Answers
9514 1404 393
Answer:
a) f(-2.5) = 62.6875; f(-1.5) = -13.0625; (-2.5, -1.5) contains a real root
b) there are 1 each of positive and negative real roots; 2 complex roots
c) -2 and 1/3 are the rational real roots
d) x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}
Step-by-step explanation:
a) f(-2.5) = 62.6875; f(-1.5) = -13.0625. The function changes sign between -1.5 and -2.5, so there is a real root in that interval.
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b) The given coefficients have one sign change, so there is one positive real root. Changing the signs of odd-degree terms makes the signs + - + - -, so there are three sign changes. There are 1 or 3 negative real roots, and possibly 2 complex roots. The constant term is non-zero, so zero is not a root. Here's your table:
positive real roots: 1
negative real roots: 1 or 3
complex roots: 2 or 0
zero roots: none
The graph is attached. It shows 2 real roots, one positive and one negative, so there are 2 complex roots. (There are 4 roots in total, so if only 2 are real, the other 2 are complex.)
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c) Possible rational roots are of the form ...
±{1, 2}/{1, 3, 9}
Listed, they are ...
±{1/9, 2/9, 1/3, 2/3, 1, 2}
The actual real roots are -2 and 1/3.
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d) The graph shows the real roots to be -2 and 1/3. The original leading coefficient of 3 is the product of the leading coefficients of the factors. Writing the factor (x -1/3) as (3x -1) lets us reduce the leading coefficient of the quadratic term from 9 to 3. The result of dividing factors (x+2) and (3x-1) from the original function is shown in the attachment. It is a parabola with vertex (-1/3, 2/3), so the factorization is ...
f(x) = (x +2)(3x -1)(3(x +1/3)² +2/3)
The roots of the quadratic term are ...
3(x +1/3)² = -2/3
x +1/3 = ±√(-2/9)
x = (-1 ±i√2)/3
So, the entire list of roots is ...
x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}
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Additional comment
The roots of a quadratic are easily found by knowing its leading coefficient and its vertex. If factoring known real roots from a higher-degree polynomial results in a quadratic, then the remaining complex roots are easily found. A graphing calculator is a wonderful tool for this process.
Related Questions
Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use pi equals 3.14 in any formulas used
Answers
Answer:
Perimeter = 65.12 in
Area = 292.48 in^2
which agrees with the second answer choice
Step-by-step explanation:
The perimeter is going to be the addition of the sides of the rectangle external to the composite figure ( 12 + 16 + 12 = 40) PLUS the length of half of the circumference or radius 8 inches (which is pi * radius = 3.14 * 8 = 25.12 in)
Then the total perimeter is:
Perimeter = 40 in + 25.12 in = 65.12 in
The are is going to be the area of the rectangle (12 * 16 = 192 square inches) PLUS the area of the semicircle of radius 8 in (pi *radius^2 /2 = 100.48 square inches).
Therefore the total area is:
Area = 192 + 100.48 = 292.48 in^2
10. Put the numbers into least to greatest order: -33/5, 3 1/3, 3.3, -3.5
Answers
Answer:
Answer:
Order from Least to Greatest
-33/5 < -3.5 < 3.3 < 3 1/3
Step-by-step explanation:
Three out of nineteen students will ride in a car instead of a van. How many ways can those three students be
chosen? Use the following formula.
n!
r
C(n, r) = r!(n-1)!
Answers
I need help please.
Answers
Answer:
D 18 percent
Step-by-step explanation:
So a percent s out of a hundred and you have 50 so it is more easy to double everything and make it a hundred
the equation should be 18 is what percent of 100 which is the same thing as 18/100
18 divided by 100 is .18
last question:) thanks guys
Answers
Answer:
5/12
Step-by-step explanation:
Probability of getting either heads or tails of a coin : 1/2
Probability of getting 1,2,3,4, or 6 on a dice: 5/6
Multiply those two probabilities : 1/2 * 5/6 = 5/12
You have a 5 out of 12 chances of getting heads on a coin AND any number but a 5 on a dice.
Hope this helps!
A singles tennis court measures (8x – 2) ft long and (3x – 3) ft wide.Which expression represents the area of the court?
Answers
Answer:
The expression that represents the area of the court is: [tex]24x^2 - 30x + 6[/tex]
Step-by-step explanation:
Area of a rectangle:
A rectangle has length l and width w. The area of a rectangle is:
[tex]A = lw[/tex]
A singles tennis court measures (8x – 2) ft long and (3x – 3) ft wide.
This means that [tex]l = 8x - 2, w = 3x - 3[/tex]
Which expression represents the area of the court?
The tennis court is rectangular, so
[tex]A = lw = (8x - 2)(3x - 3) = 24x^2 - 24x - 6x + 6 = 24x^2 - 30x + 6[/tex]
The expression that represents the area of the court is: [tex]24x^2 - 30x + 6[/tex]
Please help, I will give brainliest, I am struggling badly.
Answers
Answer:
3rd option is the amswer
Find a linear equation whose graph is the straight line with the given property.
Through (0.5, -2.25) and (1, -5.25)
Answers
Answer:
Step-by-step explanation:
-5.25+2.25 - 3
1-0.5 = 0.5
=-6 =m
y=-6x
What is the perimeter
Answers
Answer:
-2x + 3
Step-by-step explanation:
Perimeter means to add all the sides of the triangle. Simply combine like terms:
(3x) + (2x - 5) + (-7x + 8)
(3x + 2x - 7x) + (-5 + 8)
(5x - 7x) + (8 - 5)
-2x + 3
-2x + 3 is your answer.
~
Sara had $108 to spend on 8 books. After buying them she had $12 left. Let b represent the cost of each book. Which equation represents this situation?
Answers
Answer:
12
Step-by-step explanation:
you take 108-12=96
then you take 96/8=12
Please help, I will give brainliest, I am struggling badly.
Answers
Answer: y = 5/2x - 4
Step-by-step explanation:
the equation is y = ax + b (a ≠ 0)
because the slope of the line is 5/2 => a = 5/2
the line passes through (0; -4) => -4 = b
=> the equation is y = 5/2.x - 4
I need help, it’s geometry:
Answers
Answer: The area is 5x + 20
Step-by-step explanation:
Add all the numbers up.
7 + 4x - 8 = 3
13 + (x + 8) = (x + 21)
Therefore, your answer is 5x + 20
Let me know if you have any questions!
Which value for k makes the equation 42 ÷ k = 14 true? Select all that apply. A. 588 B. 62 C. 1452 D. 3 E. 23
Answers
3 is the value of k in the Linear equation .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
equation 42 ÷ k = 14
42/k = 14
42 = 14 * k
k = 42/14
k = 3
Learn more about Linear equation
brainly.com/question/11897796
#SPJ1
PLEASE ANSWER THIS QUESTION RIGHT.A ball thrown in the air has a height of h (t)
- 16t2 + 50t + 3 feet after t seconds.
Part A: What is the average rate of change for h(t) between t= 0 and t = 2?
A.36 Seconds per second
seconds per second
B.-36 feet per second
C.-18 seconds per second
D.18 feet per second
Answers
Need help don’t know what to do I’m confused
Answers
What is the inverse of the function f(x) = 2x+1
Answers
Answer:
The answer is b. h(x) = one-halfx – one-half
Step-by-step explanation:
Answer:
hey everyone its b!!!
Step-by-step explanation:
Determine the measure of ∠Z.
Question 5 options:
A)
41.76°
B)
13.29°
C)
87.71°
D)
48.24°
Answers
Answer:
A
Step-by-step explanation:
The measure of the angle Z is equivalent to 41.7°.
What is tangent function?The tangent function is one of the main six trigonometric functions and is generally written as tan (x). It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.Given is a right angle triangle XYZ.
Using the tangent function, we can write -
tan(Z) = XY/XZ
tan(Z) = 25/28
tan(Z) = 0.89
Z = tan⁻¹(0.89)
Z = 41.7°
Therefore, the measure of the angle Z is equivalent to 41.7°.
To solve more questions on angle measurements, visit the link below -
https://brainly.com/question/16570146
#SPJ2
Elena says I find 25.44 and then move the decimal point
Answers
Answer: help a homegirl out
Step-by-step explanation: let me get these points please
Simplify (3^5)^2/3^-2
Answers
Answer:
the answer would be 531441
Step-by-step explanation:
Answer:
531441
Step-by-step explanation:
Solve by elimination and show all steps please
3x=2y-7, 2x-y=10
Answers
Answer:
if you download the app photomath it will help you
Step-by-step explanation:
I promise!
Step-by-step explanation:
x=27 and y= 44
.......................
Select all that are equivalent to sin H.
1. cos H
2. cos Y
3. sin Y
4. sin W
5. tan W
6. cos(90-H)
7. sin(90-H)
Answers
Answer:
i believe 1-3-5
Step-by-step explanation:
Answer: the 2nd and 6th
Step-by-step explanation:
i did the test thing
Brandon is 5 years older than his brother Hermie. There combined age is 23. How old is Brandon?
Find Brandon's age using the following equation:
2 + (x + 5) = 23
A
9
14
15
Answers
Answer:
9
Step-by-step explanation:
9 +5 = 14
14 +9 = 23
HI, i have to turn this in by the end of the day! please help.
Answers
Answer:
Both are 77
Step-by-step explanation:
103 + 103 = 206
360 - 206 = 154
154/2 = 77
#2=77
#4=77
#3 is the same as #1, then subtract them from 360, divide that and you get 77 for the last two.
By definition, the determinant equals ad - bc. What is the value of when x = -2 and y = 3? I NEED HELP PLEASE
Answers
Answer:
B. -84Step-by-step explanation:
Taking the determinant of the matrices we will have;
= 4x(5y) - 2x(3y)
= 20xy - 6xy
= 14xy
Given x = -2 and y = 3
Determinant = 14(-2)(3)
Determinant = -28*3
Determinant = -84
Two students are reading a novel. Ashley reads 2 pages per day. Carly reads 1 page per day, but she starts early and is already on page 5. When will the two students read on the
same page?
Ashley:p=2d
Carly:p=d+5
Answers
Emmaline bought a new book for $12 with a coupon for 25% off, how much would it cost without the coupon
Answers
Answer:
$16
Step-by-step explanation:
[tex]0.75x = 12\\3x = 48\\x = 16[/tex]
What is the simplified form of (-3xy)(5xy-1)?
Answers
Answer:
-15x²y²+3xy
Step-by-step explanation:
((−3x)(y))(5xy−1)
=((−3x)(y))(5xy+−1)
=((−3x)(y))(5xy)+((−3x)(y))(−1)
=−15x²y²+3xy
Kimberly worked for 2 weeks. The shaded parts of the model represent the fraction of each week she worked from home.
Which expression can be used to determine the number of weeks Kimberly worked from home over these 2 weeks?
Answers
Answer
she worked 1 week and 1 day
Step-by-step explanation
The FitnessGram PACER Test is a multistage aerobic capacity test that progressively gets more difficult as it continues.
Answer:
Step-by-step explanation:
Two cities are 252 miles apart. How far are the two cities from one another on a map with a scale of 1/4 inches: 18 miles?
Answers
Answer:
3.5 inches
Step-by-step explanation:
create a proportion:
inches / miles = inches / miles
let 'x' = distance in inches
1/4 = x
18 252
18x = 252(1/4)
18x = 63
x = 63 / 18
x = 3.5
The area of rectangle RSTU is 36x2+25x−25. The length of the rectangle RSTU is 4x+5. Which expression describes the width of the rectangle RSTU?
Answers
Given:
The area of the rectangle RSTU = [tex]36x^2+25x-25[/tex]
Length of the rectangle RSTU = [tex]4x+5[/tex]
To find:
The width of the rectangle RSTU.
Step-by-step explanation:
We have,
[tex]36x^2+25x-25[/tex]
Splitting the middle term, we get
[tex]=36x^2+45x-20x-25[/tex]
[tex]=9x(4x+5)-5(4x+5)[/tex]
[tex]=(4x+5)(9x-5)[/tex]
We know that, the area of a rectangle is
[tex]Area=Length \times width[/tex]
Area of rectangle is product of (4x+5) and (9x-5).
Since (4x+5) is the length of the rectangle, therefore, (9x-5) is the width of the rectangle RSTU.
