Which polynomials are prime? check all of the boxes that apply. x2 9 x2 – 9 x2 3x 9 –2x2 8
Answers
Prime polynomials cannot be factorized in smaller degree polynomials. The prime polynomials out of the considered option are:
Option 1: x^2 + 9Option 3: x^2 + 3x + 9What 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 options for them being prime or not:
Option 1: [tex]x^2 + 9[/tex]Take [tex](x+a)(x+b) = x^2 + 9[/tex]
Then, expanding it gives:
[tex]x^2 + (a+b)x + ab = x^2 + 9 \implies a+b = 0, ab = 9[/tex]
or we get: [tex]a = -b, ab = -b^2 = 9, b^2 = -9[/tex]
Square of a real number doesn't exist, so this factor doesn't exist. Thus, it is prime polynomial.
Option 2: [tex]x^2 - 9[/tex]We have the identity [tex](a+b)(a-b) = a^2 - b^2[/tex]
and since 9 is square of 3, therefore, we get:
[tex]x^2 -9 = x^2 -3^2 = (x+3)(x-3)[/tex]
So it got factorized. Thus, not a prime polynomial.
Option 3: [tex]x^2 +3x + 9[/tex]Take [tex](x+a)(x+b) = x^2 + 3x + 9[/tex]
Then, expanding it gives:
[tex]x^2 + (a+b)x + ab = x^2 + 3x + 9 \implies a+b = 3, ab = 9[/tex]
That gives:
[tex]a = 3-b\\ab = b(3-b) = 3b - b^2 = 9\\b^2 -3b + 9 = 0[/tex]
Solving this quadratic equation by root formula gives:
[tex]b = \dfrac{-(-3) \pm \sqrt{(-3)^2 -4(1)(9)} }{2}\\\\b = \dfrac{-(-3) \pm \sqrt{-27} }{2}\\[/tex]
this makes 'b' a complex number and it doesn't remain a real number as its expression contains square root of a negative number.
Thus, this polynomial cannot be factorized in terms of smaller degree polynomials. Thus, its a prime polynomial.
Option 4: [tex]-2x^2 + 8[/tex]Taking -2 common out, we get:
[tex]-2(x^2 - 4) = -2(x^2 - 2^2) = -2(x-2)(x+2)[/tex]
Thus, it got factorized, and therefore not a prime polynomial.
Thus, the prime polynomials out of the considered option are:
Option 1: [tex]x^2 + 9[/tex]Option 3: [tex]x^2 + 3x + 9[/tex]Learn more about prime polynomials here:
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Answer:
A) x2 + 9
C) x2 + 3x + 9
☆
EDGE2022; Good Luck :D!!!
Related Questions
please help
photo down below
Answers
Answer:
x=102⁰
Step-by-step explanation:
180⁰-47⁰-31⁰=180⁰-78⁰=102⁰
What is the Equivalent of 9/5 and 18/10?
Answers
Answer:
Writing 9/5 as a decimal using the division method. To convert any fraction to decimal form, we just need to divide its numerator by denominator. Here, the fraction is 9/5 which means we need to perform 9 ÷ 5. This gives the answer as 1.8.
Step-by-step explanation:
hope this helps if not let me know
Work out length of x
to 3 Significant Figures
image not drawn accurately
HURRY UP TO ANSWER I HAVE 10 MINUTES REMAINING BEFORE I HAVE TO ANSWER
Answers
Answer:
3.32
Step-by-step explanation:
[tex]4.7 ^2 = 22.09[/tex]
[tex]22.09/2 = 11.045[/tex]
then we can find the square root, [tex]\sqrt{11.045} = 3.32[/tex]
now we can check our answer:
[tex]a^2 + b^2 = c^2[/tex]
[tex]3.32^2 + 3.32^2 = 4.7^2[/tex]
[tex]11.0224 + 11.0224 = 22.0448[/tex]
and [tex]\sqrt{22.0448} = 4.6951[/tex] or 4.7
How to subtract mixed numbers with unlike denominators?.
Answers
To subtract mixed numbers with different denominators, follow these steps:
1. Rename the fractions using a common denominator.
2. Subtract whole numbers from whole numbers. You might need to regroup first.
3. Subtract fractions from fractions.
4. Simplify, if needed.
Let's try it with [tex]2\frac{3}{5}-1\frac{1}{4}[/tex]
First, rename the fractions using a common denominator. The least common denominator of these fractions is 20. Multiply to make equivalent fractions with 20 as the denominator.
[tex]\frac{3x4}{5x4}=\frac{12}{20}[/tex] [tex]\frac{1x5}{4x5}=\frac{5}{20}[/tex]
Rewrite the problem and subtract the whole numbers.
[tex]2\frac{12}{20}-1\frac{5}{20}=1\frac{?}{?}[/tex]
Now, subtract the fractions. Subtract the numerators and keep the denominator the same.
[tex]2\frac{12}{20}-1\frac{5}{20}=1\frac{7}{20}[/tex]
This answer is already in its simplest form, so there is no need to simplify it.
What type of polygon is needed to use the Pythagorean theorem?
A. Acute triangle
B. Right triangle
C. Rectangle
D. Isosceles triangle
Answers
Ahh, yes, the Pythagorean Theorem!
The Pythagorean Theorem is applied to right triangles. Only right triangles. So our answer would be B.
I hope this makes sense. I can continue to expand on this if you like.
-Toremi
The correct answer is option (B) Right triangle.
What is a right triangle?A triangle with one of its angles measuring 90° is known as a right triangle.
The Pythagorean theorem is applicable only to a right triangle.
The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs of the triangle.
Hence, the correct answer is option (B) Right triangle.
Learn more about right triangles here:
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A door's shape is made by combining a rectangle and a semicircle. What is the area of the door?
Will mark brainlyest!!!
Answers
Answer:
I am not sure but I think the answer is 34.28
Step-by-step explanation:
Sorry if that is the wrong answer
Hope this helped
Answer:
34.28 ft^2
Step-by-step explanation:
Area of rectangular portion 7 x 4 = 28
area of semicircle with radius 2
1/2 * pi (2)^2
Added together = 34.28 ft^2
what two numbers add up to -12 and multiply to 36
Answers
-6 * -6 = 36
Answer:
-6 and -6
Step-by-step explanation:
[tex](-6)+(-6)=(-12)\\(-6)(-6)=36[/tex]
Adding a negative is the same as subtracting.
Multipling a negative by a negative is the same as multiply two even numbers. The negative signs cancel each other out.
Please help me asap with my grade 11 trigonometry math! I'll give brainliest, please help, thank you. *URGENT*
Answers
Answer:
37.8579
This value is approximate and rounded to four decimal places
===============================================
Explanation:
The tangent function is being applied to some unknown angle x. To isolate x, we undo whatever tangent is doing. So we apply the inverse function. Specifically the inverse tangent function. This is also known as "arctangent" and your calculator most likely shows it as a button with a "-1" exponent above the "tan"
So apply the arctangent to both sides to get
tan(x) = 0.7773
arctan(tan(x)) = arctan(0.7773)
x = 37.8579
heres a diagram to help
ANSWER ASAP!! 40 POINTS!! what is the 10% of the number 90,500
Answers
We start with 90,500
to get 10% we multiply it by .10
90,500 * .10 =
9050
Answer:
D
Step-by-step explanation:
Carly typed 180 words in two minutes enter the number of words Carly typed in five minutes at this rate
Answers
Answer:
the answer is 450
Step-by-step explanation:
180 × 2= 360. but that only gives us 4 mins we need one more min. so we divide 180 by 2 and get 90. we add 90 to 360 and get an answer of 450
A cone has a volume of 1,570 in. If
the height of the cone is 15 inches,
calculate the radius of the cone.
Answers
Step-by-step explanation:
1/3×π×r^2×15=1570. r^2=1570×21/(22×15);r=10.00
Find the least number 1008 would need to be multiplied by to give a square number.
Answers
Step-by-step explanation:
7 to make a perfect square
Solve the quadratic function by completing the square. what are the missing pieces in the steps? –32 = 2(x2 10x) –32 = 2(x2 10x 25) 18 = 2(x 5)2 9 = (x 5)2 ± = x 5 x = –2 or x =
Answers
An equation is formed of two equal expressions. The missing pieces of the solution of the quadratic equation are 50, 3, and -8.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
To fill the missing piece of the solution of the quadratic equation, you need to balance each of the equations. Therefore, the solution to the problem can be written as,
[tex]-32 = 2(x^2 + 10x)\\\\-32 + 50 = 2(x^2 + 10x + 25)\\\\18 = 2(x + 5)^2\\\\9 = (x + 5)2\\\\\pm 3= x + 5\\\\x = -2\ \ {\rm or}\ \ x = -8[/tex]
Thus, the solution of the quadratic equation is -2 or -8.
Hence, the missing pieces of the solution of the quadratic equation are 50, 3, and -8.
Learn more about Equation:
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help me guys I need It now answer it correctly no.4 and 5 pls
Answers
Answer:
4. 309.76π
5. 2500/π
Question 4
Step 1. Find radius
D = 2r
r = D/2
r = 35.2/2 = 17.6 cm
Step 2. Find area
A = πr²
A = π(17.6)²
A = 309.76π ≈ 973.14 cm²
Question 5
Step 1. Find radius
C = 2πr
r = C/2π
r = 100/2π = 50/π ≈ 15.92 m
Step 2. Find area
A = πr²
A = π(50/π)²
A = π(2500/π²)
A = 2500/π ≈ 795.77 m²
I hope this helps!
Question 4
Step 1. Find radius
D = 2r
r = D/2
r = 35.2/2 = 17.6 cm
Step 2. Find area
A = πr²
A = π(17.6)²
A = 309.76π ≈ 973.14 cm²
Question 5
Step 1. Find radius
C = 2πr
r = C/2π
r = 100/2π = 50/π ≈ 15.92 m
Step 2. Find area
A = πr²
A = π(50/π)²
A = π(2500/π²)
A = 2500/π ≈ 795.77 m²
i think these are right i hope this helped if not im sorry
PLEASE HELP ME DUE TODAY!!!!!!!!! PLEASE ANYONE
Answers
Answer:
a
Step-by-step explanation:
Answer:the answer is A 5x5=25
Step-by-step explanation:
Which shows one way to determine the factors of 12x3 – 2x2 18x – 3 by grouping? 2x2(6x – 1) 3(6x – 1) 2x2(6x – 1) – 3(6x – 1) 6x(2x2 – 3) – 1(2x2 – 3) 6x(2x2 3) 1(2x2 3)
Answers
The factor of the given expression 12x^3 - 2x² + 18x-3 is as follows (6x-1)(2x²+3).
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given expression is
12x^3 - 2x² + 18x-3
= 2x²(6x-1) + 3(6x-1)
= (6x-1)(2x²+3)
Learn more about quadratic equations;
brainly.com/question/13197897
Answer:
A.
Step-by-step explanation:
Can you help finish my trigonometry maze?? And show me the equation for each I know some of them are finding angles and I’m stuck please help.
Answers
Using the trigonometric ratios of sine, cosine and tangents will help solve navigate the maze.
What is trigonometry?Trigonometry is the study of the relationships between side lengths and angles of triangles.
The three main trigonometry functions are sine, cosine and tangent.
For right-angled triangles, the ratios of the three trigonometric functions are:
Sine = opposite/hypotenuseCosine = adjacent/hypotenuse Tangent = opposite/adjacentFor the given maze, the missing measures are found using the angles and the side given.
For example:
tan 52 = 40/x
x = 40/tan 52 = 31.3
Therefor, using the trigonometric ratios will help solve navigate the maze.
Learn more about trigonometry at: https://brainly.com/question/24236629
Hannah is experimenting with a new drawing program on her computer. She created quadrilateral MATH with coordinates M(1, 2). A(-5, 3), T(- 6,-3), and H(0,- 4). Hannah believes that she has created a square. Prove that Hannah is correct.
Answers
Answer:
It is a square, Hannah is a G.
Step-by-step explanation:
You can plug it in for visual, see attachment. You can see that it is a bit rotated square.
But real proof should be done with the points.
For it to be square all sides need to equal each other.
What's the x distance of M and A?
It is 1-(-5) = 1+5 = 6
What is the x distance of H and T?
It is 0-(-6) = 0+6 = 6
What is the y distance of M and H?
It is 2-(-4) = 2+4 = 6
What is the y distance of A and T?
It is 3-(-3) = 3+3 = 6
All are 6 so all sides are equal so it is a square.
All of the following are considered migration push factors EXCEPT...
A. Employment Opportunity
B. Violence or war
C. Outsourcing
D. Pollution
Answers
Answer:
c. outsourcing
Step-by-step explanation:
just didbthat
Answer:
b
Step-by-step explanation:
because it shows it talks about factor
Answer number 15 please. Thank you
Answers
Answer:
I got 84% increase
Step-by-step explanation:
Subtract final value minus starting value
Divide that amount by the absolute value of the starting value
Multiply by 100 to get percent increase
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds
and each large box of paper weighs 80 pounds. A total of 19 boxes of paper were
shipped weighing 1280 pounds altogether. Determine the number of small boxes
shipped and the number of large boxes shipped.
Answers
Answer:
x = 8
y = 11
Step-by-step explanation:
Total small box weight = 50x [x being the number of small boxes]
Total large box weight = 80y [y being the number of large boxes]
Total boxes = x+y = 19
Total weight = 1280
Determine x and y.
You know 2 equations. One for weight and another for number of boxes each.
1280 = 50x +80yx+y = 19Rewrite second equation:
x+y=19
y=19-x
You have to plug in one into another.
1280 = 50x + 80(19-x)
Solve for x
1280 = 50x + 1520 - 80x
-240 = -30x
x = 8
Solve for y by plugging in x into one of the equations:
8+y = 19
y = 11
PLS HELP!!! No links pls and Ty <333
Sid is making a pizza. The diameter of the pizza is 15 inches.
What is the area of the pizza (use 3.14 for pi and round to the nearest
tenth)?
Answers
Answer:
176.6 inches.
Step-by-step explanation:
15 is the diameter, so 15/2 is 7.5 which is the radius
A of a circle is 3.14 x r^2
7.5^2=56.25
56.25 x 3.14=176.625
rounded makes it 176.6
what is the following states of the pythangorean theorom triangles
Answers
Conor reads 3 pages every 4 minutes. At this rate, how many pages can he read in 30 minutes?
Answers
answer
22.5pages
example: 30÷4*3
Find the length of the third side. If necessary, round to the nearest tenth.
18
30
Answers
Answer:
24
Step-by-step explanation:
[tex]let \: the \: length \: of \: \: the \: third \: side \: = y \\ using \: pythaoras \: theorem \: \\ 30 {}^{2} = y { }^{2} + 18 {}^{2} \\ y {}^{2} = 30 {}^{2} - 18 {}^{2} \\ y {}^{2} = 900 - 324 \\ y {}^{2} = 576 \\ y = \sqrt{576} \\ y = 24 \\ lenht \: of \: the \: third \: side = 24[/tex]
Delta Math: Angle Terminology with Equations
Answers
[tex]\text{The two angles are supplementary, so their sum is~} 180^{\circ} \\\\m\angle A + m\angle B= 180^{\circ}\\\\\implies x+15+x-13 = 180\\\\\implies 2x +2 = 180\\\\\implies 2x = 180-2\\\\\implies 2x = 178\\\\\implies x = \dfrac{178}2\\\\\implies x = 89\\\\\text{Hence the measure of angle B is}~ \angle B = (89-13)^{\circ} = 76^{\circ}[/tex]
The expression (8+8+8+8+8)−(6+6+6+6+6) is equal to 10 .
Use any of the operations below to create another expression that is equal to 10 , but only uses the numbers 6 and 8 .
Addition (+)
Subtraction (−)
Multiplication (⋅)
Division (÷)
Squaring ( )2
Square Root ( )−−√
Answers
6²-(8+8)
Solution:There are plenty of expressions with numbers 6 and 8 that are equivalent to 10.Here is one of them:6²-(8+8)→36-16=10Hope it helps.
Do comment if you have any query.
HELP PLS WILL GIVE BRAINLIEST
Answers
Answer:
The answer is B and D :)
Step-by-step explanation:
It is b because the x value is getting bigger while the y value is getting smaller. :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
Options B and D
Step-by-step explanation:
Step 1: Determine what negative association is
Negative association basically means that the best-fit line for the scatter plot would be in a downwards slope which means that it has a negative association.
In the given examples, Option A wouldn't work because we can see that the best-fit line would be going up which is a positive association. Option B would work because we see the downward slope. Option C wond't work for the same reason as Option A. And finally Option D would work since we have a downward slope.
Answer: Options B and D
What is 3185 divided by 1625?
Answers
Answer:
1,96
Step-by-step explanation:
= 3185 ÷ 1625
= 1,96
#off
#thankyou:))
HELP I’M GONNA FAIL!!!!!! Pls help ASAP! I NEED TO PROMOTEEEEEE!!!!
Answers
V=4/3pi r^3
Where r is 2 in this example so,
V= 10.67 pi
V= 33.51
V≈33.51
Solution:Volume of a Sphere: [tex]V=\displaystyle\frac{4}{3} \pi r^3[/tex]π is equal to 3.14...r is equal to 2Plug in the values:V=4/3π(2)³V=4/3π×8V≈33.51 (rounded to the nearest hundredth)Hope it helps.
Do comment if you have any query.