Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Example: x²+3x+5 is a polynomial.
The polynomial whose factors are (a²-6) and (a²+4) is,
P(x) = (a²-6)(a²+4)
= a⁴ + 4a² - 6a² - 24
= a⁴ - 2a² - 24
Hence, The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.
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What is the domain of the function y=2√x-6?
88AX<∞
O 0≤x<∞
3≤x<∞
6≤x<∞
Answer:
If the x-6 is all under the sqrt, the last answer is right:
6<= x <= infinity
If only x is under the sqrt and - 6 is NOT under the sqrt, then:
0 <= x <= infinity is the correct answer.
Step-by-step explanation:
You can look at the equation and or graph to determine the domain of a function. The domain is all the x's that may go into the equation or all the x's on the graph of the function. Inside of a squareroot symbol the number inside there must be positive. While considering the equation, only x's that keep that inside positive can be used.
For sqrt(x-6), x has to be 6 or bigger.
For sqrt(x) - 6, x has to be 0 or bigger.
The amount of money spent buying packets of instant noodles varies directly
with the number of packets purchased. If 30 packets of noodles cost $34.88,
how much would 45 packets cost? Round all answers to the nearest hundredth
in your calculations.
A. $38.70
B. $52.20
C. $25.83
D. $43.00
The cost of 45 packets of instant noodles given the direct variation is $52.335
Direct variationlet
Amount spent on noodles = nNumber of Packets purchased = pn = k × p
Where,k = constant of proportionality
34.88 = k × 30
34.88 = 30k
k = 34.88/30
k = 1.16266666666666
Approximately,
k = 1.163
Find n when p = 45
n = k × p
= 1.163 × 45
n = $52.335
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find the values of x for the following equations..[tex]x^{2} +4x-98=0[/tex]
Hello !
Look at the picture
A school year begins with 24 students
trying out for the basketball team and 20
students trying out for the debate team.
Within a week, 6 students have dropped
out of the basketball tryouts and 2
students have dropped out of the debate
tryouts. What percentage of the remaining
students are trying out for the basketball
team?
Answer:
50%
Step-by-step explanation:
In rhe beginning, there were 24 + 20 = 44 students trying out in total. After a week, there are 44 - 6 - 2 = 36 students remaining. Of those 36 students, 18 of them are trying out for the basketball team. The percentage of students trying out for the basketball team would be 18/36 = 0.5 = 50%
Write an expression that is equivalent
1/2a-4
Step-by-step explanation:
Answer
a - 8
------------+
2
One number is 2 less than a second number. Twice the second number is 5 less than 3 times the first. Find the two numbers.
Answer:
9 and 11
Step-by-step explanation:
First number = x -2
Second number = x
and 2x = 3(x-2) - 5
2x = 3x - 6 - 5
x = 11
first number = 11-2 = 9
Question
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third
side of each triangle.
с
y = c =
6.5
Provide your answer below:
A
12
C
B
Z
y
4.8
3
Y
Answer:
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle
SOMEONE PLS ANSWER STEP BY STEP TY
9k-2≥88 or -34 -4> -25
Hello,
9k - 2 88
⇔ 9k - 2 + 2 ≥ 88 + 2
⇔ 9k ≥ 90
⇔ 9k/9 ≥ 90/9
⇔ k ≥ 10
S = [10 ; + ∞ [
Answer:
k ≥ 10
Step-by-step explanation:
9k - 2 ≥ 88
Step 1 : Add 2 on both sides.
9k - 2 + 2 ≥ 88 + 2
9k + 0 ≥ 90
9k ≥ 90
Step 2 : Divide 9 on both sides.
9k/9 ≥ 90/9
k ≥ 10
7. How many triangles exist when the angle measures are 90°, 90°, and 0°? 2 POINTS
Answer: None
Step-by-step explanation:
There is no triangle with an angle measure of 0 degrees.
find the least number that must be subtracted from 21 2o show the result is a perfect square
Answer:
5
Step-by-step explanation:
2 × 2 = 4
3× 3 = 9
4 × 4 =16
5 × 5 =25
16 is the only number and closest number to 21 to subtract from
Answer two questions about Systems A and B:
−3x−2y=4
5x−8y=−1
5x−8y=−1
−3x−2y=4
1) How can we get System B from System A?
Choose 1 answer:
Swap the order of the equations
(Choice A, Checked, Correct)
CORRECT (SELECTED)
Yes
For the given systems we have:
1) Just swap the equations in system A.
2) Yes, the systems are equivalent.
How can we get System B from System A?Here we have the systems:
A:
-3x - 2y = 4
5x - 8y = -1
B:
5x - y = -1
-3x - 2y = 4
Notice that we have the same equations, just in a different order. So if we swap the first and second equations in system A, we get system B.
Are the systems equivalent?
Yes, because both systems are defined by the same equations.
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twenty six thousandths in numerical form
Answer:
0.026
Step-by-step explanation:
Twenty-Six = 26 ( But for simplicity in the Next Step write it as 26.)
Tenths means to move the Decimal Point 1 Place LeftHundredths means to move the Decimal Point 2 Place LeftThousandths means to move the Decimal Point 3 Place LeftThen Twenty-Six Thousandths = 0.026
Jenny likes to paint. she estimates the number of paintings she completes using the function p of w equals one half times w plus one, where w is the number of weeks she spends painting. the function j(y) represents how many weeks per year she spends painting. which composite function would represent how many paintings jenny completes in a year?
The composite function of the paintings Jenny completes in a year is
[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]
What is a composite function?A composite function is a function made of other functions, where the output of one function is the input to the other function.
An example of the composite functions 2x+3 and [tex]x^{2}[/tex] together make the composite function [tex](2x+3)^{2}[/tex]
We have [tex]P(w)=\frac{1}{2}w+1[/tex]
Here, P(w) represents the number of paintings Jenny completes in some w weeks. and
J(y) represents the number of weeks per year.
As J(y) is the number of weeks spent per year in painting, we can calculate the paintings completed in a year by substituting
w as J(y) in the equation we have
Then the equation becomes:[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]
Hence this is the composite function that would represent the number of paintings Jenny completes in a year.
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which variable expression describes the area of the shaded region in the diagram shown below ?
Answer: B
Step-by-step explanation:
The area of entire rectangle is (9)(4)=36.
The area of the square inside is [tex]x(x)=x^2[/tex]
Subtracting the areas, we get [tex]36-x^2[/tex]
James needs to mix a 10% acid solution with a 50% acid solution to create 100 milliliters of a 26% solution. How many milliliters of each solution must James use?
James must mix _____ milliliters of 10% solution and____milliliters of 50% solution.
James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.
Given that, James needs to mix a 10% acid solution with a 50% acid solution to create 100 millilitres of a 26% solution.
Let the acid solution needs to mix with 10% be x ml and the acid solution needs to mix with 50% will be 100 - x ml.
Now,
10% x + 50% ( 100 - x ) = 26% ×100
⇒[tex]\frac{10x}{100} +\frac{50(100-x)}{100}=\frac{2600}{100}[/tex]
⇒10x + 50( 100 - x ) = 2600
⇒10 x + 5000 - 50x = 2600
⇒10 x - 50 x = 2600-5000
⇒-40 x = -2400
⇒x=60
Therefore, James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.
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The sum of two numbers is 21. Three times the larger is equal to four times the smaller.
Find them.
Below, the two-way table is given for a class
of students.
Freshmen
Sophomore
Juniors
Seniors
Total
Male
4
Female
3
6
3
Total
If a student is selected at random, find the
probability the student is a female given that it's a
junior.
Using it's concept, the desired probability is:
P(Female|Junior) = 75%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 8 Junior Students, out of which 6 are Female, hence the probability is:
P(Female|Junior) = 6/8 = 0.75 = 75%.
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HELP QUICK! You must find all intervals
where f(x) is negative.
f(x)=2(x+3)(x-7)
Answer:
any # where -2<=x<7
Step-by-step explanation:
(x-7) would be negative and (x+3) positive, resulting in f(x) being negative.
Samantha is going to run in a 5K race. To prepare, she wants
to run an average of 40 minutes a day until the marathon
on Saturday. She ran 45 minutes on Monday, 30 minutes on
Tuesday, 55 minutes on Wednesday, and 25 minutes on
Thursday. How long should she run on Friday to reach her
goal?
The number of minutes Samantha needs to run on Friday to reach her goal is 45 minutes.
AverageMonday = 45 minutesTuesday = 30 minutesWednesday = 55 minutesThursday = 25 minutesFriday = x minutesAverage = (Monday + Tuesday + Wednesday + Thursday + Friday) / 5
40 = (45 + 30 + 55 + 25 + x) / 5
40 × 5 = 155 + x
200 = 155 + x
200 - 155 = x
45 = x
x = 45 minutes
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if one adult is randomly chosen from the group, what is the probability that the adult does not use a cell phone app for shopping and is at least 40 years old?
Answer:
1/100
Step-by-step explanation:
The answer is 1/100 because we don't know how many people are in the group but do know that only 1 person has been taken from the group and the probability will be 1 out of how many people are in the group so we just put 100 there as we don't know how many people are in the group.
Ps: Sorry if this is wrong, this is just a guess.
Find the equation of a straight line which passes through the point (3, 2) and is perpendicular to the line 3x + 5y =10. Hence, determine the gradient and y-intercept of the equation.
Answer:
Step-by-step explanation:
eq of line perpendicular to 3x+5y=10 is
5x-3y=a
where a is constant.
it passes through (3,2)
5(3)-3(2)=a
a=15-6=9
reqd. eq. is 5x-3y=9
or
3y=5x-9
y=5/3 x-3
gradient=5/3
y-intercept=-3
or
5y=-3x-10
y=-3/5 x-2
slope=-3/5
slope of reqd. line=-1/(-3/5)=5/3
eq. of line through (3,2) is
y-2=5/3(x-3)
3y-6=5x-15
3y=5x-15+6
3y=5x-9
y=5/3 x-3
Instructions: Determine if AB is tangent to the circle.
AB
20
B
12
수 to the circle.
16
Step-by-step explanation:
to be a tangent, it would have to have a 90° angle with the radius (12).
and that would make the triangle ABCenter of the circle a right-angled triangle.
and then Pythagoras must apply :
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle). in our case the 20-line.
so,
20² = 12² + 16²
400 = 144 + 256 = 400
yes, it is confirmed, because the Pythagoras principle applies, it is a right-angled triangle, and therefore AB is indeed a tangent.
Answer:
the line AB is tangent to the circle
Step-by-step explanation:
we have :
16² + 12² = 256 +144 = 400
On the other hand:
20² = 400
Then
16² + 12² = 20²
Then
According to the Pythagorean theorem:
The line AB is perpendicular to the radius of the circle
Which means the line AB is tangent to the circle.
Simplify....
[tex] \frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{ {a}^{2} + 1 } - \frac{4a}{ {a}^{4} + 1 } \\ [/tex]
please help ty~
The simplified expression of [tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex] is [tex]\frac{8a}{a^8 - 1}[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]
Add the first two terms
[tex]\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]
Evaluate
[tex]\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]
Evaluate the first two terms
[tex]\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}[/tex]
Evaluate
[tex]\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}[/tex]
Take the LCM
[tex]\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}[/tex]
Evaluate the like terms
[tex]\frac{8a}{a^8 - 1}[/tex]
Hence, the simplified expression is [tex]\frac{8a}{a^8 - 1}[/tex]
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melissa worked 7 hours and 40 minutes last monday. she makes 16 dollars and hour.how much did she make for those hours she worked on that day?
Which graph represents this inequality Y is greater than or less to 4X -3
The graph of the inequality can be seen in the image at the end.
Which graph represents the inequality?
Here we have the inequality:
y ≥ 4x - 3
To graph this we need to graph the line:
y = 4x - 3
With a solid line (because the points on the line are solutions) and then shade the region above that line.
The graph of the inequality can be seen below.
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The function g(x) = 10x2 100x + 213 written in vertex form is g(x) 10(* - 5)2 - 37. Which statements are true
about g(x)? Select three options.
The axis of symmetry is the line x = -5.
The vertex of the
graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
.
The value of a, when the equation is written in vertex form, is negative.
Answer:
Step-by-step explanation:
The best way to answer a question like this one is to use a graphing program on the internet. This graph was done with desmos
It looks to me that the equation is g(x) = 10(x - 5)^2 - 37
I checked to see that this is correct, and thank goodness it is.
The vertex of the graph is (5, -37).The vertex has a minimumThe parabola opens upwardThe graph is shown below.
If [tex]\frac{w}{y} = \frac{y}{z} then what is the value of x?[/tex]
The value of x in the given expression is; x = wz/y
How to change subject of formula?We are given the expression;
w/x = y/z
Now, we want to find the value of x which means we want to make x the subject of the formula. Thus;
Multiply both sides of the given expression by x to get;
(w/x)*x = (y/z)*x
⇒ w = xy/z
Now, multiply both sides by z/y to get;
w(z/y) = (xy/z) * (z/y)
wz/y = x
Thus, the value of x in the given expression is;
x = wz/y
The correct question is;
If w/x = y/z, then what is the value of x
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Which expression is equivalent to 1/2 (2 - 5x + 6)?
0 -5/4x+2
O -5 +6 1/2
O - 5/4x+1
O-5x+8
I need help with this question please!
the price that they should charge on the 2 year extended warranty is in order to break even is $10.
what price should the company charge?the price at which the company would breakeven is:
= percentage of product that will fail x replacement cost
solving gives:
= 4% x 250
= $10
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Find f(−1) given f(x)=−3x3+2x2+24
A. -23
B. 28
C. 29
D. 23
Answer:
C. 29
Step-by-step explanation:
[tex]f(x) = -3x^3 + 2x^2 +24[/tex]
• To calculate [tex]f(-1)[/tex] , we have to replace x with -1 in the definition of [tex]f(x)[/tex] , and calculate the value:
[tex]f(-1) = -3(-1)^3 + 2(-1)^2 + 24[/tex]
⇒ [tex]-3(-1) +2(1) + 24[/tex]
⇒ [tex]3 + 2 + 24[/tex]
⇒ [tex]29[/tex]
[tex]\huge\boxed{\textsf{C.}\ 29}[/tex]
We have this equation:
[tex]f(x)=-3x^3+2x^2+24[/tex]
Substitute [tex]x=-1[/tex]:
[tex]f(-1)=-3(-1)^3+2(-1)^2+24[/tex]
Simplify to find the final answer:
[tex]\begin{aligned}f(-1)&=-3(-1)+2(1)+24\\&=3+2+24\\&=5+24\\&=\boxed{29}\end{aligned}[/tex]