The factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
The polynomial function is given as:
[tex]P(x) = x^3 + 4x^2 - 9x - 36[/tex]
Factorize the given expression.
[tex]P(x) = x^2(x + 4) - 9(x +4)[/tex]
Factor out x + 4
[tex]P(x) = (x^2 - 9)(x +4)[/tex]
Express 9 as the square of 3
[tex]P(x) = (x^2 - 3^2)(x +4)[/tex]
Apply the difference of two squares
[tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
Hence, the factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
Read more about factorization at:
https://brainly.com/question/11434122
35 out of 50 students in a class wear glasses. What percentage of students in the class wear glasses?
Answer:
70%
Step-by-step explanation:
Percentage is out of 100
35/50 change denominator
multiply both numerator and denominator by 2
70/100= 70%
6c = 2p – 10. write the equation in function notation, where c is the independent variable.
Answer:
p(c) = 3c +5
Step-by-step explanation:
Effectively, you want to solve for p.
6c = 2p -10
6c +10 = 2p
3c +5 = p
p(c) = 3c +5 . . . . function notation (p is a function of c)
-0.7=-7/9z help me pleasseeee!
Find the 62nd term of the arithmetic sequence
15, 13, 11, ...
Answer:
[tex]a_{62}=-107[/tex]
Step-by-step explanation:
This is an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
where d is the common difference and n is the index of any given term.
The common difference of the given sequence is -2:
[tex]13-15=-2\\11-13=-2[/tex]
Using the first term and the common difference, you can write the equation for this sequence:
[tex]a_n=15+(n-1)(-2)[/tex]
And using that equation, you can find the 62nd term:
[tex]a_{62}=15+(62-1)(-2)\\a_{62}=15+(61)(-2)\\a_{62}=15-122\\a_{62}=-107[/tex]
A car travels at an average rate of speed of 60 miles per hour for 72 hours. How many miles does
this car travel?
Answer:
4320 miles
Step-by-step explanation:
distance= speed× time
60 ×72= 4320
Can someone plz help me?
Answer:
d
Step-by-step explanation:
I got it right on my quiz
can anyone help me plz
Answer:
x = 24
Step-by-step explanation:
x/4 + 10 =16
-10 -10
x/4 = 6
*4 *4
x=24
hope this helps! :)
PT. 5 OF MY HW!!! ITS UNIT RATE!!!
Answer: The second pool is filled at a faster rate (3,600 gal/h) than the first pool (1,300 gal/h)
Step-by-step explanation:
A boat can travel 120 kilometers on 60 liters of gas. How far can it travel on 197 liters
Answer:
394 km
Step-by-step explanation:
197 is 197/60 times as much as 60
so the distance is also that much more: 120 km * 197/60 = 394
Oceanside Bike Rental Shop charges a 13 dollars fixed fee plus 7 dollars an hour for
renting a bike. Keith paid 69 dollars to rent a bike. How many hours did he pay to have
the bike checked out? Let h = number of hours bike was checked out
Answer:
8 hours
Step-by-step explanation:
69-13=56
56/7=8
13+7h=69
Find the surface area of the cuboid.
Answer:
62 cm²
Step-by-step explanation:
The surface area (SA) is the sum of the areas of the 6 faces.
The opposite faces are congruent, then
SA = area of front/ back + area of top/ bottom + area of 2 sides
= 2(5 × 3) + 2(5 × 2) + 2(3 × 2)
= 2(15) + 2(10) + 2(6)
= 30 + 20 + 12
= 62 cm²
PLEASE HELP
5) Which function represents the relationship between x and y?
A) y = x + 2
B) y = 2x
C) y = x + 4
D) y = x-2.
Answer:
A) y=x+2
Step-by-step explanation:
We can see that each time x increase by 2, y also increases by 2. The slope of the line formed by this equation is therefore 1. But we start out with y = 2, even when x=0. That's the definition of the y-intercept: the value of y when x is equal to zero.
The slope-intercept form of a straight line equation is y = mx + b, where m is the slope (1, in this case) and b is the y-intercept (0 in this case).
We have y = 1x + 2, or y = x + 2
Evalute the expression X=6 y=-4 -3y+x
Answer:
y= 1/2
Step-by-step explanation:
y=-4 -3y+x
<=> y + 3y = -4 + x
<=> 4y = -4 + 6
<=> 4y = 2
<=> y = 1/2
Write the equation 5x + 2y = -6 in general form.
Answer:
[tex]5x+2y+6=0[/tex]
Step-by-step explanation:
General equations are in the form [tex]Ax + By + C = 0[/tex]
So you can add 6 to both sides to make:
[tex]5x+2y+6=0[/tex]
what is 3 1/3, 3.337,33/10,3.11 from least to greatest
Answer:
1/3 < 3 < 33/10 < 3.337 < 3.11
Step-by-step explanation:
A line L is parallel to the line 2x-5y-8=0. What is the gradient of the line
Answer:
2/5
Step-by-step explanation:
1) rearrange the equation in the form y=mx+c where m is the gradient and y is the y intercept
2x-5y-8=0
add 5y to both sides
2x-8=5y
divide 5 on both sides
2/5x - 8/5 = y
overall equation is y=2/5x-8/5
the gradient is 2/5
It takes Amy twice as long to deliver papers as it does Nancy. How long would it take each girl to deliver the papers by herself if they can deliver the papers together in 36 minutes?
Answer:
so if it takes twice all long for amy as nacy that means
Amy takes 2/3 or 0.6(aprox)
Nacy takes 1/3 or 0.3(aprox)
Amy=24
Nacy=12
Hope This Helps!!!
QUICK I NEED HELP….PLZ Hurry!! ;-;
Which equation represents a liner function
Equation 1: Y=2x+1
Equation 2: Y^2= 3x+1
Equation 3: y=5x^5-1
Equation 4: Y= 4x^4-1
Answer: Equation 1: Y=2x+1
Step-by-step explanation:
Need help ASAP! Problem and directions in picture;)
What is the value of ?
[tex]50 + angle \: \: u \: \: = 115 \\ = > angle \: \: u \: = 115 - 50 \\ = > angle \: \: u \: \: = 65[/tex]
Answer:
Angle U is 65°.
Hope you could get an idea from here.
Doubt clarification - use comment section.
How do u Keep change change this number???
1.3 - -300=????
I don’t know what to do
solve for x and graph the solution on the number line
Answer:
[tex]\boxed{\sf x\ge \:-1}[/tex]
Step-by-step explanation:
[tex]\sf 4x\ge \:-4[/tex]
Divide both sides by 4:
[tex]\sf \cfrac{4x}{4}\ge \cfrac{-4}{4}[/tex][tex]\sf x\ge \:-1[/tex]__________________________________
Please help me with this problem I will give brainpower to the first person that answers this correctly with an explaination
Hi!
To solve this, we can set up an equation. If L, the length, is 3 less than 2 times W, the width, it would look like this. L = 2w - 3
Now, the perimeter equation is L + L + w + w = 48, so we plug in the L's and get this:
2w - 3 + 2w - 3 + w + w = 48
Now solve, add like terms:
6w - 6 = 48
add 6 to both sides
6w = 54
divide both sides by 6
w = 9
The width is 9, and the length is two times this minus 3, so 2(9) - 3 = 18 - 3 = 15
Therefore your width is 9 and your length is 15
Hope this helps! :D
Can someone help me with this
giving out brainliest
Answer:
C
Step-by-step explanation:
Step 1: plot your 2 known points, (-2,3) and (1,0)
Step 2: after that, you should see that your y value should be a - and your x a +. You can eliminate A and B.
Step 3: check to see if C is a correct answer, (4,-3)
C is the answer, hope that helps
Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?
Answer:
B.
Step-by-step explanation:
Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?
She bought a total of 17 apples and lemons combined.
So the equation that would represent this is,
l + a = 17.
Each apple costs 35¢ and each lemon costs 15¢. All the lemons and apples cost $3.95 togther.
So the equation that would represent this is,
0.15l + 0.35a = $3.95
Can i get some help :
Answer:
b = [tex]\frac{7}{12}[/tex]
Step-by-step explanation:
b + [tex]\frac{2}{3}[/tex] = 1 [tex]\frac{1}{4}[/tex] ← change to an improper fraction
b + [tex]\frac{2}{3}[/tex] = [tex]\frac{5}{4}[/tex]
Multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions
12b + 8 = 15 ( subtract 8 from both sides )
12b = 7 ( divide both sides by 12 )
b = [tex]\frac{7}{12}[/tex]
Answer:
The value of b is 7/12.
Step-by-step explanation:
Question :
Solve for b.
[tex]{\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]
Enter your answer as a fraction in simplest form in the box.
[tex]\implies{\sf{b = \square}}[/tex]
[tex]\begin{gathered}\end{gathered}[/tex]
Solution :
[tex]{\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]
Converting the mixed fractions into improper fraction.
[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{(1 \times 4) + 1}{4}}}}[/tex]
[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{(4)+ 1}{4}}}}[/tex]
[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{4+ 1}{4}}}}[/tex]
[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{5}{4}}}}[/tex]
Now, transporting LHS to RHS.
[tex]{\implies{\sf{b= \dfrac{5}{4} - \dfrac{2}{3}}}}[/tex]
Taking LCM of denominators and subtracting.
[tex]{\implies{\sf{b= \dfrac{(5 \times 3) - (2 \times 4)}{12}}}}[/tex]
[tex]{\implies{\sf{b= \dfrac{(15) - (8)}{12}}}}[/tex]
[tex]{\implies{\sf{b= \dfrac{15 - 8}{12}}}}[/tex]
[tex]{\implies{\sf{b= \dfrac{7}{12}}}}[/tex]
[tex]{\star{\red{\underline{\boxed{\sf{b= \dfrac{7}{12}}}}}}}[/tex]
Hence, the value of b is 7/12.
[tex]\begin{gathered}\end{gathered}[/tex]
Verification :
[tex]{\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]
Substituting the value of (b=7/12)
[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]
Converting mixed fractions into improper fraction
[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{(1 \times 4) + 1}{4}}}}[/tex]
[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{(4) + 1}{4}}}}[/tex]
[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{4 + 1}{4}}}}[/tex]
[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{5}{4}}}}[/tex]
Taking LCM of denominators in LHS and adding.
[tex]{\implies{\sf{ \dfrac{(7 \times 1) + (2 \times 4)}{12} = \dfrac{5}{4}}}}[/tex]
[tex]{\implies{\sf{ \dfrac{(7) + (8)}{12} = \dfrac{5}{4}}}}[/tex]
[tex]{\implies{\sf{ \dfrac{7 + 8}{12} = \dfrac{5}{4}}}}[/tex]
[tex]{\implies{\sf{ \dfrac{15}{12} = \dfrac{5}{4}}}}[/tex]
Cutting the fraction to simplest form.
[tex]{\implies{\sf{ \cancel{\dfrac{15}{12}} = \dfrac{5}{4}}}}[/tex]
[tex]{\implies{\sf{ \dfrac{5}{4}= \dfrac{5}{4}}}}[/tex]
[tex]{\star{\red{\underline{\boxed{\sf{LHS = RHS}}}}}}[/tex]
Hence Verified!
[tex]\underline{\rule{220pt}{3.5pt}}[/tex]
Li designed a survey to determine how comfortable students at her middle school are with fractions. There are 600 students in her middle school. The students are equally distributed among grade levels. She selected a sample of 28 students in her first-period class. Which best explains Li’s sample? random and biased random and unbiased nonrandom and biased nonrandom and unbiased.
Answer:
unbiased nonrandom
Step-by-step explanation:
By picking only people from 1st period they are not random.
They haven't said anything that would make these people biased.
Answer:
unbiased nonrandom
Step-by-step explanation:
Combine the like terms to create an equivalent expression
−4q-(-8p)+10
Answer:
Step-by-step explanation:
−4q-(-8p)+10
= -4q + 8p + 10.
(There are no like terms).
Can someone help me, please? :(((
[tex]\huge \sf༆ Answer ༄[/tex]
According to given figure ~
Area of whole is equal to :
Area of Triangle + Area of rectangleAnd,
Area of Triangle :
[tex] \sf \dfrac{1}{2} ( 7 \times 6)[/tex]Area of Rectangle :
[tex] \sf7 \times 3[/tex]Therefore, the Area of whole figure is ~
[tex] \boxed{ \sf (7 \: • \: 3) + \frac{1}{2}(7 \: • \: 6)}[/tex]So, the Correct choice is ~ A
x+1=x+2 is there a solution
Answer:
No Solution
Step-by-step explanation:
This is impossible. x+1 is not x+2
Variables are always the same: x=x
Answer:
No their isn't
Step-by-step explanation:
who was often called the father of modern mathematics because he created analytic geometry and the cartesian coordinate system?
Answer:
I believe Descartes
Step-by-step explanation:
René Descartes was one of the key figures in the Scientific Revolution of the 17th Century.