For this case we have two functions of the form y = f (x). We must find the quotient of the following functions:
[tex]f (x) = x + 2\\g (x) = 3x + 5[/tex]
So, we have by definition:
[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]
Answer:
[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]
with 3x + 5 different from zero, so that the function is defined
Answer:
[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]
where [tex]x\ne -\frac{5}{3}[/tex]
Step-by-step explanation:
The given functions are:
f(x) = x + 2 and g(x) = 3x + 5
[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]
Since this is a rational function, the function will not be defined where denominator equals zero.
We need to restrict the function or define the domain.
This is a rational function defined for [tex]x\ne -\frac{5}{3}[/tex]
Thank you for any help!
Answer: Option B.
Step-by-step explanation:
Given the system of inequalities:
[tex]y<x^2+6[/tex]
[tex]y>x^2-4[/tex]
The solution of the system of inequalities is the region between the parabolas. This region is: below the parabola [tex]y=x^2+6[/tex] and above the parabola [tex]y=x^2-4[/tex]
Then, if a point is a solution of the system, then it must be in the region between this parabolas.
You can observe in the figure attached that the point that is in this region is the point (2,6), therefore, the answer is the option B.
What are the excluded values of the function? y= 5/6x-72
Answer:
x = 12 is the excluded value
Step-by-step explanation:
An excluded value is the value/s of x that make the denominator of the rational function equal to zero as this would make the function undefined.
Equate the denominator to zero and solve for x
6x - 72 = 0 ⇒ 6x = 72 ⇒ x = 12 ← excluded value
Answer: x=12
Step-by-step explanation:
-7
-3 -4M
Solve for M
=
2
Answer:
M equals -4/3 or -1 and 1/3
Answer:
M = -4/3
Step-by-step explanation:
Begin by cross multiplying
-2*-7 = 6(-3 - 4M) Combine the left
14 = - 18 - 24M Add 18 to both sides.
14 + 18 = - 18+18 - 24M Combine
32 = -24M Divide by - 24
32/-24 = -24/-24 * M
- 4/3 = M
Tonya has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it’s width
Answer:
The length of the rug is [tex]7\ ft[/tex]
The width of the rug is [tex]3\ ft[/tex]
Step-by-step explanation:
Let
x----> the length of the rug
y----> the width of the rug
we know that
The area of the rug is
[tex]A=xy[/tex]
[tex]A=21\ ft^{2}[/tex]
so
[tex]21=xy[/tex] -----> equation A
[tex]x=y+4[/tex] -----> equation B
substitute equation B in equation A and solve for y
[tex]21=(y+4)y[/tex]
[tex]y^{2}+4y-21=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=3\ ft[/tex]
see the attached figure
Find the value of x
[tex]x=3+4=7\ ft[/tex]
therefore
The length of the rug is [tex]7\ ft[/tex]
The width of the rug is [tex]3\ ft[/tex]
I need to find AB and DE
Answer:
AB = 21 and DE = 23
Step-by-step explanation:
Given 2 intersecting chords inside the circle then
The products of the measures of the parts of one chord is equal to the products of the measures of the parts of the other chord, that is
x(x + 13) = (x + 10)(x + 1) ← distribute parenthesis on both sides
x² + 13x = x² + 11x + 10 ← subtract x² + 11x from both sides
2x = 10 ( divide both sides by 2 )
x = 5
Hence
AB = x + 10 + x + 1 = 2x + 11 = (2 × 5) + 11 = 10 + 11 = 21
DE = x + x + 13 = 2x + 13 = (2 × 5) + 13 = 10 + 13 = 23
what is 2 quarters and one nickel
1 quarter = 25 cents
1 nickel = 5 cents
2 quarters = 25*2 = 50 cents
50 cents + 5 cents = 55 cents, or $0.55
2 quarters and one nickel is 55cents
Suppose you earn $12 each time you mow the lawn. Which function describes the relationship between your total earnings E and the number of times you mow the lawn, m?
E(m) = m + 12
m = 12E
E(m) = m – 12
E(m) = 12m
Answer:
E(m) = 12m
Step-by-step explanation:
Your earnings will be the amount of times you mow the lawn * $12 per job
so if m is the amount of times and 12 is the amount your Earnings(E) = 12m
The perimeter of a square is less than 20 inches. If s is the side length of the square, which inequality can be used to model the situation?
A. 20 < s + 4
B. 20 < s – 4
C. 4s < 20
D. s ÷ 4 < 20
Help ASAP!
Answer:
C. 4s < 20
Step-by-step explanation:
One side measures s. The perimeter is the sum of the lengths of the 4 sides, so the perimeter is s + s + s + s. Since all side lengths are equal, the perimeter is simply 4s. The perimeter is less than 20 inches, so 4s must be less than 20.
The inequality is
C. 4s < 20
Answer:
The answer is C on Edge 2021
Step-by-step explanation:
C : 4s < 20
Hope this helps!
help me fast i need help a lot :3
the third option
because 1/3 is not equal to three
where as if we replace the x with one in all the other we would find that the equation is correct.
what is the interquantile range between 3 & 8?
Answer:
8 - 3 =5
5 is the range of the values given
Step-by-step explanation:
We are only given 2 values;
3 and 8
It seems more reasonable to compute the range of these values as a measure of spread.
The range of a data-set is simply the difference between the maximum and the minimum values.
In our case, the maximum is 8 while the minimum is 3. The range is thus;
8 - 3 = 5
Final answer:
The interquartile range (IQR) is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). If Q1 is 3 and Q3 is 8, the IQR is 5.
Explanation:
The interquartile range (IQR) is the range of the middle 50 percent of the data values, calculated by subtracting the first quartile (Q1) from the third quartile (Q3). If the student asks about the interquartile range between 3 and 8, it seems that they may be referring to the quartiles directly, which would be unusual since quartiles are typically values derived from the data set. However, if we assume that in this case, 3 represents Q1 and 8 represents Q3, then the IQR can be calculated simply as:
IQR = Q3 - Q1 = 8 - 3 = 5.
The IQR indicates the spread of the central half of a data set and is useful in identifying potential outliers and understanding the distribution of data.
Given that [tex]\frac{4x-y}{3y} = \frac{1}{2}[/tex] , find the value of [tex]\frac{x}{y}[/tex]
Answer:
[tex]\frac{x}{y}[/tex] = [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4x-y}{3y}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2(4x - y) = 3y ← distribute left side
8x - 2y = 3y ( add 2y to both sides )
8x = 5y ( divide both sides by 8 )
x = [tex]\frac{5}{8}[/tex] y ( divide both sides by y )
[tex]\frac{x}{y}[/tex] = [tex]\frac{5}{8}[/tex]
x + 3y = 3
2x + y = 11
Answer:
if you are looking for a possible solution
x + 3y = 3
3 + 3(0) = 3
2x + y = 11
2(4) + 3 = 11
Step-by-step explanation:
In this the solution is y = -1 and x = 6.
doyle has 20 pencils. he divided them equally between 4 table
Answer:
the answer is 3 i believe
Step-by-step explanation:
[tex]20 / 4[/tex]
The sum of the angle measures of a triangle is 180°. Find the measure of each angle
Answer:
16 and 82 degrees
Step-by-step explanation:
You can sum all of the angles together and solve for x.
(x - 1) + (5x - 3) + (5x - 3) = 180
11x - 7 = 180
11x = 187
x = 17
The first angle is 16 degrees. (17 - 1)
The other two angles are 82 degrees(5(17) - 3)
Answer:
16 and 82 degrees
Step-by-step explanation:
You can sum all of the angles together and solve for x.
(x - 1) + (5x - 3) + (5x - 3) = 180
11x - 7 = 180
11x = 187
x = 17
The first angle is 16 degrees. (17 - 1)
The other two angles are 82 degrees(5(17) - 3)
Lara found the volume of a sphere with a diameter of 10.
V = 4
3
π(103)
1. V = 4
3
π(1000)
2. V = 4000
3
πunits3
Analyze Lara’s work. Is she correct? If not, what was her mistake?
Yes, she is correct.
No, she used the diameter instead of the radius measure.
No, she should have multiplied 4 and 10 first before applying the exponent.
No, her units should be squared for volume.
Answer:
No, she used the diameter instead of the radius measure.
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=10/2=5\ units[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (5)^{3}[/tex]
[tex]V=\frac{500}{3}\pi\ units^{3}[/tex]
Answer:
No, she used the diameter instead of the radius measure.
Step-by-step explanation:
The formula for the sphere is:
[tex]\pi \frac{4}{3} r^{3}[/tex]
So she should have calculated the radius before inserting the values into the formula, the radius is half the diameter, so the radius of that sphere is 5.
In order to calculate it right you have to put 5 instead of the 10 so teh formula would look like this:
[tex]\pi \frac{4}{3} r^{3}[/tex]
[tex]\pi \frac{4}{3} 5^{3}[/tex]
[tex]\pi \frac{4}{3}(125)[/tex]
[tex]250\pi }[/tex]
The answer would be:
[tex]250\pi }[/tex]
given that (-3,6) is on the graph of f(x), find the corresponding point for the function 1/3f(x)
Answer:
The corresponding point of (-3 , 6) is (-3 , 2)
Step-by-step explanation:
* Lets talk about some transformation to solve the problem
- A vertical stretching is the stretching of the graph away from
the x-axis
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
- If 0 < k < 1 (a fraction), the graph is f(x) vertically compressed
by multiplying each of its y-coordinates by k.
* Now lets solve the problem
∵ f(x) transformed to be 1/3 f(x)
∴ The graph of f(x) is stretched or compressed vertically
∵ k = 1/3
∴ 0 < k < 1
∴ The graph is compressed vertically
- The y-coordinate must be multiplying by k
∵ The y-coordinate of the point is 6
∵ 6 × 1/3 = 2
∴ The image of the point (-3 , 6) is (-3 , 2)
* The corresponding point of (-3 , 6) is (-3 , 2)
Marie is purchasing a $105,000 home with a 30 year mortgage at 5.25%. What’s her monthly principal and interest payment?
A. $414.73
B. $503.23
C. $556.09
D. $579.81
Answer:
Her monthly principal payment is D: $579.81 and monthly interest payment is 0.4375.
Step-by-step explanation:
Ok, in order to calculate the monthly principal and interest payment, we can use this relatively simple equation. The equation is:
[tex]M=P\frac{r(1+r)^{n} }{((1+r)^{n}-1) }[/tex]
Where variables represent the following:
M is your monthly payment.
P is your principal.
r is your monthly interest rate, calculated by dividing your annual interest rate by 12.
n is your number of payments (the number of months you will be paying the loan throughout the 30 years)
Then, in this case:
M=?
P=$105,000
5.25%=5.25/100=0.0525, then [tex]r=\frac{0.0525}{12} =0.004375[/tex]
[tex]n=12*30=360[/tex]
So, [tex]M=105,000\frac{0.004375(1+(0.004375))^{360} }{((1+(0.004375))^{360}-1)}[/tex] $
Solving this,
[tex]M=105,000\frac{0.004375(1.004375))^{360} }{((1.004375))^{360}-1)}[/tex] $
[tex]M=105,000\frac{0.004375(4.8141) }{((4.8141))-1)}[/tex] $
[tex]M=105,000\frac{0.02106 }{3.8142}[/tex] $
[tex]M=105,000(0.005522)/tex] $
[tex]M=579.81[/tex] $
Her monthly principal payment is $579.81.
Answer: $579.81 APEX
Martin uses clay to make vases. He uses 750 grams of clay for each vase. How many kilograms of clay does he need to make 10 vases?
Answer:
7500
Step-by-step explanation: 750 * 10
Answer:75 kilograms
You would have to divide 750 by 10 and you would get 75
suppose that 11 inches of wire cost 66 cents at the same rate how much (in cents) will 28 inches of wire cost
Answer:
168 cents or = $1.68
Step-by-step explanation:
11 inches of wire cost 66 cents
28 inches of wire cost x? cents
x = 28 * 66 / 11 = 168 cents or = $1.68
Answer
168 cents or = $1.68
Which of the following is a term, variable, and expression. 21, ab, 5x squared, h
Term = 5x^2
h = variable
21 is a constant
I think ab is an expression or the product of two factors.
naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read
write the functions formula
Answer:
Step-by-step explanation:
The question here is "how many pages does this book have?"
In 4 hrs, at 55 pages/hr, he reads 220 pages.
Adding the number of pages read (220) to the number of pages left to read (350) yields a total of 570 pages in this book.
Next time, please try to be more specific about what you want to find. "functions formula" is very ambiguous and unhelpful.
The equation is [tex]\( y = 570 - 55x \)[/tex], where [tex]\( y \)[/tex] is pages left and [tex]\( x \)[/tex] is hours passed.
To complete the equation for the relationship between the number of pages left and the number of hours, we first need to determine the rate at which Naoya is reading the book.
Since he read 55 pages per hour, after 4 hours he would have read [tex]\( 55 \times 4 = 220 \)[/tex] pages.
Given that after 4 hours he still had 350 pages left to read, we can find out how many pages he had initially:
Initial number of pages = Total pages - Pages read
Initial number of pages = 350 pages + 220 pages
Initial number of pages = 570 pages
Now, let's use the formula for the relationship between the number of pages left and the number of hours:
[tex]\[ y = 570 - 55x \][/tex]
Where:
- [tex]\( y \)[/tex] represents the number of pages left to read after [tex]\( x \)[/tex] hours.
- [tex]\( x \)[/tex] represents the number of hours.
So, the complete equation for the relationship is:
[tex]\[ y = 570 - 55x \][/tex]
The complete question is here:
Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read.
Let y represent the number of pages left to read after x hours.
Complete the equation for the relationship between the number of pages left and number of hours.
y=
Which shapes can you use to model the log and the board
Answer:
a cylinder can model a log and a rectangular prism would model a board
Step-by-step explanation:
vocab
Answer:
a cylinder can model a log and a rectangular prism would model a board
Step-by-step explanation:
Need answer..... PLZ PLZ PLZ
Answer:
D. Gabrielle is more justified in choosing not to get insurance
Step-by-step explanation:
Gabrielle is more justified in choosing not to get insurance because she is in good heath and haven't had the need to visit a doctor in a long time.
Chances are she'll be fine, at least until he health situation changes.
Juan on the other hand should find a way to afford the insurance, because of his failing health he can't predict his health costs in short term. So, an insurance would be a great thing for him to have, it would at least give him some financial security because chances are his health costs would be higher than his premiums.
Calculate the finance charge and new balance using the previous balance method. Previous balance = $199.19 Annual rate = 14% Finance charge = $ New purchases = $97.50 Payments/credits = $75.75 New balance = $
To calculate the finance charge and new balance, first find the finance charge with the formula: Previous balance x Annual rate / 12 months. Add this to the previous balance and any new purchases, then subtract any payments or credits. The resulting figure will be the new balance. In this example, the finance charge is $2.32 and the new balance is $223.26.
Explanation:In this financial calculation, the annual rate of 14% is used to calculate the finance charge on the previous balance of $199.19. The formula to calculate the finance charge is: Previous balance x Annual rate / 12 months. Moving forward, the finance charge will be added to the previous balance and any new purchases, then any payments or credits will be subtracted from this total to find the new balance.
Calculate the finance charge. Finance charge = (199.19 x 0.14) / 12 = $2.32.Add the finance charge to the previous balance and new purchases. $199.19 (previous balance) + $2.32 (finance charge) + $97.50 (new purchases) = $299.01.Subtract payments or credits from the previous total to find the new balance. New balance = $299.01 - $75.75 (payment) = $223.26.Learn more about Finance charge calculation here:https://brainly.com/question/15720230
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The finance charge is $75.75.
Explanation:To calculate the finance charge and new balance using the previous balance method, you can follow these steps:
Calculate the finance charge by multiplying the previous balance by the annual interest rate.Add any new purchases to the previous balance.Subtract any payments or credits from the new balance.In this case, the finance charge would be $27.89, calculated as $199.19 * 0.14.
The new balance would be $321.84, calculated as ($199.19 + $97.50) - $75.75.
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math help please ????
Answer:
4 (as in 25/4)
Step-by-step explanation:
Write and solve an equation of ratios:
x 15
------ = ------
10 24
Then 24x = 150, and x = 150/24 = 6.25. This is equivalent to 25/4.
Answer:
x = 25/4
Step-by-step explanation:
If the rectangles are similar, the ratio of the side lengths have to be similar
10 24
------ = --------
x 15
Using cross products
10*15 = 24*x
150=24x
Divide each side by 24
150/24=24x/24
150/24=x
Divide the top and bottom by 6
25/4 = x
125.315 to standard form
Answer:
1.25315*102
Step-by-step explanation:
The number 125.315 is already in standard form. This form, also known as scientific notation, simplifies the representation of large or small numbers. However, 125.315 doesn't need this kind of simplification.
Explanation:The number 125.315 is already in standard form. In Mathematics, standard form, also known as scientific notation, refers to expressing a number as a number between 1 and 10 multiplied by a power of 10. The purpose is to simplify the representation of very large or very small numbers. For instance, 2000 would be written as 2 x 10^3 in scientific notation. However, 125.315 is not a large enough number that needs to be simplified in such a manner.
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Jack earns $300 per week selling cars. He makes an additional 2% commission on all of his sales. Last week he sold $53, 850 worth of cars. What was Jack’s income for the week?
Answer:
1377 dollars
Step-by-step explanation:
Problem 6
Jessie has some chickens and rabbits. There are 30 heads and 76 legs in all. How many chickens
does Jessie have and how many rabbits does Jessie have?
Answer:
8 rabbits
22 chickens
Step-by-step explanation:
c = chickens
r = rabbits
heads - c + r = 30
legs - 2c + 4r = 76
We can now use these two equations to create one by isolating the variable (c) in the first equation.
c = 30 - r
2c + 4r = 76
2(30 - r) + 4r = 76
60 - 2r + 4r = 76
2r = 16
r = 8
Now we know that there are 8 rabbits, which means that there has to be 22 chickens in order to have 30 heads.
To solve the problem of finding the number of chickens and rabbits, we can use a system of equations.
Explanation:To solve this problem, we can use a system of equations. Let's consider the number of chickens as 'c' and the number of rabbits as 'r'.
We know that there are a total of 30 heads, which means that c + r = 30.
We also know that there are a total of 76 legs, which means that 2c + 4r = 76.
We can solve this system of equations by substitution or elimination to find the values of c and r. From there, we can determine the number of chickens and rabbits that Jessie has.
Let's solve it using the elimination method: Multiply the first equation by 2 to match the coefficient of 'c' in the second equation. You will get 2c + 2r = 60. Subtract this equation from the second equation to eliminate 'c', and you will get 2r - 2r = 76 - 60. Simplifying, we have 0 = 16, which is not true.
There is no solution for this system of equations. Therefore, the problem may be set up incorrectly.
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Please solve!!!!
-x=2-3x+3
-x=2-3x+3
add 3x to both sides
2x=2+3
combine like terms
2x=5
divide by 2
x= 5/2
Answer:
The answer is x = 5/2.
Step-by-step explanation:
Add the like terms which are 3 & 2. Add like variables which would be 3x added to both sides then you get 2x = 5. Divide by 2 on both sides to get x = 5/2.
Number seven omg I am done with math!!! Please help to solve for m
Answer:
m∠1 = 123°
Step-by-step explanation:
Since a straight line is always a supplementary angle, it equals 180°. To solve for the unknown angle, we can subtract the known angle from 180°.
180° - 57° = 123°
So m∠1 = 123°
180-57= 123 is the measurement for angle 2
All straight line is equal to 180