Answer:
x
4
−5x
2
+4
To factor the expression, solve the equation where it equals to 0.
x
4
−5x
2
+4=0
By Rational Root Theorem, all rational roots of a polynomial are in the form
q
p
, where p divides the constant term 4 and q divides the leading coefficient 1. List all candidates
q
p
.
±4,±2,±1
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
x=1
By Factor theorem, x−k is a factor of the polynomial for each root k. Divide x
4
−5x
2
+4 by x−1 to get x
3
+x
2
−4x−4. To factor the result, solve the equation where it equals to 0.
x
3
+x
2
−4x−4=0
By Rational Root Theorem, all rational roots of a polynomial are in the form
q
p
, where p divides the constant term −4 and q divides the leading coefficient 1. List all candidates
q
p
.
±4,±2,±1
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
x=−1
By Factor theorem, x−k is a factor of the polynomial for each root k. Divide x
3
+x
2
−4x−4 by x+1 to get x
2
−4. To factor the result, solve the equation where it equals to 0.
x
2
−4=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. Substitute 1 for a, 0 for b, and −4 for c in the quadratic formula.
x=
2
0±
0
2
−4×1(−4)
Do the calculations.
x=
2
0±4
Solve the equation x
2
−4=0 when ± is plus and when ± is minus.
x=−2
x=2
Rewrite the factored expression using the obtained roots.
(x−2)(x−1)(x+1)(x+2)
the set of non integers
Step-by-step explanation:
A non negative integer is an integer that that is either positive or zero. It's the union of the natural numbers and the number zero
Can whoever answers this give a full explanation of what numbers i'm supposed to put (screenshot is there)
Long division is easier than you think. Here's how to solve this problem:
1. See how many times 36 can go into 66.
Multiply until you reach a number that is closest (or exact) to 66.
36 x 1 = 36; 36 x 2 = 72.
72 is over 66, so 2 doesn't work. Therefore, we'd put "1" in the first space on the shelf (right above the 6).
2. Subtract.
Now that we have "1" on the shelf, you need to subtract 36 by 66. We do this because 36 x 1 is 36. If it were the number "2" on the shelf, we'd subtract 72, and so on.
66 - 36 = 30.
3. See how many times 36 can go into 30.
Since it can't go into 30, we bring the 3 down (hence the arrow pointing down). The number is now 303.
4. See how many times 36 can go into 303.
I won't write it all out, but after multiplying 1-7 by 36, we find that the closest solution is 36 x 8 = 288.
We put "8" on the shelf, next to "1".
5. Subtract.
Now that "8" is on the shelf, we subtract 288 by 303, which gives us 15.
Since 36 cannot go into 15, and there are no more numbers we can drag down, your remainder is 15.
Your answer is:
36 R 15
The first two boxes under 663 should be filled with 36, the next three under that should have 303, the next three should have 288, and the final two boxes should have 15.
I hope this helped!
Jayana is trying to run a certain number of miles by the end of the month. If Jayana is 30% of the way to achieving her goal and she has already run 9 miles, how many miles is she trying to run by the end of the month?
Find the exact length of the third side.
68
51
Answer:
The value of c is:
c=85 unitsStep-by-step explanation:
Given the right-angled triangle
a=68b=51And we have to determine the value of the hypotenuse 'c'.
c=?
Pythagorean Theorem:
For a right-angled triangle with sides a and b the hypotenuse c
[tex]c=\sqrt{a^2+b^2}[/tex]
[tex]a=68[/tex]
[tex]b=51[/tex]
[tex]c=\sqrt{68^2+51^2}[/tex]
[tex]c=85[/tex] units
Thus, the value of c is:
c=85 units
can someone help, please! also i'm giving brainliest
2 = Distributive Property (you are distributing the -5 to the x and the -6)
1 = Given (its the original equation)
3 = Addition Property of Equality (you add 5x to both sides)
4 = Division Property of Equality (you divide both sides by 15)
17 people over max capacity as an expression is what?
Answer: x + 17
Step-by-step explanation:
if capacity is x, 17 is added to x, hence x + 17
The cost to rent a car is $25 plus an additional $0.15 for each mile the car is driven. How many miles was a car driven if it had a bill of $71.80? 479 645 454 312
Answer:
The answer is 312.
Step-by-step explanation:
Because you would start with 71.80 minus 25 to get 46.8 then do 46.8 divided by 0.15 to get 312.
Answer:
312
Step-by-step explanation:
What is the average rate of change of f over the interval -7 < or equal to x
Give an exact number
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
The average rate of change can be found by using the following formula
[tex]\frac{f(x_{2}) - f(x_{1}) }{x_{2} - x_{1}}[/tex]
Since the interval goes from -7 to 2, we should find the y-values that correspond to x=-7 and x=2.
By inspection of the graph, we can clearly see that when x is -7, y is -7 as well and when x is 2, y is 5.
Now that we know this, we can simply plug these values into the formula!
[tex]\frac{f(2) - f(-7) }{2 - (-7)} = \frac{5 - (-7)}{2 - (-7)} = \frac{5 +7}{2+7} = \frac{12}{9} = \frac{4}{3}[/tex]
Good luck!
Solve the equation by finding the common multiple.
three fourths minus two sixths plus seven twenty fourths equals blank
Help!
1253/9997 or 0.12534
My explanation~3/4 - 2/6 + 7/24
convert into decimals3/4 = 0.75
2/6 = 0.333
7/24 = 0.29166
then use PEMDAS add first0.333 + 0.29166 =
0.62466
then subtract0.75 - 0.62466 =
0.12534
then convert back or leave as is1253/9997
what you would get when converting back to a fractionhope i helped :P---------------------------------------------------------------Answer: 11/6 that is it!
Write the translation notation for 2 units left and 3 units up
Answer:
(-2,3)
Step-by-step explanation:
The left and down is negative and right and up is positive
Solve for theta to the nearest degree
Step-by-step explanation:
So first thing is to determine which trigonometric ratio we use here. Theta is adjacent to 5 and 8 is the hypotenuse, so we should be using Cosine.
So we set up the equation
cos θ = adj/hype
cos θ = 5/8
θ = [tex]cos^{-1} (5/8)[/tex]
θ=51.3178125...
θ=51°
1
A line has a slope of -2 and a y-intercept of -2.
7
6
6
4
3
1
3-7-6-5-4-3-2-1
1 2 3
6 67
X
-3
4
-
--7-
What is the x-intercept of the line?
Answer:
-1
Step-by-step explanation:
When writing an equation in slope-intercept form, you need the values of the
Answer:
slope, m
y-intercept
Step-by-step explanation:
When writing an equation in slope-intercept form, there will be need for slope and y- intercept.
What is the slope intercept form of an equation ?When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.
Here m is slope and c is constant.
To writing the slope intercept form of the equation,
There will be requirement of slope,
and y intercept, it will be in form of (0, a), here a will be value of y coordinate.
To know more about Slope intercept form :
https://brainly.com/question/9682526
#SPJ2
Anyone know how to do identify the features?
Adams High School is going to select a committee. The committee will have a faculty member, a male student, a female student, a parent, and a school board member. Here are the positions and the people interested in each. Position People interested Faculty member Mr. Jackson, Mrs. Washington Male student Tom, Omar, Keith, Justin Female student Donna, Charmaine, Rita, Keiko Parent Dr. Ward, Ms. Allen, Mrs. Flores, Mrs. Smith School board member Dr. Davis, Ms. Young, Mrs. King, Mr. Adams Based on this list, how many ways are there to fill the five committee positions?
Answer:
512 ways
Step-by-step explanation:
Given
Selection
Faculty Member = 1
Male Student = 1
Female Student = 1
Parent = 1
School Board Member = 1
Select from:
Faculty Member = 2
Male Student = 4
Female Student = 4
Parent = 4
School Board Member = 4
Required
Determine how many ways they can be selected
There are 2 faculty members of which 1 will be selected from.
Any of these two members may be selected.
So, Selection = 2
There are 4 male students of which 1 will be selected from.
Any of these four students may be selected.
So, Selection = 4
There are 4 female students of which 1 will be selected from.
Any of these four students may be selected.
So, Selection = 4
There are 4 parents of which 1 will be selected from.
Any of these four parents may be selected.
So, Selection = 4
There are 4 school board members of which 1 will be selected from.
Any of these four members may be selected.
So, Selection = 4
Total number of selection is then calculated as thus:
[tex]Selection = 2 * 4 * 4 * 4 * 4[/tex]
[tex]Selection = 512[/tex]
Hence, there are 512 ways
What is the slope of the line that passes through the points (1,-6) and (-8,9)
Answer:
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1) = (9+6)/(-8-1) = -15/9
= -5/3
The next event requires each runner to jump 8 hurdles that are spaced 12.3 meters
apart. If there are 15 meters from the starting line to the first hurdle and 10.5 meters
from the last hurdle to the finish line, how long is the race? Show your work.
Answer:The race is 111.6
Step-by-step explanation:The race is 111.6 m long.
8 hurdles spaced 12.3 m apart means 7 spaces that are 12.3 m in length; 7*12.3 = 86.1
Add to this the distance to the first hurdle and the distance from the last hurdle:
86.1+15+10.5 = 111.6 m
Step-by-step explanation:
Answer:
If I am incorrect, please let me know.
Step-by-step explanation:
This is the work I did.
Please mark me brainliest :)
find the slope of the line passing through each pair of points. if the slope is undefined, write undefined. (5,9) and (5,-3)
Answer:
i believe undefined
Step-by-step explanation:
Slope
m= −3−9
5−5
-12/0
Find the distance between 5 + 4i and 9 + 3i.
Answer:
Distance = √17
Step-by-step explanation:
We are looking for the distance between 5 + 4i and 9 + 3i.
This is as equal to saying we have two points in the plane, whose coordinates are; (5, 4) and (9, 3)
Distance between the 2 points will be;
D = √[(5 - 9)² + (4 - 3)²]
D = √(16 + 1)
D = √17
same question again. ugh
Answer:
-3
Step-by-step explanation:
the slope is -3 because it goes down 3 y for every 1 forward on x
Answer:
[tex]m=-3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula (Rate of Change): [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (1, -3)
Point (-1, 3)
Step 2: Find slope m
Substitute: [tex]m=\frac{3+3}{-1-1}[/tex]Add/Subtract: [tex]m=\frac{6}{-2}[/tex]Divide: [tex]m=-3[/tex]The answer. X=7 Ik that
Answer:
C: 147°
Step-by-step explanation:
Based on looking, the most appropriate answer should be C, which is 147°.
will mark brainliest
ONE question with picture included^^^^
Answer:
The third option is wrong becuase x isn't a defined variable, and they specified that the book must be at least 250 pages, which means that it can't be less.
A grocery store sells a bag of 3 oranges for $1.71. How much does one orange cost?
Answer: 57 cents each
Answer:
57 cents
Step-by-step explanation:
divide the amount of money by the amount of oranges to find the amount each of them are. so if each of them are 57 then 1 is 57.
What value of x is in the solution set of 2x. 3 > 11 - 5x?
a. -3
b. 0
c. 2
d. 4
Answer:
i think option d
Answer:
The answer is D : 4.
Step-by-step explanation:
=2x-3>11-5x
=2x-3+5x>11
=7x-3>11
=7x>11+3
=7x>14
=7x/7>14/7
=x>2
By simplifying the problem, you can see that "x" must be greater than 2. Therefore, eliminating all other possible answers that are shown, but 4.
I answered the same questions with the same exact wording and explanation so please don't report any answers that are the same as this one, they are all mine and written by me.
There are 72 female performers in a dance recital. The ratio of men to women is 2:9. How many men are in the dance recital?
Answer:
48
Step-by-step explanation:
72 ÷ 3 = 24
so you know that the men is 24 × 2 = 48
48:72 = 2:3
i looked it up and it says x=4 and theres 12 men but i dont think that helps im so sorry i couldnt find anything:(
find the midpoint of the segment with the following endpoints. (8,10) and (1,4) ?
Mark uses 19 gallons of gas while traveling 399
miles at a constant rate in his car. How many
miles is Mark able to travel on 9 gallons of gas?
Answer:
189
Step-by-step explanation:
If mark uses 19 gallons to travel 399 miles, that means he was able to travel 21 miles per gallon.
We get this by taking 399 divided by 19.
So if mark travels on 9 gallons of gas and goes 21 miles per gallon, he will have traveled 189 miles.
We get this by taking 21 times 9
Jackson is at colletibles fair. He has exactly $8 and will purchase a collectibles card from a vendor for $5. What percentage will jackson spend on the purchase?
A. 0.625%
B. 3%
C. 40%
D. 62.5%
Please help me out or explain how do i do it, but if you give me the answer ill give you brainliest!
What is the y-intercept of the function f(x) = -2/9x + 1/3x?
Answer:
Step-by-step explanation:
THE DOTS SHOWN REPRESENT WHAT KIND OF SEQUENCE?
D is for difference
R is for ratio
Arithmetic is Adding
Geometrical is Multiplying
