Factor completely 4x5 − 20x4 − 36x3. (1 point)
Answers
Answer:
The factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]
Step-by-step explanation:
Given the polynomial [tex]4x^5 - 20x^4 - 36x^3[/tex]
We have to factor the above polynomial completely.
[tex]4x^5 - 20x^4 - 36x^3[/tex]
Take [tex]x^3[/tex] common from each term.
[tex]x^3(4x^2-5x-9)[/tex]
Here, the quadratic polynomial is prime i.e it cannot be factored into lower degree polynomial. It has complex roots.
Hence, the factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]
Answer: 4x^3(x^2 - 5x - 9)
Proof of validity is shown below.
Related Questions
Suppose that you work part-time as a sales representative at a car dealership. You earn a base salary of $125 per week plus a 18% commission on all sales that you make. Your best friend has exactly the same job at another car dealership but earning a base salary of 85$ per week plus a 21% commission on all sales. How much do you and your friend need to sell in order to earn the same amount in any given week?
Answers
Let x = the sales in a week.
Person A:
$125 per week plus 18% commission on sales.
Earnings in a week on x sales is
125 + 0.18x
Person B:
$85 per week plus 21% commission on sales.
Earnings in a week on x sales is
85 + 0.21x
For the two earnings to be equal,
85 + 0.21x = 125 + 0.18x
0.03x = 40
x = 40/0.03 = $1333.33
Answer: $1,333.33
Kim, Laura and Molly share £385
The ratio of the amount of money Kim gets to the amount of money Mollley gets is 2:5
Kim gets £105 less than Molly gets
What percentage of the £385 does Laura get ?
With working out
Answers
x = 2/5y, since the ratio is 2:5.
y = 105 + x, since Molly has 105 more pounds than Kim.
Substitute x into this equation, so that y = 105 + 2/5y. Subtract 2/5y from both sides to get 3/5y = 105. Divide each side by 0.6 (equivalent to 3/5) and you get y = 175, which is how much Molly has. Kim gets 2/5 of Molly's share (or 105 fewer pounds), so she has 70.
70 + 175 (Kim and Molly's shares) is equal to 245. Therefore, Laura receives the remaining 140 pounds.
140/385 = a/100
Cross multiply so that 385a is 14000. Divide by 385 to get 36.4 (rounded).
Thus, Laura receives about 36.4% of the total money. Hope this helps (:
Consider the following system of equations.
Which statement describes why the system has two solutions?
A. Each graph has one y-intercept, which is a solution.
B. Each graph has one vertex, which is a solution.
C. The graphs of the equations intersect the x-axis at two places.
D. The graphs of the equations intersect each other at two places.
Answers
The solution of a system of equations is the set of points of intersection of the graphs of the equations.
The answer is D.
Answer:
D. Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines equivalent.
Step-by-step explanation:
If you look at the graph (Firstly), you can see that both lines look similar, which is one big hint to this question. But (secondly), like the other person said, both have equivalent y-intercepts in each problem. I saw an open spot for me to answer this so I took it UuU!
Also Just Realized This Is A Totally Diff Question On My Quiz, So The Question That Goes With This Answer Is "Consider the equations and graph below.
y = negative 3 (x minus 1). Y = negative 3 x minus 1
On a coordinate plane, 2 lines are parallel to each other.
Which explains why this system has no solution?"
The table shows the outputs, y, for different inputs, x:
Input (x) 2 5 9 12
Output (y) 20 15 12 8
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)
Answers
[tex]\bf \begin{array}{l|lllll} x&2&5&9&12\\ y&20&15&12&8 \end{array} \begin{array}{llll} \impliedby \textit{notice the x-values do not re} peat\\ \qquad \textit{therefore is a function} \end{array}[/tex]
b)
[tex]\bf \begin{array}{l|lllll} x&2&5&\stackrel{\downarrow }{9}&12\\ y&20&15&\boxed{12}&8 \end{array}\qquad \qquad \begin{array}{llll} f(x)=5x+14\\\\ x=9\\\\ 5(9)+14\implies 45+14\implies \boxed{59} \end{array}[/tex]
well, notice, which is larger?
c)
[tex]\bf \stackrel{f(x)}{64}=5x+14\implies 50=5x\implies \cfrac{50}{5}=x\implies 10=x[/tex]
PLEASE ANSWER THIS
Classify each expression as a polynomial or not. If the expression is a polynomial, name it according to its degree and its number of terms.
f(x)=x^2sqrt3+x-5
I already know it is a polynomial because the highest variable is 2. Please help me with the rest. The question itself confuses me
Answers
The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?
b = –16
b = –8
b = 8
b = 16
Answers
Answer:
Option B is correct.
value of b = -8
Step-by-step explanation:
Given the equation: [tex]x^2+bx+16= 0[/tex]
As per the condition: The only solution for the given equation is, x = 4.
Substitute this value of x =4 in given equation, to solve for b;
[tex](4)^2+b(4)+16= 0[/tex]
Simplify:
[tex]16+4b+16= 0[/tex]
or
[tex]32 + 4b= 0[/tex]
Subtract 32 on both sides, we get;
32 + 4b -32 = 0-32
Simplify:
4b = -32
Divide both sides by 4 we get;
b = -8
therefore, the value of b = -8
someone please help me! thank you so much
Answers
I believe the answer would be 5. Let me explain.
For the equation f(x) = -2x +3, I plugged in "-1" from the ordered pair into the equation as "x".
f(x) = -2 (-1) +3, and that would simplify to f(x) = 5,
so then y = 5.
Hope this helps!
May
A website-hosting service charges businesses a onetime setup fee of $275 plus d dollars for each month. If a business owner paid $1,091 for the first 12 months, including the setup fee, what is the value of d? a. Create an equation to represent this situation.
b.Solve
your equation above to find the value of d. Show all work to receive full
credit
Answers
S = 275 + dx
where S is the total amount paid, d is the monthly fee and x is the number of months. Substituting the known values from the given,
1091 = 275 + d(12)
or, 1091 = 12d + 275
(b) To determine the value of d, follow the steps given below,
Substract 275 in each side of the equation,
1091 - 275 = 12d + 275 - 275
Simplifying,
816 = 12d
Divide both sides of the equation by 12,
816/12 = 12d/12
Simplifying,
68 = d
or d = 68
Hence, d = 68
*PLEASE HELP, BRAINLIEST* A salesman must commute 1 hour and 48 minutes from his house to the airport, fly to another city and take a bus to his destination. What is the total travel time one way?
Answers
The total travel time one way is 288 minutes.
Explanation:To find the total travel time one way, we need to add up the time spent on each part of the journey. The salesman spends 1 hour and 48 minutes commuting from his house to the airport. Let's convert this to minutes, which gives us 60 + 48 = 108 minutes.
Next, we add the flight time. The question doesn't specify the duration of the flight, so we can't determine that. We'll assume it takes 2 hours, which is 120 minutes. Finally, we add the time spent on the bus. Again, the question doesn't provide this information, so let's assume it takes 1 hour (60 minutes) by bus.
Adding up the commute time, flight time, and bus time, we get 108 + 120 + 60 = 288 minutes. Therefore, the total travel time one way is 288 minutes.
At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12. For her party, Arpitha purchased the minimum number of hot dog packages and bun packages that she could while making sure to have the same number of hot dogs and buns. How many hot dogs can Arpitha serve at her party?
Answers
It is stating that she, Arpitha, bought the MINIMUM packs of hotdogs AND minimum packs of buns to get an equal number of buns to hotdogs.
We can find the multiples they have in common.
8, 16, 24, 32, 40
12, 24, 36, 48, 60
They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.
Hope this helped!
They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.
We have given that,
At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12.
Let's first analyze the word problem we have here.
It is stating that she, Arpitha, bought the minimum packs of hotdogs and minimum packs of buns to get an equal number of buns to hotdogs.
We can find the multiples they have in common.
8, 16, 24, 32, 40
12, 24, 36, 48, 60
They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.
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Decide which of the two points lies on the graph of the line
3x+y=10
A.3,1
B. 1,3
Answers
3(3) + 1 = 10
9 + 1 = 10
10 = 10 (true)
A. 3, 1
hope this helps
PLEASE HELP ME!!!!!! 20pts
Given: Circle P with a point O outside of the circle. How many tangent lines can be drawn from point O to the Circle P?
0
1
2
Infinite
Answers
The best way to determine how many tangent lines can be created is to actually draw the circle and point itself. Given circle and a point outside, extend lines going from the point to the circle where the line is tangent to the circle. From this, we can get only 2 tangent lines, nothing more. (See attached)
Answer:
2
Answer:
I think its 2
Step-by-step explanation:
If $2500 is invested at an interest rate of 4.5% per year, compounded daily, find the value of the investment after the given number of years. (round your answers to the nearest cent.)
Answers
$2500 is invested at an interest rate of 4.5% per year, compounded daily for 2 years will amount to $5225.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, $2500 is invested at an interest rate of 4.5% per year, compounded daily, and assuming it is for 2 years.
∴ The amount compounded daily will be,
A = P(1 + (r/365)/100)ⁿˣ³⁶⁵ as compounded daily.
A = 2500(1 + (4.5/365)/100)²ˣ³⁶⁵.
A = 2500( 1 + 0.00101)⁷³⁰.
A = 2500(1.00101)⁷³⁰.
A = 2500×2.09 dollars.
A = 5225 dollars.
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To calculate the future value of an investment of $2500 at a 4.5% interest rate compounded daily for 5 years, we use the compound interest formula. Assuming 5 years of growth, the future value would be approximately $3117.14.
Explanation:If $2500 is invested at an interest rate of 4.5% per year, compounded daily, we need to find the value of the investment after a certain number of years. The formula to calculate the future value of an investment with daily compounding is given by:
FV = P × (1 + r/n)^(n×t)
where:
FV is the future value of the investment,P is the principal amount ($2500),r is the annual interest rate (4.5% or 0.045),n is the number of times the interest is compounded per year (365 for daily),t is the time the money is invested for, in years.To calculate the future value, we plug in the values into the formula. However, the number of years, t, has not been specified, so we'll need that to give a final answer. For our purposes, let's assume the student asks for the value after 5 years. Using the formula:
FV = $2500 × (1 + 0.045/365)^(365×t)
FV = $2500 × (1 + 0.00012328767)^(1825)
FV = $2500 × 1.246856823
FV = $3117.14 (rounded to the nearest cent)
After 5 years, the investment would be worth approximately $3117.14.
What is the length of BC
Answers
The Earth's circumference measured at the equator is approximately 1.3148 × 108 feet. What is the number written in standard form?
Answers
Answer:
The number written in standard form is [tex]131,480,000[/tex]
Step-by-step explanation:
we have
[tex]1.3148*10^8[/tex]
we know that
[tex]10^8=100,000,000[/tex]
substitute
[tex]1.3148*10^8=1.3148(100,000,000)[/tex]
Remember that
When multiplying decimals by 10, move the decimal point one space to the right
In this case move the decimal point eight spaces to the right
[tex]1.3148(100,000,000)=131,480,000[/tex]
therefore
The number written in standard form is [tex]131,480,000[/tex]
Solve for N.
-n/5 = -5
N = -25
N = -1
N = 25
Answers
-n = -25
Divide -1 on both sides,
n = 25
Hope this helps!
-n = -25
n = 25
Answer: C) or the third option.
Wall posters are usually sold curled up in cylindrical cardboard tubes. if the length of the tube is 84.5 cm, and the diameter of the tube is 2.40 cm, what is the area of the poster, in cm2? (assume the poster doesn't overlap itself.)
a. 637 cm2
b. 203 cm2
c. 382 cm2
d. 1529 cm2
e. 605 cm2
Answers
Diameter of the cylinder = 2.40 cm
The circumference is
π(2.40 cm) = 2.4π cm.
The area is
A = (2.4π cm)*(84.5 cm) = 637.1 cm²
Answer: a. 637 cm²
What is (5,9) reflectes across the Y and X axis
Answers
(5, 9) reflected across the x axis is (-5, 9)
I hope this helps. (:
The reflection of points across Y and X axis will be equal to (-5, 9), (5, -9).
What is reflection of points?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image.
A line, called the line of reflection, will allow an image to reflect through it. Every element inside a figure is thought to reflect another figure when they are all equally spaced apart from one another.
As per the mentioned data in the question,
The given point is (5, 9).
Under the reflection in the y-axis, points are converted as,
(x, y) ⇒ (-x, y)
So,
(5, 9) ⇒ (-5, 9)
Under the reflection in the x-axis, points are converted as,
(x, y) ⇒ (x, -y)
So,
(5, 9) ⇒ (5, -9)
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Bob bought a bike for $250 and repaired it . He can now sell the bike for $300. What is the percent increase in the value bike ?
Answers
Answer:20%
Step-by-step explanation:
250*20%=50
50+250=300
Answer:
20%
Step-by-step explanation:
What is the area of a parallelogram whose vertices are A(−4, 9) , B(11, 9) , C(5, −1) , and D(−10, −1) ?
Answers
Which value of a would make the following expression completely factored?
x2 – a
a 12
b 36
c 49
d 81
Answers
Answer:
The correct answer is twelve.
Step-by-step explanation:
The values of a would make the expression 36, 49 and 81.
The correct options are b, c, and d.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
To factor the expression x² - a completely, we need to write it as a product of two binomials.
This can be done using the difference of squares formula, which states that a² - b² = (a + b)(a - b).
If we apply this formula to x² - a, we get:
x² - a = (x + sqrt(a))(x - sqrt(a))
This is a factorization of x² - a into two binomials, where the constant term a is represented by the square root of a.
For the expression x² - a to be completely factored, both factors must be irreducible (meaning they cannot be factored any further). This requires that a be a perfect square.
Out of the given options, 36, 49, and 81 are perfect squares.
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What is the value of x?
Answers
all angle = 60 degrees
so 2x-4 =60
2x=64
x = 64/2 = 32
x = 32
A rectangle has perimeter 84 cm and length 35 cm. What is its width?
Answers
84 = 2(35 + W)
84/2 = 35 + W
42 = 35 + W
W = 42 - 35
W = 7
answer
its width 7 cm
Answer: The required width of the rectangle is 7 cm.
Step-by-step explanation: Given that a rectangle has perimeter 84 cm and length 35 cm.
We are to find the width of the rectangle.
Let w represents the width of the rectangle.
According to the given information,
length, l = 35 cm and perimeter, P = 84 cm.
Therefore, we get
[tex]P=2(l+b)\\\\\Rightarrow 84=2(35+w)\\\\\Rightarrow 42=35+w\\\\\Rightarrow w=42-35\\\\\Rightarrow w=7.[/tex]
Thus, the required width of the rectangle is 7 cm.
For the given functions f and g, find the requested composite function value. (15 pts!!!)
f(x) = √x+3, g(x) = 5x; Find (f ×g)(3).
a. 3√2
b. 5√30
c. √30
d. 5√6
Answers
Solve for b 2(b-2)=2b+9
Answers
Distribute.
2b-4=2b+9
Subtract 9 on both sides.
2b-13=2b
Subtract 2b on both sides.
-13=0
Because -13 is not equal to 0, there are no values of b that satisfy the equation.
The width of a rectangle is 3 less than twice its length. if the area of the rectangle is 193 cm 2 cm2, what is the length of the diagonal
Answers
W*L=193
replace W with 2L-3: (2L-3)L=193
2L^2-3L-193=0
Cannot factor
are you sure the numbers are correct?
If it cannot be factored, use the quadratic formula to find out L, then you can find out W
use the Pythagorean theorem to find the diagonal. I don't see an easier way.
How to write an equation of a line in slope intercept form with two points?
Answers
y = mx + b
1) Use the two points to find the slope.
Subtract the y-coordinates.
Subtract the x-coordinates int eh same order.
Divide the difference in y by the difference in x.
That is the slope, m.
2) Now you need to find b.
Rewrite y = mx + b with your value of m in the equation.
Now use one of the two points and replace x and y with the x- and y-coordinates and solve for b.
3) Finally, rewrite y = mx + b with the values of m and b you found.
Find the constant of variation k for the direct variation. 3x+5y=0
Answers
3x+5y=0
5y=-3x
y=(-3/5)*x
k=-3/5.
Answer:
The constant of variation is
-3/5
your welcome XD
BRAINLIESTTTT aSAP!
i only need part b :)
Answers
A life insurance policy costs $11.61 for every $1,000 of insurance. At this rate, what is the cost of $75,000 of insurance?