PLEASE HELP!! please do all steps! i’ll mark as brainliest!!!
Answer the following questions using what you've learned from this unit. Write your
responses in the space provided.
1. Factor the polynomial. (2 polnts)
-3x4 - 9x3 + 15x2
2. Use the grouping method to factor the polynomial below completely. (4 points)
10x3 - 35x2 + 6x - 21
Answers
Answer: 1. 3x^2(-x^2-3x+5). 2. (2x-7)(5x^2+3)
Step-by-step explanation:
(1) Find the greatest common factor - 3x^2. Simplify as much as possible.
(2) Split 10x^3 - 35x^2 and 6x-21 into two separate groups. Factor each group separately to get 5x^2(2x-7) and 3(2x-7). The numbers in the parentheses should be the same for each group - (2x-7). Take the numbers outside of the parentheses and put them together to get (5x^2+3). Your final answer will be (2x-7)(5x^2+3).
1. The required factor of the polynomial is
(-3x²)(x²+3x-5).
2. The required factor of the polynomial using grouping method, the answer is (5x²+3)(2x-7).
What is a polynomial?"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."
What is factorization of a polynomial?"The factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
There are six different methods to factorizing polynomials. One of those methods is factorization of a polynomial by grouping method."
1. The given polynomial is
[tex]-3x^{4} - 9x^{3} + 15x^{2} \\= - 3x^{2}(x^{2}+3x-5)\\[/tex]
Therefore, by factorizing the given polynomial, we get:
[tex]- 3x^{2}(x^{2}+3x-5)[/tex].
2. The given polynomial is
[tex]10x^{3}-35x^{2} +6x-21[/tex]
We need to factorize it using grouping method.
Therefore,
[tex]10x^{3}-35x^{2} +6x-21\\= 5x^{2}(2x-7)+3(2x-7)\\= (5x^{2} +3)(2x-7)[/tex]
Hence,
1. The required factor of the polynomial is
(-3x²)(x²+3x-5).
2. The required factor of the polynomial using grouping method, the answer is (5x²+3)(2x-7).
Learn more about the factorization of a polynomial here: https://brainly.com/question/10499871
#SPJ2
Related Questions
equation of the line through point (5,4) and perpendicular to y=−4/3x−2.
Answers
Answer:
y=3/4x+1/4
Step-by-step explanation:
Perpendicular lines have slopes that are negative and reciprocal. If you multiply them together, the result is -1.
So, to find the slope of the new line, we can use this equation:
-4/3m=-1
multiply both sides by 3/-4
m=3/4
So the slope of the new line is 3/4
Here's the equation so far:
y=3/4x+b (b is a placeholder)
we can substitute the point (5,4) into the equation, since the line is going to pass through it.
4=3/4(5)+b
4=15/4+b
1/4=b
So the line is y=3/4x+1/4
Hope this helps!
Josslyn needs to earn at least $420 a week during her summer break to pay for college. She works two jobs, one at a restaurant that pays $18 an hour and the other tutoring for $16.50 per hour.
Let x be the number of hours she works at the restaurant and let y be the number of hours she works tutoring. Write an inequality that models this situation.
Answers
Answer:
x+y[tex]\geq[/tex]420
18x+16.50y[tex]\geq[/tex]420
Step-by-step explanation:
Answer:
18x + 16.50y ≥ 420
Step-by-step explanation:
6,6,5,5, 4, 7,4,8, 4, 6, 5, 7,8
Find the modes of this data set.
what’s the mode?
Answers
Answer: 6, 5, 4
Step-by-step explanation:
The mode is the number that you see the most. 6, 5, and 4 appear 3 times in the set.
Answer:
6,5,4
Step-by-step explanation:
the all tie in repeating 3 times. The mode is what repeats the most. since 6,5,4 all repeats 3 times they tie for mode.
Please help me ASP with this I got 2 minutes to do it
Answers
Answer: 5/6
Step-by-step explanation:
Answer:
I believe the answer is 1 1/6
Step-by-step explanation:
Here is how I got 1 1/6
4 1/3 - 3 1/2
4 - 3 = 1
1/3 - 1/2 = 2/6 - 3/6 = 1/6
Answer = 1 1/6
simplify -8z^8+(-14z^8)
Answers
Answer:
-22x^8
Step-by-step explanation:
-8z^8 + (-14z^8)
z^8 = z^8
-8 - 14 = -22
-22z^8
I really really really really need help 9(7)/3
Answers
Answer:
21
Step-by-step explanation:
9*7 is 63 divided by 3 should get you 21.
Answer:
21
Step-by-step explanation:
Could someone help with me his before I go to sleep and I hope when I wake up the answer is here pls
Answers
inverse laplace of L^-1 {5s/s^2 + 3s - 4}
Answers
Answer:
[tex]L^{-1} (\frac{5s}{s^{2}+ 3 s -4 } )[/tex] = [tex]4e^{-4t} + e^{t}[/tex]
Step-by-step explanation:
Step(i):-
Given
[tex]L^{-1} (\frac{5s}{s^{2}+ 3 s -4 } )[/tex]
Factors of s² + 3s - 4
= s² + 4s - s -4
= s( s +4 ) -1 (s +4)
= (s-1)(s+4)
[tex]L^{-1} (\frac{5s}{s^{2}+ 3 s -4 } )[/tex]
= [tex]L^{-1} (\frac{5s}{s+4)(s-1) } )[/tex]
By using partial fractions
[tex](\frac{s}{s+4)(s-1) } ) = \frac{A}{s+4} + \frac{B}{s-1}[/tex] ..(i)
s = A ( s-1) + B( s+4) ....(ii)
Put s= 1 in equation (ii) , we get
1 = B(5)
[tex]B = \frac{1}{5}[/tex]
s = -4 in equation (ii) , we get
-4 = -5A
[tex]A =\frac{4}{5}[/tex]
Step(ii):-
now the equation (i) , we get
[tex](\frac{s}{s+4)(s-1) } ) = \frac{4}{5(s+4)} + \frac{1}{5(s-1)}[/tex]
[tex]L^{-1} (\frac{s}{s+4)(s-1) } ) = 5( L^{-1} \frac{4}{5(s+4)} + 5L^{-1} \frac{1}{5(s-1)}[/tex]
By using inverse Laplace transform formula
[tex]L^{-1} (\frac{1}{s-a} ) = e^{at}[/tex]
[tex]L^{-1} (\frac{1}{s-1} ) = e^{t}[/tex]
[tex]L^{-1} (\frac{1}{s+4} ) = e^{-4t}[/tex]
[tex]L^{-1} (\frac{s}{s+4)(s-1) } ) = 5( L^{-1} \frac{4}{5(s+4)} + 5L^{-1} \frac{1}{5(s-1)}[/tex]
= [tex]4e^{-4t} + e^{t}[/tex]
1) Integers get bigger the further left they are located on a number line.
True
False
I need help!!!!!!!
Answers
Answer:
False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
The left of the number line is the domain of negative numbers. As you go left on the number line, the integers are smaller.
Evaluate b - y for b= -13 and y= -50.
Answers
Answer:
37
Step-by-step explanation:
because you are basically adding -13 to 50 because the minus and the -50 cancel eachother out
Best and Correct answer gets Brainliest!!!
Answers
Answer:
Line A
Step-by-step explanation:
Line A crosses 5 at y when it hits 1 at x, meaning that constant of proportionality is 5. Trust me ; D.
help asap i’ll give brainliest
Answers
Answer:
answers in this order
5
4
3
2
1
6
Step-by-step explanation:
i kno that the way these numbers are are kinda sus but this is correct
hope this helps <3
A zookeeper took a random sample of 30 days and observed how much food an elephant ate on each of those days. The sample mean was 350 kg and the sample standard deviation was 25 kg. Find the 95% confidence interval for how much food the elephant eats.
Answers
Answer:
341.95≤x≤358.95
Step-by-step explanation:
The confidence interval formula is expressed as;
CI = xbar±(z×s/√n)
xbar is the mean sample
s is the standard deviation
z is the z score at 95% confidence interval
n is the sample size
xbar = 350kg
z = 1.96
s = 25kg
n = 30
Substitute
CI = 350±(1.96×25/√30)
CI = 350±(1.96×4.564)
CI = 350±(8.946)
CI = (350-8.946, 350+8.946)
CI = (341.05, 358.95)
Hence the 95% confidence interval for how much food the elephant eats us 341.95≤x≤358.95
Drag and drop each number to its correct position on the number line.
PLEASE HELP!
Answers
Answer:
where is the numberline miss
Answer:
you forgot the picture
:-(((
Find the value of 0 and round to the nearest whole degree
Answers
Answer:
57°
Step-by-step explanation:
[tex] \theta = {sin}^{ - 1} \bigg( \frac{36}{43} \bigg) \\ \\ \theta = 56.846591584 \degree\\ \\ \theta \approx 57 \degree\\ \\ [/tex]
What is special about y coordinate that goes with the x coordinate of 1on a proportional gragh
Answers
Answer:
The first coordinate (usually the x-coordinate) is called the domain and the second (usually the y-coordinate) is called the range. If tou remember from earlier chapters the domain contains values that correspond to the independent variable whereas the range contains values corresponding to the dependent variable.
Step-by-step explanation:
I majored in Mathematics
Exam Guidelines
Exam Instructions
Question 15 of 20:
Select the best answer for the question.
15. Simplify: (3 x 22) = 6 + [28 – (4)?1
A. 55
B. 23
ООО
C. 32
D. 46
Answers
Mike measured the height of an art frame as 6.33 feet, but the actual height was 7 feet. What is the percent of error in Mike's measurement? (5 points)
a
9.45%
b
9.57%
c
10.58%
d
13.33%
Answers
Step-by-step explanation:
Difference between measured vs actual
= 7ft - 6.33ft = 0.67ft.
Percent of error = (0.67ft/7ft) * 100% = 9.57%. (B)
Answer:
9.57%
Step-by-step explanation:
What is the slope of the line y=3
A. 3
B. -3
C. 0
D. Undefined
Answers
Answer:
0
Step-by-step explanation:
Slope is the rise (change in y) over the run (change in x).
y=3 is simply a horizontal line.
hope this helps!
5x + 7 (-7) = 2x + 6 (-7)
What property is being shown above?
O Multiplication Property of Equality
Division Property of Equality
O Addition Property of Equality
Subtraction Property of Equality
Answers
Answer:
so sorry i had too
Step-by-step explanation:
someone passed this to me) 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you
Helpppppppppppppppppppppplppoollooppp
Answers
Answer:
I wouldn't advise putting answers from test on brainly its against the honor of code and you will get warned.
Step-by-step explanation:
Help please! I’ll give brainliest!
Answers
Solve for n.
d=4m + 7n
n
Answers
Answer:
n = [tex]\frac{d-4m}{7}[/tex]
Step-by-step explanation:
Given
d = 4m + 7n ( subtract 4m from both sides )
d - 4m = 7n ( isolate n by dividing both sides by 7 )
[tex]\frac{d-4m}{7}[/tex] = n
Answer:
n = d - 4m ÷ 7
Step-by-step explanation:
d = 4m + 7n
d - 4m = 7n
7n = d - 4m
n = d - 4m ÷ 7
Thus, n = d - 4m ÷ 7
-TheUnknownScientist
The original cost of an item is $64 but you have to pay $78.08. What is the markup of the item as a percent
Answers
Answer:
22%
Step-by-step explanation:
$78.08 - $64 = $14.08
$14.08 * 100% / $64 = 22%
please help me wth this
Answers
A druggist has two mixtures of a certain chemical and water, one containing 10% of the chemical and the other containing 40% of the chemical. How much of each mixture should he use to make 10 ounces that contain 25% of the chemical? How many ounces of chemical are in the final mixture? 1 2.5 7.5
Answers
0.10x + 0.40(10 - x) = 0.25(10)
The value of x is 5. Hence, the druggist should mix 5 ounces of each. There are 2.5 ounces of chemical in the final mixture.
Answer:
the answer is= 2.5
Step-by-step explanation:
good luck!
If I do my maths homework at a rate of 1.6 questions per minute, it will take me 47 minutes to complete. What rate is needed to complete it in 34 minutes?
Give your answer correct to 1 decimal place.
Answers
Answer:
Step-by-step explanation:
reqd. rate=(1.6)×47÷34≈2.2 questions per minute.
The required rate to complete the question in 34 minutes is given as 2.2 questions per minute.
What is the rate of change?Rate of change is defined as the change in value with rest to the time is called rate of change.
As mentioned in the question, in homework rate of doing questions is 1.6 questions per minute.
It took 47 minutes to complete the whole expression,
Total questions in the homework given by,
Total question = rate × time
Total question = 1.6 × 47
Total questions ≈ 75 questions
Now,
If the time to complete the question is 34 minutes, the rate required is given by,
Rate = total question/time
Rate = 75/34
rate = 2.2 questions per minute.
Thus, the required rate to complete the question in 34 minutes is given as 2.2 questions per minute.
Learn more about the rate of change here: https://brainly.com/question/13103052
#SPJ2
50!!! Points Paul needs 27 plants to fill his garden and has $99 to
spend. Lilies cost $5 each and tulips cost $2 each. Which
system represents the number of lilies (1) and tulips (t)
Paul can buy?
Answers
[tex]\boxed{\boxed{\pink{\bf \leadsto Option \ A \ is \ correct .}}}[/tex]
Step-by-step explanation:Given that , Paul needs 27 plants to fill his garden and has $99 to spend. Lilies cost $5 each and tulips cost $2 each.
Tulips are represented by t .Lilies are represented by l .Now we need to find which set of linear equations represent the above situation. So ,
Sum of number of lilies and tulips is 27 .
[tex]\implies \bf n( Tulips) + n(Lilies ) = 27 \\\\\bf\implies \boxed{ \bf l + t = 27 }[/tex]
Now , cost of each lily is $5 and tulip is $2 . And he has $99 in total . So ,
[tex]\bf\implies n_{tulips} \times cost_{tulip} + n_{lilies} \times cost_{lilies} = Money \ that \ Paul \ has. \\\\\bf \implies t\times \$2 + l \times \$5 = \$ 99 \\\\\implies \boxed{\bf 2t + 5l =\$ 99 }[/tex]
Hence we can see that our ans matches with option (a) which is ,
[tex]\red{\bf Option \ A}\begin{cases} \bf l + t = 27 \\\\\bf 2t + 5l = 99 \end{cases}[/tex]
Hence option (A) is correct .The scatter plot shows the heights x (in inches) and the weights y (in pounds) of 10 people. Find the weight of the person who is 70 inches
tall. Then find the height of the person who weighs 125 pounds.
Answers
Answer:
70 inches weighs 160
125-pound person is 66 inches tall
Step-by-step explanation:
2. The graph below shows how the water level of a swimming pool changes as the pool is
filled with water. What does the slope of the graph represent?
7
6
Depth of Water In
Swimming Pool (In foot)
N
1 2 3 4 5 6 7
Time (in hours)
A the time it takes to fill the pool completely
B. the maximum depth of the water in the pool
C. the rate at the pool fills in feet per hour
D. the rate at which the pool fills in hours per foot
Answers
Answer:
C. the rate at the pool fills in feet per hour
Step-by-step explanation:
Given
The attached graph
Required
What does the slope represent?
The slope of any graph can be calculated using:
[tex]Slope = \frac{Rise}{Run}[/tex]
Where:
Rise = The change in the vertical axis
Run = The change in the horizontal axis within the same interval as the Rise
The vertical axis measures depth in feet and the horizontal axis measures time in hour.
So:
[tex]Slope = \frac{Depth}{Time}[/tex]
or
[tex]Slope = \frac{Feet}{Hour}[/tex]
This means that the slope measures rate in feet per hour