Answer:
y= -1/2x +5
Step-by-step explanation:
The ratio of fiction to nonfiction books in a classroom library is 2 to 3 . If there are 24 books nonfiction books in the classroom library , how many fiction books are there?
Answer:
16Step-by-step explanation:
Given the ratio of fiction to nonfiction books in a classroom library is 2 to 3, then the total ratio of both books will be 2+3 = 5. If there are 24 books non fiction books in the library, to get the amount of fictionbooks that are there we will follow the following steps.
First we will calculate the total number of books in the shelf;
3/5 * Total number of books = total non fiction books
3/5 * Total number of books = 24
3*Total number of books = 5*24
3*Total number of books = 120
Total number of books = 120/3
Total number of books = 40
Therefore there are 40 total of books on the shelf.
Total number of fiction books = 2/5 * 40
Total number of fiction books = 2* 8
Total number of fiction books = 16 books
Hence there are 16 fiction books on the shelf.
can someone please help me with this question :)
Solve the system of equations.
y = x2 - 2
y = -2x + 1
Answer:
x = -3 and y = 7 or x = 1 and y = -1
Step-by-step explanation:
Evaluate the expression, given functions f and g: f(x) = 3x – 2, g(x) = 7 – x2.
3f(1) - 49(-2)
f(x) = 3x – 2, g(x) = 7 – x2.
3f(1) - 49(-2)
Substitute the given value into the function and evaluate.
101
The value of 3f(1) - 49(-2) for the given function f(x) = 3x – 2 will be 101.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
Given the function,
f(x) = 3x – 2
Now,
f(1) = 3(1) - 2 = 1
So,
3f(1) - 49(-2) = 3×1 - 49(-2)
⇒ 3 + 98 = 101
Hence "The value of 3f(1) - 49(-2) for the given function f(x) = 3x – 2 will be 101".
For more about the function,
brainly.com/question/23712366
#SPJ2
find the value of x and y if y-2x=3 and x+y=3
Answer:
x= 0 y = 3
Step-by-step explanation:
i hope it helped u!!
Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.) 1. x^3-7x+6=0;1 2. x^3-3x^2+25x+29=0;-1 3.x^3-4x^2-3x+18=0;3 Find all the zeros of the function 4. f(x)=x^2+4x-12 5.f(x)=x^3-3x^2+x+5 6. f(x)=x^3-4x^2-7x+10 Write the simplest polynomial function with integral coefficients that has the given zeros. 7. -5,-1,3,7 8. 4,2+3i (thank you so much in advance, it would mean a lot, and it is urgently needed, hence the high reward, thank you! Have a great day)
Step-by-step explanation:
"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"
Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic. I'll use grouping.
Then, we can either factor or use the quadratic equation to find the remaining two roots.
1. x³ − 7x + 6 = 0; 1
x³ − x − 6x + 6 = 0
x (x² − 1) − 6 (x − 1) = 0
x (x + 1) (x − 1) − 6 (x − 1) = 0
(x² + x − 6) (x − 1) = 0
(x + 3) (x − 2) (x − 1) = 0
The remaining two roots are both real: -3 and +2.
2. x³ − 3x² + 25x + 29 = 0; -1
x³ − 3x² + 25x + 29 = 0
x³ − 3x² − 4x + 29x + 29 = 0
x (x² − 3x − 4) + 29 (x + 1) = 0
x (x − 4) (x + 1) + 29 (x + 1) = 0
(x² − 4x + 29) (x + 1) = 0
x = [ 4 ± √(16 − 4(1)(29)) ] / 2
x = (4 ± 10i) / 2
x = 2 ± 5i
The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.
3. x³ − 4x² − 3x + 18 = 0; 3
x³ − 4x² − 3x + 18 = 0
x³ − 4x² + 3x − 6x + 18 = 0
x (x² − 4x + 3) − 6 (x − 3) = 0
x (x − 1)(x − 3) − 6 (x − 3) = 0
(x² − x − 6) (x − 3) = 0
(x − 3) (x + 2) (x − 3) = 0
The remaining two roots are both real: -2 and +3.
"Find all the zeros of the function"
For quadratics, we can factor using either AC method or quadratic formula. For cubics, we can use the rational root test to check for possible rational roots.
4. f(x) = x² + 4x − 12
0 = (x + 6) (x − 2)
x = -6 or +2
5. f(x) = x³ − 3x² + x + 5
Possible rational roots: ±1/1, ±5/1
f(-1) = 0
-1 is a root, so use grouping to factor.
f(x) = x³ − 3x² − 4x + 5x + 5
f(x) = x (x² − 3x − 4) + 5 (x + 1)
f(x) = x (x − 4) (x + 1) + 5 (x + 1)
f(x) = (x² − 4x + 5) (x + 1)
x = [ 4 ± √(16 − 4(1)(5)) ] / 2
x = (4 ± 2i) / 2
x = 2 ± i
The three roots are x = -1, x = 2 − i, x = 2 + i.
6. f(x) = x³ − 4x² − 7x + 10
Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1
f(-2) = 0, f(1) = 0, f(5) = 0
The three roots are x = -2, x = 1, and x = 5.
"Write the simplest polynomial function with integral coefficients that has the given zeros."
A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c). Remember that imaginary roots come in conjugate pairs.
7. -5, -1, 3, 7
f(x) = (x + 5) (x + 1) (x − 3) (x − 7)
f(x) = (x² + 6x + 5) (x² − 10x + 21)
f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)
f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105
f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105
8. 4, 2+3i
If 2 + 3i is a root, then 2 − 3i is also a root.
f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))
f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))
f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))
f(x) = (x − 4) (x² − 4x + 13)
f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)
f(x) = x³ − 4x² + 13x − 4x² + 16x − 52
f(x) = x³ − 8x² + 29x − 52
Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x)
Complete Question
Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = 12e^x, [−6, 6] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
Answer:
The average is
[tex]AV = 403[/tex]
The value of x is
[tex]x = 4[/tex]
Step-by-step explanation:
From the question we are told that
The equation is [tex]f(t) = 12e^x[/tex]
The points consider is [-6 , 6]
Generally the average value of the function over the given interval is mathematically represented as
[tex]AV = \frac{1}{z-w} \int\limits^ z_w {f(x)} \, dx[/tex]
[tex]AV = \frac{1}{ 6 - (-6)} \int\limits^{6}_{-6} { 12e^x} \, dx[/tex]
[tex]AV = \frac{1}{12 } e^x| \left 6} \atop {-6}} \right.[/tex]
[tex]AV = e^6 -e^{-6}[/tex]
[tex]AV = 403[/tex]
Generally when the function equal the average we have that
[tex]f(x) = 12e^{x} = 403[/tex]
[tex]e^{x} = 34[/tex]
[tex]x = ln(34)[/tex]
[tex]x = 4[/tex]
What is the solution Set to 2a+6=2a+5+1
Answer:
Infinite Amount of Solutions
Step-by-step explanation:
Step 1: Write out equation
2a + 6 = 2a + 5 + 1
Step 2: Combine like terms
2a + 6 = 2a + 6
Here we see that we have the same slope and same y-intercept or the same equation. When this happens, our solution set is infinite amount of solutions, as any value a can be plugged in and would be true.
3. The minimum payment on a credit card is based on the total amount owed. A credit card company uses the following rules: For a bill less than $20 the entire amount is due, for a bill of at least $20 but less than $500, the minimum due is $20. For a bill of at least $500 but less than $1000 the minimum due is $40 and for a bill of at least $1000 but less than $1500 the minimum due is $80 dollars. For a bill of $1500 or more the minimum due is 1/10th of the bill.
a. Write a function to describe the minimum payment due.
b. What is the minimum payment due if the bill is $345?
c. What is the minimum payment due if the bill is $1410?
d. What is the minimum payment due if the bill is $1700?
Answer:
b
Step-by-step explanation:
x + 2y = 33
x-y = 11
Answer:
[tex]x=\frac{55}{3},\:y=\frac{22}{3}[/tex]
Step-by-step explanation:
Solve by Substitution ;
[tex]\begin{bmatrix}x+2y=33\\ x-y=11\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:x+2y=33:\quad x=33-2y\\\\\mathrm{Subsititute\:}x=33-2y\\\\\begin{bmatrix}33-2y-y=11\end{bmatrix}\\\\Simplify\\\begin{bmatrix}33-3y=11\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:33-3y=11:\quad y=\frac{22}{3}\\\mathrm{For\:}x=33-2y\\\\\mathrm{Subsititute\:}y=\frac{22}{3}\\x=33-2\times\frac{22}{3}\\\\x=\frac{55}{3}\\\\x=\frac{55}{3},\:y=\frac{22}{3}[/tex]
if you apply the changes below to the quadratic parent function, f(x)=x2, what is the equation of the new function shift 3 units left vertically stretch by a factor of 4 reflect over the a axis
Answer: B. g(x) = –4(x – 3)2
Step-by-step explanation: To apply the changes to the equation of a vertical stretch of 4 and a translation of 3 units to the right, as well as the correct answer would be choice B.
The reason for this is when you apply a vertical stretch, because it changes the y-values (which causes it to vertically stretch or appear skinnier when graphed), you would multiply 4 to f(x) which would look like 4x^2.
Then, since you have a reflection over the x-axis, you must multiply a -1 to f(x) to reflect it over the x-axis which would result in -4x^2.
Finally, it also asks to shift the graph right 3 which by moving it right, you change the x values meaning you will perform f(x-3) to achieve this (subtract the value from x when you move right, and add the value to x when you move left).
Find the equation of a Horizontal line containing the point (-1,3)
Answer:
y = 3
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
We know that a horizontal line has a slope of zero:
Slope m = 0
y = 0x + b
y = b
Since we are trying to find a line that fits with (-1, 3), we look solely at the y-value.
y = 3
We want to find the equation of a horizontal line such that it passes through a given point.
The answer is: y = 3
We know that the general form of a horizontal line is:
y = a
Where a is a real number.
Now, we also want that our line passes through the point (-1, 3).
Notice that the y-value of the point is 3, and in a horizontal line we can have only one value of y, so the horizontal line must be:
y = 3
The graph of the line and the point can be seen below
If you want to learn more you can read:
https://brainly.com/question/10863938
A number cube numbered 1-6 is rolled once. What is the probability that the side facing up shows a 4
Answer:
it will be one out six to roll a four
Step-by-step explanation:
there is one being rolled to be a 4 out of six
Select the correct inequality to make a true statement
Please help
Answer:
2/5 is greater
Step-by-step explanation:
to compare you need to make them common denominator, and that could be10. to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2. this will turn it into 4/10. 4/10 is greater than 3/10
The solution is : 2/5> 3/10
2/5 is greater than 3/10
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Here, we have,
the given fractions are,
2/5 and 3/10
now, we have,
to compare you need to make them common denominator,
and that could be10.
to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2.
i.e. 2*2/5*2
=4/10
this will turn it into 4/10.
now, we get,
4/10 is greater than 3/10
Hence, 2/5> 3/10 , 2/5 is greater than 3/10.
To learn more on fraction click:
brainly.com/question/10354322
#SPJ2
Solve xy - 3 = k solve for x
Answer:
x=(k+3)/y
Step-by-step explanation
First, we simplify by adding 3 to both sides of the equation
xy-3+3=k+3
Now it's xy=k+3
To get x we divide both sides by y
So x=(k+3)/y
Answer:
[tex]x = \frac{k + 3}{y} [/tex]
Step-by-step explanation:
Do all u can to make x stand alone.
Just obey the rules of fhe operations when they cross the equal sign.
What is two plus two?
Answer:
4 you dumba**. Jesus christ
Step-by-step explanation:
PLS ANSWER BEST ANSWER GETS BRAINLIEST Tim wants to decorate a rectangular card with a width of 1/2 inch and an area of 7/4 square inches. Find the length of the card in inches?
Answer:
[tex]\frac{7}{2}[/tex]in
Step-by-step explanation:
First you must set up an equation. [tex]\frac{1}{2}x=\frac{7}{4}[/tex]
Then, you must solve for x. [tex]x=\frac{7}{2}[/tex]
Which expression is equivalent to 10i/2-i
Answer:
A reduce the fraction is
5\1
Answer:
C. 4i-2
Step-by-step explanation:
EDGE 2020
find the area of the blue shaded shape
Answer:
Hey there!
The big square has an area of 6x6 or 36 units.
However, we subtract 8 to get 28 because the 8 white squares do not count.
Let me know if this helps :)
Answer:
28units²
Step-by-step explanation:
6² = 36
36 - 8 = 28
please show the work.
What is the area of this figure? 15 yd 4 yd 7 yd 25 yd 21 yd 22 yd
Answer:
45
Step-by-step explanation:
y’all pls help me :(
Answer: B
Step-by-step explanation:
When you are multiplying exponents, if the base is the same, then you can directly add the exponents together.
We can see that both bases are 6. That means we can add the exponents.
[tex]3+\frac{1}{4}[/tex] [common denominator]
[tex]\frac{12}{4}+\frac{1}{4}[/tex] [add]
[tex]\frac{13}{4}[/tex]
Now, we know that the answer will be [tex]6^1^3^/^4[/tex].
Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g compose f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true?
Answer:
a=-1
b=10
Step-by-step explanation:
Answer:
a: -1
b: 10
edge 2020
What is 2 ×2×6×6×9×0×6×9×4×6÷4+1-9
Answer:
-8
Step-by-step explanation:
just put in in a calculator
Step-by-step explanation:
2×2×6×6×9×0×6×9×4×6÷4+1-9= -8
its simple just calculate in a calculater....
Find the radius of a sphere with a volume of 456cm^3
(show work)
Answer:
r≈4.775
Step-by-step explanation:
the formula for this is: r=(3V /4π)^⅓
The average daily sleep time for a domestic cat is 11.5 hours. What is this in hours and minutes?
b) An African lion sleeps 20% more than the cat. What is the sleep time of the African lion?
mathematics PLEASE HELP
Part A
1 hour = 60 minutes
0.5 hours = 30 minutes (multiply both sides by 0.5)
11.5 hours = 11 hours + 0.5 hours
11.5 hours = 11 hours + 30 minutes
11.5 hours = 11 hours, 30 minutes is the answer
========================================
Part B
20% = 20/100 = 0.20
The lion sleeps 20% more than the cat, which means the lion sleeps 0.20*11.5 = 2.3 hours more
This leads to 11.5 + 2.3 = 13.8 hours being the total time the lion sleeps
1 hour = 60 minutes
0.8 hours = 48 minutes (multiply both sides by 0.8)
13.8 hours = 13 hours + 0.8 hours
13.8 hours = 13 hours + 48 minutes
13.8 hours = 13 hours, 48 minutes is the amount of time the lion sleeps
If you go on a road trip of 270 miles in the mountains and 7/10 of the trip is downhill, how many miles of the trip are not downhill? Reduce to the lowest terms.
Answer:Answer:
81 miles
Step-by-step explanation:
From the question 7/10 of the trip has been said to be downhill. It therefore means that 3/10 is not downhill.
Miles = 270
Downhill = 7/10
Not downhill = 3/10
Now we have To calculate Miles that are not downhill (uphill)
But first I calculated for the number of downhill miles
270x7/10
Downhill = 189 miles
To get the number of not downhill miles
I subtracted 189 from the total number of miles on the question.
270 - 189
= 81 Miles.
Therefore 81 Miles of the trip are not downhill.
If you have anymore questions or need clarity please let me know on the comment section. Thank you and Good luck!
Step-by-step explanation:
15m + (- 5m) combine like terms
Answer:
10 m
Step-by-step explanation:
15m - 5m = 10 m
both numbers have m which are alike
Answer: 10m
Step-by-step explanation: you subtract five from fifteen
Please help me out with this!
third
hope it helps you
Answer: (6^-8/7^-12)
Step-by-step explanation:
In this type of problems, you apply the laws of indices which stated that
( a²/b²)³ =( a²×³/b²×³)
= ( a6/b6)
From this question now, applying the above principle
(6²/7³)-4
= (6²×-⁴/7³×-⁴)
= (6^-8/7^-12)
So the answer is C
Which numbers are factors of 32? Check all that apply.
1
2
3
4
6
8
Answer:
The answer is, 1,2,4, and 8
Step-by-step explanation: