Using the monthly payment formula, it is found that:
A. You can afford a car at a price of $13,742.36.
B. The monthly payments are of $109.15.
What is the monthly payment formula?The monthly payments are given by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The variables involved in the equation are listed and explained as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For item a, the parameters are given as follows:
A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
Hence the maximum value of the car is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
0.0181919241P = 250
P = 250/0.0181919241
P = $13,742.36
For item b, the parameters are given as follows:
P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).
Hence the monthly payments are given as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
A = 6000 x 0.0181919241
A = $109.15.
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Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|
B.1-41 <1-3/<13<|4|
C. 1211-51> |-7|>1-81
D. 1-41>19> |-31 >|-10|
In actuality, "absolute value" refers to thinking of all numbers as positive and removing all negative signs from front of them (or zero). Symbol for absolute value. -71<181<|9|<1-10| set of absolute values
Explain about the absolute values?Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0.
The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.
The exact distance of an integer or number from zero on a number line is its absolute value. As a result, the absolute value is never negative and is always positive.
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Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam 5 inches wide, 2 inches high, and 10 feet long can support a maximum of 8 tons. What is the maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long?
The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33.
How to find the maximum weight ?G = C×(w×h²/l)
Where,
C = constant
C = G×l/(w²h²)
Weight (w) = 6 in
Height (h) = 2 in
Length (l)= 10 ft
Maximum ton (G) = 8 t
C = 8×10/(6×2²)
C = 80/24
C = 10/3
G = (10/3)×(w×h²/l)
So, Maximum weight
G = (10/3)×(6×2²/24)
G = 10/3 t
G = 3.33 tones
The maximum weight is 3.33 tones.
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Find g(x), where g(x) is the translation 1 unit up of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
g(x)=
The value of the translated function g(x) will be x²+1.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.
Given that the function is f(x) = x². The function g(x) in the form of a(x–h)²+k will be written as below,
The function is translated to the 1 unit up which means that the value of k will be equal to the positive 1.
The function is,
g(x) = a(x–h)²+k
g(x) = 1(x-0)² + 1
g(x) = x² + 1
Therefore, the value of the translated function g(x) will be x²+1.
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How Is The Problem Shown The Picture Done
Answer:
instead of X, we replace 9.
So we have: f(9)=4*9^2-2*9+4.
Again, f(9)= 4*81-18+4=324-14=310.
18
8. Carey bought a $2,100 computer system on the installment plan. He made a $400 down
payment, and he has to make monthly payments of $79.50 for the next two years. How much
interest will he pay?
Answer:
$208
Step-by-step explanation:
$79.50 x 24 = 1908
$1908 + 400 = 2308
$2100/2308 = 9%
Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.
What is Interest?Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.
Total number of monthly payments
= 12 months/year x 2 years
= 24 months
and, Monthly payment amount = $79.50
Total amount paid in monthly installments
= Monthly payment amount x Total number of monthly payments
= $79.50 x 24
= $1,908
Next, we can subtract the initial down payment from the total amount paid to find the interest paid:
Total interest paid = Total amount paid - Down payment
= $1,908 - $400
= $1,508
Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.
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Use the product-to-sum identities to rewrite the following expression as a sum or difference.
2sin(2x)sin(2x)
The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.
How to transform a product of trigonometric functions into a sum of trigonometric functions
Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:
sin α · sin β = [cos (α - β) - cos (α + β)] / 2
First, write the trigonometric function defined in the statement:
2 · sin 2x · sin 2x
Second, use the product-to-sum formula by considering α = β = 2 · x:
2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]
cos 0 - cos 4x
1 - cos 4x
Third, write the resulting expression:
2 · sin 2x · sin 2x = 1 - cos 4x
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The sum of two numbers is 130 and their difference is 34 Let x be the first number and y be the second
number Set up a system of equations and use the elimination method to find the numbers. You must
show your work
10. A theater sold 800 tickets for Friday night's performance, One child ticket costs $4.50 and one adult
ticket costs $6.00. The total amount collected was $4.500. How many of each type of ticket were sold?
11. The postal service offers flat-rate shipping for priority mail in special boxes. Malia shipped 4 small
boxes and 2 medium boxes, which cost her $54 to ship. Meanwhile, Stephen shipped 1 small box and
2 medium boxes, and paid $33. How much does it cost to ship these two sizes of boxes?
Step-by-step explanation:
9)=
By the question:-
x + y = 130-i
x - y = 34-ii
Now,
Add i and ii,
x + y + x -y = 164
or, 2x = 164
so, x = 82
Now,
x -y = 34
or, 82 - y = 34
so, y = 48
The numbers are 82 and 48.
10) =
Let adults ticket be x and childs ticket be y.
x + y = 800
x = 800 - y - eqn i
4.5x + 6y = 4500
Substituting x's value from eqn i,
4.5(800-y) + 6y = 4500
or, 3600 - 4.5y + 6y = 4500
or, 1.5y = 900
so, y = 600
Now,
x + y = 800
or, x + 600 = 800
so, x = 200
Hence, 600 adult tickets were sold and 200 child tickets were sold.
11)=
Let cost of one small box be x and one medium box be y.
So,
4x + 2y = 54-eqn i
x + 2y = 33-eqn ii
subtracting eqn i from ii,
x + 2y - 4x - 2y = - 21
or, -3x = - 21
so, x = 7
Now,
x + 2y = 33
or, 2y = 33 - 7
or, y = 26/2
so, y = 13
So, cost of one small box is $7 and medium box is $13.
Graph g(x) = -2x - 3.
The graph of the function g(x) = -2x - 3 is attached below.
Graph:
Graph refers a diagram that represents the variation of a variable in comparison with that of one or more other variables.
Given,
Here we have the function g(x) = -2x - 3
Now, we need to plot the graph of the function.
In order to plot the graph for the given function,
First we have to take some sample values for the given function and then apply it on the given function to generate the table to plot the graph.
Now, we have to take -2, -1, 0, 1, 2 are the samples value for x.
Then we get the value of the function as,
x = -2 => g(-2) = -2(-2) - 3 = 4 - 3 = 1
x = -1 => g(-1) = -2(-1) - 3 = 2 - 3 = -1
x = 0 => g(0) = -2(0) - 3 = 0 - 3 = -3
x = 1 => g(-2) = -2(1) - 3 = -2 - 3 = -5
x = 2 => g(2) = -2(2) - 3 = -4 - 3 = -7
Now, we can get the table like the below
Now, we have to plot the graph through this table, then we get the graph like the following.
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find quotient of 5 divided by 3/10
The quotient of 5 divided by 3/10 is equal to 50/3
How to divide by a fraction?When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.
So, if we want to divide A by the fraction (b/c), then we can write:
A÷(b/c)
That will be equal to A*(c/b), so:
A÷(b/c) = A*(c/b)
Here we want to divide 5 by 3/10, then we need to solve:
5÷(3/10)
Using the above rule we will get:
5÷(3/10) = 5*(10/3) = 50/3
That is the quotient.
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What is the equivalent equation to the given equation?
x = x² - 20
The equivalent equation to the given equation i.e, x = x² - 20 is x² - x - 20 = 0
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is,
x = x² - 20
We have to make the equation in quadratic form i.e, ax² + bx + c = 0
so, first take x to the right side
0 = x² - 20 - x
Now swap the equation,
x² - 20 - x = 0
put 'x' term in middle and constant term at last like this,
x² - x - 20 = 0
Hence, The equivalent equation to the given equation i.e, x = x² - 20 is x² - x - 20 = 0
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Joey has 80 pens and 30 of them are red. What percent are red?
Answer:
Step-by-step explanation:
some help me pls with this
Solve the equation: r - 535 = 175
Step-by-step explanation:
r - 535 = 175
r = 175 + 535 = 710
Answer:
take - 535 to the other side (over equal to side)
which makes it +535
r = 175 + 535
r = 710
Find the value of n(AnB) if
n(A)=5 n(B)=7 and n(AUB)= 10
what is n(AnB)=?
PLEASE HELP
By using the concept of set operation, the result obtained is
[tex]n(A \cap B) = 2[/tex]
What is a set?
Set is a well defined collection of distinct objects. The members of a set are called elements of a set. Set can be empty as well as non empty.
Set can be finite as well as infinite.
The number of elements inside a set is known as cardinal number of the set
Operations on set are union, intersection, set difference and symmetric difference
Concept of set operation has been used here
n(A)=5 n(B)=7 and n(AUB)= 10
[tex]n(A \cap B) = n(A) + n(B) - n(A \cup B)[/tex]
[tex]n (A \cap B) = 5 + 7 -10\\n(A \cap B ) =2[/tex]
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Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller. Which equation below could be used to find the smaller number?
(1) 2x-3(x+1)=x+4
(2) 3(x+1)-2x = x+4
(3) 2x-3(x+2) = x+4
(4) 3(x+2)-2x = x+4
Answer:
(4)
Step-by-step explanation:
Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.
Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x
Then, since the result of this is four more than the smaller, this expression is x+4.
Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.
Hence, the option (4) is correct.
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.
Let us assume the smaller number is [tex]x[/tex].
The larger number is [tex](x+2)[/tex].
Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is
[tex]3(x+2)-2x[/tex]
So, the result is four more than the smaller.
i.e., [tex]3(x+2)-2x=x+4[/tex]
Hence, the option (4) is correct.
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There are 4 squares and 16 triangles. What is the simplest ratio of squares to
triangles?
Answer:
1 : 4
Step-by-step explanation:
There are 4 squares and 16 triangles.
That is,
Squares : Triangles
4 : 16
To write it in its simplest ratio, divide both by 4.
Squares : Triangles
1 : 4
Write a coordinate rule for the dilation.
Answer: 584390
Step-by-step explanation: the r4u819
Write a quadratic function f whose zeros are 7 and -5.
Answer:
f(x) = x² -2x -35
Step-by-step explanation:
You want a quadratic function that has zeros 7 and -5.
FactorsEach zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).
f(x) = (x -7)(x +5)
f(x) = x² -2x -35
__
Additional comment
You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.
sum: 7-5 = 2
product: (7)(-5) = -35
quadratic: f(x) = x² -2x -35
help please for brianlest???
Answer:
Step-by-step explanation:
domain: 1,2,3,4
Range: 8,6,4,2
D=-2
[tex]a_{n}=a_{1}+(n-1)-2[/tex] formula
How does knowing the x-intercepts and the vertex of a
function help you graph a quadratic function?
A graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
With the help of the vertex and the x-intercept, the equation of the parabola can be formed which helps to graph a quadratic function because the equation of the parabola resembles the quadratic function,
Thus, a graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
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what is -3 > -2x + 7 ?
Mark earns a salary of £28000 per annum. At the end of the on increase first year he is given he is of 3%.. At end of the second given an increase of 2.5%. Work out Mark's salary at the end of the two years.
Answer:
£27839
Step-by-step explanation:
O×M=N (original x multiplier = original value)
£28000×0.97%=£27160< 1st year decrease
£27160x1.025=£27839<2nd year increase
1 A father is three times as old as his daughter. If the father is 31 years older than his daughter, what are their ages?
father age 46.5
daughter age 15.5
46.5 - 15.5 = 31
332x39 how do you work it out
what is 100÷200 need help
on dividing 100 by 200 we get answer as 0.5 or we can also write it as 1/2 in fraction.
What is division?
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.
To divide 12 donuts into three similar groups in the aforementioned case, you would need to put four doughnuts in each group. Consequently, 12 divided by 3 will equal 4.
We need to find 100/200,
on solving this division problem we get answer as 1/2 (in fraction) or 0.5 (in decimal).
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Which graph represents the function f(x) = –|x + 3|?
Answer:
The answer would be A. (Not sure if its A B C or D question but I will have picture below)
Step-by-step explanation:
Hope this helps you! :))
Alma ran a marathon. The graph shows the distance she ran during the marathon. Use the drop-down menus to complete the statements based on the graph.
From the proportional relationship graphed, it is found that:
The labeled point means that in 2 hours she ran 16 miles.In 1 hour, Alma ran 8 miles.Her distance changed at a unit rate of 8 miles per hour, so Alma's speed was of 8 miles per hour.If Alma ran faster, the slope of the graph would be greater.What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.
When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:
y = kx.
From point (2,16) in this problem, the constant is given as follows:
k = 16/2 = 8.
Hence the equation is:
y = 8x.
Meaning that her rate is of:
8 miles per hour.
If she ran faster, the slope = constant would increase, as it represents the velocity.
Missing InformationThe problem is given by the image at the end of the answer.
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Mrs. Boyer is buying folding chairs that are on sale for $8. She has $56. Which inequality
can be solved to show the number of chairs c Mrs. Smith can buy?
a. 8c ≤ 56
b.8 >56
c. 56c<58
d. 56c>28
An inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56
In this question we have been given Mrs. Boyer is buying folding chairs that are on sale for $8.
She has $56
We need to find an inequality that can be solved to show the number of chairs c Mrs. Smith can buy.
A price of one chair is $8
So, the price of 'c' number of chairs would be 8c
But she has $56
So, to find the number of chairs she can buy, we need to divide 56 by 8
We can write is as 8c = 56
⇒ c = 7
But she might buy less that 7 chairs.
So, we write above relation in inequality form as,
8c ≤ 56
Therefore, an inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56
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Change 4 1/6to an improper fraction.
Answer:
4 1/6 = 25/6
Why?:
Multiply the denominator with the mixed number 4.
Add the numerator 1 and get 25.
Then, you keep the denominator (Which is 6) on the bottom.
And finally, you get
25/6
Answer:
25/6
Step-by-step explanation:
first start by multiplying 6 and 4, which leads you to 24
then add the 1 from the numerator and you get 25 as your numerator.
for the denominator, leave six as it is so it becomes 25/6
Estimate 17.140 - 03.179 by first rounding each number to the nearest tenth.
Answer: 13.9
Step-by-step explanation:
17.140 rounded to the nearest tenth is 17.1
03.179 rounded to the nearest tenth is 3.2
17.1 - 3.2 = 13.9
Use the diagram to complete the statement.
The value of the side CB in the right angled triangle is found as 4√2 units.
Describe the Pythagorean theorem?The Pythagoras theorem, commonly known as the Pythagorean theorem, says that if a triangle has a right angle (90 degrees), the square of the hypotenuse equals equal to the sum of a squares of the opposite two sides.It describes the connection between the three sides of such a right-angled triangle.For the given question,
The diagram is given;
AB = 7 units.
AG = 3 units.
GB = 7 - 3 = 4 units.
GC = 4 units.
In right angled triangle GCB, apply Pythagorean theorem.
CB² = GB² + GC²
CB² = 4² + 4²
CB² = 2(4)²
Taking square root both side.
CB = 4√2
Thus, the value of the side CB in the right angled triangle is found as 4√2 units.
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