Answer:
1512
LCM = 2 × 2 × 2 × 3 × 3 × 3 × 7
= 1512
Approximate the root by using a linearization centered at an approximate nearby number
√101
Linearization is the idea in calculus where if you zoom in really close onto a section of the graph, the curve and the tangent line will be extremely similar to each other.
We can use this idea and approximate nearby values to the tangent line.
The parent graph of a square root function is [tex]f(x)=\sqrt{x}[/tex].
There are two methods in which we can calculate the approximate value of [tex]\sqrt{101}[/tex] by using linearization techniques.
Method 1:Write equation of tangent line.Find the value of y at x = 101.Let's use the nearest perfect square to [tex]\sqrt{101}[/tex], which is [tex]\sqrt{100}[/tex]. When drawing the graph of the square root function, we use the point (100, 10) because where x = 100, y = 10 on a square root function.
Now, we have a point that the tangent line passes through, and we want to find the slope.
We can do so by taking the derivative of [tex]f(x) =\sqrt{x}[/tex].
[tex]f'(x)=x^\frac{1}{2}[/tex] [tex]f'(x)=\frac{1}{2} x^-^\frac{1}{2}[/tex] [tex]f'(x)=\frac{1}{2x^\frac{1}{2} }[/tex] [tex]}f'(x)=\frac{1}{2\sqrt{x} }[/tex]Plug in x = 100 to find the slope of the tangent line here.
[tex]f'(100)=\frac{1}{2\sqrt{100} }[/tex] [tex]f'(100)=\frac{1}{2(10)}=\frac{1}{20}[/tex]The slope of the tangent line at x = 100 is 1/20. Now, we can use the point and the slope of the tangent line to determine the equation for the tangent line.
(100, 10), m = 1/20
Point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex] [tex]y-(10)=\frac{1}{20}(x-(100))[/tex] [tex]y=\frac{1}{20}x-5+10[/tex] [tex]y=\frac{1}{20}x+5[/tex]To find the value of y at x = 101, plug this into the tangent line equation.
[tex]y=\frac{1}{20}(101)+5[/tex] [tex]y=\frac{101}{20}+5[/tex] [tex]y=\frac{101}{20} +\frac{100}{20} = \frac{201}{20}[/tex]201/20 is equal to 10.05. Let's estimate the error of this calculation to the actual value of [tex]\sqrt{101}[/tex], inputted into a calculator.
We get [tex]\sqrt{101}=10.04987562[/tex], which is extremely close to 10.05. Our estimate using linearization only has an error of 0.00012.
Method 2:You may have noticed that the first method uses little calculus, apart from taking the derivative of f(x).
The more "calculus-y" method involves finding the change in y in terms of the change of x.
We know that dy/dx is the the change in y due to a change in x, so we can use this to find the change in y when x = 101.
[tex]\frac{dy}{dx} =\frac{1}{2\sqrt{x} }[/tex]Solve for dy by mutliplying dx to both sides of the equation.
[tex]dy=\frac{1}{2\sqrt{x} } \cdot dx[/tex]The change in x is 1, because 101 - 100 = 1.
We want to find the change in y when x = 100, and has a change of 1. Therefore, we have:
[tex]dx=1[/tex] [tex]x=100[/tex]Plug these values into the equation [tex]dy=\frac{1}{2\sqrt{x} } \cdot dx[/tex] and solve for dy.
[tex]dy=\frac{1}{2\sqrt{200} } \cdot 1[/tex] [tex]dy=\frac{1}{2(10)}[/tex] [tex]dy=\frac{1}{20}[/tex]The change in y when x = 100 with a change of 1 is 1/20. We know when x = 100 the y-value is 10. Therefore, when x = 101, the change in y is 1/20, so y = [tex]10\frac{1}{20} = \frac{201}{20} = 10.05[/tex].
You can see that we get the same answer with either method.
Write the slope intercept form of the equation of the line through the given point plz
Answer: [tex]y=-x-5[/tex]
Step-by-step explanation:
Slope intercept form is [tex]y=mx+b[/tex], so we have to find a way to substitute the given information into the equation. We have [tex]m[/tex] because it gives us the slope. The slope is -1, as the directions state. Now, we substitute it in and solve for b:
Substitute -1 in for m⇒ [tex]y=-x+b[/tex] Substitute in the point (-1, -4) in for [tex]x[/tex] and [tex]y[/tex] respectively to get [tex]-4=-(-1)+b[/tex] Solve the equation to get b= -5After getting the y-intercept, you have the full equation!
Which number line represents the solutions to lx - 5| = 1?
Answer:
The answer is B, or the second one
Step-by-step explanation:
Write the sentence as an inequality 8 is less than 6 more than 3 times a number x
Answer:
Sometimes you have to think a little out of order to do this type of problem.... but here goes an explanation.
Step-by-step explanation:
8 is less than looks like this: 8 <
6 more than looks like this: +6
3 times a number x is: 3x
So
8 < 3x+6 meets the criteria
The inequality will be 8 < 3x+6 if the 8 is less than 6 more than 3 times a number x; the answer is 8 < 3x+6.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The sentence as an inequality 8 is less than 6 more than 3 times a number x:
From the question:
Here x is any real number:
The inequality will be:
8 < 3x+6 which represents 8 is less than 6 more than 3 times a number x
Thus, the inequality will be 8 < 3x+6 if the 8 is less than 6 more than 3 times a number x; the answer is 8 < 3x+6.
Learn more about inequality here:
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The system of equations can be solved using linear combination to eliminate one of the variables.
2x − y = −4 → 10x − 5y = −20
3x + 5y = 59 → 3x + 5y = 59
13x = 39
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
2x – y = –4
10x – 5y = –20
7x = 39
13x = 39
Answer:
D
Step-by-step explanation:
X2+6x-16) divided (x-2)
Answer:
let's hope for the best ....XD
Answer:
ummmm....iam sorry I tried but failed ,umm...I think he got your answer see from there!! sorry!!
Look at the figure below:
Make a two-column proof showing statements and reasons to prove that triangle NMT is similar to triangle PMN. (10 points)
Answer:
Step-by-step explanation:
Given:
m∠NPT = m∠TNM = 50°
To prove:
ΔNMT ~ ΔPMN
Solution:
Statements Reasons
1). m∠NPT = m∠TNM 1). Given
2). ∠NMP ≅ ∠NMP 2). Reflexive property
3). ΔNMT ~ ΔPMN 3). By AA property of similarity of two
triangles
11) Find the value for x for both diagrams please help me
Answer:
Step-by-step explanation:
11 a).
20x + 5 + 24x - 1 = 180
44x = 176
x = 176 / 44
x = 4
b). 6x = 5x + 10
x = 10
Is -3/4 greater or less than or equal-.75
Answer:
Equal to
Step-by-step explanation:
If you think of both numbers compared to 1 whole then they can be converted to each other.
What does the digit 6 represent in ?
Answer:
6 is in ten place and its place value is 60, 3 is in ones place and its place value is 3.
solve the system of linear equations by substitution.
x + 4y = 6
x - y = 1
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Answer:
(x, y) = (2, 1)
Step-by-step explanation:
Use the second equation to write an expression for x:
x = 1 +y
Substitute that into the first equation:
(1 +y) +4y = 6
5y = 5 . . . . . . . . subtract 1, collect terms
y = 1 . . . . . . . divide by 5
x = 1 +1 = 2 . . . use the expression for x to find x from y
The solution is (x, y) = (2, 1).
A waffle recipe calls for two and one over 4 cups of flour if John wants to make 1 1/2 times recipe how much flour does he need
Answer:
3 3/8
Step-by-step explanation:
U multiply 2 1/4 times 1 1/2 and it equals 3 and 3/8
Evaluate 5|7 - 9| - 2.
Answer:
5|7 - 9| - 2 = 8
Form a perfect-square trinomial. y = x2 + 2x + − 1−
Answer:
y = x^2+2x+1
Step-by-step explanation:
x^2+2x+1
= (x+1)^2
Answer:
The correct answer is y = x2+ 2x+ 1 − 1− 1
The blank spaces are positioned here for the problem:
y=x2+2x+___-1-___
I just did the assignment on Edge and got it correct.
Hope this helped!
Graphing Linear Equations Using a Table
Y=1/2x+2
plz help
Use the function below to find f(-4)
f(x) = 2^x
A. -8
B. 1/16
C. -16
D. 1/8
Answer:
B. 1/16
Step-by-step explanation:
f(-4) = 2^(-4) = 1/(2^4) = 1/16
If you get this, you are a critical thinker. I enter the garden. There are 44 people. You kill 40. How many people are in the garden?
Answer:
There are 5 people left in the garden because since you entered in the garden, that makes 44 people into 45 people. Then I killed 40 (as in me, not you).
Step-by-step explanation:
A giant tortoise can travel 0.14 miles in 1 hours .At this rate ,how long would it take to travel 2 miles ?
Answer:
about 14.3 hours
Step-by-step explanation:
The relation between time, speed, and distance can be written any of three ways:
time = distance/speeddistance = speed×timespeed = distance/time__
Here, the question asks for the travel time, so the relevant relation is the first one. Filling in the given values, we have ...
time = (2 mi)/(0.14 mi/h) ≈ 14.29 h
It would take about 14.3 hours to travel 2 miles.
Rebotar Inc.makes basketballs.Their fixed costs are $3,450.
Variable costs are $12per basketball.
if the basketball is priced at $25 and 300 basketballs are sold,did Rebotar break even?How do you know?Show all work.
Answer:
Since the profit is positive, Rebotar not only broke even, they had earnings.
Step-by-step explanation:
Function Modeling
The costs, incomes, and profits of Rebotar Inc. can be modeled by means of the appropriate function according to known conditions of the market.
It's known their fixed costs are $3,450 and their variable costs are $12 per basketball produced and sold. Thus, the total cost of Rebotar is:
C(x) = 12x + 3,450
Where x is the number of basketballs sold.
It's also known each basketball is sold at $25, thus the revenue (income) function is:
R(x) = 25x
The profit function is the difference between the costs and revenue:
P(x) = 25x - (12x + 3,450)
Operating:
P(x) = 25x - 12x - 3,450
P(x) = 13x - 3,450
If x=300 basketballs are sold, the profits are:
P(300) = 13(300) - 3,450
P(300) = 3,900 - 3,450
P(300) = 450
Since the profit is positive, Rebotar not only broke even, they had earnings.
Which is the best estimate for the percent equivalent to 3/8?
o26%
o27%
o37%
o38%
Answer:
o37%
Step-by-step explanation:
3/8 is 37%, 4/8 is 50% because it's half full, for eights just go up 13, or subtract 13, it's a little hard for me to explain, sorry
Need help pls!!!!! anyone?
Answer:
D
Step-by-step explanation:
First multiply by t
at = vf -vi
Then subtract vf
at - vf = -vi
Then multiply by -1
Vi = vf - at
someone pleaseeeeeee answer :)))
Answer:
You would have to rent 10 movies for the cost to be the same.
Step-by-step explanation:
20+1.5x=3.5x
-1.5x on both sides
20=2x
x=10
Answer:
You would have to rent 8 movies at the first store and 10 movies at the second
Step-by-step explanation:
A company makes 100 bags. 32 of the bags have buttons but no zips. 32 of the bags have zips but no buttons. 35 of the bags have neither zips nor buttons. How many bags have zips on them?
Answer:
32.
Step-by-step explanation:
The first 32 have buttons but NO zips.
Then 35 have NEITHER buttons OR zips.
Then 32 have ZIPs, but no buttons.
The question only asks for zips. The other bag is unaccounted for.
Expand (-2x+4)^5 using the binomial theorem (Pascals triangle)
Will award brainiest, (show work)
100 points, silly answers will be reported immediately.
Answer:
[tex]-32x^5+320x^4-1280x^3+2560x^2-2560x+1024[/tex]
Step-by-step explanation:
We must expand [tex](-2x+4)^5[/tex] using the Binomial Theorem.
To do so, we need Pascal's Triangle. Seeing that the exponent is 5, we look at the 5 + 1 = 6th row of Pascal's Triangle. The numbers here are:
1, 5, 10, 10, 5, 1
These will be the numbers to multiply all the distinct terms in the expansion by.
Remember that when expanding this out, we always start by taking the first term (-2x here) to the nth power (here, it's 5th power) and multiplying that by the second term (4 here) to the 0th power:
(-2x)^5 * 4^0 = -32x^5 * 1 = -32x^5
Since this is our first term, we multiply it by the first Pascal number from above: 1. Then, we simply get -32x^5 as our final first term of the expansion.
We repeat this process, each time lowering the first power by 1 and increasing the second power by 2.
2nd term:
(-2x)^4 * 4^1 = 16x^4 * 4 = 64x^4
Multiply by 5:
64x^4 * 5 = 320x^4
3rd term:
(-2x)^3 * 4^2 = -8x^3 * 16 = -128x^3
Multiply by 10:
-128x^3 * 10 = -1280x^3
4th term:
(-2x)^2 * 4^3 = 4x^2 * 64 = 256x^2
Multiply by 10:
256x^2 * 10 = 2560x^2
5th term:
(-2x)^1 * 4^4 = -2x * 256 = -512x
Multiply by 5:
-512x * 5 = -2560x
6th term:
(-2x)^0 * 4^5 = 1 * 1024 = 1024
Multiply by 1:
1024 * 1 = 1024
Hence, our expansion is:
[tex]-32x^5+320x^4-1280x^3+2560x^2-2560x+1024[/tex]
can someone show me how to do this step by step (part c pls) :)
Answer:
The student scores 20 pts
Step-by-step explanation:
A student answers 10 Q's correct, this earns the student 30 points (3 x 10)
The other 5 Q's are presumably wrong since they did answer the question
If every question wrong loses 2 pts then the student lost 10 points from wrong answers (2x5) =10
Take the total amount of secured points and subtract the points for questions that the student got wrong
30 pts - 10 pts = 20 pts
Answer:
20
Step-by-step explanation:
15 questions answered
10 are correct so they get 30 or 3*10
5 are incorrect so the get a -10 or -2*5
Total score is 30-10 or 20
Find the area of a regular polygon with 9 sides that has a perimeter of 135 inches and an apothem of 6 inches
Answer:
The area of regular polygon with 9 sides is 405 square inches.
Step-by-step explanation:
Given
Perimeter of Polygon = P = 135 inches
Apothem = a = 6 inches
We know that the sides of regular polygon are equal. Let s be the side of the polygon then
[tex]P = 9*s\\135 = 9*s\\s = \frac{135}{9}\\s = 15\ inches[/tex]
Now the formula for area of polygon when apothem, sides and number of sides is known:
[tex]A = \frac{a*n*s}{2}\\A = \frac{6*9*15}{2}\\A=\frac{810}{2}\\A = 405\ in^2[/tex]
Also the formula can be written as:
[tex]A = \frac{1}{2}P*a[/tex]
Hence,
The area of regular polygon with 9 sides is 405 square inches.
Three friends went for dinner and ordered Pizza for $12, Salads for $6 and Drinks for $6. If they divide the total cost equally, how much did each friend pay?
Answer:
Step-by-step explanation:
Total = 12 + 6 + 6 = 24
Divided in 3 friends = 24 ÷ 3 = 8
Each should pay 8
Select the correct answer
A company is interested in learning if employees are satisfied with their jobs. To find out the company hires an independent market research
company to conduct a survey. Every survey filled out by an employee is anonymous. Which of the following statements is correct?
A This method of sampling is biased.
B This method of sampling is unbiased.
C This method of sampling is neither biased nor unbiased. D This method of sampling can be considered both biased and unbiased.
The statement (B) is correct because it is anonymous, it does not focus on a specific ethnicity, gender, or other factor.
What is a survey?A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.
We have:
A company is interested in learning if employees are satisfied with their jobs.
Every survey that an employee fills out is completely anonymous.
The statement (B) this method of sampling is unbiased because it is anonymous, it does not focus on a specific ethnicity, gender, or other factor.
Thus, the statement (B) is correct because it is anonymous, it does not focus on a specific ethnicity, gender, or other factor.
Learn more about the survey here:
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Please help I'll give brainliest
Answer:
b
Step-by-step explanation:
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Answer:
b. The cost of orange juice is $3 per jug.
Step-by-step explanation:
A "unit rate" is a rate that is "per <single item>" The rates given are per the following numbers of items:
a: 3
b: 1 . . . a unit rate
c: 10
d: 2 (dozen) or 24 (single roses)
The rate of selection B is the only unit rate.
8
1 point
The table below represents a linear relationship. Find the slope of the line.
1
3
22
14
6
-6
- 10
6
17