Answer: B) 5, −3, 1 over 2 are the zeros of f(x).
Step-by-step explanation:
Given function f(x)=[tex]2x^3-5x^2-28x+15[/tex]
If a is a zero of f(x) then f(a)=0
Let's check all the options
[tex]f(5)=2(5)^3-5(5)^2-28(5)+15\\=2(125)-5(25)-28(5)+15=250-125-140+15=0[/tex]
[tex]f(-3)=2(-3)^3-5(-3)^2-28(-3)+15\\=2(-27)-5(9)-28(-3)+15=-54-45+84+15=0[/tex]
[tex]f(\frac{-1}{2})=2\frac{-1}{2}()^3-5(\frac{-1}{2})^2-28(\frac{-1}{2})+15\\=2(\frac{-1}{8})-5(\frac{-1}{4})+14+15=\frac{-1}{4}-\frac{5}{4}+29=\frac{110}{4}=\frac{55}{2}\neq 0[/tex]
Therefore , 5 and -3 are zeroes of f(x).but -1/2 is not.
[tex]f(\frac{1}{2})=2\frac{1}{2}()^3-5(\frac{1}{2})^2-28(\frac{1}{2})+15\\=2(\frac{1}{8})-5(\frac{1}{4})-14+15=\frac{1}{4}-\frac{5}{4}-14+15=0[/tex]
⇒ 1/2 isthe third zero of f(x).
Here we got our three zeroes as 5,-3,1/2,rest other will not satisfy f(a)=0
Therefore B represents the zeroes of f(x).
The function f(t) = 5*cos ((pi/4)*t) + 11 represents the tide in Dark Sea. It has a maximum of 16 feet when time (t) is 0 and a minimum of 6 feet. The sea repeats this cycle every 8 hours. After six hours, how high is the tide?
A. 11 feet
B. 6 feet
C. 8.5 feet
D. 10.5 feet
After six hours, the tide is 11 feet high.
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."For given question,
We have been given a function [tex]f(t)=5\times cos((\frac{\pi}{4} )t)+11[/tex]
which represents the tide in Dark Sea and t represents the time in hours.
We need to find the height of the tide after 6 hours.
For t = 6, we need to find the value of function f(t)
[tex]\Rightarrow f(6)=5\times cos((\frac{\pi}{4} )6)+11\\\\\Rightarrow f(6)=5\times cos((\frac{3\pi}{2} ))+11\\\\\Rightarrow f(6)=0+11\\\\\Rightarrow f(6)=11[/tex]
Therefore, after six hours, the tide is 11 feet high.
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Write the slope-intercept form of the given line. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
n - (-24) =12 find the value
6.4 rounded to the nearest whole number
Which of the following values does not satisfy the inequality-2x-6is less than or equal to 1 A)-4 B)-3 C)-2 D)-1
Answer:
-4
Step-by-step explanation:
What is the product of −3 1/4 and −1 1/2 ? Enter your answer as a mixed number, in simplified form, in the box.
Answer:
Mixed number is [tex]4\frac{7}{8}[/tex] and the simplified form of this mixed number is [tex]\frac{39}{8}[/tex].
Step-by-step explanation:
The two mixed numbers are
[tex]-3\frac{1}{4}=-\frac{13}{4}[/tex]
and [tex]-1\frac{1}{2}[/tex]
= [tex]-\frac{3}{2}[/tex]
Now we will multiply these negative fractions.
[tex](-\frac{13}{4})(-\frac{3}{2})[/tex]
When two negative signs get multiplied they become positive.
= [tex]\frac{13}{4}\times \frac{3}{2}[/tex]
= [tex]\frac{39}{8}[/tex]
= [tex]4\frac{7}{8}[/tex]
Therefore, mixed number is [tex]4\frac{7}{8}[/tex] and the simplified form of this mixed number is [tex]\frac{39}{8}[/tex].
Two weeks ago, Star bought 3 cans of tennis balls. Last week, she bought 4 cans of tennis balls. This week, she brought 2 cans of tennis balls. The tennis balls cost d dollars per can. Write an expression in simplest form that represents the total amount that star spent.
For this case we have to:
d: Represents the cost in dollars for each can of tennis
Then we have according to the data that:
[tex]3d + 4d + 2d[/tex]
The above expression represents the total cost of the tennis cans that Star bought.
We simplify, adding the similar terms of the expression:
[tex]9d[/tex]
ANswer:
[tex]9d[/tex]
Edwin walks for 2 1/2 hours. He walks 1 2/3 miles in the first hour, 1 3/4 miles in the second hour and 1/4 of the total distance in the last 1/2 hour.What is the total distance Edwin walks?
Answer:
The total distance is 41/9 = 4 5/9 miles
Step-by-step explanation:
Total time is 2 1/2 hours.
First hour, he walks 1 2/3 = 5/3 miles.
Second hour, he walks 1 3/4 = 7/4 miles.
The last half hour he walks 1/4 of total distance. If we call total distance x.
[tex]\frac{5}{3} + \frac{7}{4} +\frac{x}{4} = x[/tex]
Now, we can eliminate the denominator, multiplying by four and by three.
[tex]5*4 + 7*3 + 3*x = 4*3*x\\20 + 21 + 3x = 12 x\\41 +3x = 12x \\41 = 12x - 3x\\41 = 9x\\x = 41/9\\x = 4 \frac{5}{9}[/tex]
Total distance is 4 5/9 miles
Use a five-step plan to solve the following word problem. Show all five steps in your response:
Doug is twice Anne's age. Doug is 34 years old. How old is Anne?
(01.02 MC)Betty had $70. She bought a necklace for $9 and a ring for $7. Which expression correctly shows the total money Betty has left?
A $70 − (−$9) + (−$7)
B $70 + (−$9) + (−$7)
C $70 − (−$9) − (−$7)
D $70 + (−$9) − (−$7)
answer choices
A
B
C
D
The expression correctly shows the total money Betty has left is $70 + (−$9) + (−$7). The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Betty had $70. she bought a necklace for $9 and a ring for $7. The expression for the amount left will be written below,
The amount of the necklace and ring will be deducted from the initial amount,
E = $70 + (−$9) + (−$7)
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There are three liters Of apple juice at a school party. 10 students want to drink all of the apple juice, and they all want to get exactly the same amount. How much apple juice can each student have?
To calculate the amount of apple juice each of the 10 students can have, divide the total volume of 3 liters by 10, resulting in 0.3 liters per student.
The question involves dividing a total volume of liquid evenly among a number of participants, which is a basic arithmetic problem in mathematics, specifically dealing with division.
To find out how much apple juice each student can have, you need to divide the total amount of apple juice by the number of students. There are 3 liters of apple juice and 10 students. So, each student can have 3 liters / 10 students = 0.3 liters of apple juice. A liter is a unit of capacity, and it's comparable to a jug of milk or a bottle of soda, which also holds a similar amount of liquid. Hence, the volume in this context is measured in liters. When you divide the total volume of apple juice by the number of students, you get the volume that each student will receive.
Gina bought six containers of yogurt for four dollars how many containers of yogurt could you to buy for $12
does each set of side lengths form a right triangle 10 m, 11 m, 15 m or 15 m, 8 m, 17 m,
10m, 11m, 15m is not a right triangle
15m, 8m, 17m is a right triangle
The perimeter of a rectangle is 24 inches. Find the dimensions if it’s length is 3 inches greater than its width
Isaiah’s family drove 348.2 miles per day on their vacation across county. How many miles did Isaiah’s family travel in 2.5 days?
multiply miles per day by number of days
348.2 * 2.5 = 870.5 miles
What are the factors of the expression? 6/7cd
Answer:
The factors of the expression are 6/7, c and d.
Step-by-step explanation:
The given expression is
[tex]\frac{6}{7}cd[/tex]
We need to find the factors of the expression.
Factors: Numbers and variables multiplied to get an expression, then these numbers and variables are known as factors.
The factor form of given expression is
[tex]\frac{6}{7}cd=\frac{6}{7}\times c\times d[/tex]
Therefore, the factors of the expression are 6/7, c and d.
What's the sum & classification of 3/10 and square root of 10?
3.31227766,irrational
3.31227766,rational
18.16227766,irrational
18.16227766,rational
Answer:
3.46227766; irrational
Step-by-step explanation:
The sum of 3/10 and √10 can be written mathematically as:
3/10 + √10
Taking the LCM which is 10
3/10 + √10 = 0.3 + 3.16227766
= 3.46227766
Since we cannot express the resulting value as a ratio of two integers, therefore the value is classified as an irrational number.
Grandma Jean is preparing the turkey for Thanksgiving dinner.The turkey weighs 12 lbs and there will be a total of 18 people at sinner.If each person eats the same amount of turkey,how much turkey will each person get
The temperature was 29*F. By the end of the day, the temperature dropped TO -7*F. what was the total distance in the temperature change?
at the animal shelter 5/8 are cats. Of the cats, 2/3 are kittens. What fraction of animals at the shelter are kittens?
How do you solve this?
maya tried to play a new video game.on her first 4 tries,she lost 14 points,lost 8 points,and finnaly gave up.write and find the value of an integer expression to show her final score
Mr. O’Brian is paid $7.30 per hour for 40 hours he works in a week. He is paid 1.5 times that rate for each hour after that
The length of a rectangle is three centimeters less than the width. If one area of the rectangle is 53 cm^2, find the dimensions of the rectangle. (explain how you got step by step)
Simplify: (13x + 10y) - (6x - 7y) +5x
John made $195 for 13 hours of work. At the same rate, how much would he make for 17 hours of work?
Final answer:
John's hourly wage is calculated to be $15 per hour. For 17 hours of work at this rate, John would earn $255.
Explanation:
John made $195 for 13 hours of work, which means his hourly wage is the total amount earned divided by the total hours worked. To find John's hourly wage we calculate $195 ÷ 13 hours = $15 per hour. To determine how much he would make for 17 hours of work at this same rate, we multiply his hourly wage by 17 hours.
$15 per hour × 17 hours = $255
Therefore, at the same hourly rate, John would make $255 for 17 hours of work.
Each row in a window display of compact disk cartons contains two more boxes than the row above. The first row has one box. How many rows will make to where there is 144 boxes
You have two fractions, 2/5 and 3/10, and you want to rewrite them so that they have the same denominator (and whole number numerators). What number(s) could you use for the denominator?
Choose the 2 answers that apply:
A. 15
B.5
C.20
D.10
HELP PLS I WILL GIVE BRAINLIEST AND TWENTY POINTS PLS HELP
How do I start the second part of this problem?
A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water wasted varies directly with the amount of time the faucet drips. What is the constant of variation?
A. 1/3
B. 2
C. 1/2
D. 3
Answer:
A. 1/3
Step-by-step explanation:
Suppose x represents the amount of the water ( in cups ) wasted in t minutes,
∵ The amount of water wasted varies directly with the amount of time the faucet drips,
⇒ x ∝ t
⇒ x = kt
Where,
k = constant of variation,
If x = 1, t = 3,
[tex]\implies 1 = k(3)\implies k = \frac{1}{3}[/tex]
Hence, the constant of variation is [tex]\frac{1}{3}[/tex]
OPTION A is correct.