The polynomial that is prime is given by Option C: [tex]10x^2 - 4x +3x +6[/tex]
What are prime polynomials?Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
Checking all the listed polynomials for them being prime or not:
Case 1: [tex]x^3+3x^2+2x+6[/tex]Rewriting it as:
[tex]x^3+3x^2+2x+6 = x^2(x+3) + 2(x+3) = (x^2 + 2)(x+3)[/tex]
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 2: [tex]x^3 + 3x^2 -2x -6[/tex]Rewriting it as:
[tex]x^3 + 3x^2 -2x -6 = x^2(x+3) -2(x+3) = (x^2-2)(x+3)[/tex]
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 3: [tex]10x^2 - 4x +3x +6[/tex]We can rewrite it as:
[tex]10x^2 -4x + 3x -6 = 10x^2 -x -6 = f(x) \: \rm (say)[/tex]
This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.
Case 4: [tex]10x^2 -10x + 6x - 6[/tex]
It can be factored as:
[tex]10x(x-1) + 6(x-1) = (x-1)(10x-6)[/tex]
This is not a prime polynomial.
Thus, the polynomial that is prime is given by Option C: [tex]10x^2 - 4x +3x +6[/tex]
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Answer:
The polynomial that is prime is given by Option C:
What are prime polynomials?
Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
Checking all the listed polynomials for them being prime or not:
Case 1:
Rewriting it as:
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 2:
Rewriting it as:
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 3:
We can rewrite it as:
This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.
Case 4:
It can be factored as:
This is not a prime polynomial.
Thus, the polynomial that is prime is given by Option C:
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Step-by-step explanation:
What is an equation of the line that passes through the points (-6,-4) and
(-4,0)? Put your answer in fully reduced form.
Answer:
-4=-6a+b /×(-1)
0=-4a+b
4=6a-b
0=4a+b
4=10a
10a=4 /÷10
a=4/10 =2/5
4=6×2/5-b
4=12/5-b
8/5=-b
b=-8/5
[tex]f(x) = \frac{2}{5} x - \frac{8}{5} [/tex]
Answer:
y=2x+8
Step-by-step explanation:
Renee, Susan, and Martha will share the cost to rent a vacation house for a week. • Renee will pay 40% of the cost. • Susan will pay 0.35 of the cost. • Martha will pay the remainder of the cost. Martha thinks that she will pay 13 of the cost. Is Martha correct?
Answer:
Martha is wrong.
Step-by-step explanation:
Let the cost of the house is C.
Payment by Ranee = 40% of the cost
=40% of C
=[tex]\frac{40}{100}\times C[/tex]
=0.40 C
Payment by Susan = 0.35 of the cost
=0.35 C
Combined payment by Ranee and Susan = 0.40C + 0.35C=0.75C
The remaining payment will be done by Martha.
So, the remaining payment = C- 0.75C=0.25 C
Hence, Martha will have to pay 0.25 of the cost or 25% of the cost.
So, Martha is wrong.
3-) Martha O'Brien made a deposit to her checking account at an ATM and received
$75 in cash. The checks deposited totaled $50 less than twice the currency amount,
and the total deposit was $25 more than the check amount. Determine the amounts
Martha deposited in checks and in currency as well as the total deposit.
Answer:
The amount Martha deposited in checks is $150
The amount Martha deposited in cash is $100
The total deposit is $175
Step-by-step explanation:
Since Total deposit (T) = currency (C) + coins + check (Ck) - cash received (Csh)
T = C + Ck - Csh. (1)
Given that cash received (Csh) = $75,coins = 0 and the checks deposited totaled $50 less than twice the currency amount. So,
Ck = 2C - $50 (2)
Also, total deposit was $25 more than the check amount. So,
T = Ck + $25 (3)
Substituting equation (2) into (1), we have
T = C + Ck - Csh
T = C + 2C - $50 - Csh
T = 3C - $50 - $75
T = 3C - $125 (4)
Substituting equation (2) into (3), we have
T = Ck + $25
T = 2C - $50 + $25
T = 2C - $25 (5)
Equating equations (4) and (5), we have
3C - $125 = 2C - $25
Collecting like terms, we have
3C - 2C = $125 - $25
C = $100
Substituting C into (2), we have
Ck = 2C - $50
Ck = 2($100) - $50
Ck = $200 - $50
Ck = $150
We now compute T
T = C + Ck - Csh.
T = $100 + $150 - $75.
T = $250 - $75
T = $175
So, the amount Martha deposited in checks is $150
The amount Martha deposited in cash is $100
The total deposit is $175
Unit 11 Homework 5
Please help me solve these, will give brainliest. I’m failing and need this assignment to pass.
Answer:
1.=872.00
2.=3782.48
3.=121.84
5.=486.00
7.=9248.85
8.=121.50
Step-by-step explanation:
i tried my best hope this helps
The Surface Area of Prisms are shown below.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
We have,
1. Surface area of cuboid
= 2(lw+ wh + lh)
= 2(144 + 204 + 96)
= 888 in²
2. Surface Area of Cylinder
= 2πrh
= 2,549.68 mm²
3. SA of Triangular prism
= 2 bh + (a+ b+ c)H
= 154.337 cm²
4. SA of Trapezoidal prism
= (b1 + b2)h + PH
= (5+ 19)12.1 + (8+ 19+ 8 + 19)14
= 290.4 + 756
= 1,046.4 ft²
5. SA of Cuboid
= 324 m²
6. SA of Triangular prism
= 1274.86 yd²
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This is a shape whose base is a circle and whose sides taper up to a point.
This shape is known a cone
If Rafael earns $18/hr working 40 hours each week. How much will he earn in 6 months?
Answer:
Step-by-step explanation:
6 months=26 weeks
=>26x18=468
This zigzag crystal vase has a height of 12 inches. The cross sections parallel to the
base are always rectangles that are 5 inches wide by 4 inches long.
(a) If we assume the crystal itself has no thickness, what would be the volume of the
base?
A cubic inches
(b) The crystal is actually half an inch thick on each of the sides and on the bottom.
Approximately how much space is contained within the vase?
A cubic inches
The volume of the vase when the crystal itself has no thickness will be 240 inches³.
How to calculate the volume?The volume of the vase when the crystal itself has no thickness will be calculated thus:
V = Bh
V = (4in × 5in) × 12
V = 240 inches³
When the crystal is half an inch thick on each of the sides and on the bottom, the volume will be:
= 1/2 × 240 inches ³
= 120 inches³
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help me please. ASAP UNDER 5 MINUTES, thank you
Answer:
39
Step-by-step explanation:
I had the same exact question on a test I took
Can anyone tell me if The last one is right?
Answer:
See below.
Step-by-step explanation:
All linear dimensions are in ft, and all areas are in ft².
Pyramid:
Lateral area: 4 × 6 × 5 / 2 = 60
Base area: 6 × 6 = 36
Total surface area: 96
Hidden surface area (the square base): 36
Actual surface area in the composite solid: 60
Square prism:
Lateral area: 4 × 20 × 6 = 480
Base area: 2 × 6 × 6 = 72
Total surface area: 552
Hidden surface area (both square bases): 72
Actual surface area in the composite solid: 480
Cube:
Total surface area: 6 × 6 × 6 = 216
Hidden surface area (one base): 36
Actual surface area in the composite solid: 180
The surface areas above are for each of the above solids if each were free standing and unattached to other solids.
The way the three components are above, you must deduct some areas of bases (as shown above in the actual surface areas) since they are internal.
Pyramid actual visible area: 60
Square prism actual visible area: 480
Cube: 180
Total surface area: 720
Which of the following is / are the solution(s) of the equation |x+3|= −10?
Answer:
(no solutions)
Step-by-step explanation:
Solve for x:
abs(x + 3) = -10
Hint: | Show the equation has no solution.
By definition, absolute value is positive. Therefore abs(x + 3) = -10 has no solution:
Which expression best estimates Negative 18 and one-fourth divided by 2 and two-thirds
Answer:
-18 divided by 3
Step-by-step explanation:
help pls area of base is 15.6 feet and 6ft and 7ft are the others
Answer:
655.2 feet (655 feet 213⁄32 inches)
Step-by-step explanation:
Solve for x what is t=m/x
Answer:
— x=pm+n. Explanation: Take x out as a common factor on the left side of the equation. ⇒x(m+n)=p. To solve for x, divide both sides by (m + n).
1 answer
Step-by-step explanation:
Which of the following is NOT true about the following equation? y=−3
A) It is the equation of a horizontal line.
B) Its slope is zero.
C) It is perpendicular to the equation y=13x+2.
D) The line does not cross the x-axis.
Answer:
The statement which is NOT true about the equation y = -3 is
It is perpendicular to the equation y = 1/3x + 2 ⇒ C
Step-by-step explanation:
Let us revise the facts of the horizontal line:
The line is horizontal if all points on it have the same y-coordinatesThe horizontal line is parallel to the x-axisThe slope of the horizontal line is zeroThe equation of the horizontal line is y = b, where b is the y-coordinate of all points on the lineThe y-intercept of the horizontal line is (0, b)∵ The equation of the line is y = -3
→ Which means the value of y = -3 at any value of x
∴ The line is horizontal
∴ Its slope = 0
∵ The horizontal line is parallel to the x-axis
∴ The line does not intersect the x-axis
∴ The true statements are:
It is the equation of a horizontal lineIts slope is zeroThe line does not cross the x-axisThe statement which is NOT true about the equation y = -3 is
It is perpendicular to the equation y = 1/3x + 2
Find the total amount given the original price, tax rate and tip rate. Round to the nearest hundredth if necessary.
Original price: $101.33
Tax rate: 6.7%
Tip: 18%
Enter the correct answer in the box.
Answer:
126.360
Step-by-step explanation:
Which of this best describes the relationship of the data shown on this scatterplot?
Answer:
B No correlation
Step-by-step explanation:
Positive correlation = as x increases, y increases
Negative correlation = as x increases , y decreases
Constant correlation = as x increases, y stays the same
Find the future value and the compound interest if $7000 is invested for 5 years at 14% p.a.
Answer:
14,039
Step-by-step explanation:
The interest gets you about 980 dollars a year but the compound get you around 4k on the since it doubles each year
Which expression is equivalent to −(4−3)?
A. −22−3
B. −22+3
C. −3−22
D. −3+22
Answer:
B.
Step-by-step explanation:
-(4 - 3) = -1.
If by 22 you mean 2^2 ( 2 squared) then it is B. -22 + 3 = -1.
domnics video game has a perimeter of 18 inches the width is 4 inches what is the height of the video game
please help me with it due today
Answer:
-9x
Step-by-step explanation:
trust me it’s -9x
Answer:
13x - 22
Step-by-step explanation:
combine like terms 8x + 5x= 13x and 15-37= -22, so the simplified expression is 13x-22
Write k/3 + 16 as words
Answer:
k divided by three plus sixteen
Step-by-step explanation:
3. Boynton Beach recreation center has collected a total of 510 donated tickets for free ice
cones. Beginning on the second day of summer vacation, the recreation center randomly
selects 9 children to each receive one of the free ice cream tickets. Assuming the
recreation center continues this pattern of giving away tickets to 9 children each day,
which explicit formula shows the
number of ice cone tickets remaining at the end of the
day, after n number of days?
a.=510-9n
B.=510+9(n-1)
C.510-9(n-1)
D.9(n-1)-510
Answer:
Hence, in this case, it is concluded that the correct answer is "N = 618 - n x 7"
Step-by-step explanation:
Considering the situation described above, the explicit formula that shows the number of ice cream tickets remaining at the end of the day, after n number of days is "N = 618 - n x 7."
This is based on the idea that each day of the ice cream ticket is defined as 7 tickets taken.
Thus the ticket listing for each day is described as
Day 1. 618 - 7 OR 618 - 1 × 7;
Day 2. 618 - 14 OR. 618 - 2 × 7;
Day 3. 618 - 21 OR 618 - 3 × 7;
Therefore, from this illustration above, the formula needed is: "N = 618 - n x 7."
PLEASE HELP ASAP! 70 POINTS!
Given the parent function f(x)=|x| , write the equation of the function g(x) whose graph is pictured.
(GRAPH W/ BLACK LINE IS THE PARENT FUNCTION FOR REFERENCE. Graph w/ the orange line is the one that needs an equation)
ANSWER:
g(x) = _____
Answer:
g(x) = 3|x - 2| - 4
Step-by-step explanation:
f(x) = |x|
vertex: (0, 0) → (2, -4)
point: (1, 1) → (3, -1)
⇒ g(x) = 3f(x - 2) - 4
⇒ g(x) = 3|x - 2| - 4
x- intercept of - 4 and y-intercept of -3
Answer:
(-4,-3)
Step-by-step explanation:
Not sure if tht was what you were asking, but that's how u write it as a point or vertex
Write a function t(I) that determines the number of
toothpicks in any given level of the pyramid.
Using the table, we will see that the function is:
t(l) = 3*l
How to write the function?
Here we only have a table to work with, so we need to use that.
In the table, we can see the pairs:
t(1) = 3t(2) = 6t(3) = 9t(4) = 12So, in each new level, we just add 3 more toothpicks. Even more, we can see that the number of toothpicks is 3 times the value of l (the level) for all the cases in the table. So this is a linear function.
From that we can conclude that the function will be:
t(l) = 3*l
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A rectangular prism has a length of 13ft and a width of 16ft.
If the prism has a volume of 936ft3, calculate the height of
the prism. Make sure your answer includes the proper units.
Considering the volume of the rectangular prism, it is found that it's height is of 4.5 ft.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by:
[tex]V = lwh[/tex]
In this problem, the measures given are as follows:
l = 13 ft, w = 16 ft, V = 936 ft³.
Hence, the height, in ft, is found as follows:
[tex]V = lwh[/tex]
[tex]13 \times 16 \times h = 936[/tex]
[tex]h = \frac{936}{13 \times 16}[/tex]
[tex]h = 4.5[/tex]
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Line CD passes through points C(1, 3) and D(4, –3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
–5
–2
1
5
Answer: 5
Step-by-step explanation:
YALL BETTER HELP ME LOLLL
Explain how you could use the dimensions of a reduced rectangle and one given measurement of an original rectangle to find a missing measure?
Answer:
You find out the answer.
Step-by-step explanation:
But, the answer is one side cause three - four is one
Answer:
you can cross multiply Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position.
Step-by-step explanation:
i got this riight.
stephan invested $950 in an account that grows continuously at an annual rate of 4.2%. write a function that represents the situation, where A is the value Stephan’s investment after t years. what will his investment be worth to the nearest cent after 10 years
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$950\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &10 \end{cases} \\\\\\ A=950e^{0.042\cdot 10}\implies A=950e^{0.42}\implies A\approx 1445.86[/tex]
What is the radius of circle P?
Diameter = 2.75
Radius(p) = 2.75/2
Answer 1.375