Which polynomials are prime? check all of the boxes that apply. x2 9 x2 – 9 x2 3x 9 –2x2 8
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!!!
please help me i will give brainliest
Answer:
Look below
Step-by-step explanation:
We know QS is parallel to RT, so that will be the first one. We also know that r is congruent to s, so add that if possible
Next, we have to use the alt. int. angles are congruent theorem, so we can say that angle QTR and angle SOT are congruent due to this rule.
Next we have to use reflexive property, and the only thing that fits is the transversal intersecting the parallel lines. So we can say that QT is congruent to TQ.
Then we can say that triangle SQT and triangle ROT are congruent due to SAS.
Finally, we can say angle QTS is congruent to angle TQR because of corresp. parts of congruent triangles are congruent(CPCTC for short)
I hope this helped!
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The length of the base of a triangle is four more than twice the height. the area of the triangle is 80 m^2. find the lengths of the base and the height of the triangle.
can someone help me out with this? none of my friends understand this question either.
Which of the following is an equivalent expression to the expression “T?
a
a
Answer:
a^1/12
Step-by-step explanation:
a ^1/3 / a^1/4 = a ^ (1/3 - 1/4) = a^ 1/12
find the value of x from the square
Answer:
X = 5
Step-by-step explanation:
From the given figure,
one length of a square(l)= x
Area of the square(A) = 25cm^2
We know,
Area of square(A)= l^2
or, 25=x^2
or, √25 = x
or, 5cm = x
Step-by-step explanation:
Side = x cmGiven, that the area of the square = 25cm^2
therefore,area of square = (side)^2
25 = x^2
x = √25
x = 5 cm.
Hope it helps you!!PLEASE HELP ASAP! WILL GOVE BRAINLIEST!!! I NEED THIS DONE PLEASE FOLLOW DIRECTIONS!
Answer:
I'm not sure but
Step-by-step explanation: The area is 9.5 feet.
mode is 7. find the missing value for this list: 1,4,7,5,7,X,3,6,3,5,9
Answer:
the missing value is 7
Step-by-step explanation:
mode means the highest occuring number and from the figures above, the numbers the occured the most are 3,5and7. they appeared two times and since from the question it's said that 7 is the mode, it means that 7 should occure more than 3 and 5. so the missing value is 7.
Which of the following is the equation of a line in slope-intercept form for a
line with slope = { and y-intercept at (0.-2)?
y
O A. y=-x-2
ОВ
O B. y=x-2
{
O C. y=-x+
OD. y=-2x
2
SUBMIT
Answer:
Option B is the correct answer
Step-by-step explanation:
Hope it helps you in your learning process.
Alia bought a home for her pet turtle. The rectangular tank is 3 feet long, 1 foot wide, and 2 feet high. What is the volume of the tank?
The volume of the tank is Blank
cubic feet
Answer:
Volume of tank = l×b×h
=3ft.×1ft.×2ft.
=6 ft³
Step-by-step explanation:
Hope it helps you. Please Mark me brilliant.
On a coordinate plane, line M N goes through points (2, 3) and (negative 3, 2). Point K is at (3, negative 3). Which point could be on the line that is perpendicular to Line M N and passes through point K? (0, −12) (2, 2) (4, 8) (5, 13)
MN goes through
(2,3)(-3,2)Slope:-
m=2-3/-3-2=-1/-5=1/5Slope of perpendicular line:-
-5Passes through k(3,-3)
Equation in point slope form
y-y1=m(x-x1)y+3=-5(x-3)y+3=-5x+15y=-5x+12Check one by one
0=-5(-12)+12=60+12=722=-5(2)+12=-10+12=2Yes option B is correct
Answer:
(2, 2)
Step-by-step explanation:
First find the slope of the line MN, using the two given points:
[tex]\sf let\:(x_1,y_1)=(2,3)[/tex]
[tex]\sf let\:(x_2,y_2)=(-3,2)[/tex]
[tex]\implies \sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-3}{-3-2}=\dfrac15[/tex]
If two lines are perpendicular to each other, the product of their slopes will be -1.
Therefore, the slope (m) of the line perpendicular to MN is:
[tex]\implies \dfrac15 \times m=-1[/tex]
[tex]\implies m=-5[/tex]
Using the point-slope form of the linear equation with point K (3, -3), we can construct the linear equation of the line perpendicular to MN:
[tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-(-3)=-5(x-3)[/tex]
[tex]\implies \sf y=-5x+12[/tex]
Now we have the equation of the line perpendicular to MN, we can input the x-values of the solution options to see which once is correct:
[tex]x=0\implies \sf y=-5(0)+12=12\implies (0,12)[/tex]
[tex]x=2\implies \sf y=-5(2)+12=2\implies (2,2)[/tex]
[tex]x=4\implies \sf y=-5(4)+12=12\implies (4,-8)[/tex]
[tex]x=5\implies \sf y=-5(5)+12=-13\implies (5,-13)[/tex]
Therefore, the point that is on the line that is perpendicular to MN and passes through point K is (2, 2)
An empty box weighs 13 ounces. The box is packed with large and small apples. Each large apple, I, weighs 4. 5
ounces and each small apple, s, weighs 3 ounces.
Enter an equation that can be used to determine the total weight, w, in ounces, of the loaded box containing / large
apples and s small apples.
Answer:
W = 13 + 4.5l + 3s
Step-by-step explanation:
We would have to add 13 because it's the natural weight. We don't know how many apples there are, but we know much weight is in each one. We will use the letters as the unknown. Then we will use 4.5 for L, and 3 for s
What specific measure of a geometric figure is shown in the image?
Answer:
A 140 degree angle. Think about where 90 degree angle is, where 180 degree angle is, and recognize that 140 degree angle is in between those. Also, when it's saying side length, it's just saying how long the line itself is;)
Step-by-step explanation:
Answer:
A 140° angle
Step-by-step explanation:
It can be seen that the angle between 2 rays is being measured. Conveyor scale indicates 140° angle.
Hope this helps
One sector has an area of 167 square inches and an arc measure of 110°.
The area of the circle that contains the sector is 546.5 in² (rounded to the nearest tenth)
Calculating area of a circleFrom the question, we are to determine the area of the circle.
The area of a circle can be determined by using the formula,
[tex]A = \pi r^{2}[/tex]
From the given information,
Area of the sector = 167 in²
Arc measure = 110°
Using the formula,
[tex]Area\ of\ sector = \frac{\theta}{360 ^\circ} \times \pi r^{2}[/tex]
Then,
[tex]167= \frac{110 ^\circ}{360 ^\circ} \times \pi r^{2}[/tex]
[tex]167= \frac{11}{36} \times \pi r^{2}[/tex]
[tex]\pi r^{2} =\frac{167 \times 36}{11}[/tex]
[tex]\pi r^{2} = 546.5 \ in^{2}[/tex]
Since area of the circle, A, is given by πr²
Then,
A = 546.5 in²
Hence, the area of the circle that contains the sector is 546.5 in²
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Here is the complete question:
Find the area of the circle that contains sector. Round to the nearest tenth, if necessary. One sector has an area of 167 square inches and an arc measure of 110°.
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Keisha's gym charges a one-time initial fee to join plus a monthly fee to maintain
membership. The graph below shows the cost of Keisha's gym membership.
select all the statements that are true about her gym membership costs.
The cost for 6 months is $120.00.
The initial fee to join the gym is $20.00.
The initial fee to join the gym is $30.00.
The gym membership fee is $20.00 per month.
The gym membership fee is $30.00 per month
Answer:
B and E
Step-by-step explanation:
^
Can someone help me with this one
Answer:
15
Step-by-step explanation:
i belive its 15 i think you should look where the dot is
Please answer number 8
Answer:
0.05%
Step-by-step explanation:
(6x1000)+(1x10)+(8x1/1)+(9x1/10)+(4/100)=
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
[tex]\qquad \tt \dashrightarrow \:(6 \times 1000) + (1 \times 10) + (8 \times \frac{1}{1} ) + (9 \times \frac{1}{10} ) + \frac{4}{100} [/tex]
[tex]\qquad \tt \dashrightarrow \:6000 + 10 + 8 + \frac{9}{10} + \frac{4}{100} [/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{600000 + 1000 + 800 + 90 + 4}{100} [/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{601894}{100} [/tex]
or
[tex]\qquad \tt \dashrightarrow \:{6018.94}{} [/tex]
Simplify: 5(x - 12)
5x - 12
5x - 60
65x
7x
Answer:
5x - 60
Explanation:
[tex]\dashrightarrow \sf 5(x - 12)[/tex]
using distributive method : a(b + c) = a(b) + a(c)
[tex]\dashrightarrow \sf 5(x) +5(- 12)[/tex]
[tex]\dashrightarrow \sf 5x -60[/tex]
5. A bank has outstanding loans worth $10,000. Some were loan at 10% and some
were loaned at 7%. If the income from these loans was $820, how much was
loaned at 10%?
The total amount of the outstanding loan that the bank loaned at 10% interest rate is $4,000.
What are the linear equations that represent the question?a + b = $10,000 equation 1
0.1a + 0.07b = 820 equation 2
Where:
a = amount loaned at 10%b = amount loaned at 7%How much was loaned at 10%?Multiply equation 1 by 0.07
0.07a + 0.07b = 700 equation 3
Subract equation 3 from equation 2
0.03a = 120
Divide both sides of the equation by 0.03
a = 120 / 0.03
a = $4000
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what is the volume of this shape
Answer:
C -- 72
Step-by-step explanation:
Formula B x W x H
B = base
W = with
H = hight
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
Factor by grouping. (Pleaseeee helpppp lolll I don’t remember how to do this)
Answer:
(2v+3) (v^2+7)
Step-by-step explanation:
2v^3 + 3v^2 + 14v +21
v^2 (2v+3) + 7(2v+3)
= (2v+3) (v^2+7)
I think this is the correct answer from what I remeber, sorry if I may have it wrong.
Can someone please help me ? Thank youu !
Answer:
B
Step-by-step explanation:
Giving Brainliest! 10 Points! Select all the correct answers.
Each of these scatter plots has a line of fit for its data points. Which graphs have a line that is a line of best fit for the data points?
Answer:
A and D
Step-by-step explanation:
Plato/Edmentum answer
The graphs have a line that is a line of best fit for the data points are:
scatter plot of options A and D.
What is a scatterplot?A scatterplot is a type of graphical display that is used to represent the relationship between two continuous variables.
In a scatterplot, each point represents the values of the two variables, with one variable being plotted along the x-axis and the other variable being plotted along the y-axis.
The position of each point on the graph represents the values of both variables for that particular observation.
We have,
The line of best fit, also known as the regression line, is a straight line that is drawn through a scatter plot of data points to represent the trend or relationship between two variables.
In a scatter plot, the horizontal axis represents one variable, and the vertical axis represents the other variable.
The line of best fit is drawn in such a way that it minimizes the distance between the line and the data points.
We see that,
The scatter plot of option A and D graphs have a line that is a line of best fit for the data points.
Thus,
The scatter plot of option A and D graphs have a line that is a line of best fit for the data points.
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28.2
с
45.8
В
о
mzB =
Answer:
17.6
I hope this helps :)
The probability that juliana will take a particular type of dance class is shown in the chart below. She will definitely take either ballet or jazz, but not both. The probability that she will take jazz on wednesday night is 27%. If the probability that she will take ballet is 70%, what is the probability that she will take jazz on saturday morning?.
The probability that Juliana will take jazz on Saturday morning based on the decision tree given is 3%.
What is the probability that jazz is taken on Saturday morning?The probability that jazz is taken is:
= 1 - Probability of ballet
= 1 - 70%
= 30%
The probability that if jazz is taken, it will be taken on Wednesday is:
= Probability that jazz is taken on Wednesday night / Probability that Jazz is taken
= 27% / 30%
= 90%
The probability that Jazz is taken on Saturday morning is therefore:
= Probability that jazz is taken x (1 - Probability of Wednesday night)
= 0.3 x ( 1 - 90%)
= 3%
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Hunter earned a grade of 66% on his multiple choice math final that had a total of 200 problems. How many problems on the final exam did Hunter get wrong?
There are 68 problems on the final exam did Hunter get wrong.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Hunter earned a grade of 66% on his multiple choice math final that had a total of 200 problems.
Now,
Since, Hunter earned a grade of 66% on his multiple choice math final that had a total of 200 problems.
Hence, The correct problem = 66% of 200
= 66/100 x 200
= 66 x 2
= 132
Thus, The incorrect question = 200 - 132
= 68
Therefore, There are 68 problems on the final exam did Hunter get wrong.
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X^2 +8x+7
What is the vertex?
(X= -b/2a)
What is the Y intercept?
Step-by-step explanation:
any quadratic equation has the form
y = ax² + bx + c
so, we can see in our case
a = 1
b = 8
c = 7
the x value of the vertex is indeed camcorders by
x = -b/(2a) = -8/2 = -4
the corresponding y we get then
y = (-4)² + 8×-4 + 7 = 16 - 32 + 7 = -9
the vertex = (-4, -9).
the y- intercept is simply the point with x = 0 (and the corresponding y value).
which is c, because
y = 0² + 8×0 + 7 = 7
the y-intercept = (0, 7)
Jaime has a board that is 8 feet long. He cuts the board into three equal pieces. How long is each piece.
SHOW WORK PRETTY PLEASE WITH SUGARCANE JUICE!!!
A furniture store has a sale during which the sale price of a sofa is 1/3 off its original price. The original price
of the sofa is $1,029. A customer can get an additional 5% discount off the sale price for paying with cash. At
checkout, a 6.5% sales tax on the final price is added to the cost of the sofa. What is the total cost of the sofa,
including sales tax, for a customer paying with cash?
Answer:
$694.06
Step-by-step explanation:
OG price= 1,029
discount=.05
sales tax =.065
1/3(og price)=1/3(1029)=343
one third of $1,029 is 343, hence we take off $343 from the orginial price
1029-343= $686--> sales price
.05*salesprice= .05*686=34.3
subtract 5% discount: 686-34.3= $651.71
=find 6.5% tax: .065*651.71= $42.36
add 6.5% tax: 651.81+42.36=694.06
MAKE THIS INTO A TESTABLE QUESTION!!
"What do milkweed bugs eat"
pleasd help
Answer: what do milky buggies munch on UWU
Step-by-step explanation: