Find the intervals where f(x) is increasing or decreasing: √x -2x. Ans: increasing (0, 1/4) Decreasing (1/4, ∞)

The equivalent expression of (10⁻² . 4⁵)⁻² is 10⁴ / 4¹⁰

We have to find the expression that is equivalent to the expression below:

(10⁻² . 4⁵)⁻².

Therefore, using the law of indices,

[tex](x^{a} )^{b} = x^{ab}[/tex]

Hence, let's find the equivalent expression by applying the laws of indices.

(10⁻² . 4⁵)⁻² = 10⁴ . 4⁻¹⁰

Also, applying the law of indices,

[tex]x^{-b} = \frac{1}{x^{b} }[/tex]

Therefore,

10⁴ . 4⁻¹⁰ = 10⁴ / 4¹⁰

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Answer:

===========================

y is greater by 100 times

Answer:

2^2×3×5

Step-by-step explanation:

hope this works :)

The water that a bobcat drink in 1 day will be 3x.

Let the amount of water be represented by x.

From the information, it was stated that each day a bobcat drinks about 3 times as much water as a canada goose drinks.

Let the water that the Canada goose drank be represented as x

Therefore, the water that a bobcat drink in 1 day will be 3x.

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The equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .

Let the equation of line passes through the point (-2, 8) be y = mx + b.

Where m is the slope of the line and b is the y intercept of the line.

According to the given question.

A line passes through the points (-2, 8).

And it is also perpendicular to the line containing (0, 1) and (4, 5).

Since, the line is perpendicualr to the line conatining (0, 1) and (4, 5).

So, the slope of the line whose equation is to be find is given by

m = -1/(5 - 1/4-0)

⇒ m = -1/4/4 = -1

Thereofre, the equation of line with slope -1 is

y = -1x + b

Also, it passes through (-2, 8)

So,

8 = -1(-2) + b

⇒ 8 - 2 = b

⇒ b = 6

Thereofore, the equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .

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Answer: 0.17

Step-by-step explanation:

Plug the equation into a calculator (17 divided by 100).

You can also think of the problem like this; move both decimal places to the left twice since, in 100, there are two 0's.

17 -> 0.17

100 -> 1

This can also work with 17 and 1000, but you would have to move the decimal place three times.

17 -> 0.017

1000 -> 1

Since the values on both sides of the expression are different, hence the equation has no solution.

Linear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b

Given the expression 4x+3x-x=-5+6x

Collect the like terms

4x+3x-x = -5+6x

4x+3x-x-6x = -5

7x - 7x = -5

Simplify

-0x = -5

0x = 5

x = 5/0

Since the values on both sides of the expression are different, hence the equation has no solution.

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The value of x is -5

Algebraic expressions are expressions that comprised of;

They are also made of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc

Given the equation;

4x + 3x = -5 + 6x

Let's solve for x

We have;

collect like terms

4x + 3x - 6x = -5

Add or subtract like terms

7x - 6x = - 5

x = -5

Thus, the value of x is -5

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Answer:

4 and 5

Step-by-step explanation:

We need 2 positive numbers that are right beside each other, like 1 and 2. When the problem is translates into number format we get:

y^2+4x=41

x = 1st # and y = 2nd #

so if we do 4 (x) and 5 (y)

5^2+4(4)=41

the statement is true.

Answer:

[tex]\mathrm{b = 2\frac{A}{h} - a}[/tex]

Translation:

Option C.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

An equation represents a represents only when there is a unique value of x for every value of y. when it represents u as a function of x.

i.e if we draw lines parallel to y axis and it cuts the curve two or more than two times at a particular value of x then it doesn't represent a function at all.

And as we can see in the given tables,

1.) 12.23 is the value of x for both 5.4 and 6.4

2.) 0.31 is the value of x for both 55 and 59

4.) 20 is the value of x for both 245 and 255

So, the only table representing y as a function of x is table 3.

Answer:

table 3 is correct i took the test

Step-by-step explanation:

8 x 10^16/4 x 10^11

do exponents first

8 x 10,000,000,000,000,000/4 x 100,000,000,000

than multiply

80,000,000,000,000,000/4 x 100,000,000,000

than divide

20,000,000,000,000,000x 100,000,000,000

2,000,000,000,000,000,000,000,000,000

Answer:

x = 23

Step-by-step explanation:

The two angles are supplementary angles.

Supplementary angles sum 180°

(6x+4) + 38 = 180

6x + 42 = 180

6x = 180 - 42

6x = 138

x = 138/6

x = 23

Check:

6*23  + 4 + 38 = 180

138 + 42 = 180

Answer:

Step-by-step explanation:

We know that the sum of angles of a linear pair is always equal to 180°. These angles are also known as supplementary angles.

[tex]\bf 6x+4+38^o=180^o[/tex] (Add numbers)

[tex]\bf 6x+42=180[/tex] (Simplify)

[tex]\bf 6x+42-42=180-42[/tex](Subtract both sides by 42)

[tex]\bf 6x=138[/tex] (Simplify)

[tex]\bf \cfrac{6x}{6}=\cfrac{138}{6}[/tex] (Divide both sides by 6)

[tex]\bf x=23[/tex]

Therefore, x = 23.

_____________________

Hope this helps!

Have a great day!

Answer: x = 4

Step-by-step explanation:

   Given:

3x - 1 = 11

   Add 1 to both sides of the equation:

3x = 12

   Divide both sides of the equation by 3:

x = 4

Answer:

True

Step-by-step explanation:

Because you never expect when something may show up once your doing something and forget about what you lost a while back. Sometimes it just pops up and we're like, "Oh that's where it was".

Can't say true or false because both can be answers in different cases, mathematically speaking you can select one thing from a set of similar things having similar chance to be selected. and again you can also select one thing at random from a set of things having different chance of being selected. in my perspective:)

and maybe the question has more chance to be false because if a statement is false at least in one case it is false.

By doing some changes of units, we can see that we will need 22.61 gallons of paint to cover 800 square meters.

We know that with one liter of interior paint we can cover 100 square feet.

Remember the relation between square feet and square meeters:

1ft^2 = 0.092 m^2

Then with one liter we can cover:

100ft^2 = 100*0.092 m^2 = 9.2 m^2

So the number of liters of paint that we need to cover the 800 m^2 is given by the quotient:

L = 800m^2/9.2m^2 = 86.96

We need 86.96 liters of paint, and the relation between liters and gallons is:

1 L = 0.26 gal

Then we need:

86.96 L = 86.96*(0.26 gal) = 22.61 gal

We will need 22.61 gallons of paint to cover 800 square meters.

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Answer:

17

Step-by-step explanation:

We can substitute x = -4 and y = 1 since the point lies on the line.

[tex]5(-4)-3(1)=B \\ \\ B=17[/tex]

Answer:

$4,218.75

Step-by-step explanation:

The formula for computing simple interest I on a principal amount P for t years at an interest rate of R% is given by

I = Prt

The ending balance amount is found by adding the principal to the interest computed

Ending balance = P + I

Here r is the interest rate in % converted to a decimal. This is done by dividing by 100

r = R/100 = 2.75%/100 = 0.0275 per year

I = 2500 x 0.0275 x 25 = 1718.75

So interest I = $1718.75

Ending balance = $2,500 + $1718.75 = $4,218.75

Main Answer:1) (x + 2)

                     2) The numbers are 19 and 21.

Concept and definitions should be there:

An odd integer n is an integer which is not a multiple of 2 (or equivalently one more than a multiple of 2). The odd integers are ..., -5, -3, -1, 1, 3, 5, ... Every odd integer can be written in the form 2k + 1 for some unique integer k.

The product of any two odd integers is odd and the result of a division where both the dividend and the divisor are odd is odd. But the sum and difference of any two odd integers are even.

The sum and difference of an even integer and odd integer are odd. Besides 2, all prime numbers are odd. Also, odd integers are really cool

This article is a stub. Help us out by expanding it.

Given data:

1) We have two consecutive odd integers.

Solving part:

Remember that the distance between any two consecutive odd numbers is 2.

5 - 3 = 2

7 - 5 = 2

13 - 11 = 2

etc.

So if the smaller of the two odd numbers is x, then the larger one will be (x + 2).

Given that:

2) We have two consecutive odd numbers, let's write them as:

Solving part:

(2*n + 1) and (2*n + 3)

Where n is an integer number.

We know that the smaller one is 12 more than one third of the larger one, so we have:

(2*n + 1) = 12 + (2*n + 3)/3

Now we can solve this for n

2*n + 1 = 12 + (2/3)*n + 1

2*n - (2/3)*n = 12 + 1 - 1

(4/3)*n = 12

n = (3/4)*12 = 9

n = 9

Then the two consecutive odd integers are:

(2*n + 1) = (2*9 + 1) = 19

(2*n + 3) = (2*9 + 3) = 21

Final Answer:1) (x + 2)

                      2) The numbers are 19 and 21.

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The shape of the distribution of the given data set is : Bell shaped

What is Frequency distribution ?

Frequency distribution, in statistics, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. Simple examples are election returns and test scores listed by percentile. A frequency distribution can be graphed as a histogram or pie chart.

Data: 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1

Classes = 5

Class  Frequency

1-3      →3

4-6     →4

7-9     →9

10-12  →2

13-15   →2

The shape of the distribution is peak at the center and down at both the ends,

Therefore, we can say that the shape of the distribution is bell shaped.

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I think you are supposed to add the the numbers in that row and if it's more that 18 and less that 37 that's the answer. exapmle:

2,8,3,9,5

Add those together and get 27. 27 is less than 37 and more that 18 so it would be one of the answers.

I could be wrong but I'm pretty sure that is what you do

The fraction that is greater is 36/104 since 34.62% is greater than 32.11%

Fractions are written as the ratio of two integers. For instance a/b is a fraction.

In order to determine which of the fractions is greater, we will express them as percentage as shown:

35/109 * 100

3500/109

32.11%

Similarly;

36/104 * 100

3600/104

34.62%

Hence the fraction that is greater is 36/104 since 34.62% is greater than 32.11%

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Answer:

  26.0 cm

Step-by-step explanation:

Given quadrilateral ABCD with diagonal BD forming triangles ABD and BCD, and angles A=90°, C=52°, ADB=35°, and CBD=52°, you want the length of CD to 3 significant figures.

The law of sines tells you the relation between sides and opposite angles is ...

  a/sin(A) = b/sin(B) = c/sin(C)

This lets us write two proportions that can be solved for the measure of CD.

In triangle ABD:

  BD/sin(A) = AB/sin(D)

  BD = AB·sin(90°)/sin(35°) = 12 cm/sin(35°) ≈ 20.921 cm

In triangle BCD:

  CD/sin(B) = BD/sin(C)

  CD = BD·sin(B)/sin(C) = 20.921 cm·sin(102°)/sin(52°) ≈ 25.969 cm

The length of CD is about 26.0 cm.

Answer:

5/3 + 15/4 are the fractions

Answer:

Step-by-step explanation:

400

30

1

400 FOR HUNDREDS