Answer:
Step-by-step explanation:
Comment
How many 3 digit numbers are divisible by 4, but do not contain the digit nine?
If you know a computer language, then the main line would be
for x = 100 to 999 do
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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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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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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2[3x] = [1/2(4x+20)]2
Answer:x=10
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
Multiply the numbers
2⋅3x=[12(4x+20)]⋅22⋅3=[12(4+20)]⋅2
6x=[12(4x+20)]⋅26=[12(4+20)]⋅2
Combine multiplied terms into a single fraction
6x=[12(4x+20)]⋅26=[12(4+20)]⋅2
6x=[1(4x+20)2]⋅26=⎣⎡1(4+20)2⎦⎤⋅2
Multiply by 1
6x=[1(4x+20)2]⋅26=⎣⎡1(4+20)2⎦⎤⋅2
6x=[4x+20/2]⋅26=[4+20/2]⋅2
Re-order terms so constants are on the left
6x=4x+20/2⋅26=4+20/2⋅2
6x=2⋅4x+20/2
Cancel multiplied terms that are in the denominator
6x=2⋅4x+20/2
6x=4x+20
Subtract 4x from both sides
6x=4x+20
6−4=4+20−4
Simplify
6x-4x=4x+20-4x
2x=4x+20-4x
Combine like terms
2x=20
Divide both sides by the same factor
2x=20
2x/2=20/2
cancel 2 on both sides
20 divided by 2 is 10
so therefore,
x=10
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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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
Do this thing please I will be very thankful
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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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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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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Choose the multiplication equation that is represented by the model (will give brainlist thingy)
0.9 x 0.8 = 0.72
0.9 x 0.2 = 0.18
0.1 x 0.8 = 0.08
0.9 x 0.6 = 0.54
Answer:
0.9*0.8=0.72
Step-by-step explanation:
there are 9 squares across the top and 8 square downward so the only equation similar to this is the first equation.
Answer: 0.9 x 0.8 = 0.72
Step-by-step explanation:
dark gray is 9 x 8, divide both numbers by 10, you get 0.9 x 0.8 = 0.72
Vani went to the store to buy some chicken. The price per pound of the
chicken is $3.50 per pound and she has a coupon for $3.25 off the final
amount. With the coupon, how much would Vani have to pay to buy 3 pounds
of chicken? Also, write an expression for the cost to buy p pounds of chicken,
assuming at least one pound is purchased.
PLEASE PROVIDE THE AMOUNT FOR P AND FOR 3 POUNDS
The cost is the cost per pound times the number of pounds minus the coupon.
If [tex]p[/tex] pounds are purchased, she will pay [tex]3.50p-3.25[/tex].
If 3 pounds are purchased, she will pay 3.50(3)-3.25=7.25.
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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Given that 25% of a certain volume is 30cm^3, calculate the total volume
Answer:
Step-by-step explanation:
[tex]x[/tex] x 25/100=30
25/100[tex]x[/tex]=30
25[tex]x[/tex]=3000
[tex]x[/tex]=300/25
[tex]x[/tex]=120
Chapter 3/4 test i need help please
Answer:
Answer number 3
y=-9x+5
pleaseeeee help me asap
Answer: x=30 degrees
Step-by-step explanation:
A triangle has 180 degrees, so:
90+x+20+x+10=180
90+2x+30=180
2x+30=90
2x=60
x=30
PLEASE I REALLY NEED THIS ANSWER
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]
help needed asap !!!!
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
Tasha plants seeds in clay pots. She has 40 seeds to plant. She plants 6 seeds in each pot. How many seeds does Tasha have left over?
she would have four seeds left because 6 seeds times six pots would equal 36 seeds so subtract 36 from forty to get four
Step-by-step explanation:
Answer:4
Step-by-step explanation:6x6=36+4=40
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].Translate this sentence into an equation.
Six more than the quotient of a number and 7 is equal to 9.
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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(a)Bill invests Rs 75000 for 10 years at a rate of 6 % per year simple interst. Calulate the total interest he will receive.
(b) Harry invests Rs 24 000 at a rate of 7 % per annum at simple interest.After how many months will Ravi gain Rs 1260 as interst?
Answer:
Step-by-step explanation:
A = 75000(1 + (0.06 × 10)) = 120000
A = $120,000.00
B = 24000(1 + (0.07 × 0.75)) = 25260
B = $25,260.00
B=9 months
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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Write the equation in standard form using integers
(no fractions or decimals): = −
2
3
− 1
Answer: 2x3-1
Step-by-step explanation:
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
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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An ostrich egg has a width of 12.9 cm to the nearest tenth of a centimeter. Find the minimum and maximum possible measurements.
The minimum measurement is 12.85 and the maximum measurement is 12.94 that would be equal to 12.9.
What is rounding of decimal numbers?
Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up. The term "rounding decimals" describes the accurate rounding of decimal figures. To the nearest whole, tenth, or hundredth, we can round decimals.
Given, An ostrich egg has a width of 12.9 cm to the nearest tenth of a centimeter.
We have to find the minimum and maximum possible measurements.
If you're rounding to the nearest tenth of a centimeter, 12.85 centimeters is the smallest measurement that would equal 12.9 centimeters.
And 12.94 centimeters is the maximum measurement that would be equal to 12.9.
Therefore, the minimum measurement is 12.85 and the maximum measurement is 12.94.
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