The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:
x = 5, x = -1 + i, x = -1 - i.
How to obtain the solutions to the equation?The equation is defined by the rule presented as follows:
f(x) = 2x³ - 6x² - 16x - 20.
One solution for the equation is given as follows:
x = 5.
Because f(5) = 0.
Then (x - 5) is a linear factor of the function f(x), which can be written as follows:
2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).
This is because the product of a linear function and a quadratic function results in a cubic function.
Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:
2x³ - 6x² - 16x - 20 = = ax³ + (b - 5a)x² + (c - 5b)x - 5c.
Then these coefficients are obtained comparing the left and the right side of the equality as follows:
a = 2.-5c = -20 -> c = 4.b = -6 + 5a = 4.Hence the equation is:
2x² + 4x + 4.
Using a quadratic equation calculator, the remaining zeros are given as follows:
x = -1 + i.x = -1 - i.More can be learned about the solutions of an equation at brainly.com/question/25896797
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-7x + 6y = -4
14x-12y = 8
Answer:
Step-by-step explanation:
Using the equation of the function p(x) below, determine which of the statements below is true. Show your work.
*
1 point
Captionless Image
p(-2) > p(0)
p(-2) < p(0)
p(-2) and p(0) cannot be compared because p(-2) is undefined.
p(-2) and p(0) cannot be compared because p(0) is undefined.
The true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.
The given function is a logarithmic function and it is undefined at x = 0.
First, let us understand the logarithmic function:
A logarithmic function is a function of the form which is read as “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1.
We are given:
p(x) = log 5x
substitute x = 0 in the above equation, we will get;
p(0) = log 5 * 0
p(0) = log 0
p(0) = undefined
Thus, the true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.
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Three-eights of the seven grade students were taking advanced math at the beginning of the year, but seven dropped out by the end of the year. If there were 140140 students taking advanced math at the end of the year, how many total 7th grade students are there?
Answer:
147 * 3/8
1176/3 = 392
Kareem Abdul-Jabbar is the all-time leader in points scored in professional
basketball. He averaged 1,919.35 points scored each season. About how many points
did Kareem score during his twenty-year career?
Kareem Abdul-Jabbar scored a total of 38387 point in his career
MultiplicationIn math, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.
To find the number of points he had in his total career, we just need to multiply his points per season with the total number of years he spent play game.
This becomes 1919.35 * 20 = 38387 points
He had a total of 38387 points all time in his career
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what happens to the width of two-sided confidence interval as each of these attributes changes? - the confidence level increases - the sample size increases a. increases b. decreases
The width of two-sided confidence interval decreases as the sample size increases and increases as the confidence level increases.
Confidence interval : In Statistic, confidence interval is a range of estimates for unknown parameters.
The formula for the interval can be expressed as:
Confidence Interval (CI ) = X bar +_ Z( S/√n)
Where,
X bar ---> the sample mean
S ---> the sample standard deviation
n --> the sample size Z---> Z-value which comes from normal distribution
From the formula we can conclude the below points about confidence interval :
The increases in confidence level leds to increase the width of the confidence interval also. A larger confidence level means the interval is larger. the width of confidence interval varies inversely to sample size i.e increase in sample size implies decrese in width of confidence interval. .Confidence interval increases with increase of sample standard deviationsSo, Confidence interval varies with sample mean, confidence level and standard deviations.
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Multiply. Simplify the answer and write as a whole number.
7 1/2-1 1/5
The answer is in the form of whole number is 6 .
Given,
In the question:
The number is given as:
= [tex]7\frac{1}{2} - 1\frac{1}{2}[/tex]
Now, According to the question:
= [tex]7\frac{1}{2} - 1\frac{1}{2}[/tex]
Convert to fraction into mixed fraction:
= 15/2 - 3/2
Calculate the sum or difference:
= 12/2
Cross out the common factor:
= 6
Hence, The answer is in the form of whole number is 6 .
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1. Evaluate-[34+ (-16)-12].
a. 16
b. -16
C.-6
16
Step-by-step explanation:
[34-16-12]
[18-12]
16
a couple has 3 children. they sit in 5 adjacent seats in the same row while watching a movie. if the mother must sit in between the two youngest children, how many seating arrangements are possible?
Answer: well about 3
Step-by-step explanation:
father(youngest)mom(middle child)oldest
oldest(youngest)mom(middle child)father
father(middle child)mom(youngest)oldest
hope this helps:)
The table below shows results of a survey about who uses the World Wide Web.
User Percent
Business 34%
Education and Government 12%
Home 54%
If 600 people were surveyed, how many people used the World Wide Web for Business?
PLEASE HELP ASAP FOR 30 POINTS! !!!! Two Pony Express riders each rode part of a 336-mile trip. Each rider rode the same number of miles. They changed horses every 12 miles. How many horses did each rider use?
Answer:
28 horses
Step-by-step explanation:
336/12=28
because every 12 miles they change the horse.
Square LMNO has vertices L(-2, 2) M(2, 2) N(2, -2) O(-2, -2). Find the coordinate of the image after a 180 degree rotation around (0,0) for point L.
Check the picture below, assuming counter-clockwise rotation.
PLEASE HELP ME!
Show that quadrilateral ABCD is a parallelogram. A(-3,-2) B(-1,2) C(1,1) D(-1,-3)
Answer:
Step-by-step explanation:
With corners as
A
(
−
2
,
−
1
)
,
B
(
1
,
2
)
,
C
(
5
,
2
)
and
D
(
2
,
−
1
)
, let us find slopes of each side of the parallelogram
A
B
C
D
.
Slope of
A
B
is
2
−
(
−
1
)
1
−
(
−
2
)
=
3
3
=
1
Slope of
B
C
is
2
−
2
5
−
1
=
0
4
=
0
Slope of
C
D
is
(
−
1
−
2
2
−
5
=
−
3
−
3
=
1
Slope of
D
A
is
−
1
−
(
−
1
)
2
−
(
−
2
)
=
0
4
=
0
As slopes of alternate sides of quadrilateral are equal, alternate sides are parallel to each other
and
A
B
C
D
is a parallelogram.
Please solve the question below
Answer:
be chill bro but which subject is this
For each value of X, determine wether it is a solution to
The solutions of -1 + 3x ≥ 14 are 5 and 8.
Linear Inequality:A linear inequality is a Mathematical expression that represents that both sides are not equal. In simple words, we can say that If the relationship makes a non-equal comparison between any two numbers or expressions, then it is known as Linear inequality.
Here we have
-1 + 3x ≥ 14
To determine the solutions of a given linear inequality substitute each value of x and check if the value satisfies the given expression
At x = 5 ⇒ -1 + 3(5) ≥ 14
⇒ -1 + 15 ≥ 14
⇒ 14 ≥ 14
∴ x = 5 is a solution to -1 + 3x ≥ 14
At x = 8 ⇒ -1 + 3(8) ≥ 14
⇒ -1 + 24 ≥ 14
⇒ 23 ≥ 14
∴ x = 8 is a solution to -1 + 3x ≥ 14
At x = -4 ⇒ -1 + 3(-4) ≥ 14
⇒ -1 - 12 ≥ 14
⇒ - 13 ≥ 14 [ which is not true ]
∴ x = - 4 is not a solution to -1 + 3x ≥ 14
At x = 2 ⇒ -1 + 3(2) ≥ 14
⇒ -1 + 6 ≥ 14
⇒ 5 ≥ 14 [ which is not true ]
∴ x = 2 is a solution to -1 + 3x ≥ 14
Therefore,
The solutions of -1 + 3x ≥ 14 are 5 and 8
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The original price of the flowers was $80, but with discount she paid $60. What percent of the flowers she did NOT pay?
The percentage of flowers she did not pay for is 25% (option A)
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
For instance, 25% means 25/100. This means that 25% of a 50mangoes is 25/100× 50 =12.5mangoes
Similarly, the discount when she paid $60 instead of $80 is $80-$60= $20
therefore %discount = 20/80 ×100= 2000/80= 25%
therefore the percentage she did not pay for is 25%
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HELP PLEASE SOLVE ITS SLOPE!
Step-by-step explanation:
1. gradient=y2-y1/x2-x1
=21-9/-7-(-12)
=21-9/-7+12
=12/5
2.consider any two coordinates:
(13,32),(7,33)
gradient:
=33-32/7-13
=1/-5
If a fair die is rolled 6 times what is the probability rounded to the nearest thousandth of getting at least 5 fours?
To get 1 four, probability is 1/6
To get 2 fours, probability is (1/6)^2
So
To get 5 fours, probability is (1/6)^5 = 0.0001286
please help i have a test tomorrow and i dont know how to do this
Answer:
90 - 2x
Step-by-step explanation:
Angle A and B are both equal as both connect to the middle of the circle
ABO = [tex]x[/tex]
BAO = [tex]x[/tex]
Look at the diagram I attached
Angle ABC is = [tex]x+90[/tex]
Angle BAC = [tex]x[/tex]
Total Angle in a Triangle = 180
[tex]x + 90 + x + ACB = 180[/tex]
[tex]180 - 90 - 2x = ACB[/tex]
[tex]ACB = 90 - 2x[/tex]
Determine which set of side measurements could be used to form a right triangle. square root of 19 comma square root of 35 comma 54 square root of 15 comma 6 comma square root of 51 5, 8, 30 5, 6, 7
As per the concept of right angled triangle, the set of side measurements that could be used to form a right triangle is √15, 6, and √51
Right-angle triangle:
Right angle triangle means a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Given,
√19, √35, 54
√15, 6, √51
5, 8, 30
5, 6, 7
Now, we have to determine which set of side measurements could be used to form a right triangle.
Here we know that, according to the Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
So, by using Pythagoras' theorem:
Option (2) √15, 6, √51
Makes the right angle triangle,
Because when we verify these by using the Pythagoras theorem,
(√15)² + (6)² = (√51)²
15 + 36 = 51
51 = 51
Therefore, the set of side measurements that could be used to form a right triangle is √15, 6, and √51 option (2) is correct.
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if the same number is added to both numerator and denominator of the fraction 3/5. the result is 2/3 what is the number?
Answer:
2
Step-by-step explanation:
Decribe and correct the error in fining the um 2 5/6(-8/15)=12/6(-8/15)=65(-16)/30=49/30=1 19/30
Error free in finding the sum of 2 is 9/30
we need to correct the error and find the sum of 2
= [tex]\frac{5}{6}[/tex] + ([tex]\frac{-8}{15}[/tex])
let's find the l.c.m of both
LCM stands for 'Least Common Multiple'. The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers. It can be calculated for two or more numbers as well. There are different methods to find the LCM of a given set of numbers. One of the quickest ways to find the LCM of two numbers is to use the prime factorization of each number and then the product of the highest powers of the common prime factors will be the LCM of those numbers.
= 25 -16 / 30
= 9/30
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bro someone help me i dont understand anything
Answer:
pretty sure its the 2nd, 3rd, and 5th one
(Sorry if im wrong)
Step-by-step explanation:
with explanation if possible .
part a and b.
The coordinates on the x-axis (the x-intercepts) and y-axis (the y-intercepts) are;
(a) (i) The point, A = (6, 0)
(ii) The point B = (0, 6)
(b) The point A = (4, 0)
The point B = (0, 3)
What are the x and y-intercepts of a graph?The x and y-intercepts are the points at which the graph intersects the x-axis and the y-axis respectively. The coordinates of the points are (x, 0) and (0, y) respectively.
(a) (i) The equation of the line of the graph is; x + y = 6
The x-intercept of the line is at point A
The y-intercept of the line is at point B
At the x-intercept, the y-coordinate is 0, from the equation, x + y = 6, when y = 0, we get;
x + y = 6
x + 0 = 6
x = 6
The coordinate of the x-intercept, A = (6, 0)
(ii) The y-coordinate of the y-intercept is the value c of the equation of the line y = m·x + c
The x-coordinate at the y-intercept is 0
Rearranging the equation, x + y = 6, we get;
y = -x + 6
The y-coordinate at the y-intercept is therefore, c = 6
The point B is therefore; (0, 6)
(b) (i) The equation of the line is 4·y + 3·x = 12
The equation can be rearranged so that we get;
4·y + 3·x = 12
4·y = 12 - 3·x
y = (12 - 3·x) ÷ 4 = 3 - (3/4)·x
y = 3 - (3/4)·x
At the x-intercept, the value of y is 0. Plugging in y = 0 in the equation, y = 3 - (3/4)·x, we get;
0 = 3 - (3/4)·x
3 = (3/4)·x
x = 3 ÷ (3/4) = 4
x = 4,
y = 0 and x = 4, therefore the coordinate of the point A is (4, 0)
(ii) The y-intercept is point B
The x-value at the y-intercept is 0
Plugging the value x = 0 in the equation y = 3 - (3/4)·x, we get;
y = 3 - (3/4)× 0 = 3
x = 0 and y = 3
The coordinate of the point B is (0, 3)
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what is the volume of the following rectangular prism? 1 1/3 units 4 1/2 units2
indicate the answer choice that best completes the statement or answers the question. 1. how many different samples of size 3 (without replacement) can be taken from a finite population of size 10? a. 30 b. 1,000 c. 720 d. 120
The correct option is option (d).
Using Combination,
Total 120, different samples of size 3 (without replacement) can be taken from a finite population of size 10.
Population size: The population is the entire group of guesses. A sample is a specific group for which you collect data. It is denoted by N.
Sample Size: The sample size is always smaller than the total size of the population. A sample is a subset of the population set. It is denoted by n.
we have given that , n = 3 and N = 10
Using the following formula for calculating the possible number of different samples of size 3 (without replacement) can be taken from a finite population of size 10.
Number of possible different samples of size n from Population size N = NCn = N!/n! (N-n)!
then we have, 10C3 = 10!/3! × 7!
=> 10×9×8/3×2 = 15×8 = 120
Hence, 120 different samples of size 3 (without replacement) is possible from Population of size 10.
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Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges for each box of seeds. The equation p = -0.5x^2 + 36x -113 models the profit of the fundraiser. What's the smallest amount, in dollars, that you can charge and make a profit of at least $409?
The smallest amount that can be charged per box of seeds to make a profit of $409 is $20.125
What is a profit?A profit is the financial gain from a business transaction when the revenue from the transaction exceeds the expenses and taxes.
The function for the profit from the fund raiser is; p = -0.5·x² + 36·x - 113
When the profit is $409, we have;
p = 409 = -0.5·x² + 36·x - 113
-0.5·x² + 36·x - 113 = 409
-0.5·x² + 36·x - 522 = 0
The solutions of the above quadratic function, found using the quadratic formula are as follows;
x = (-36 ± √(36² - 4×(-0.5)×(-522)))/(2×(-0.5))
From which we have;
x = (-36 + √(36² - 4×(-0.5)×(-522)))/(2×(-0.5)) ≈ 20.125
x = (-36 - √(36² - 4×(-0.5)×(-522)))/(2×(-0.5)) ≈ 51.875
Therefore, when the profit is $409, the amount charged are x ≈ 51.875 or x ≈ 20.125
The smallest amount charged when the profit is $409 is therefore;
x ≈ $20.125
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Write an equation in slope-intercept form for the line that passes through (9, 12) and is perpendicular to y=4
Answer:
[tex]x=9[/tex]
Step-by-step explanation:
First, let's determine the slope! We know that the line is perpendicular to [tex]y=4[/tex]. This line is just a horizontal line that crosses the y-axis with a slope of 0. The line perpendicular to this will have the form [tex]x=?[/tex]. This is a straight, vertical line with indeterminate slope.
The line passes through the point (9, 12). If the line is going straight up and down, it will intercept every y-value, but only one x-value. The x-value in this ordered pair is 9. Therefore, the equation of the line is [tex]x=9[/tex].
The shape below is made of two rectangles joined together. 5 cm 9 cm 8 cm 5 cm Find the total area of the shape. Optional working Answer: cm²
Answer:
length × width
5×9=45cm²
45cm²×2=90cm²
Tthe total area of the shape is 85 cm².
How to solve for the areaRectangle 1:
Length = 9 cm
Width = 5 cm
Area of Rectangle 1 = Length * Width
= 9 cm * 5 cm
= 45 cm²
Rectangle 2:
Length = 8 cm
Width = 5 cm
Area of Rectangle 2 = Length * Width = 8 cm * 5 cm = 40 cm²
Total area of the shape
= Area of Rectangle 1 + Area of Rectangle 2 = 45 cm² + 40 cm²
= 85 cm²
Therefore, the total area of the shape is 85 cm².
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If f(x) = 3x -121, find the sum of values when f(x) = 4.
Write your answers for x as simplified fractions.
I
and x =
The sum of the values when f(x) = 4 is
The required value of the function x is 41.6
What is a function ?This relationship is typically represented as y = f(x), or "f of x," where y and x are coupled such that for each value of x, there is a specific value of y. This means that f(x) can only have one value for a given x. In set theory jargon, a function connects an element x to an element f(x) in another set.
Given : f (x ) = 3x - 121
to find ; value of f ( x ) when f (x) = 4
Since two values of f(x ) are given
we can simply equate these two values
and the answer which we will get is the final answer
thus we get
3x - 121 = 4
3x = 121 + 4
3x = 125
x = 125/ 3
x = 41.6
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Which function has x-intercepts at 4 and -6?
Function for which x -intercepts is at 4 and -6 is given by
y = k (x - 4)( x + 6).
As given in the question,
Let us consider f(x) be the required function.
y = f(x)
Standard form of a function whose x- intercepts is defined as x = a and
x = b is given by ;
f(x) = k (x - a ) ( x -b)
⇒ y = k (x - a ) ( x -b)
Where 'k' is constant which can be evaluate when quadratic function passes through point ( x₁ , y₁).
Here x - intercept is at 4 and -6
a = 4 and b = -6
Function for which x -intercepts is at 4 and -6 is given by :
y = k (x - 4) ( x -(-6))
⇒ y = k ( x - 4 ) ( x+ 6 )
Therefore, function for which x -intercepts is at 4 and -6 is given by
y = k (x - 4)( x + 6).
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