To find all zeros of f(x) = x^3 - 2x^2 - 4x + 8, we can use the Rational Root Theorem to test possible rational roots. The only rational root is x = 2. The complex roots can be found by dividing the equation by (x - 2) and solving the resulting quadratic equation.
Explanation:To find all zeros of the equation f(x) = x^3 - 2x^2 - 4x + 8, we can use the Rational Root Theorem to test possible rational roots. By factorizing the constant term, 8, and the leading coefficient, 1, we find that the possible rational roots are ±1, ±2, ±4, ±8. By testing these values in the equation, we can find that the only rational root is x = 2. To find the complex roots, we can use polynomial long division or synthetic division to divide the original equation by (x - 2) and solve the resulting quadratic equation.
Learn more about Zeros of a Polynomial Function here:https://brainly.com/question/29780212
#SPJ2
2. A package of paper towels contains 3 rolls. Each package of paper towels costs $2.79. A function, f(x), is written to represent the cost of purchasing x packages of paper towels. What is the practical domain for the function f(x)?
A. All real numbers
B. All whole numbers
C. All positive numbers
D. All whole numbers that are multiples of 3
Answer:
B
Step-by-step explanation:
Let x be the number of packages of paper towels.
Each package of paper towels costs $2.79.
Then x packages of paper towels cost $2.79x.
Hence, a function f(x) is
[tex]f(x)=2.79x[/tex]
Practically, you can buy 0 packages, 1 package, 2 packages and so on, only whole numbers of packages, so practical domain is all whole numbers.
(2b/3)^4 simplify the expression
Answer:
[tex]\large\boxed{\left(\dfrac{2b}{3}\right)^4=\dfrac{16b^4}{81}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{2b}{3}\right)^4\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{2^4b^4}{3^4}=\dfrac{16b^4}{81}[/tex]
Answer:
16b^4/81
Step-by-step explanation:
y=37*1.26^x is rhis a growth or a decay
Answer:
If x is greater than 1 it is growth, if it less than it is decay
Step-by-step explanation:
Write the equation of the circle with center (0, 0) and (−1, −3) a point on the circle. A) x2 + y2 = 4 B) x2 + y2 = 5 C) x2 + y2 = 10 D) x2 + y2 = 16
ANSWER
C)
[tex] {x}^{2} + {y}^{2} = 10[/tex]
EXPLANATION
The center of the circle is (0,0).
The circle passes through (-1,-3).
The radius can be obtained using the distance formula:
[tex]r = \sqrt{(0 - 1)^{2} + {(0 - - 3)}^{2} } = \sqrt{10} [/tex]
The equation is given as:
[tex]( {x - h)}^{2} + ( {y - k)}^{2}= {r}^{2} [/tex]
Where (h,k) is the center and r is the radius.
This implies that;
[tex]( {x - 0)}^{2} + ( {y - 0)}^{2}= {( \sqrt{10)} }^{2} [/tex]
[tex] {x}^{2} + {y}^{2} = 10[/tex]
pleeeeeeeeaaaseeeeee help meeeeeeee!!!!!!!!!
Answer:
Option D.
[tex]A =96\pi\ cm^2[/tex]
Step-by-step explanation:
The area of the circular bases is:
[tex]A_c = 2\pi(a) ^ 2[/tex]
Where
[tex]a=4\ cm[/tex] is the radius of the circle
Then
[tex]A = 2\pi(4) ^ 2[/tex]
[tex]A = 32\pi\ cm^2[/tex]
The area of the rectangle is:
[tex]A_r=b * 2\pi r[/tex]
Where
[tex]b=8\ cm[/tex]
b is the width of the rectangle and [tex]2\pi r[/tex] is the length
Then the area of the rectangle is:
[tex]A_r=8 * 2\pi (4)[/tex]
[tex]A_r=64\pi\ cm^2[/tex]
Finally the total area is:
[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]
[tex]A =96\pi\ cm^2[/tex]
Answer:
The correct answer is option B. 96π
Step-by-step explanation:
Points to remember
Surface area of cylinder = 2πr(r + h)
Where r is the radius of cylinder and h is the height of cylinder.
From the figure we get r = 4 cm and h = 8 cm
To find the surface area of cylinder
Surface area = 2πr(r + h)
= 2π * 4(4 + 8)
= 96π
The correct answer is option B. 96π
Which table of values represents the relationship between Roberts age and Julia’s age
Answer:
Option C is correct
Step-by-step explanation:
The relationship between Roberts age and Julia’s age is given by:
r = j+3 ....[1]
where,
r is the Robert's age and j represents the Julia's age in years
We have to find the table of values represents the relationship between Roberts age and Julia’s age
if r = 9 years
then;
[tex]9 = j+3[/tex]
Subtract 3 from both sides we have;
6 = j
or
j = 3 years
Similarly:
if r = 15 years
then;
[tex]15= j+3[/tex]
Subtract 3 from both sides we have;
12 = j
or
j = 12 years
If r = 21 years
then;
[tex]21= j+3[/tex]
Subtract 3 from both sides we have;
18 = j
or
j = 18 years
Therefore, the table of values represents the relationship between Roberts age and Julia’s age is, Table C
option c is the right answer
Can someone help me to solve this number 9?
I will say 1 block is 1 something okay cause I don’t have a key mini has an area of 2 (2x2=4/2=2) And the giant has an area of 32 (8x8=64/2=32) I don’t know if the small one became big or the big one became small so if the small to big is 16 big to small is 0.0625 or the numbers the other way around
Answer:
Area of left triangle = 2 * 2 / 2 = 2
Area of triangle on the right = 8 * 8 / 2 =32
32 / 2 = 16
Therefore the triangle on the right has 16 times the area than the triangle on the left.
Step-by-step explanation:
Let f(x) = 3x + 2 and g(x) =7x + 6. Find f ·g and its domain.
Answer:
[tex]f * g = 21x ^ 2 + 32x +12[/tex]
Domain: all real numbers [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
We have the functions [tex]f (x) = 3x + 2[/tex] and [tex]g (x) = 7x + 6[/tex]
We want to find f*g. Then we must multiply the function f by the function g.
Note that the function [tex]f (x) = 3x +2[/tex] is a linear function, therefore its domain is all real numbers. In the same way the function [tex]g (x) = 7x + 6[/tex] is also a linear function and its domain is all real numbers.
The multiplication of f * g will be
[tex]f * g = (3x + 2) (7x + 6)\\\\f * g = 21x ^ 2 + 18x + 14x +12\\\\f * g = 21x ^ 2 + 32x +12[/tex]
The function g(x) is a quadratic function and its domain is the intercept of the domain of f(x) with the domain of g(x), that is, all real numbers.
Kevin recorded the ages of the next 12 people who entered his grocery store. He asked his brother John to find the mean, median, and the mode of the data set: [ 6,18,8,4,18,20,10,10,21,6,17,18]. John's results are shown. mean =156/12=13. median = 20+10/2=15, mode=10. I'll post a picture of the questions.
Answer:
Step-by-step explanation:
6,18,8,4,18,20,10,10,21,6,17,18
Arrange the data in ascending order
4,6,6,8,10,10,17,18,18,18,20,21
Part A
Mean = 156/12 = 13 is correct
Median = 15 is incorrect because the data is not arranged. Median when there are even numbers will be: 10+17/2 = 13.5
Mode = 10 is incorrect, because mode is most repeating value and in the data set it is 18 so, Mode = 18
Part B
10,12 and 52 should be added in data set in ascending order
4,6,6,8,10,10,10,12,17,18,18,18,20,21,52
Mean = 230/15 = 15
Median = Middle term as odd numbers = 8th term = 12
Mode = 10 and 18
Part C
Both median and mean are used to measure central tendency.
The best measure of central tendency is considered median because the mean is affected by the presence of outliers while median is not affected by outliers.
Answer:
He is correct.
Step-by-step explanation:
I got 100% on my paper
(8-(-9))^2 + ((-3)-(-6))^2
Answer:
298
Step-by-step explanation:
Given
(8 - (- 9))² + (-3 - (- 6))² ← evaluate the parenthesis before squaring
= (8 + 9)² + (- 3 + 6)²
= 17² + 3²
= 289 + 9
= 298
Answer: (8+9)^2 + (-3 + 6)^2
= 17^2 + 3^2
= 289 + 9
= 298. ANS.
Find the missing lengths of the sides
Answer: option c
Step-by-step explanation:
You can use these identities:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]
Then, using the angle that measures 30 degrees, you know that:
[tex]\alpha=30\°\\opposite=8\\adjacent=b[/tex]
Substituting:
[tex]tan(30\°)=\frac{8}{b}[/tex]
Now you must solve for b:
[tex]b=\frac{8}{tan(30\°)}\\\\b=8\sqrt{3}[/tex]
Using the angle that measures 30 degrees, you know that:
[tex]\alpha=30\°\\opposite=8\\hypotenuse=c[/tex]
Substituting:
[tex]sin(30\°)=\frac{8}{c}[/tex]
Now you must solve for c:
[tex]c=\frac{8}{sin(30\°)}\\\\c=16[/tex]
ANSWER
The correct answer is C
EXPLANATION
The side adjacent to the 60° angle is 8 units.
The hypotenuse is c.
Using the cosine ratio, we have
[tex] \cos(60 \degree) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos(60 \degree) = \frac{8}{c} [/tex]
[tex] \frac{1}{2}= \frac{8}{c} [/tex]
Cross multiply
[tex]c = 8 \times 2 = 16[/tex]
Also
[tex]\cos(30 \degree) = \frac{b}{c} [/tex]
[tex]\cos(30 \degree) = \frac{b}{16} [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{b}{16} [/tex]
Multiply both sides by 16
[tex]b = 16 \times \frac{ \sqrt{3} }{2} [/tex]
[tex]b = 8 \sqrt{3} [/tex]
The correct answer is C
What is the sum of the integers below?
-9, 4, 10, -4, 8, -4
The sum of the integers -9, 4, 10, -4, 8, -4 is calculated by adding the numbers together, which totals 5.
To find the sum of the integers -9, 4, 10, -4, 8, -4, we add them together:
-9 + 4 + 10 + (-4) + 8 + (-4) = 5.
We can group the positive and negative numbers to make this simpler:
(4 + 10 + 8) = 22
(-9 - 4 - 4) = -17
Adding the results of the positive and negative groups gives us:
22 + (-17) = 5.
Therefore, the sum of the given integers is 5.
Victoria read a 160-page historical fiction novel followed by a science fiction novel of the exact same length. Her average reading speed of the science fiction novel was 2 pages per hour more than her average reading speed of the historical fiction novel. Victoria models her novel reading marathon with the following expression, where x represents her average reading speed of the historical fiction novel. What does x + 2 represent in this situation? A. the total time taken to read the novels B. the average reading speed of the historical fiction novel C. the average reading speed of the science fiction novel D. the number of pages of the science fiction novel
The answer is C: the average reading speed of the science fiction novel.
If x is her reading speed for the historical fiction novel, and her reading speed for the sci-fi novel is just two pages more than that of the historical fiction novel, then the equation to find out how fast she reads the science fiction novel would be x + 2, as you’re adding 2 to the reading speed of the historical fiction book (x)
Answer:
The answer to this question is correct but on PLATO the answer choice is actually A.
Step-by-step explanation:
PLATO
Write a parallel and perpendicular equation that passes through the point (6,-2)?
Answer:
y=x-8 and y=-x+4
Step-by-step explanation:
The slopes of the lines can be anything, as long as they are the opposite reciprocals of each other. Then you can plug in the point for x and y to solve for b in both lines (for y=mx+b where m is the slope)
a local city collects 8% sales tax if the total purchase was $216 then how much was collected for sales tax
If a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.
What is Percentage?A relative value indicating hundredth parts of any quantity is known as Percentage.
Given that a local city collects 8% sales tax
The total purchase was $216.
We need to find the amount collected for sales tax.
To find this we have to find 8% of 216.
Convert 8% to the decimal value.
8/100=0.08
Now multiply 0.08 with 216
0.08×216
$17.28
Hence, if a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ3
The amount collected for sales tax is $16.
Step 1: Understand the Problem
The total purchase amount ($216) includes the sales tax. We need to find how much of this amount is the sales tax itself.
Step 2: Convert the Percentage to a Decimal
Convert the sales tax rate from a percentage to a decimal.
[tex]\[ \text{Sales Tax Rate} = \frac{8}{100} = 0.08 \][/tex]
Step 3: Set Up the Equation
Let ( P ) be the pre-tax purchase amount and ( T ) be the total amount including tax. The relationship can be written as:
[tex]\[ T = P + \text{Sales Tax} \][/tex]
Since the sales tax is 8% of the pre-tax amount,
[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]
Thus, the total amount is:
[tex]\[ T = P + 0.08P = 1.08P \][/tex]
Step 4: Solve for the Pre-Tax Amount
We know the total amount ( T ) is $216.
[tex]\[ 216 = 1.08P \][/tex]
To find ( P ):
[tex]\[ P = \frac{216}{1.08} \][/tex]
[tex]\[ P \approx 200 \][/tex]
Step 5: Calculate the Sales Tax
Now, find the sales tax:
[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]
[tex]\[ \text{Sales Tax} = 0.08 \times 200 \][/tex]
[tex]\[ \text{Sales Tax} = 16 \][/tex]
Therefore the amount collected for sales tax is $16.
In 26 years, Peter will be 54 years old. In how many years will he be 75 years old?
Peter will be 75 years old in 47 years.
Answer:
In 47 years Peter will be 75 years old
Step-by-step explanation:
If Peter will be 54 years old in 26 years then subtract 26 from 54
54-26=28
This means that Peter is 28 right now, if you want to double check that work then add 26 to 28 implying that in 26 years Peter with be 54 years old
28+26=54
This shows that your calculations are correct! Now you have to figure out how many years from now will Peter be when he turns 75 years old, so you subtract his current age which is 28 from 75
75-28=47
Now to double check this add 47 to his current age which is 28
28+47= 75
This shows that your calculations are correct and it will take 47 years for Peter to be 75 years old!
pls help!! will give thx and 5star and brainliest
Answer:
12.A.) Heptagon
Step-by-step explanation:
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.
y = 7.5x
y = 5.5x + 10
1. Substitute: 7.5x = 5.5x + 10
How many classes could Anna take so that the total cost for the month would be the same?
5
classes
What is the total monthly cost when it is the same for both gyms?
$
How many classes could Anna take so that the total cost for the month would be the same?
5 classes
What is the total monthly cost when it is the same for both gyms?
$37.50
Step-by-step explanation:
The number of classes Anna could take so the total cost for the month would be the same is 5.
The total monthly cost when it is the same for both gyms would be $37.50.
What is the number of classes that the total cost would be the same?When the total cost is the same, both equations for the gym would be equal to each other.
7.5x = 5.5x + 10
In order to determine the value of x, take the following steps:
Combine similar terms
7.5x - 5.5x = 10
Add similar terms together
2x = 10
Divide both sides by 2
x = 5
Total cost = 7.5 x 5 = $37.50
To learn more about total cost, please check: https://brainly.com/question/25879561
#SPJ2
Someone please help I promise to mark brainlest!!!
Answer:
A
Step-by-step explanation:
Substitute the values of n into the recursive formula and check result against values in table
A
[tex]a_{2}[/tex] = 3 + 5 = 8 ← correct
[tex]a_{3}[/tex] = 8 + 5 = 13 ← correct
[tex]a_{4}[/tex] = 13 + 5 = 18 ← correct
[tex]a_{5}[/tex] = 18 + 5 = 23 ← correct
Answer:
the answer is A
Step-by-step explanation:
Which is the image of (-2, -5) reflected across X=2?
(-6, 5)
(-2,9)
(6,-5)
(2,9)
Answer:
(6,-5)
Step-by-step explanation:
As the point is 4 units to the left of X=2, the reflection must be 4 units to the right of X=2
A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.2 in. The slant height of the pyramid is 90.1 in. What is the height of the pyramid?
Answer:I THINK 89.3 in.
You can solve this problem with the Pythagorean Theorem. The base is a square. So half way across the middle will the right under the tip of the pyramid.
What is the reciprocal of 4 5/8
Answer:
8/45
Step-by-step explanation:
Write 4 5/8 as an improper fraction: 45/8.
Then invert this result, obtaining:
. This is the "reciprocal" of 4 5/8.
Answer:
37/8
Step-by-step explanation:
attachement ---
Use the quadratic formula to determine the exact solutions to the equation.
2x2−5x+1=0
Enter your answers in the boxes.
x =
or x =
ANSWER
[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]
or
[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]
EXPLANATION
The given equation is:
[tex]2 {x}^{2} - 5x + 1= 0[/tex]
Comparing this to
[tex]a {x}^{2} + bx + c = 0[/tex]
we have a=2, b=-5, c=1
The quadratic formula is given by
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
We substitute the values to get,
[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)(2)} }{2(2)} [/tex]
[tex]x = \frac{ 5 \pm \sqrt{ 17} }{4} [/tex]
[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]
or
[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]
What is the factored or of 25y^4 - 4z^2
Answer:
[tex](5y^2+2z)(5y^2-2z)[/tex]
Step-by-step explanation:
Use the difference of squares formula.
[tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]a=5y^2 \\ b=2z[/tex]
[tex](5y^2+2z)(5y^2-2z)[/tex]
The function f(x) is shown on the provided graph. Graph the result of the following transformation on f(x).
Answer:
Observe the attached image
Step-by-step explanation:
We have the graph of a line that passes through the points (0,5) and (2, 1).
The equation of the line that passes through these points is found in the following way:
[tex]y = mx + b[/tex]
Where
m = slope
[tex]m = \frac {y_2-y_1}{x_2-x_1}\\\\m = \frac{1-5}{2-0}\\\\m = -2\\\\b = y_2-mx_2\\\\b = 1 -(-2)(2)\\\\b = 5[/tex]
So
[tex]y = -2x + 5[/tex]
We must apply to this function the transformation[tex]f (x-4)[/tex].
We know that a transformation of the form
[tex]y = f (x + h)[/tex] shifts the graph of the function f(x) h units to the right if [tex]h <0[/tex], or shifts the function f(x) h units towards the left if [tex]h> 0[/tex].
In this case [tex]h = -4 <0[/tex] then the transformation [tex]f(x-4)[/tex] displaces the graph 4 units to the right.
Therefore if f(x) passes through the points (0,5) and (2,1) then [tex]f (x-4)[/tex] passes through the points (4, 5) (6, 1)
And its equation is:
[tex]y = -2(x-4) +5\\\\y = -2x +13[/tex]
Observe the attached image
Help me answer this question please
For this case we must find the inverse of the following function:
[tex]f (x) = x ^ 2 + 7[/tex]
For this we follow the steps below:
Replace f(x) with y:
[tex]y = x ^ 2 + 7[/tex]
We exchange the variables:
[tex]x = y ^ 2 + 7[/tex]
We solve the equation for "y", that is, we clear "y":
[tex]y^ 2 + 7 = x[/tex]
We subtract 7 on both sides of the equation:
[tex]y ^ 2 = x-7[/tex]
We apply square root on both sides of the equation to eliminate the exponent:
[tex]y = \pm\sqrt {x-7}[/tex]
We change y by[tex]f ^ {- 1} (x):[/tex]
[tex]f ^ {- 1} (x) =\pm\sqrt {x-7}[/tex]
Answer;
Option A
Jack and Nina are graphing two equations on a coordinate grid. Jack has graphed the equation y = 2x.
If Nina graphs y = 5x, where will her graph be in relation to the graph Jack made?
A) For all x > 0 the graph will be higher.
B) For all x > 0 the graph will be lower.
C) For all x the graph will be higher.
D) For all x the graph will be lower.
ANSWER
A) For all x > 0 the graph will be higher.
EXPLANATION
Jack's graph has equation
y=2x
This graph passes through the origin and has slope 2.
Nina's graph is y=5x.
This graph also passes through the origin and has slope 5.
Since 5 is greater than 2, for all x>0, Nina's graph will be higher.
Answer: A
Step-by-step explanation: Changing the 2 to a 5 makes an exponential growth function increase at a faster rate. Therefore, for all x > 0 the graph will be higher. At x = 0 the graphs will have the same value and for all x < 0, Nina's graph will be lower.
solve -30+15y/2+2y=-11
Answer:
[tex]\large\boxed{y=\dfrac{8}{37}}[/tex]
Step-by-step explanation:
[tex]Domain:\ 2+2y\neq0\to y\neq-1\\\\\dfrac{-30+15y}{2+2y}=-11\\\\\dfrac{-30+15y}{2+2y}=\dfrac{-11}{1}\qquad\text{cross multiply}\\\\(-30+15y)(1)=(-11)(2+2y)\qquad\text{use the distributive property}\\\\-30+15y=(-11)(2)+(-11)(2y)\\\\-30+15y=-22-22y\qquad\text{add 30 to both sides}\\\\15y=8-22y\qquad\text{add}\ 22y\ \text{to both sides}\\\\37y=8\qquad\text{divide both sides by 37}\\\\y=\dfrac{8}{37}[/tex]
5 x 3 x 2 +3/0 -45/3+1 =
options:
a)12
b)0
c)-1
d)impossible
PLEASE PLEASEEEEE HELPPP
I WILL MARK YOU BRAINLEST
[tex]5 \times 3 \times 2 + \frac{3}{0} - \frac{45}{3} + 1 = \\ \\ = \frac{3}{0} \\ \\ or \\ \\ 1. \: 30 + \frac{3}{0} - \frac{45}{3} + 1 \\ 2. \: 30 + \infty - \frac{45}{3} + 1 \\ 3. \: 30 + \infty - 15 + 1 \\ 4. \: \infty [/tex]
Yeah it's Impossible
Answer:
Yeah it's Impossible
Step-by-step explanation:
What is the sum of all odd numbers 10 to 55
Answer:
To sum consecutive numbers we use the formula:
n * (n+1) / 2
1 through 55 = (55 * 56) / 2 = 1,540
1 through 9 = (9 * 10) / 2 = 45
10 through 55 = 1,540 -45 = 1,495
********************************************************
EDITED
Gee, it seems I added ALL numbers from 10 through 55
ALL ODD numbers from 10 through 55 sum to
759
Step-by-step explanation: