Answers
Answer:
option B should be correct
Related Questions
Solve the system by substitution.
x – 4y = -8
5у – 1 = x
Submit Answer
Answers
Answer:
y = -7 and x = -36
Step-by-step explanation:
x - 4y = -8
5y - 1 = x
→ Substitute 5y - 1 into x - 4y = -8
5y - 1 - 4y = -8
→ Simplify
y - 1 = -8
→ Add 1 to both sides
y = -7
→ Substitute y = -7 into 5y - 1
( 5 × -7 ) - 1 = -36
Answer:
The solution is (-36, -7)
Step-by-step explanation:
Since 5y - 1 = x, we can replace x in the first equation by 5y - 1:
5y - 1 - 4y = -8
Collecting like terms, we get:
y = -7
If y = 7, then by the second equation x = 5(-7) - 1 = -36
The solution is (-36, -7)
Let f(x) = (1/2)^x. Find f(2), f(0), and f(-3), and graph the function.
Answers
The calculated values of the functions are f(2) = 1/4, f(0) = 1 and f(-3) = 1/8
How to calculate the values of the functionsFrom the question, we have the following parameters that can be used in our computation:
f(x) = (1/2)ˣ
Using the above as a guide, we have the following:
f(2) = (1/2)² = 1/4
Also, we have
f(0) = (1/2)⁰ = 1
Lastly, we have
f(-3) = (1/2)⁻³ = 1/8
The graph of the function is attached
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HELP ME ASAP!!!!!!!!!!!!
See picture attached.
Please friend request me if you get it right.
Thanks xx
Answers
Answer:
Number of cubes = 8 large and 32 small, or 40 total
Step-by-step explanation:
each layer = 2 large and 8 small cuboids.
each layer = 128 cm³
512/128 = 4 layers
so:
4 x 2 = 8 large cuboids
4 x 8 = 32 small cuboids
Victoria earns a gross annual income of $124,482 and is buying a home for $225,500. She is making a 20% down payment and financing the rest with a 30-year loan at 4.5% interest.
(a) What is the mortgage amount she will borrow?
(b) Can she afford this mortgage?
(c) What will her monthly mortgage payment be?
(d) What will her total payment for the house be?
(e) What is the amount of interest she will pay?
Answers
Answer:
(a) The mortgage amount she will borrow is $180,400
(b) Yes she can
(c) Her monthly payment will be approximately $914.06
(d) Her total repayment is approximately $329,061.6
(e) The amount of interest is approximately $148,661.6
Step-by-step explanation:
The details of the transactions are;
The gross annual income Victoria earns = $124,482
The cost price of the home she is buying, C = $225,500
The amount she is making as down payment = 20%
The duration the loan she id financing the rest with, t = 30-years
The interest rate on the loan, r = 4.5%
(a) The mortgage amount she will borrow, 'P', is the cost of the home less the down payment
The down payment = 20% of the cost of the home
∴ The down payment = (20/100) × $225,500 = $45,100
∴ P = $225,500 - $45,100 = $180,400
The mortgage amount she will borrow, P = $180,400
(b) Using the 2× to 2.5× gross income rule, we have;
2 × her annual income = 2 × 124,482 = 248,964
∴ 2 × her annual income > The mortgage = 180,400
She can afford the mortgage
(c) The monthly fixed payment for the mortgage is given as follows;
[tex]M = P \times \dfrac{r}{n} \times \dfrac{\left(1+ \dfrac{r}{n} \right)^{n \cdot t}}{\left[\left(1 + \dfrac{r}{n} \right)^{n\cdot t} - 1\right]}[/tex]
Where;
n = The number of periods per year = 12 monthly periods per year
180,400*0.045*(1 + 0.045)^(30)/((1 + 0.045)^(30) - 1)
[tex]M = 180,400 \times \dfrac{0.045 }{12} \times \dfrac{\left(1+\dfrac{0.045 }{12}\right)^{30 \times 12}}{\left[\left(1 + \dfrac{0.045 }{12}\right)^{30 \times 12} - 1\right]} \approx 914.060298926[/tex]
Her monthly payment will be M ≈ $914.06
(d) The total repayment is given as follows;
n × t × M
∴ 12 × 30 × 914.06 = 329061.6
The total payment for the house = $329,061.6
(e) The amount of interest = The total payment - The principal loan amount
∴ The amount of interest = $329061.6 - $180,400 = $148,661.6
The copy machine runs for 20 seconds and then jams. About how many copies were made before the jam occurred? Round your answer to the nearest tenth
Answers
Answer:
10.7
Step-by-step explanation:
A polynomial of degree 3 is multiplied by a polynomial of degree 5. What is the degree of the product?
Answers
Answer:
8
Step-by-step explanation:
The degree of a polynomial refers to the term with the highest exponent. Thus the highest exponent in a degree 3 polynomial is x3; for a degree 5 polynomial, it's x5. When you multiply
x3*x5 = x3+5 = x8.
So the product of a degree 3 polynomial and a degree 5 polynomial is a degree 8 polynomial.
Your leading term will result from the 3-degree term of the first polynomial, and the 5-degree term of the second. So you'll have something like ax3 * bx5. That will result in x3*x5=x8, so your product will have degree 8.
HELPPP!!
Find the value of x in the parallelogram!
Answers
Answer:
x = 17
Step-by-step explanation:
Area of a parallelogram:
A = bh
Given:
A = 153
b = 9
Work:
A = bh
h = A/b
h = 153/9
h = 17
Bayshore College staff are planning an end of the year meeting between students, parents and staff. They are to seat 5 parents, 5 students and 1 teacher in a circular arrangement around a table. In how many ways can this be done if no student is to sit next to another student and no parent is to sit next to another parent? (b) (4 pt) There are 20 student representatives who are already seated in a row of 20 seats. Out of the 20 representatives, 6 are to be chosen to give a speech. How many choices are there if no two of the chosen representatives occupy neighbouring seats?
Answers
The total number of choices for selecting 6 representatives without any two occupying neighboring seats is 77597520 .
(a) The number of ways to arrange 5 parents, 5 students, and 1 teacher in a circular arrangement around a table such that no student sits next to another student and no parent sits next to another parent, we can use the principle of inclusion-exclusion.
First, let's consider the arrangements without any restrictions. We have a total of 11 people to arrange around the table (5 parents + 5 students + 1 teacher), which can be done in (11 - 1)! = 10! ways.
Now, let's consider the arrangements where at least two students sit next to each other. We can treat the two adjacent students as a single entity, resulting in 10 entities to arrange around the table (4 parents + 5 student pairs + 1 teacher). This can be done in (10 - 1)! = 9! ways. However, within each student pair, the students can be arranged in 2! ways. Therefore, the total number of arrangements with at least two students sitting next to each other is 9! × 2! ways.
Similarly, we consider the arrangements where at least two parents sit next to each other. Again, we treat the two adjacent parents as a single entity, resulting in 10 entities to arrange around the table (4 parent pairs + 5 students + 1 teacher). This can be done in (10 - 1)! = 9! ways. Within each parent pair, the parents can be arranged in 2! ways. Therefore, the total number of arrangements with at least two parents sitting next to each other is 9! × 2! ways.
By the principle of inclusion-exclusion, the number of valid arrangements is given by
Valid arrangements = Total arrangements - Arrangements with at least two students sitting next to each other - Arrangements with at least two parents sitting next to each other
Valid arrangements = 10! - 9! × 2! - 9! × 2!
Valid arrangements = 2177280
(b) The number of choices for selecting 6 representatives out of 20, where no two chosen representatives occupy neighboring seats, we need to use a combination of counting techniques.
First, choose 6 seats out of the 20 seats in which the representatives will be seated. This can be done in C(20, 6) ways.
Now, since no two chosen representatives can occupy neighboring seats, we can think of the remaining 14 seats as dividers between the chosen representatives. We need to place these dividers in such a way that each chosen representative occupies a separate section.
To ensure that no two representatives occupy neighboring seats, we need to place the dividers such that each section contains at least one seat. We have 6 chosen representatives, so we need to place 5 dividers among the 14 remaining seats. This can be done in C(14, 5) ways.
Therefore, the total number of choices for selecting 6 representatives without any two occupying neighboring seats is given by:
Total choices = C(20, 6) × C(14, 5)
Total choices = 38760 × 2002
Total choices = 77597520
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The speed of a garden snail is about 8.5×10−6 miles per second. If a garden snail moves at this speed in a straight line for 2×103 seconds, how far would the snail travel in standard notation and scientific notation.
Answers
Answer:
17*10^-3 miles
Step-by-step explanation:
Given data
Speed= 8.5×10^−6 miles per second
Time taken=2×10^3 seconds
We know that the expression for the speed is given as
speed= distance/time
distance= speed* time
substitute
distance= 8.5×10^−6* 2×10^3
distance= 8.5*2*(10^-6+3)
distance= 17*10^-3 miles
Use multiplication to explain why 3/4 ÷ 2/5 =15/8 please help me
Answers
Answer:
See below
Step-by-step explanation:
[tex] \frac{3}{4} \div \frac{2}{5} \\ \\ = \frac{3}{4} \times \frac{5}{2} \\ \\ = \frac{3 \times 5}{4 \times 2} \\ \\ = \frac{15}{8} [/tex]
A solid wooden cone of a diameter 14 cm and vertical length 24 cm is vertically cut into two equal halves. One half is to be covered by colourful paper at the rate of Rs. 7 per sq. cm, find the total cost of the paper required.
(The answer must come Rs. 5950)
plz anyone ASAP help.
Answers
Answer:
The answer given is incorrect
The correct answer is Rs. 3640
The total cost of the paper required to cover one-half of the wooden cone is Rs. 3846.5.
What is the surface area of a cone?The surface area of a cone is given by the formula:
surface area = π x r x s
where r is the radius of the base of the cone and s is the slant height of the cone. The slant height of the cone is the distance from the apex of the cone to the base, measured along the surface of the cone.
In this case, the diameter of the base of the cone is 14 cm, so the radius is half the diameter or 14 cm / 2 = 7 cm.
The vertical length of the cone is 24 cm, so the slant height of the cone is the square root of the vertical length squared plus the radius squared:
s = √(24² + 7²)
s = √(576 + 49)
s = √(625)
Which simplifies to:
s = 25 cm
Now that we have the radius and slant height of the cone, we can use the formula for the surface area of a cone to find the surface area of one-half of the cone:
surface area = π x 7 cm x 25 cm = 175π cm²
To find the total cost of the paper required, we need to multiply the surface area by the cost per square centimeter:
total cost = 175 x 3.14 cm² x Rs.7/cm² = Rs. 3846.5
Therefore, the cost of the paper needed to cover one-half of the wooden cone is Rs. 3846.5.
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Find the matrix representation of the derivative map P3(R) → P3(R), with respect to the basis {1, x, x2, x}. 21. Suppose h : P1(R) + R² is a linear transformation with the following matrix representation with respect to the bases B = {1+2, X} and D - = = {(1),(-1)} Repp,p(h) = [ [Ź 2 2 1 4 2 Find the image of the polynomial 2x – 1 under h.
Answers
After considering the given data we conclude that the matrix representation of the derivative map [tex]P_3(R) - - - > P_3(R)[/tex]with respect to the basis[tex](1, x, x^2, x)[/tex]is:
[0 1 0 0]
[0 0 2 0]
[0 0 0 3]
[0 0 0 0]
And the image of the polynomial is [tex]3 + 3x + 10x^2.[/tex]
The first part of the question asks for the matrix representation of the derivative map [tex]P_3(R) - - - > P_3(R)[/tex]with respect to the basis [tex](1, x, x^2, x)[/tex] To find this matrix, we have to apply the derivative map to each basis vector and express the result as a linear combination of the basis vectors. The coefficients of these linear combinations will form the columns of the matrix representation.
Applying the derivative map to each basis vector, we get:
[tex]d/dx(1) = 0 = 0(1) + 0(x) + 0(x^2) + 0(x^3)[/tex]
[tex]d/dx(x) = 1 = 0(1) + 1(x) + 0(x^2) + 0(x^3)[/tex]
[tex]d/dx(x^2) = 2x = 0(1) + 0(x) + 2(x^2) + 0(x^3)[/tex]
[tex]d/dx(x^3) = 3x^2 = 0(1) + 0(x) + 0(x^2) + 3(x^3)[/tex]
Therefore, the matrix representation of the derivative map [tex]P_3(R) - - - > P_3(R)[/tex]with respect to the basis [tex](1, x, x^2, x)[/tex] is:
[0 1 0 0]
[0 0 2 0]
[0 0 0 3]
[0 0 0 0]
The second part of the question concerns for the image of the polynomial 2x - 1 under the linear transformation h with matrix representation:
[0 2]
[2 1]
[4 2]
with respect to the bases B = {1+2, x} and D = {(1), (-1)}.
To evaluate the image of 2x - 1, we first need to express it as a linear combination of the basis vectors in B:
[tex]2x - 1 = (-1/2)(1+2) + (2)(x)[/tex]
Next, we need to evaluate the coordinate vector of this linear combination with respect to the basis B. The coordinate vector is:
[-1/2]
Now, we can evaluate the image of 2x - 1 under h by multiplying the matrix representation of h by the coordinate vector:
[0 2]
[2 1]
[4 2]
[-1/2]
Therefore, the image of 2x - 1 under h is [tex]3 + 3x + 10x^2.[/tex]
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draw a hypothetical demand curve for tickets to a particular rock concert. use the drop box to upload an image or file containing your demand curve.
Answers
The hypothetical demand curve for tickets to a particular rock concert is given in the image attached.
What is the hypothetical demand curve
According to Samuelson: theory, the law of demand states that people buy more at lower prices and less at higher prices when other things remain constant.
Note that by using the image,
Prices of ticket (cent) Demand by consumer
5 35
4 30
3 70
2 80
1 95
Therefore, "Demands curves show how much people will buy the ticket at different prices over time." The Curve shows consumer purchases at different prices.
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Catherine Destivelle was the first woman rock climber to complete a solo ascent in 1992. She is helping to design an inside rock-climbing wall on which other climbers can practice. She draws the figure
below on the coordinate grid to represent part of the wall. Each square represents one foot
Answers
Answer:
count the unit squares
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
find Measure angle WZY QUICK PLEASE
Answers
Answer:
<WZY = 31°
Step-by-step explanation:
First, we can see that <XZW is equal to <WZY.
Given that, we know we can set the two equations equal to each other to find "x".
8x - 1 = 5x + 11
Now that the two equations are set equal to each other, all we have to do is simplify to find x.
Bring 5x over and subtract it from 8x.
3x - 1 = 11
Bring -1 over and add it to 11.
Since you're subtracting a negative, it becomes positive allowing you to add it to 11.
3x = 12
Now you need to get x by itself. Do do that, you need to divide three by itself, and whatever you do to one side, you must do to the other.
3x/3 = 12/3
Now you have:
x = 4
____________________________________________________
Now that you know the value of x, all you need to do is plug x back into the equation for <WZY
5(4) + 11
20 + 11
31.
And there is your answer - <WZY = 31°
The options are -63/16, -61/16,-59/16, -31/8, -15/4, -29/8
Answers
Answer:
-31/8. That's the answer to your question
i need help with this questionnnn
Answers
What is the other measure of the other acute angle? Pls explain how you got your answer !
Answers
Answer:
[tex]65^{o}[/tex]
Step-by-step explanation:
Angles in a triangle add up to 180
An acute angle is any angle smaller than 90
Since it is a right angle triangle, one of the angles is a right angle and therefore 90
So 180 - 90 - 25 = 65
please whats the answer?
Answers
Answer:
=93
Step-by-step explanation:
[tex]7 \frac{5}{6} + 5 \frac{1}{9} [/tex]Then mutiply 6 x7 with will give you 42 then add 5 which will equal =47please help me ........
Answers
F is a function that describes a sequence and is therefore defined over the positive
integers. Find the first four terms of the sequence.
f(n) = 100(-0.1)n-1
f(0) = -1000, f(1) = 100, f (2) = -10, f(3) = 1
f(1) = -10, f (2) = 1, f (3) = -0.1, f (4) = 0.01
f(1) = 100, f (2) = 10 f(3) = 1, f (4) = 0.1
f(1) = 100, f (2) = -10, f(3) = 1, f (4) = -0.1
Answers
Answer:
Suppose we add up alternate Fibonacci numbers, Fn-1 + Fn+1; that is, what do ... L(1)=1 and L(3)= 4 so their sum is 5 whereas F(2)=1; L(2)=3 and L(4)= 7 so their ... What is the relationship between F(n-2), and F(n+2)? You should be able to find a ... Fib(N); K (an EVEN number!), Lucas(K) and Fib(K) in each expression like ...
Step-by-step explanation:
IO. Write an
an equation
m=4
(0,0)
y=-
Please don’t use those link things they don’t work for me please just answer the question, brainliest for the first
Answers
Since the formula is y=mx+b, m is 4 and from (0,0) b is 0.
HELP ASAP! first one to answer gets brainliest and 15 points
No links or fake answers
5 questions attached
Answers
Answer:
1st: x-120
2nd: 0
3rd: x+12
4th: 120 + x
5th: x+12
im pretty sure that's right...?
I won't get brainliest lol
If x≠-4, which answer choice represents the following in simplified form (question attached)
A. X+3
B. X-4
C. 2x+6
D. X-3
Answers
Answer:
[tex]A) x+3[/tex]
Step-by-step explanation:
[tex]\frac{2x^{2}+14x+24 }{2x+8}[/tex]
[tex]=\frac{2(x^{2}+7x+12)}{2(x+4)}[/tex]
[tex]=\frac{x^{2} +7x+12}{x+4}[/tex]
[tex]=\frac{(x+4)(x+3)}{x+4}[/tex]
[tex]=x+3[/tex]
Find the value of x to the nearest tenth.
Answers
Answer:
2.8
Step-by-step explanation:
√(4² - 2²) = √12
=> √[(√12)² - 2²] = √8 ≈ 2.8
Korey kept track of the number of miles he ran each week for five weeks. The median number of miles he ran during the five weeks was 20, and the mean was 21. Which list could show the number of miles Korey ran each of the five weeks?
Answers
Options:
A. 18, 20, 20, 22, 25
B. 20, 20, 20, 25, 25
C. 16, 19, 21, 22, 22
D. 20, 20, 21, 22, 22
Answer:
A. 18, 20, 20, 22, 25
Step-by-step explanation:
Required
Which list has a mean of 21 and median of 20
Each of the list have 5 numbers and they've all been sorted.
The median is the number at the 3rd position (i.e. the middle number)
So, list C and D are out because they do not have a median of 20.
Next, calculate the mean of lists A and B
[tex]\bar x = \frac{\sum x}{n}[/tex]
A. 18, 20, 20, 22, 25
[tex]\bar x = \frac{18 + 20 + 20 + 22 + 25}{5}[/tex]
[tex]\bar x = \frac{105}{5}[/tex]
[tex]\bar x = 21[/tex]
B. 20, 20, 20, 25, 25
[tex]\bar x = \frac{20 + 20 + 20 + 25 + 25}{5}[/tex]
[tex]\bar x = \frac{110}{5}[/tex]
[tex]\bar x = 22[/tex]
Only list A has a median value of 20 and a mean value of 21
Molly drew this sketch of a house. Which of the following best describes the shape
of the roof?
A Rectangle
B Trapezoid
C Parallelogram
D Rhombus
Answers
Answer:
the trapezoid .it is the only one that resembles that of a roof.hope this helped
What is the value of x?
Answers
Answer:
A
Step-by-step explanation:
the total angles can only add up to 180°, therefore 35 + 70 = 105, 180 - 105 = 75°. 75° = A.
On the highway, the gas mileage of Jesse’s motorcy- cle is twice that of his car. If his car gets 28 mpg on the highway, what is the gas mileage of his motor- cycle on the highway?
Answers
Based on the ratios of gas mileage of Jesse's motorcycle to that of his car, 2x and x respectively, we have found out that the gas mileage of Jesse’s motorcycle on the highway is 56 mpg.
To solve the problem of finding out the gas mileage of Jesse’s motorcycle on the highway, it is necessary to use ratios. The first ratio is based on the gas mileage of Jesse’s car on the highway which is 28 mpg, then the ratio for his motorcycle is set as 2x, where x is the mileage per gallon of Jesse’s car, 28.
Therefore, the second ratio is 2x. Then we can equate these ratios in order to solve the problem. This can be done as follows: 2x/28 = y/1, where y represents the gas mileage of Jesse’s motorcycle on the highway.
Solving for y yields the following:
2x/28 = y/1
2x * 1 = 28 * y
2x = 28y
2x/2 = 28y/2
x = 14y
So the gas mileage of Jesse’s motorcycle on the highway is 14 times the mileage of his car. Therefore, to find out the gas mileage of his motorcycle on the highway, we need to multiply 28 by 2 and then divide the result by 1 which is equal to 56. Therefore, the gas mileage of Jesse’s motorcycle on the highway is 56 mpg.
In conclusion, based on the ratios of gas mileage of Jesse's motorcycle to that of his car, 2x and x respectively, we have found out that the gas mileage of Jesse’s motorcycle on the highway is 56 mpg. This has been calculated using the equation 2x/28 = y/1, where y is the gas mileage of Jesse’s motorcycle on the highway.
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Fifty students in an Italian class were surveyed about how they listen to music. Of those asked:
34 listen to Spotify (S)
30 listen to Pandora (P)
18 listen to the radio (R)
22 listen to Spotify and Pandora
13 listen to Spotify and the radio
4 listen to Pandora and the radio
o 2 listen to Spotify, Pandora, and the radio
(a) Represent this information in a Venn diagram:
(b) How many liked none of these types of music?
(c) How many students liked exactly two of these types of music?
(d) How many liked at least two of these types of music?
Answers
In the Italian class survey, 50 students were asked about how they listen to music. A Venn diagram was used to represent the information. Five students liked none of the types of music, 37 students liked exactly two types of music, and 39 students liked at least two types of music.
(a) The information can be represented in a Venn diagram as follows:
In the diagram, S represents the number of students who listen to Spotify, P represents the number of students who listen to Pandora, and R represents the number of students who listen to the radio. The overlapping regions show the number of students who listen to multiple platforms.
___________
| |
| S |
|___________|
| |
R | SP | P
|___________|
| |
| RP |
|___________|
(b) To determine the number of students who liked none of these types of music, we need to find the students who did not fall into any of the three categories. This can be calculated by subtracting the total number of students who liked at least one type of music from the total number of students surveyed.
Total number of students surveyed = 50
Students who liked at least one type of music = S + P + R - (SP + SR + PR) + SPR
Substituting the given values:
Students who liked at least one type of music = 34 + 30 + 18 - (22 + 13 + 4) + 2 = 45
Students who liked none of these types of music = Total number of students surveyed - Students who liked at least one type of music
Students who liked none of these types of music = 50 - 45 = 5
Therefore, 5 students liked none of these types of music.
(c) To find the number of students who liked exactly two types of music, we need to calculate the sum of the students in the overlapping regions of the Venn diagram.
Students who liked exactly two types of music = SP + SR + PR - (SPR)
Substituting the given values:
Students who liked exactly two types of music = 22 + 13 + 4 - 2 = 37
Therefore, 37 students liked exactly two types of music.
(d) To determine the number of students who liked at least two types of music, we need to add the students who liked exactly two types of music to the number of students who liked all three types of music.
Students who liked at least two types of music = Students who liked exactly two types of music + Students who liked all three types of music
Students who liked at least two types of music = 37 + 2 = 39
Therefore, 39 students liked at least two types of music.
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