Answer:
5/8
Step-by-step explanation:
1/4=2/8
2/8+1/8=3/8
8/8-3/8=5/8
3. How many y-values are there
for each x-value in the function
represented by the graph?
(A) 0
(C) 2
(B) 1
0 infinitely many
Simplify.
4x + 2(x + 5) + 1
A) 6x + 6
B) 4x + 8
C) 6x + 11
D) 5x + 8
Answer:
C is your answer for your question
Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3
What is lim f(x)?
Answer:
\(\displaystyle 51\)
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringFunctionsFunction NotationAlgebra II
Piecewise functionsCalculus
Limits
Right-Side Limit: \(\displaystyle \lim_{x \to c^+} f(x)\)Limit Rule [Variable Direct Substitution]: \(\displaystyle \lim_{x \to c} x = c\)
Limit Property [Addition/Subtraction]: \(\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)\)
Limit Property [Multiplied Constant]: \(\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)\)
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.\)
Step 2: Solve
Substitute in function [Limit]: \(\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3\)Factor: \(\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1]\)Rewrite [Limit Property - Multiplied Constant]: \(\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1\)Evaluate [Limit Property - Variable Direct Substitution]: \(\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1]\)Simplify: \(\displaystyle 51\)Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Lets find the square of the no. from 1 to 10. Then observe the digits at one's place of each square no. what did you notice Write a short note.
The observation of the pattern is discussed below.
When we calculate the squares of the numbers from 1 to 10 and observe the digits at the one's place of each square, we notice a pattern:
1²=1
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
9²=81
10²=100
If we focus on the digits at the one's place, we can see that they form a repeating pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. This pattern repeats itself as we calculate the squares of higher numbers.
This observation is known as the "digit at one's place pattern" or the "units digit pattern." It occurs because the square of any number depends only on the digit at the one's place of that number. Hence, when we square numbers that have the same digit at the one's place, we get the same digit at the one's place in the result.
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Find the other endpoint of the line segment with the given endpoint and midpoint.
Endpoint 1: (−3,−5)
Midpoint: (9,6)
Endpoint 2=
Answer:
Step-by-step explanation:
(x - 3)/2 = 9
x - 3 = 18
x = 21
(y - 5)/2 = 6
y - 5 = 12
y = 17
(21, 17)
Almonds are sold in 8-ounce and 20-ounce packages. What is the least number of ounces you can buy of each package to have equal amounts of each package size?
The least number of ounces you can buy of each package to have equal amounts of each package size is ounces
Answer:
40
Step-by-step explanation:
\(8=2^3 \\ \\ 20=2^2 \times 5 \\ \\ \lcm(8,20)=2^3 \times 5=40\)
Please answer I really need help!!
what is 0.01 as a fraction
Answer:
hey! this is simple! .01 is 1 out of 100.
Step-by-step explanation:
so the answe is, 1/100
Note: When solving for k, round to four decimal places. A culture started with 5,000 bacteria. After 3 hours, it grew to 6,500 bacteria. Predict how many bacteria will be present after 13 hours. Round your answer to the nearest whole number. P = Aekt Enter the correct answer. DONE + ?
Answer:
5000 * (e^((1 /4) * ln(55 / 50) * (13))) = 6,815.47 from My text book
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP!
19
The water ski club plans to build a new ramp for their ski shows in the shape of a triangular prism shown below
Answer:
24.8!
Step-by-step explanation:
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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3,864,950 rounded to the nearest ten thousand
Answer:
3,870,000
Step-by-step explanation:
The 5 rounds the 9 into a 10
The 10 rounds the 4 into a 5
The 5 rounds the 6 into a 7
Put them all together and you get 3,870,000
I hope this helps, and have a great day! :)
Each of students reported the number of movies they saw in the past year. Here is what they reported.10, 20, 11, 4, 10, 10 Find the mean number of movies that the students saw.If necessary, round your answer to the nearest tenth.
Answer:
10.8
Explanation:
Given the reported data
10, 20, 11, 4, 10, 10
We are to find the mean number of movies
Mean = Sum of the data/sample size
Sum of data = 10+20+11+4+10+10
Sum of data = 65
Sample size = 6
Mean number = 65/6
Mean number = 10.83
Mean number to nearest tenth is 10.8
The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5. Model the normal range of pH values of lemon juice, using a compound inequality.
1.5 > x > 4
1.5 < x < 4
1.5 ≤ x ≤ 4
1.5 ≥ x ≥ 4
The normal range using a compound inequality is 1.5 < x < 4
How to model the normal range using a compound inequality.From the question, we have the following parameters that can be used in our computation:
pH values less than 4
pH values greater than 1.5
Represent the pH values with x
Using the above as a guide, we have the following:
x is less than 4
x is greater than 1.5
When represented as inequality, we have
x < 4 and x > 1.5
Combine the inequalities
1.5 < x < 4
Hence, the normal range is 1.5 < x < 4
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For what values of theta do maximum r-values occur on the graph the polar equation r = 2 cos4 theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole
Answer:r=2 cos^4(theta)
Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.
First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:
r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.
Next, we can take the derivative of r with respect to theta, using the chain rule:
dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).
Setting this equal to zero and factoring out sin(2theta), we get:
sin(2theta)(-1 - 2cos(2theta)) = 0.
This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.
When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.
When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.
These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).
Write a two column proof (Given: x is the midpoint of WY and VZ) (Prove: VW=ZY)
Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.
To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.
By simplifying the equation, we can see that the equation becomes:
6x - 5x = 17 - 2
Simplifying further, we have:
x = 15
Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.
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A pool has the perimeter of 36
meters. The length of one side
is 10 meters. What is the width
of the pool?
Determine the measure of x in the diagram below:
x = °
The measure of angle x on the straight line is 130 degrees.
What is the measure of angle x?The sum of interior angles in a triangle equals 180 degrees.
To determine the value of x, we first determine its suplemetary angle x .
Hence:
40 + 90 + ( suplemetary angle of x ) = 180
Solve for the suplementary angle:
130 + ( suplemetary angle of x ) = 180
Suplementary angle of x = 180 - 130
Suplemetary angle of x = 50 degree
Now, we can find the measure of angle x.
Note that, sum of angles on a straight line equals 180 degree.
Hence:
x + ( suplemetary angle of x ) = 180
x + 50 = 180
Solve for x
x = 180 - 50
x = 130 degrees.
Therefore, the value of x is 130 degrees.
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(8x4+2x2−1)+(3x3−5x2+7x+1)=
Answer: 41 (i'm not really sure. but i was trying to help so please don't be mad
Step-by-step explanation:
8 * 4 = 32 3 * 3 = 9 and 5 * 2 = 10
2 * 2 = 4 9 - 10 = -1
32 + 4 = 36 -1 + 7 = 6 + 1 = 7
36 - 2 = 34
34 + 7 = 41
Help help please math almost done
Answer:
√113 is
Step-by-step explanation:
please mark me as brainlest
can u pls help me i am really stuck this is a geo problem pls get to me as soon as possible thanks.
Question: find the value of x.
Answer:
Please refer to the attachment
Tamika has $800 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $482.62.
She buys 3 bicycle reflectors for $10.84 each and a pair of bike gloves for $24.49.
She plans to spend some or all of the money she has left to buy new biking outfits for $52.93 each.
Which inequality can be used to determine o, the maximum number of outfits Tamika can purchase while staying within her budget?
The inequality that can be used to determine x, the number of outfits Tamika can purchase is; 539.63+ 52.93x ≤ 800
The given parameters are:
Budget = $800
New bicycle = $482.62
3 bicycle reflectors = $10.84 each
Pair of a bike gloves = $24.49.
New biking outfits = $52.93each.
Let the number of new biking outfits be x So, we have;
New bicycle + 3 . price of bicycle reflectors + Pair of a bike gloves + New biking outfits <= Budget
This gives;
482.62 + 3( 10.84) + 24.49+ 52.93x ≤ 800
This gives;
539.63+ 52.93x ≤ 800
Solve the inequality;
52.93x ≤ 260.37
Divide by 52.93
x ≤ 4.91
Hence, the inequality is 539.63+ 52.93x ≤ 800
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A trawler A is 40km west of another trawler B. A set off at 20kmh travel at 25kmh. What course should trawler B take to intercept trawler A
Trawler B should take a course that is 18 degrees east of north.
How to explain the angleIn order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.
Here are the steps to find the course that Trawler B should take:
Draw a diagram of the situation.
Label the two trawlers A and B.
Draw a line representing the direction that Trawler A is traveling.
Draw a line representing the direction that Trawler B should travel.
Measure the angle between the two lines.
The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.
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15 minutes before 7:00
Answer:
6:45
Step-by-step explanation:
Because 45 + 15 is 60 and since 6:60 isn't an actual way to express time, you would say 7:00
Have a nice day!!!
Answer:
15 minutes before 7:00 in the morning is 6:45 a.m.
Step-by-step explanation:
A square is drawn on the coordinate plane. The endpoints of one of its sides are located at (-2,4) and (-2,-11). What is a perimeter?
Answer:
60
Step-by-step explanation:
see attachment for explanation
What is the area of the obtuse triangle below?
Answer:
eleven times nine is ninety nine
Answer:
B.
Step-by-step explanation:
Ron's yearly income is $44,300 and has $4,400 withheld for taxes and $2,400 for personal deductions. If he gets paid biweekly, what is his net pay for each paycheck?
Answer:
Net biweekly pay for each paycheck is \(\$1442\)
Step-by-step explanation:
Employees paid biweekly are paid 26 times a year.
So, Required Biweekly net pay \(=\frac{44300-4400-2400}{26}\)
\(\approx 1442\)
Best Regards!
Since my uncles farmyeard apperas to be overrun with gos and chickens i asked him hom many of each did he have he responded that his dog and chicked had a total of 148 legs and 60 heads. hime mmay of each does he have
There are 14 dogs and 46 chickens in the farmyard.
The supposition that there are d dogs and c chickens.
Each chicken has two legs, but each dog has four.
Consequently, the total number of legs may be written as follows:
4d + 2c
Since we are aware that there are 148 legs in total, we can construct the following equation:
4d + 2c = 148
We may create another equation since we know that there are a total of 60 heads (dogs and chickens):
d + c = 60
Now that we have two equations with two variables, we may answer them both at the same time.
2d + 2c = 120 is the result of multiplying the second equation by two.
When we deduct this from the first equation, we obtain 2d = 28.
So, d = 14.
Reintroducing this into the second equation, we get:
14 + c = 60
So, c = 46.
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Mrs. Santos bought a dozen roses for P50.75 each. Each rose was matched with a handkerchief worth P100.25. How much did she spend in all?