Answers
( negative infinity , -3)U( -3, 0 )
To find the intervals over which a function is increasing, you need to find its derivative, set it greater than 0 and solve for x. The solutions give the intervals where the function is increasing.
Explanation:In mathematics, to find the intervals over which a function is increasing, you first need to find its derivative. The derivative of a function at a certain point gives the slope of the tangent line at that point. If the derivative is positive, the function is increasing. If it's negative, the function is decreasing.
For example, let's say we have a function f(x) = x^3 - 3x. The derivative of this function is f'(x) = 3x^2 - 3. To find the interval where the function is increasing, we set the derivative greater than 0 and solve for x: 3x^2 - 3 > 0. The solution to this inequality gives the intervals over which the function is increasing .
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Related Questions
48 out of 120 equals what percent
Answers
48 * 2,5 = 120
np ;)
The map scale is 1in: 40 miles . the distance on the map is 3.5 inches . what is the actual distance
Answers
3.5 inches is 40 miles*3.5 inches or 140 miles
Please help! Create a set of five positive numbers (repeats allowed) that have a median of 10 and a mean of 14. What thought process did you use to create your numbers?
Answers
What is the remainder of 4^31 when divided by 10
Answers
[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides
[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]
[tex](4^1)^2 \equiv 4^2 \ (\text{mod} \ 10)[/tex]
[tex]4^2 \equiv 16 \ (\text{mod} \ 10)[/tex]
[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides again
[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex](4^2)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]
[tex]4^4 \equiv 36 \ (\text{mod} \ 10)[/tex]
[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides again
[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex](4^4)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]
[tex]4^8 \equiv 36 \ (\text{mod} \ 10)[/tex]
[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
Square both sides again
[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex](4^8)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]
[tex]4^{16} \equiv 36 \ (\text{mod} \ 10)[/tex]
[tex]4^{16} \equiv 6 \ (\text{mod} \ 10)[/tex]
----------------------------
So far we have found that,
[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]
[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]
[tex]4^{16} \equiv 6 \ (\text{mod} \ 10)[/tex]
Multiply out all of the left sides of those equations above. Multiply out the right sides as well to balance things out
[tex](4^1)*(4^2)*(4^4)*(4^8)*(4^{16}) \equiv 4*6*6*6*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{1+2+4+8+16} \equiv 24*36*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 4*6*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 24*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 4*6 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 24 \ (\text{mod} \ 10)[/tex]
[tex]4^{31} \equiv 4 \ (\text{mod} \ 10)[/tex]
-------------------------------------------------------------------------
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The final answer is 4
Final answer:
The remainder of 4^31 when divided by 10 is 4, determined by examining the repeating last-digit pattern of powers of 4.
Explanation:
To find the remainder of 4^31 when divided by 10, we can use the concept of powers and properties of numbers related to modulo arithmetic. Specifically, we look at the last digit pattern that emerges when calculating powers of 4, since the remainder when dividing by 10 depends solely on the final digit of the number.
The powers of 4 have a cycle: 4^1 ends with 4, 4^2 ends with 6, 4^3 ends with 4 again, and so on. This cycle repeats every two powers, so we only need to consider the power of 4 modulo 2 to determine the last digit of 4^31. Since 31 is an odd number, we know that 4^31 will end with a 4. Hence, the remainder of 4^31 divided by 10 is 4.
Joseph’s garden is 9 feet wide and 12 feet long. Alana’s garden is 7 feet wide and 25 feet long.
How much greater is the area of Alana’s garden than Joseph’s garden?
Please help!! Will give 15 points!
Answers
area of Josephs garden = 9*12 = 108 square feet
area for Alana's garden = 7 *25 = 175 square feet
175/108 = 1.62
Alan's garden is 1.62 times larger
A rectangle has a length of 8 cm and breadth 6cm . What is the perimeter in cm of the rectangle
Answers
8+8+6+6=28cm
So we have to do 2*(8+6)=2*14=28
So the perimeter is 28
Find the slope of a line parallel to the line through the given points. P(-2, 4), Q(6, -2) 4/3 3/4 -3/4
Answers
Answer:
Option 3 - [tex]m=-\frac{3}{4}[/tex]
Step-by-step explanation:
Given : P(-2, 4), Q(6, -2)
To find : The slope of a line parallel to the line through the given points?
Solution :
First we find the slope of the line passes through given points P(-2, 4), Q(6, -2)
The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-2-4}{6-(-2)}[/tex]
[tex]m=\frac{-6}{8}[/tex]
[tex]m=-\frac{3}{4}[/tex]
When two lines are parallel then there slope are equal.
Therefore, The slope of a line parallel to the line through the given points is
[tex]m=-\frac{3}{4}[/tex]
So, Option 3 is correct.
Suppose you have 74 feet of fencing to enclose a rectangular dog pen. The function a=37x-x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary
Answers
Standard form: ax² + bx + c
Given equation: -x² + 37x + 0
Since the "a" coefficient is negative, the parabola is flipped upside down making the maximum point the vertex.
Vertex = (-b/2a, y)
-b/2a = -37/(-1*2) = 37/2 = 18.5
This is the x-value, width which gives the maximum area
put in x = 18.5 and solve for maximum area, A.
A = -(18.5)² + 37(18.5)
A = -342.25 + 684.5
A = 342.25
round to nearest tenth
A = 342.3
Answer: width = 18.5 ft; area = 342.3 ft2
Step-by-step explanation:
you plug in the width with the function , where ever there is an x replace it with the width for the maximum area
Graph the equation 5x+2y=10
Answers
5x+2y=10: Displayed in the image below
An athlete eats
60
grams of protein per day while training. How much is this in milligrams?
Be sure to include the correct unit in your answer.
Answers
The area of a rectangle is 24 square cm. the length of the rectangle is 8 cm. find the perimeter
Answers
what is the square root of 49
Answers
7^2 = 49
The range for a set of data is estimated to be 36.
a. what is the planning value for the population standard deviation?
Answers
Given that the range of a data set is 36, the planning value for the population standard deviation is given by [tex]\sigma= \frac{1}{6} (36)=6[/tex].
The planning value for the population standard deviation can be found by dividing the range by 4.
Explanation:To estimate the population standard deviation, we can use the planning value formula. The planning value for the population standard deviation is equal to the range divided by 4. Thus, in this case, if the range is estimated to be 36, the planning value for the population standard deviation would be 9.
PLEASE HELP!!!
WILL GIVE BRAINIEST TO FIRST ANSWER
Which of the following inequalities is graphed on the coordinate plane?
A. y > 1/2x - 1/2
B. y is less than or equal to 1/2x - 1/2
C. y is greater than or equal to 1/2x - 1/2
D. y < 1/2x - 1/2
Answers
Answer:
Option C
Step-by-step explanation:
Equation of any line is of the form y=mx+b where m is the slope and b the y intercept.
The given line has y intercept [tex]\frac{-1}{2}[/tex] and slope as [tex]\frac{1}{2}[/tex]
Hence equation of given line is :
[tex]y= \frac{1}{2}x-\frac{1}{2}[/tex]
Taking point (0,0) to check the inequality we have:
0≥[tex]\frac{-1}{2}[/tex]
The statement is true so option C [tex]y\geq \frac{1}{2} x-\frac{1}{2}[/tex] is right .
The length of the base of a triangle is twice its height. if the area of the triangle is 100 square kilometers, find the height.
Answers
a=1/2b·h
If h=x
b=2x
a=1/2(2x)·x
a=x²
100=x²
x=10
h=x=10
Tom usually earns $40.85 per hour. he has a 6% pay raise. which keys must he press on his calculator?
Answers
total pay raise= (6/100)x40.85
Total pay raise= $2.450
This can be a final answer. Your question is incomplete I think.
"+" & "=" button key Tom will press in the calculator.
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
To calculate Tom's pay raise, he can perform the following calculation on his calculator:
= 40.85 x 0.06
= 2.4510
So Tom's pay raise is $2.45 per hour.
To calculate Tom's new hourly rate, he can perform the following calculation:
= 40.85 + 2.45
= 43.30
So Tom's new hourly rate is $43.30.
Here is how the calculation can be done on most calculators:
Enter 40.85 and then press the "+" button.
Enter 2.45 and then press the "=" button.
The result should be 43.30, which is Tom's new hourly rate with a 6% pay raise.
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In a rhombus, which of the following are always equal? Select all that apply.
opposite angles
diagonals
opposite sides
consecutive angles
Answers
opposite angles
hope it helps
If 5x + 5 =25 + 3x then x = ? (im in pre algebra)
Answers
[tex]5x+5 = 25+3x[/tex]
Isolate the variables
[tex]5x -3x = 25 -5[/tex]
[tex]7x = 21[/tex]
[tex]x=21/7[/tex]
[tex]x=3[/tex]
Hope I helped (:
Have a great day!
To solve the equation 5x + 5 = 25 + 3x, subtract 3x from both sides, subtract 5 from both sides, and divide by 2 to find x = 10.
Explanation:To solve the equation 5x + 5 = 25 + 3x, you need to isolate the variable x. First, subtract 3x from both sides of the equation to combine like terms: 5x - 3x + 5 = 25. Simplify: 2x + 5 = 25. Next, subtract 5 from both sides of the equation to isolate the variable: 2x = 20. Finally, divide both sides of the equation by 2 to solve for x: x = 10.
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How do you solve cot^2x + cscx= 1
(0,2pi)
Answers
[tex]\bf csc(x)-2=0\implies csc(x)=2\implies \cfrac{1}{sin(x)}=2\implies \cfrac{1}{2}=sin(x) \\\\\\ sin^{-1}\left( \frac{1}{2} \right)=\measuredangle x\implies \frac{\pi }{6}~~,~~\frac{5\pi }{6}=\measuredangle x\\\\ -------------------------------\\\\ csc(x)+1=0\implies csc(x)=-1\implies \cfrac{1}{sin(x)}=-1 \\\\\\ \cfrac{1}{-1}=sin(x) \implies -1=sin(x)\implies sin^{-1}(-1)=\measuredangle x\implies \frac{3\pi }{2}=\measuredangle x[/tex]
brainiest to best answer!
The deepest part of the Mariana trench (the deepest trench in the world’s oceans) is at an elevation of -11.033 kilometers. The elevation of the deepest part of the Atacama trench is -8.065 kilometers. What is the net change in elevation from the Atacama trench to the Mariana trench?
19.098 kilometers
2.968 kilometers
-2.968 kilometers
-19.098 kilometers
Answers
The net change in elevation from the Atacama trench to the Mariana trench is 2.968km.
What is the net change in elevation from the Atacama trench to the Mariana trench?
We know that the deepest part of Mariana trench is at -11.033 km, while the deepest part of the Atacama trench is -8.065km.
To find the net change, we need to find the difference between the largest value and the smallest value.
So we get:
D = -8.065km - (-11.033 km) = 2.968km
Then the correct option is the second one.
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If a set of data is in the direction of a downward line, which of the following would be the best model for this data?
Quadratic regression model
Exponential regression model
Linear regression model
None of the above
Answers
What classification best represents a triangle?
Answers
a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244
c^2 < a^2 + b^2
Triangle is acute triangle
answer is A.
acute because 10^2 + 12^2 > 15^2
whats 10 minutes plus 7minutes plus 48minutes plus 1 hour and 29 minutes equal?
Answers
Answer: 2 hours and 34 minutes
Step-by-step explanation:
10 minutes plus 7 minutes plus 48 minutes plus 60 minutes plus 29 minutes equals 154 minutes. 154 minutes equals 2 hours and 34 minutes.
least common denominator of 3/s and -3/6s
Answers
2s
15 - (-3) - 4
-16
22
-8
14
Answers
15 - [-3]- 4
Note that when two minuses come together the product is a plus sign.
15 +3 - 4
You have to add before you subract
18 - 4 =14
Therefore, 15- [-3] - 4 = 14.
Jonah and his friends went to the movie theater. He bought a movie ticket, and he split the cost of a giant popcorn with his friends. Jonah's costs are represented by the expression 11+15/x . What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description. Cost of movie ticket Total cost of popcorn Jonah's portion of popcorn cost
Answers
Answer:
Cost of movie ticket = 11
Total cost of popcorn = 15
Jonah's portion of popcorn cost = 15/x
Step-by-step explanation:
1. I
2. Took
3. The
4. Test
60 POINTS!!
What are the missing parts that correctly complete the proof?
Answers
3.definition of perpendicular
4.∠AXP=~∠AXQ
6.SAS congruence postulate
7.Corresponding parts of congruent triangles are congruent
the guy below/above is correct
Would x + x + x +x be 4 or 4x?
Answers
Answer:
x+x+x+x = 4x.
Step-by-step explanation:
x + x + x + x can represent 4x since there are 4 x’s. Those 4 x’s represent x being multiplied by 4, since there are 4 x’s.
Therefore, your answer is 4x.
What is the result of dividing 2x3+6x2+6x+22x3+6x2+6x+2 by x+1x+1 ? A")2x2+4x+102x2+4x+10
B) 2x2+4x+22x2+4x+2
C:)2x2+6x+22x2+6x+2
D)2x2+6x+12
Answers
Answer:
[tex]2x^2+4x+2[/tex]
Step-by-step explanation:
[tex]2x^3+6x^2+6x+2[/tex] divide by x+1
Divide the first term of numerator by the first term of denominator and put it at the top. then multiply the answer by x+1 . write the expression at the bottom and subtract it. Repeat the process till we get remainder.
[tex]2x^2+4x+2[/tex]
-------------------------------------------------------
[tex]x+1[/tex] [tex]2x^3+6x^2+6x+2[/tex]
[tex]2x^3+2x^2[/tex]
-----------------------------------------(subtract)
[tex]4x^2+6x[/tex]
[tex]4x^2+4x[/tex]
-------------------------------------------Subtract
[tex]2x+2[/tex]
[tex]2x+2[/tex]
------------------------------------------Subtract
0
Simplify 5(a - b) + 6(a + b) - 7(a - 2b)