Answers
Answer: The zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Step-by-step explanation: We are given to find the zeroes of the quadratic function below:
[tex]f(x)=8x^2-16x-15.[/tex]
To find the zeroes, we must find the roots of the following equation
[tex]f(x)=0\\\\\Rightarrow 8x^2-16x-15=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex].
We know that the roots of the quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
In the given quadratic equation , a = 8, b = -16 and c = - 15.
Therefore, the roots of the equation are
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-16)\pm\sqrt{(-16)^2-4\times 8\times (-15)}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{256+480}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{786}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm4\sqrt{46}}{16}\\\\\\\Rightarrow x=\dfrac{4\pm\sqrt{46}}{4}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{46}{16}}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{23}{8}}\\\\\\\Rightarrow x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Thus, the zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Option (C) is correct.
The zeroes of the given polynomial f(x) = 8x^2-16x-15 are x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8 Thus, Option C is correct.
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.
We are given to find the zeroes of the quadratic function f(x) = 8x^2 - 16x-15
f(x) = [tex]8x^2-16x-15[/tex] = 0
We know that the roots of the quadratic equation ax² + bx + c = 0 is
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
In the given quadratic equation , a = 8, b = -16 and c = - 15.
So,
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
x = -(-16) ± [tex]\sqrt{(-16)^2 - 4(8)(-15)}[/tex] / 2(8)
x = 16 ± [tex]\sqrt{256+ 480}[/tex] / 16
x = 16 ± [tex]\sqrt{786}[/tex] / 16
x = 4 ± [tex]\sqrt{46}[/tex] / 4
x = 1 ± [tex]\sqrt{23}[/tex] / 8
Thus, the zeroes of the given polynomial f(x) are
x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8. Option C is correct.
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Related Questions
How do I use the graph of the function to find the domain and range of f.
Answers
A cyclist rides his bike at a rate of
11
feet per second. What is this rate in miles per hour? How many miles will the cyclist travel in
3
hours? In your computations, use the fact that
1
mile is equal to
5280
feet. Do not round your answers.
Answers
First you would multiply 60 by 60 because there is 60 minutes in an hour and 60 seconds in a minute. Then you would multiply by 11 then divide by 5280 because there’s 5280 feet in a mile
In 3 hours they would travel: 22.5 miles
You would multiply 7.5 times 3
What is the justification for each step in the solution of the equation 3(2x + 7) - 4 = 53 - 3x?
Step 1: 3(2x + 7) - 4 = 53 - 3x
Step 2: 6x + 21 - 4 = 53 - 3x
Step 3: 6x + 17 = 53 - 3x
Step 4: 9x + 17 = 53
Step 5: 9x = 36
Step 6: x = 4
Answers
Final answer:
The equation 3(2x + 7) - 4 = 53 - 3x is solved through algebraic processes: distributing, combining like terms, transposing terms, isolating the variable, and dividing to solve for x, resulting in the solution x=4.
Explanation:
The justification for each step in solving the equation 3(2x + 7) - 4 = 53 - 3x involves algebraic manipulation:
Distribute the 3 into the parenthesis: 3(2x) + 3(7) - 4 = 53 - 3x becomes 6x + 21 - 4 = 53 - 3x.Combine like terms on the left side: 6x + 17 = 53 - 3x.Add 3x to both sides to get all x terms on one side: 9x + 17 = 53.Subtract 17 from both sides to isolate the term with x: 9x = 36.Divide both sides by 9 to solve for x: x = 4.Each step is justified by the rules of algebra which allow us to simplify and rearrange equations to isolate the variable. The final step gives us the solution x = 4.
Evaluate the expression when x = -15
-4x -11
A. -71
B. -49
C. 49
D. 71
Answers
Grandpa schmidt is 75 years old. this is 9 years less than seven times the age of junior schmidt. how old is junior
Answers
Seven times the age of junior = age of grandpa + 9 jears = 75 + 9 = 84 years
Hence, the age of junior will be 84 / 7 = 12 years. (Since 84 is seven times his age, you have to devide by seven).
--> Junior is 12 years old.
I hope I've been helpful, MarkV
Please i really need help on this one please!!!! :( I need an answer ASAP
Multiply r^2 + 7r + 10 / 3 by 3r - 30 / r^2 - 5r - 50
A. r + 2
B. 7r^2 - 20r - 300 / -5r - 5
C. (r + 5)( r + 2) / (r + 10)
D. 3r + 6 / 2
Answers
By factoring and simplifying the given polynomials, we found that the expressions simplify to r + 2. Therefore, the correct answer is option A. This process involves cancelling out common factors from the numerator and the denominator.
Polynomial Multiplication and Simplification
To solve the problem, we need to multiply the given rational expressions and simplify the result. The expressions are:
(r^2 + 7r + 10) / 3 and (3r - 30) / (r^2 - 5r - 50)
First, let's factor the polynomials where possible:
Factor the numerator of the first expression:[tex]r^2 + 7r + 10 = (r + 2)(r + 5)[/tex]Factor the denominator of the second expression: [tex]r^2 - 5r - 50 = (r - 10)(r + 5)[/tex]Now, the problem can be written as:
([tex](r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
Next, we simplify by canceling out the common factors:
[tex]=( (r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
The (r + 5) terms and the (r - 10) terms can be canceled:
[tex]= (r + 2) / 1[/tex]
So, the simplified answer is r + 2,
The correct option is A. r+2
If the hypotenuse is 41 inches and one of the legs is 40 inches, what is the lengh of the other eleg in inches
Answers
Which regular polygon can be used to form a tessellation?
octagon
decagon
triangle
nonagon
Answers
The regular polygon that could be used for tessellation is:
Triangle.
Step-by-step explanation:Tessellation is a geometry that is formed by a repeating pattern of same shape without any gaps.
We can use only three regular polygon for the formation of Tessellation:
1) Equilateral Triangle
2) Square
3) Regular Hexagon.
Hence, from the given option the regular polygon that can be used to form a tessellation is:
Triangle.
The rule (x, y)→(x+2, y−4) represents a translation 2 units ______
left
right
up
down
and 4 units _______
left
right
up
down
Answers
Since the x is positive and the x axis goes from left to right, it would go right.
But the Y is negative and goes up and down, it would go down.
The rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units down.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The rule (x, y)→(x+2, y−4)
As we know, when we go right side of the x-axis we add to the x-coordinate, and when we go left side of the x-axis we subtract to the x-coordinate.
The rule (x, y)→(x+2, y−4) represents a translation of 2 units right.
When we go upside of the y-axis we add to the y-coordinate, and when we go down the side of the y-axis we subtract to the y-coordinate.
The rule (x, y)→(x+2, y−4) represents a translation 4 units down.
Thus, the rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units down.
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Plz help! True or False. The response variable is plotted along the y-axis.
Answers
A probability distribution for all possible values of a sample statistic is known as a _____.
Answers
Answer:
Sampling Distribution
Step-by-step explanation:
A sample is a portion of the population chosen randomly or with certain techniques.
A statistic is a property of sample that describes the sample
Sampling distribution of statistic is a collection of all possible values of statistics for samples taken from the population. To be more precise it is probability distribution of all the outcomes of statistics of samples from the population.
Sample distribution of mean:
It can be defined as the probability distribution of all the feasible or possible means of samples of same size size taken from the population.
can somebody help me with these please ☺
Answers
This problem can be solved with a proportion.
Use x for the unknown height of the tree.
If 2 foot tall casts a shadow 5 ft long as x foot tall casts a shadow 55 ft long.
2/5 = x/55
Cross multiply:
5x = 110
x = 22
The tree is 22 ft tall.
Right problem
Look at the table. The input goes up by 1 each step. The corresponding output goes up by 3 each step. For each change of 1 in the input, the output changes 3.
Now look at the table, and fill in the output for inputs of 2, 1, and 0.
Each time the input goes down by 1, the output goes down by 3.
We have input 3 with output 10.
Then we can calculate:
input 2 with output 7
input 1 with output 4
input 0 with output 1
Since for each change of 1 in the input, the output changes 3, the slope is 3.
That means the equation is
y = 3x + b
b is the y-intercept. Since we calculated the output of 1 for an input of 0, the y-intercept is 1.
The equation is
y = 3x + 1
That means the expression for the output is 3n + 1
Answer: D. 3n + 1
if (2x-3) and (x+5) are multiplied to form the trinomial ax^2 +bx+c, what is the value of b
Answers
After using the trinomial The required value of b is 7.
What is a trinomial?
An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions use separators like +, -,, and that are symbols or operations. This algebraic expression encompasses polynomials, monomials, binomials, and trinomials. An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax2 + bx + c. Real numbers a, b, and c are present here, and a 0. Take the binomial (x + 2), for instance, and multiply it by (x + 2). The outcome is equal to x2 + 4x + 4.
Given, [tex](2x-3)[/tex] and [tex](x+5)[/tex] are multiplied [tex]= (2x-3)(x+5)[/tex]
[tex]= 2x(x+5) -3(x+5)[/tex]
[tex]= 2x^{2} +10x -3x-15\\= 2x^{2} +7x-15[/tex]
Now, comparing the calculated expression [tex]2x^{2} +7x-15[/tex] with the given equation [tex]ax^{2} +bx+c[/tex] , then we get, [tex]b=7[/tex]
Therefore, the required value [tex]b[/tex] is 7.
To learn more about trinomials
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I can't figure this out I need helppp!!!!
Answers
Darryl has $5 left in his pocket. He spent $16 on a book, $20 on a compact disc, and $2 on a magazine. How much money did he have at the beginning of the day?
Answers
Darryl had $43 at the beginning of the day.
Let's denote the initial amount of money Darryl had as [tex]\( M \)[/tex].
He spent $16 on a book, which we can denote as [tex]\( S_{book} = \$16 \)[/tex].
He spent $20 on a compact disc, which we can denote as [tex]\( S_{CD} = \$20 \)[/tex].
He spent $2 on a magazine, which we can denote as [tex]\( S_{magazine} = \$2 \)[/tex].
He has $5 left at the end of the day, which we can denote as [tex]\( L = \$5 \)[/tex].
The total amount spent, [tex]\( S_{total} \)[/tex], is the sum of the amounts spent on the book, the compact disc, and the magazine:
[tex]\[ S_{total} = S_{book} + S_{CD} + S_{magazine} \][/tex]
[tex]\[ S_{total} = \$16 + \$20 + \$2 \][/tex]
[tex]\[ S_{total} = \$38 \][/tex]
The initial amount of money Darryl had, [tex]\( M \)[/tex], is the sum of the total amount spent and the amount left:
[tex]\[ M = S_{total} + L \][/tex]
[tex]\[ M = \$38 + \$5 \][/tex]
[tex]\[ M = \$43 \][/tex]
How many solutions are ther to this equation.
Answers
Hope this helps!
Can u plz mark me as brainliest? I really need it!
Which graph represents the solution set of the system of inequalities?
{3y≥x−9
3x+y>−3
Answers
the solid line passes through (0,-3) and (0,9)
dotted line passes through (0,-3) and (0,-1)
see attached sketch
Answer:
The image shows the solution for the given inequalities.
Step-by-step explanation:
We are given the following information in the question:
[tex]3y \geq x-9\\3x+y>-3[/tex]
We have to plot the solution for the given inequality.
The image attached shows the solution to the given inequalities.
The red shaded portion is the solution to the first inequality and the blue shaded region is the solution for the second inequality.
The common shaded portion is the solution common to both the inequalities.
The dotted blue line is not a part of the solution for both the inequality.
the base is 12 the height is 17. and the apothem is 10 inches they are all inches. Triangular pyramid volume
Answers
If the slope and a point of a line are given, then the equation of the line can be written in point-slope form.
True
False
Answers
Becasue Point - slope form : y - y1 = m ( x - x1 )
( x1 , y1 ) is the point given ; m = slope is given .
You review a lease for a new apartment. The lease requires you pay the first month's rent, last month's rent and a security deposit of one month's rent, at the time of signing. The monthly rent is $500. How much will you need at the time of signing?
Answers
Sasha can mow 3/8 of an acre of grass in 45minutes.how many acres of grass does Sasha now per hour?
Answers
[tex]\bf \begin{array}{ccll} \stackrel{acre}{grass}&\stackrel{minutes}{time}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{3}{8}&45\\ g&60 \end{array}\implies \cfrac{\frac{3}{8}}{g}=\cfrac{45}{60}\implies \cfrac{\frac{3}{8}}{\frac{g}{1}}=\cfrac{45}{60}\implies \cfrac{3}{8}\cdot \cfrac{1}{g}=\cfrac{45}{60} \\\\\\ \cfrac{3}{8g}=\cfrac{45}{60}\implies 180=360g\implies \cfrac{180}{360}=g\implies \cfrac{1}{2}=g[/tex]
A spinner has 4 equally-sized sections, labeled A, B, C, and D. It is spun and a fair coin is tossed. What is the denominator of the simplified fraction representing the probability of spinning “C” and flipping “heads”? P(spinning C and flipping heads) =
Answers
Answer:
1/8
Step-by-step explanation:
how do you do number 10?
Answers
*note that complementary = 90, supplementary = 180
9x + 9 = 90
9x = 90 - 9
9x/9 = 81/9
x = 9
hope this helps
By graphing the system of constraints, find the values of x and y that maximize the objective function. 25<=x<=75 y<=110 8x+6y=>720 y=>0 minimum for c=8x+5y a. c=100 b. c=225 2/3 c. c=633 1/3 d. c=86 2/3
Answers
x = 25
x = 75
y = 110
6y = 720 - 8x
and C = 8x + 5y
The minimum point for C is the point of intersection between 8x + 6y = 720 and x = 25
Substitute x = 25 into 8x + 6y = 720 we have:
8(25) + 6y = 720
200 + 6y = 720
6y = 720-200
6y = 520
y = ²⁶⁰/₃
Substitute x = 25 and y = ²⁶⁰/₃ into C
C = 8(25) + 5(²⁶⁰/₃) = 633¹/₃
Answer: Option C
What is gk can someone solve for gk
Answers
Answer:
7
Step-by-step explanation:
12 on the bottom right is 1 up the 11 on the bottom left, so 7 must be the right answer.
The sum of two consecutive odd integers is 24. find the integers. which equation can be used to find the first integer n
Answers
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. the probability of a player weighing less than 250 pounds is closest to:
Answers
μ = 200 lb, the mean
σ = 25, the standard deviation
For the random variable x = 250 lb, the z-score is
z = (x-μ)/σ =(250 - 200)/25 = 2
From standard tables for the normal distribution, obtain
P(x < 250) = 0.977
Answer: 0.977
Using the normal distribution, it is found that there is a 0.9772 = 97.72% probability of a player weighing less than 250 pounds.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 200[/tex].The standard deviation is of [tex]\sigma = 25[/tex].The probability of a player weighing less than 250 pounds is the p-value of Z when X = 250, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{250 - 200}{25}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
0.9772 = 97.72% probability of a player weighing less than 250 pounds.
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Which statement best describes how to determine whether f(x)=9-4x^2 is an odd function
Answers
the function 9-4x^2 only has one x with an exponent of two making it even
Can somebody help me with this?
Answers
Solve 3c − 5f = 55 for f. Show your work.
Answers
[tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for the given expression.
To solve the equation 3c - 5f = 55 for f, you need to isolate the variable f by performing a series of mathematical operations. Let's go step by step:
Start with the equation:
3c - 5f = 55
Add 5f to both sides to move the term involving f to one side of the equation:
3c = 5f + 55
Subtract 55 from both sides to isolate the term with f:
3c - 55 = 5f
Now, divide both sides by 5 to solve for f:
(3c - 55) / 5 = f
f = (3c - 55) / 5
So, [tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for (f).