail mix is 2. 5 ounces.
1 serving = 2.5 ounces
Number of servings = 22.5 ounces / 1 serving
= 22.5 / 2.5
= 225/10/25/10
= 225/25
= 9 servings.
Therefore 9 servings are there in 22.5 ounces of trail mix.
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Write the equation in standard form using integers
(no fractions or decimals): = −
2
3
− 1
Answer: 2x3-1
Step-by-step explanation:
Bill is driving on the highway he begins the trip 12 gallons of gas in his car. the car use miles let represent the number of gallons of gas he has left in his tank and let D represent the total distance (in miles) traveled. Write an equation relating G to D and then graph your equation using the axes below.
graph and make a equation to support your awenser
Answer:
12 - D = X
Step-by-step explanation:
Im not REALLY x2 sure but hope its helpful
help needed asap !!!!
If the time is 10:05, what time will it be in 1000 minutes?
Answer:
2:45
Step-by-step explanation:
1 hour has 60 minutes so:
number of hours in 1000minutes:
1000/60=16.6666hours
so 16 hours + 0.6666 hours
convert 0.6666 hours to minutes;
0.6666x60=39.99minutes=40 minutes(rounded)
10:05+16hours+40 minutes
2:05+40minutes=2:45
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A line has a slope of -9 and includes the points (-9, n) and (-10, 5). What is the value of n?
n=
The value of n is calculated as -14 which was found using the slope formula and given data.
How to calculate the slope?When coordinates are provided, the following formulae can be used to determine a line's slope:
Step 1: Determine the line's coordinates.
Step 2: Enter their values into the equation slope(m) = (y₂-y₁)/(x₂-x₁).
Given: There is a line that contains the points (-9, n) (-10, 5).
We need to find the value of n.
We know that,
slope(m) = (y₂-y₁)/(x₂-x₁)
-9 = (5-n)/(-10+9)
-9(-10+9) = 5-n
90-81 = 5-n
9+5 = -n
n = -14
Therefore, the value of n is -14 which was found using the slope formula and given data.
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56 women make up an all female choir in a church. Two women are chosen to sing together for a duet. How many possible pairs could be chosen for the duet?
it is due now!!! 20 points
The per capita consumption (in pounds) of all poultry in a country is approximated by the function C(x) = 2.97x +92.19, where x is the number of years since 2014. Find and interpret C(1)
By evaluating the function in x = 1 we get:
C(1) = 95.16
This means that the per capita consumption of all poultry in 2015 was 95.16 pounds.
How to find C(1)?Here we have the linear function:
C(x) = 2.97*x+ 92.19
We know that it models the consumption of all poultry in a country as a function of x, the number of years since 2014.
Then C(1) will be the consumption of all poultry in that country one year after 2014 (this would be on 2015).
To evaluate we just need to replace the variable x in the equation by 1, we will get:
C(1) = 2.97*1+ 92.19 = 95.16
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In thi triangle, angle W equal (3x-24) degree, and angle C equal (4x-11) degree, and angle T equal 2x degree, what doe angle W equal?
The angle W equal to 24.3
In a triangle sum of three angles is equal to 180
W = (3x-24) degree
C = (4x-11) degree
T = 2x degree
3x-24+4x-11+2x=180
9x-35=180
9x=180-35
9x= 145
x=16.1
substitute the value of x in W equation
W = 3(16.1)-24 = 24.3
The value of angle W is 24.3
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Show algebraically that the sum of 2 consecutive numbers is always odd.
Answer:
Two consecutive numbers can be written as x and x+1
if we add those two equations together we get 2x+1
And since any number times two is an even number if you add one to any even number you always get an odd number
Chapter 3/4 test i need help please
Answer:
Answer number 3
y=-9x+5
5. Solve each of the following:
4 movie tickets cost $36. At this rate, what is the cost per ticket? S
a.
In my oping the onswer is 95
b. 3 ice cream cones cost $8.75. At this rate, how much do 5 ice cream cones cos
In my oping the avviciu, col
c. 5 bananas cost $2.00. At this rate, how much do 12 bananas cost? $
The cost per ticket is $9, the cost of 5 ice cream cones is $14.58 and the cost of 12 bananas is $4.8.
a.
4 movie tickets cost $36.
cost per ticket = 36/4
= $9,
The cost per ticket is $9.
b.
3 ice cream cones cost $8.75.
1 ice cream cost = 8.75/3
= 2.916
5 ice cream cost = 2.916*5
= $14.58.
The cost of 5 ice cream cones is $14.58.
c.
5 bananas cost $2.00.
1 banana cost = 2/5
= 0.4
12 bananas cost = 0.4*12
= $4.8.
The cost of 12 bananas is $4.8.
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true or false: if the eigenvalues of a are 2, 2, 5, then the matrix is certainly (a) invertible. (b) diagonalizable. (c) not diagonalizable.
The claim of invertible metrix is true and others are false.
In the given value we have to check which is true and which is false for the eigenvalues.
The eigenvalues are 2, 2, 5.
(1) First check the matrix is certainly invertible.
The matrix is invertible when the probuct of eigenvalues does not equal to zero.
invertible of A = 2*2*5
invertible of A = 20 which is not equal to zero.
So the matrix is certainly invertible. The claim is true.
(2) Now we check the matrix is certainly diagonalizable.
We note that the eigen value 2 has an algebraic multiplicity of 2 (number of repetitions), but we are unsure if the accompanying eigen vectors likewise have a count of two (geometric multiplicity)
The sum of the algebraic multiplicities must equal the sum of the geometric multiplicities in order for A to be diagonalizable.
In this instance, there is no evidence to support the geometric multiplicity of the eigenvalue 2. Therefore, we are unable to affirm that A is diagonalizable.
Consequently, the claim is false.
(3) Now we check the matrix is certainly not diagonalizable.
If the homogeneous equation from (A-⋋I)x=0 when the eigen value ⋋=2 is substituted x+y+z=0, then the solution set is x=-k-m where y=k, z=m are the parameters.
So it can be written as
[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =k\left[\begin{array}{ccc}-1\\1\\0\end{array}\right] +m\left[\begin{array}{ccc}-1\\0\\1\end{array}\right][/tex]
Putting k=1 and m=1, then the corresponding eigen vectors for ⋋=2 are [tex]\left[\begin{array}{ccc}-1\\1\\0\end{array}\right],\left[\begin{array}{ccc}-1\\0\\1\end{array}\right][/tex]
So the geometric multiplicity of the eigen value ⋋=2 is 2.
The algebraic multiplicity = Geometric multiplicity we can see the given matrix A is diagonalizable.
So the statement is false.
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An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile.
Five minutes into the descent the airplane has an altitude of 500 feet.
Given that an airplane at 3,000 feet begins to descend at a rate of
500 feet per minute, it is required to write an equation to model the situation and find the altitude of the airplane after 5 minutes.
First, we can model the situation through a linear equation of the form
y = mx + b.
Then, we must identify each variable:
y = A = Altitude
m = decrease per minute = 500
x = t = minute-time
b = Airplane height = 3,000
Now, we set up the equation, substituting y, m, x, and b into the linear equation, as the situation models the descent of the airplane the slope must be negative; thus:
A(t) = 3,000 − 500t
Lastly, we must find the altitude when if t = 5:
A(5) = 3,000 − 500(5)
Solving, we obtain:
A(5)=3,000 − 2,500 = 500
Hence the answer is, Five minutes into the descent the airplane has an altitude of 500 feet.
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Describe domain and range
F(x)= -2x^2-3x+9
Answer:
First, know that this is a downwards parabola graph.
Domain is (-∞, ∞) because x can be any value.Range has to be (−∞, [tex]\frac{81}{8}[/tex]] because the graph reaches a maximum y-value at [tex](-\frac{3}{4}, \frac{81}{8} )[/tex].What is the output for y=x-4 if the input is 13
Answer:
9
Step-by-step explanation:
y = x - 4
y = 13 - 4
y = 9
in triangle abc, AB=6.2, AC=9.5, and BC=5.1. Which is the smallest angle of the triangle?
The smallest angles of the triangle is angle A
In triangle ABC
The length of the side AB = 6.2 units
The length of the side AC = 9.5 units
The length of the side BC = 5.1 units
The opposite angle of AB is angle C, the opposite angle of AC is angle B and the opposite angle of BC is angle A
We know length of the line is BC which is 5.1 units which is the smallest side of the triangle. Then the opposite angle of BC will be the smallest angle in the triangle ABC
The opposite angle of the side BC is angle A, which is the smallest angle in the triangle
Hence, the smallest angles of the triangle is angle A
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Guided Problem Solving You have a class photo that is 10 in. long and 8 in. wide. If you want to enlarge your photo to be 15 in. long, how wide will the photo be?
Understand the Problem You know the dimensions of the original photo and the length of the enlarged photo. Find the width of the enlarged photo.
Make a Plan Draw the figures and label their sides.
The width of the enlarged photo is 12 inches
The length of the original photo = 10 inches
The width of the original photo = 8 inches
The length of the enlarged photo = 15 inches
The width of the enlarged photo = x
Then the proportion of the length and width of the original and enlarged photo will be
10 / 8 = 15 / x
Cross multiply the terms
10x = 15 × 8
Multiply the terms in the equation
10x = 120
Divide both side of the equation by 10
10x / 10 = 120 / 10
x = 120 / 10
Divide the terms
x = 12 inches
Hence, the width of the enlarged photo is 12 inches
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though the cri gin
10) Consider the graph shown. Determine the slope and write an equation in the form y = mx + b to
represent the line.
-8
A
h
8
6
Y
-2-
-4-
-6
-8
0 2
4
6
8
Answer:
Y= x+1
Step-by-step explanation:
m=2-1/ 1-0; m=1
Y-2= 1(x-1)
Y= x-1+2
Y= x+1
Mark sells a car that has been marked up $450, which was 25% of the buying price. He also has to charge a 9% sales tax on the selling price of the car. What is the final price of the car?
The final price of the car when Mark sells a car that has been marked up $450 is $2452.50.
How to calculate the price?From the information, Mark sells a car that has been marked up $450, which was 25% of the buying price.
He also has to charge a 9% sales tax on the selling price of the car. The final price of the car will be:
= Original price + Mark up + Tax
= $1800 + $450 + (9% × $1800 + $450)
= $1800 + $450 + $202.50
= $2452.50
The price is $2452.50.
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An artist charges $980 for a portrait but gives 5% discount for cash. Calculate the cash Price for portrait
Answer: $931
Step-by-step explanation:
Since $980 is 100% of the price and the cash discount is 5% we can calculate the cash price of the portrait like this:
$980 full price* (1 - .05 discount) = $931
Mike's Fitness Center charges $30 per month for a
membership. All-Day Fitness Club charges $22 per month
plus an $80 initiation fee for a membership. After
type your answer...
months will the total amount
paid to the two fitness clubs will be $
type your answer...
Answer:
the cheaper plan is Mike's until month 10. At month 10 the plans are equal after month 10 All Day is cheaper
Step-by-step explanation:
30x = 22x + 80 Set the equations equal to each other and subtract 22 from both sides of the equal sign
8x = 80 Divide both sides by 8
x = 10
At 10 months the plan are equal.
Maria will spin the arrow on the spinner 2 times. What is the probability that the arrow will stop on the same letter twice?.
Probability that the arrow will stop on the same letter twice = 1/3 (c).
What is probability?
The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that an announcement is true.
Main body:
Given : Maria will spin the arrow on the spinner 2 times.
To find : What is the probability that the arrow will stop on the same letter twice.
Solution : We have given a spinner that spin twice and stop on the same letter.
Formula for probability = no. of favourable outcome/ total outcomes
Here, total part of spinner = 3 and it spin two times
So, total possible outcome = 6. Arrow stay on same letter twice( favorable outcome) =2.
Plugging the values in formula :
Probability = 2/6
Probability = 1/3
Therefore, probability that the arrow will stop on the same letter twice = (c).
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Find the prime factorization of
the number 68.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [ ] × [ ]
X
X
Enter the number that belongs in the green box.
Answer:
[tex]68 = 2 \times 2 \times 17[/tex]
the quadratic equation x2 mx n has roots twice those of x2 px m, and none of m, n, and p is zero. what is the value of n/p?
The value of n/p is 8.
What is quadratic equation?
A quadratic equation in algebra is any equation that can be written in standard form as where x is an unknown and where a, b, and c denote known numbers, where a ≠ 0.
Let, for x^2 + mx + n = 0
⇒ x = 2α or 2β
From the given condition,
for x^2 + mx + n = 0 ⇒ x = α or x = β
Then,
2(α + β) = -m ..(1)
4αβ = n ..(2)
and α + β = -p ..(3)
αβ = m ..(4)
From equation (1) and (3),
-m/2 = -p
⇒ p = m/2
and from equation (2) and (4),
n/4 = m
⇒ n = 4m
Therefore,
n/p = 4m / (m/2) = 4 x 2 = 8
Hence, n/p = 8.
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An elevator can carry 24 adults or 40 children at one time during the course of a day the elevator Carrie’s a full passenger load 74 times if all the passengers were children how many people would the elevator Carry than if all the passengers were adults
Using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.
What do we mean by mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
parentheses, exponents, multiplication, division, and PEMDAS.
So, to calculate how many more children the lift carries in a day:
The number of adults the lift can carry is 24.
The number of children the lift can carry is 40.
The lift carries people at full capacity 70 times.
Now, calculate as follows:
24 × 70 = 1,680
40 × 70 = 2,800
Difference:
2,800 - 1,680 = 1,120
Therefore, using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.
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In the past month, Chau rented 5 video games and 4 DVDs. The rental price for each video game was $3.30. The rental price for each DVD was $3.80. What is the total amount that Chau spent on video game and DVD rentals in the past month?
Does anyone know how to do that?
The total amount that Chau spent on video game and DVD rentals in the past month is $31.70.
How to calculate the cost?Given that Chau rented 5 video games and 4 DVDs and the rental price for each video game was $3.30 while the rental price for each DVD was $3.80.
The Total amount that was spent will be:
= Amount spent on video games + Amount on DVD
= (5 × $3.30) + (4 × $3.80)
= $16.50 + $15.20
= $31.70
The amount is $31.70.
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