Simon is factoring the polynomial. x2−4x−12 (x−6)(x ______) what value should simon write on the line? −6 −2 2 6
Answers
To factor the polynomial x^2-4x-12 using the method of factoring by grouping, we can first find two numbers whose product is -12 and whose sum is -4. These numbers are -6 and 2, because (-6) * (2) = -12 and (-6) + (2) = -4.
Using this information, we can rewrite the polynomial as:
x^2 - 6x + 2x - 12
Next, we can group the first two terms and the last two terms and factor out the common factors:
x(x - 6) + 2(x - 6)
Notice that both terms have a common factor of (x - 6), so we can factor it out:
(x - 6)(x + 2)
Therefore, the factored form of the polynomial x^2-4x-12 is (x-6)(x+2).
So, Simon should write the value -2 on the line.
Related Questions
at a school pep rally, a group of sophomore students organized a free raffle for prizes. they claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. the results do not seem that random to you. you think it is a little fishy that sophomores organized the raffle and also won the most prizes. your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. a. what are the expected frequencies of winners from each class? b. conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. report your chi square and p values.
Answers
The winners of the prizes are distributed throughout the classes as per the percentage of students in the respective group.
The total number of surveyed students is 36.
We calculate the expected number of students for each class is:
Class
Expected Frequency
Freshman
30% of 36 = 10.8
Sophomore
25% of 36 = 9
Junior
25% of 36 = 9
Senior
20% of 36 = 7.2
(b)
We set up:
H0: The number of observed winners is indifferent to the number of expected winners.
H1: The number of observed winners is not indifferent to the number of expected winners.
The Test Statistic Calculation Table:
Class Observed Frequency (fi) Expected Frequency (ei) (fi -ei )² /ei
Freshman 6 10.8 2.1333
Sophomore 14 9 2.7778
Junior 9 9 0
Senior 7 7.2 0.0056
Total = 36 36 4.9167
The calculated
\(x^{2}\) = 4.9167
The p-value for 4 - 1=3 degree of freedom for the above test score is 0.177999.
(c)
Since p-value (=0.177999) > α0..05 (standard level of significance),
H0 is failed to be rejected.
The number of observed winners is concluded to be indifferent to the number of expected winners, i.e., the winners of the prizes are distributed throughout the classes as per the percentage of students in the respective group.
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In the U.S., shoe sizes are defined differently for men and women, but in Europe, both sexes use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. What might be the problem with either the mean or the median as a measure of center?
Answers
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.
The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.
For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.
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PLS HELP ME ! ! ! ! !
Answers
Answer:
D (0, 2)
General Formulas and Concepts:
Algebra I
The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = 3/4x + 2
Step 2: Break Function
Identify Parts
Slope m = 3/4
y-intercept b = 2
CHOOSE ALL THAT APPLY
Which statements about geometric sequences are true?
There is more than one correct answer. Select all that apply.
-Geometric sequences have a common difference between terms.
-Geometric sequences can have a first term of 0.
-Geometric sequences are restricted to the domain of natural numbers.
-Geometric sequences have a common ratio between terms.
PLSSSS HELPPPPP
Answers
Answer:
Geometric sequences have a common ratio between terms. TRUE
hope it helped ;-;''
1. What is the linear scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³ (Record your
Answers
The linear scale factor of the enlargement is 6.7 (580 cm³/87 cm³). To the nearest hundredth, the linear scale factor of the enlargement is 6.70.
The surface area scale factor of the enlargement is 33.2 (290 cm³/8.7 cm³). To the nearest hundredth, the surface area scale factor of the enlargement is 33.17.
Surface area is the combined area of all the faces of a three-dimensional object. It is the area that is visible when looking at the outside of the object. It is often used to calculate the amount of material needed for a certain project or product. It is also used to calculate the cost and energy required to heat or cool a certain space. Surface area can be calculated using geometry and calculus, or it can be measured directly.
1. Linear scale factor: The linear scale factor of the enlargement is the ratio of the volume of the larger jar to the volume of the smaller jar. The volume of the larger jar is 0.58 L which is equivalent to 580 cm³. The volume of the smaller jar is 87 cm³. Therefore, the linear scale factor of the enlargement is 6.7 (580 cm³/87 cm³). To the nearest hundredth, the linear scale factor of the enlargement is 6.70.
2. Surface area scale factor: The surface area scale factor of the enlargement is the ratio of the surface area of the larger jar to the surface area of the smaller jar. The surface area of a jar depends on its radius. Since the radius of the larger jar is larger than the radius of the smaller jar, the surface area of the larger jar is larger than the surface area of the smaller jar.
Therefore, the surface area scale factor of the enlargement is greater than 1. To calculate this factor, we can use the formula for the surface area of a cylinder: A = 2πrh, where r is the radius and h is the height. The height of both jars is the same, so we can calculate the surface area scale factor by dividing the radius of the larger jar by the radius of the smaller jar. The radius of the larger jar is 0.29 L, which is equivalent to 290 cm³. The radius of the smaller jar is 8.7 cm³.
Therefore, the surface area scale factor of the enlargement is 33.2 (290 cm³/8.7 cm³). To the nearest hundredth, the surface area scale factor of the enlargement is 33.17.
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Complete questions as follows-
Use the following information to answer the next two questions Raj Jars Ltd. Sells different types of similar jars. One of their jars has a volume of 87 cm³ and another has a volume of 0.58 L. 1. What is the linear scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³ 2. What is the surface area scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³
Work out the length x. 14 cm 7 cm
Answers
Answer:
14 x 7 = 98 divided by 3= 32.6
Step-by-step explanation:
Are you trying to find the length of x?
i dont know if this is the right answer
3. Given the equation 2(4x+1)=qx+5, what value of q would result in the
equation having No Solution?
A. q=1
B. q=2
C. q=5
D. q=8
Answers
A shipping box has a volume of 1,000 cubic inches. What is the length of one side of the box?
Answers
The length of one side of the box is 10 inches.
How to find the volume of a cube?Suppose that: The side length of the considered cube is L units.
Then, we get the Volume of that cube = L³ cubic units.
The volume of a cube is of the form V = L³, where L is the side length.
Given that the shipping box has a volume of 1,000 cubic inches.
Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:
1000 = L³
Cube root both sides:
L = \(\sqrt[3]{1000}\)
Therefore, each side is 10 inches.
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Louisa wants to buy an online movie subscription that is on sale for
15% off. She writes the expression - 0.15c to represent the cost of
the subscription. Rewrite this expression in a different form to show
what percent of the original price she will pay for the online movie
subscription. Then compare your expression with Louisa's. How are
the expressions related? What does each expression tell you about
the problem situation?
Answers
Answer:
0.85cone is the cost; the other is the discountStep-by-step explanation:
a) As a fraction of the original price Louisa will pay ...
0.85c . . . . 85% of the subscription price
__
b) Louisa's expression (-0.15c) tells the amount of the discount, not the cost of the subscription. If Louisa were to write the cost of the subscription, her expression would be ...
c - 0.15c
__
c) The expression of (a) is the cost of the subscription; the expression Louisa wrote is the amount of cost reduction due to the discount.
There are 25 different dogs that need to be walked. Ashley randomly chooses 5. How many different combinations are there?
Answers
Answer:5?
Step-by-step explanation:
Answer:
53130
Step-by-step explanation:
It's a combination question.
You just have to calculate:
\(C=\frac{25P5}{5P5}\)
That means: \(\frac{25x24x23x22x21}{5*4*3*2*1}\)
And that would equal: \(\frac{6375600}{120} = 53130\)
Write down the order of rotational symmetry of the shape.
Answers
Answer:
the order of rotational symmetry of the shape is 2
Violet throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. How many seconds have gone by when the ball is at it's highest point?
Answers
From this graph , it takes 0.75 seconds to reach the highest position.
What exactly is graph?A graph is a visual representation of the relationship between two sets of data or variables, typically via lines or curves. A diagram or pictorial representation of facts or values that is arranged might be referred to as a graph in mathematics. The relationship between two or more items is frequently represented by the points on the graph
The graph indicates that the peak is at (0.75, 9)
The x-axis displays the time in seconds, while the y-axis displays the height in feet.
Consequently, it takes 0.75 seconds to reach the highest position.
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Please help me with edge question .
Answers
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)
(q12) Find the volume of the solid obtained by rotating the region under the curve
over the interval [4, 7] that will be rotated about the x-axis
Answers
To find the volume of the solid obtained by rotating the region under the curve over the interval [4, 7] about the x-axis, we can use the method of cylindrical shells.
The formula for the volume of a solid generated by rotating a curve f(x) about the x-axis, over an interval [a, b], is given by:
V = ∫[a, b] 2πx * f(x) * dx
In this case, the interval is [4, 7], so we need to evaluate the integral:
V = ∫[4, 7] 2πx * f(x) * dx
To find the function f(x), we need the equation of the curve. Unfortunately, you haven't provided the equation of the curve. If you can provide the equation of the curve, I will be able to help you further by calculating the integral and finding the volume.
Please provide the equation of the curve so that I can assist you in finding the volume of the solid.
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What are the values of the three trigonometric ratios for angle l, in simplest form? sin(l) = 4/5 cos(l) = 3/5 tan(l) = 4/3
Answers
The values of the three trigonometric ratios for angle L, in simplest form, are:
\(sin(L)=\frac{4}{5}\)\(cos(L)=\frac{3}{5}\)\(tan(L)=\frac{4}{3}\)To find the values of the three trigonometric ratios for angle L, in the simplest form:Given -
The triangle LMN is given in the question.
The measurement of side LM is 15 unitsThe measurement of side LN is 25 unitsThe measurement of side MN is 20 unitsAs the trigonometric properties of a triangle state that the value of sin, cos, and tan for the respective angle can be written as:
sin(L) = perpendicular / hypotenusecos(L) = base / hypotenusetan(L) = perpendicular / baseUsing the above trigonometric properties, the value of sin(L):
\(sin(L) =\frac{20}{25} =\frac{4}{5}\)Similarly, the value of cos(L):
\(cos(L)=\frac{15}{25} =\frac{3}{5}\)And, the value of tan(L) is:
\(tan(L)=\frac{20}{15} =\frac{4}{3}\)Therefore, the values of the three trigonometric ratios for angle L, in simplest form, are:
\(sin(L)=\frac{4}{5}\)\(cos(L)=\frac{3}{5}\)\(tan(L)=\frac{4}{3}\)Know more about trigonometric ratios here:
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The question you are looking for is given below:
What are the values of the three trigonometric ratios for angle L, in simplest form?
What is the greatest common
factor of the following three
numbers?
12, 18,32
Answers
hope this helps
Answer:
2
Step-by-step explanation:
12:1,2,3,4,6,12
18:1,2,3,6,9,18
32:1,2,4,8,16,32
h.c.f = 2
The diagram below shows part of the graph of the equation y=\(2x^{2}+ax+b.\) the graph intersects the x-axis at the points \((-\frac{7}{2}, 0) and (2,0)\). Find the value of a and the value of b
![The diagram below shows part of the graph of the equation y=[tex]2x^{2}+ax+b.[/tex] the graph intersects](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/YwYLuW7uDWzWPsV7UUhm0V4pOGEqefU9.jpeg)
Answers
The value of a is 3.
The value of b is -14.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The function of the graph is,
y = 2x² + ax + b
The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).
Now,
Since, The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).
Hence, The points must satisfy the graph of the function.
So, Points (-7/2, 0) and (2, 0) are satisfy the function y = 2x² + ax + b.
When point (-7/2, 0) satisfy the function y = 2x² + ax + b
Then,
0 = 2 × (-7/2)² + a × (-7/2) + b
0 = 49/2 - 7a/2 + b
7a/2 - b = 49/2 .... (i)
And, When point (2, 0) satisfy the function y = 2x² + ax + b
Then,
0 = 2 × (2)² + a×2 + b
2a + b = -8 .... (ii)
Add equation (i) and (ii) we get;
7a/2 - b + 2a - b = 49/2 + (-8)
11a/2 = 33/2
11a = 33
a = 3
And, 2a + b = -8
2 × 3 + b = -8
b = -8 - 6
b = -14
Hence, The value of a is 3.
The value of b is -14.
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Leonardo wrote an equation that has an infinite number of solutions. One of the terms in Leonardo's equation is missing, as shown below. Negative (x minus 1) + 5 = 2 (x + 3) minus box Which could be the missing term that Leonardo put into the box? x 3x 1 5
Answers
Answer:
The missing term is 3x
Step-by-step explanation:
Given
-(x - 1) + 5 = 2(x + 3) - _
Required
Find _
For proper identification of the parameters, represent _ with Z
So, the equation becomes
-(x - 1) + 5 = 2(x + 3) - Z
Open bracket (start from the left hand side)
-x + 1 + 5 = 2(x + 3) - Z
-x + 1 + 5 = 2x + 6 - Z
Solve like terms
-x + 6 = 2x + 6 - Z
Subtract 6 from both sides
-x + 6 - 6 = 2x + 6 - 6 - Z
-x = 2x - Z
Subtract 2x from both sides
-x - 2x = 2x - 2x - Z
-3x = -Z
Multiply both sides by -1
-3x * -1 = -Z * -1
3x = Z
Reorder
Z = 3x
Hence, the missing term is 3x
Answer:
answer is 3x
Step-by-step explanation:
look at image for question and answer
Answers
Please Answer! I have been working on this for an hour and can't get it!
Given A (4,2) and B (-1,y), what is y when the slope of AB is -7/5?
Answers
Because -1 to 4 is 5 which is the run from
rise/run
So we would apply 2 - 7
Which would be - 5
Give me brainliest if this helped
The circumference of a circle is 12.56 millimeters. What is the circle's radius?
C=12.56 mm
Use 3.14 for .
Answers
The radius of the circle is 2mm
How to determine the circumferenceIt is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.
The equation is written as;
C = 2πr
Such that the parameters are;
C is the cicumference of the circle.r is the radius of the circle.πtakes the constant value of 22/7From the information given, we have thatt;
The radius of the circle = r
The circumference = 12.56mm
Substitute the values, we have;
12. 56 = 2×3.14r
Multiply the values
r = 12. 56/6. 28
divide the values
r = 2mm
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help on this please
Answers
Answer: 382
You put the 3 in the hundred then add 70+12=82 So this is right
Just add 70+12 then add 300
Which of the following processes in the water cycle causes the formation of clouds?condensation evaporation infiltration transpiration
Answers
It is A: Condensation.
Condensation is the process by which water vapor in the air is changed into liquid water. Condensation is a apart of the water cycle because it is responsible for the formation of clouds.
Graphically, a point is a solution to a system of two inequalities if and only if the point
o lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality
O lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality
O lies in the shaded regions of both the top and bottom inequalities
x does not lie in the shaded region of the top or bottom inequalities.
Intro
Done
Answers
Answer:
Lies in the shaded regions of both the top and bottom inequalities.
Step-by-step explanation:
The point of solution for BOTH systems of inequalities must work for both equations. Therefore, the point has to lie in both top and bottom shaded regions or it won't work for both, but just one.
Answer:
C: Lies in the shaded regions of both the top and bottom inequalities.
Step-by-step explanation:
Hope this helps!
Me pueden ayudar con estos ejercicios porfa.
Answers
Step-by-step explanation:
a. 3x²+10x+8 = (3x+4)(x+2)
b. 4x²+21x-18 = (4x-3)(x+6)
c. 3x²+8x+5 = (3x+5)(x+1)
d. 6x²+5x-4 = (2x-1)(3x+4)
e. 15x⁴-23x²+4 =(5x²-1)(3x²-4)
f. 15x⁴+23x²+4 =(5x²+1)(3x²+4)
g. 6x²-7x-3 = (2x-3)(3x +1)
h. 6x²-43x+72 = (3x-8)(2x-9)
the hypotenuse of a right triangle is 29, and the legs are consecutive numbers, what is the sum of the legs
Answers
The sides are 20 and 21 in right triangle.
What defines a right triangle?
The term "right triangle" refers to a triangle with an interior angle of 90 degrees.
The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.The term "right triangle" refers to a triangle with an interior angle of 90 degrees. The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.
29² = x² + (x+1)²
x²+ x² +2x +1 = 841
2x² +2x -840 =0
x² + x -420 =0
(x+21)(x-20)=0
x=20
the sides are 20 and 21
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Use the rules of measurement to divide
Answers
Answer:
\( \frac{ {m}^3{} }{25} \)
Step-by-step explanation:
that is the answer
Correct answer gets brainliest!!!
Answers
The correct statements about a line segment are; they connect two endpoints and they are one dimensional.
option C and D.
What is a line segment?A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.
The following are characteristics of line segments;
A line segment has two definite endpoints in a line. The length of the line segment is fixed.The measure of a line segment is its lengthThe have one unit of measure, either meters, or centimeters etc.From the given options we can see that the following options are correct about a line segment;
They connect two endpoints
They are one dimensional
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every item is 80% off and the regular price of a t-shirt is 10$ what is its sale price
Answers
Answer:
2$
Step-by-step explanation:
10$ - 80%=2$
The sale price is 2$.
Each side length of the parallelogram at the right is multiplied by 4. Describe the change in the parameter. Justify your answer.
Answers
side length1 = x
side length2 = y
2x + 2y = perimeter
2(4x) + 2(4)y = new perimeter
8x + 8y = new perimeter
new perimeter = 4 times the old perimeter