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The greatest common factor of 38 and 30 is 2

We have given two numbers 38 and 30 .

Prime factorization of 38 is given by

   [tex]38=2\times19[/tex]

Prime factorization of 30 is given by

   [tex]30=2\times3\times5[/tex]

Prime factorization of 30 and 38 contains 2 as common primes factors so , GCF will be [tex]2[/tex] .

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Answer:

Physical Property

Step-by-step explanation:

Physical Property. A physical property is a characteristic of a substance that can be observed or measured without changing the identity of the substance. Silver is a shiny metal that conducts electricity very well.

after simplifying yhe expression 2 x ⁵ - 7 x ⁵ / 2 + 6, we get the result as - 3 / 2 ( x⁵ - 4).

We are given the expression :

2 x ⁵ - 7 x ⁵ / 2 + 6

We need to factorize the expression completely.

Taking LCM, we get that,

4 x⁵ - 7 x⁵ + 12 / 2

combining the like terms, we get that,

- 3 x ⁵ + 12 / 2

taking - 3 common from the expression, we get that

- 3 / 2 ( x⁵ - 4)

Therefore, after simplifying yhe expression 2 x ⁵ - 7 x ⁵ / 2 + 6, we get the result as - 3 / 2 ( x⁵ - 4).

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Answer:

x=2.35930...

i hope this is the answer

The value of the expression 8 × 1 plus 5 × 1/1000 plus 9 × 1/1000 is 8.014.

Consider the expression,

8 × 1 plus 5 × 1/1000 plus 9 × 1/1000

Now,

8 × 1 = 8 and;

5 × 1/1000 = 5/1000

and;

9 × 1/1000 = 9/1000

Now,

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + 5/1000 + 9/1000

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + [ ( 9 + 5 ) / 1000 ]

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + 14 / 1000

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = ( 8 / 1 ) + ( 14 / 1000 )

Now, LCM of 1 and 1000 is 1000.

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 × ( 1000/1000) + 14/1000

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8000/1000 + 14/1000

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = ( 8000 + 14 ) / 1000

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8014/1000

8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8.014

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Answer: -17

Step-by-step explanation:

f(x) = -x - 9 and g(x) = 3x + 8

(f + g)(−8)=

f(-8)+g(-8)=

-(-8)-9+3(-8)+8=

8-9-24+8=

-1-16=-17

The derivative of the given expression is as follows   = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]

The derivative is the rate of change in a function without respect to a variable in mathematics. Derivatives are essential for solving calculus as well as differential equations problems.

Options, forwards, futures, and swaps are the four primary types of derivative contracts. Options represent derivative contracts that provide the buyer the right to buy or sell the underlying asset at a predetermined price during a specific time period. The purchaser is not required to execute the option.

Let f:(0,∞)→R;

f(x)=√x, and x₀∈(0,∞) be an accumulation point of (0,∞).

We must find f′ such that for all x₀, f′(x₀) defined as:

limx→x₀(f(x)−f(x₀))/(x−x₀) exists.

Now,

x−x₀=(√x−√(x₀))(√x +√(x₀)).

Then:

[tex]\lim _{x \rightarrow x_0} \frac{f(x)-f\left(x_0\right)}{x-x_0}[/tex] = [tex]\lim _{x \rightarrow x_0} \frac{\sqrt{x}-\sqrt{x_0}}{\left(\sqrt{x}-\sqrt{x_0}\right)\left(\sqrt{x}+\sqrt{x_0}\right)}[/tex]

                            = [tex]\lim _{x \rightarrow x_0} \frac{1}{\sqrt{x}+\sqrt{x_0}}[/tex]

                            = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]

The derivative of the given expression is as follows   = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]

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The question you are looking for is:

Use the definition to find the derivative of f(x)=(√x), for x>0. Is f differentiable at zero? Explain.

Its formed  an obtuse triangle  with side lengths 4 in, 5 in, and 8 in.

What is obtuse triangle?

When given 3 sides of a triangle, the longest side must be less than the sum of the other 2 sides.

8 < 4 + 5 so a triangle can be formed.

In fact it will be an obtuse triangle.

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Using the Empirical Rule, it is found that:

It states that, for a normally distributed random variable:

Hence, the middle 95% of values is within 2 standard deviations of the mean, with bounds given as follows:

The middle 95% of the distribution of moonsoon rainfall amount: (688 mm, 1016 mm).

For the driest 2.5% of years, considering the symmetry of the normal distribution, we have to look at 2 standard deviations below the mean, as 5/2 = 2.5%, hence:

The driest 2.5% of monsoon rainfall amount are less than: 688 mm.

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The correct decreasing order of the given numbers is : 3.32 > 2.25 > -2.25 > -3.98

What is Descending Order ?

Descending order is a way to arrange numbers from largest to smallest. When we arrange things in order, from a higher value to a lower value, it is known as the descending order or the decreasing order.

√11 = 3.316 = 3.32 (rounding off to two decimal places)

2 1/4 = 9/4 = 2.25 (by solving mix fraction)

-2.25 (negative number is written in negative x- axis)

-3.97621 = -3.98 (negative number is written in negative x- axis)

arranging the numbers in descending order

3.32 > 2.25 > -2.25 > -3.98

therefore, the highest number is 3.32 and the lowest number is -3.98

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Answer: Julie is 8 years old. Ann is 12 years old.

Step-by-step explanation:

A=Ann's age. J=Julie's age

A=J+4

A-4=(J-4)*2

A-4=2(J-4)

A=2(J-4)+4

2(J-4)+4=J+4

2J-8+4=J+4

2J-4=J+4

2J=J+8

J=8

A=J+4

A=8+4

A=12

Julie is 8 years old. Ann is 12 years old.

Julie's present age (x) is 8 years old, and Ann's present age (x + 4) is 12 years old. Julie is 8 years old and Ann is 12 years old.

Let's denote Julie's age as x.

Since Ann is 4 years older than Julie, her age can be represented as x + 4.

Four years ago, Julie's age was x - 4 and Ann's age was (x + 4) - 4 = x.

Since Ann was twice as old as Julie, we can write the equation

: x = 2(x - 4).

Simplifying the equation, we get: x = 2x - 8.

Rearranging the terms, we find: x - 2x = -8.

Combining like terms, we have: -x = -8.

Finally, solving for x, we get: x = 8.

Therefore, Julie's present age (x) is 8 years old, and Ann's present age (x + 4) is 12 years old.

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A percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

The percentage of the students who go to the movies three times a month or more is given by:

Total students = 30 + 55 = 85 students.

Percentage = 85/250 × 100

Percentage = 0.34 × 100

Percentage = 34%.

The percentage of the students who prefer dramas is given by:

Total students = 85 + 55 = 140 students.

Percentage = 140/250 × 100

Percentage = 0.56 × 100

Percentage = 56%.

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Complete Question:

A movie club surveyed 250 high school students. The students were asked how often they go to the movies and whether they prefer comedies or dramas. Their responses are summarized in the following table.

(a) What percentage of the students go to the movies three times a month or more?

(b) What percentage of the students prefer dramas?

Answer:

Subtract two sides

Step-by-step explanation:

Answer:

k = 2

Step-by-step explanation:

in such a case we look immediately at the cases y = 0 and/or x = 0

only if that does not lead us to an answer, do we need to look further.

y = 0, that means according to the graph that x = -2.

so, we have

0 = |x + k| = |-2 + k|

that can only be the case, if k = 2

and we are done.

Answer:

the horizontal and vertical lines passing through the point (1,6)

y-6=

x-1=

Step-by-step explanation:

Answer:

x=1 and =

Step-by-step explanation:

The value of the function  (h+k)(2) is 1

A function can be defined as an expression or rule that shows relationship between an independent and dependent variable.

Given the functions;

To determine ( h + k), we have

( h + k) = x² + 1 + x - 2

Then,

(h+k)(2), substitute the value of x as 2

(h+k)(2) = (2)² + 1 - (2) - 2

(h+k)(2) = 4 + 1 - 4

(h+k)(2) = 1

Thus, the value of the function (h+k)(2) is 1

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The average speed of stefan is 0.57 miles per hour.

Given, In heavy traffic, Stefan covered just 25 miles in 1 hour and 8 minutes on his way to work.

He left work early to beat the rush hour and made it home in 32 minutes using the same route.

speed of steven in heavy traffic = distance/ time

distance = 25 miles

time = 1 hour and 8 minutes = 68 minutes

therefore, speed = 25/68 = 0.36 miles per hour.

speed of steven while returning back to home.

distance = 25 miles

time = 32 minutes.

speed = 25/32 = 0.78 miles per hour.

average speed = 0.36 ₊ 0.78/2

= 1.14/2

= 0.57 miles per hour.

hence we get the average speed as 0.57 miles.

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The system of inequalities is:

x + y ≤ 120

x*3 + y*6 ≥ 480

And one possible solution to it is x = 20 and y = 80.

First, we need to define two variables, we will be using:

We know that she can make at most 120 units, then:

x + y ≤ 120

And she wants to win at leastt $480, then:

x*3 + y*6 ≥ 480

So our system of inequalities is:

x + y ≤ 120

x*3 + y*6 ≥ 480

And the graph can be seen in the image below, the solution set of the system is given by the region where both shaded areas intersect.

There we can see that one possible solution is x = 20 and y = 80, in that case the total number of items made is:

20 + 80 = 100, which is less than 120

And the income is:

20*3 + 80*6 = 540.

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Answer:

T = 3.67 years

Step-by-step explanation:

Answer: 381704, because math

The system of equations we need to solve is:

x*90 + y*50 = 860

y = x + 6

Solving that we will see that there are 4 mini hot dogs and 10 pizza rolls.

First, we need to define the variables we will be using, these are:

x = number of mini hotdogs.

y = number of pizza rolls.

We know that the combination has 860 calories in total, so:

x*90 + y*50 = 860

We also know that there are 6 more pizza rolls than mini hotdogs, so:

y = x + 6

Then the system of equations is:

x*90 + y*50 = 860

y = x + 6

Replacing the second equation into the first one, we will get:

x*90 + (x + 6)*50 = 860

Now we can solve this for x.

x*90 + x*50 + 300 = 860

x*140 + 300 = 860

x*140 = 860 - 300

x*140 =  560

x = 560/140 = 4

So there are 4 mini hotdogs, and:

y = x + 6

y = 4 + 6 = 10

There are 10 pizza rolls.

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Answer:

Both

Step-by-step explanation:

(5, 3) and (-5, -1)

To get the equation of two points(coordinate)

(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)

(5, 3) --- (x₁, y₁)

(-5, - 1) --- (x₂, y₂)

(- 1 - 3)/(- 5 - 5) = (y - 3)/(x - 5)

-4/-10 = (y - 3)/(x - 5)

4/10 = (y - 3)/(x - 5)

⅖ = (y - 3)/(x - 5)

5(y - 3) = 2(x - 5)

5y - 15 = 2x - 10

5y = 2x - 10 + 15

5y = 2x + 5

Divide through by 5

5y/5 = 2x/5 + 5/5

y = ⅖x + 1

Option 2 is correct

let's see if option 1 is correct

y = ⅖x + 1

add 1 to both sides.

y + 1 = ⅖x + 1 + 1

y + 1 = ⅖x + 2

y + 1 = ⅖(x + 5)

So, option 1 is also correct

Answer:

Both

Step-by-step explanation:

(5, 3) and (-5, -1)

To get the equation of two points(coordinate)

(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)

(5, 3) --- (x₁, y₁)

(-5, - 1) --- (x₂, y₂)

(- 1 - 3)/(- 5 - 5) = (y - 3)/(x - 5)

-4/-10 = (y - 3)/(x - 5)

4/10 = (y - 3)/(x - 5)

⅖ = (y - 3)/(x - 5)

5(y - 3) = 2(x - 5)

5y - 15 = 2x - 10

5y = 2x - 10 + 15

5y = 2x + 5

Divide through by 5

5y/5 = 2x/5 + 5/5

y = ⅖x + 1

Option 2 is correct

let's see if option 1 is correct

y = ⅖x + 1

add 1 to both sides.

y + 1 = ⅖x + 1 + 1

y + 1 = ⅖x + 2

y + 1 = ⅖(x + 5)

So, option 1 is also correct

The 9th term of this arithmetic sequence is 6.

In an Arithmetic Progression (AP), the nth term is given by the formula-

a9 = a + (n-1)d

where a = first term of the AP

d = common difference

Here, we are given that a= 10 and d = - ½

Let the 9th term of the AP be a9

Therefore, according to the formula for finding the nth term of an AP, we get-

a9 = a + (9-1)d

a9 = a + 8d

Substituting the values of a and d given in the question-

a9 = 10 + 8(-1/2)

a9 = 10 - 4

a9 = 6

Thus, the 9th term of the arithmetic sequence is 6.

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if only one-fourth the amount of brown sugar in the recipe were used

When adding 1/4 cup of brown sugar to a recipe, you would use

twelve teaspoons

0.015625 gallons

0.0625 quarts

0.125 pints

59.147 ml

3.086472 pounds

Volume, or how much liquid a container can hold, is measured in quarts in both British Imperial and US customary measurements. A quart is equal to two pints or one-fourth of a gallon.

One standard imperial quart, which is equal to two imperial pints or one-fourth of an imperial gallon, is used in the British imperial system for both dry and liquid measurements. The US Customary system has two units called quarts, one for measuring liquids and the other, a little bigger, for measuring dry goods.

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Answer:

XY=2/5

Step-by-step explanation:

Given the reciprocal of x is 0.25, that is then

x = 1/ 1/4 = 4

Given the reciprocal of y is 10 then

y = 1/10

xy = 4 ×1/10 =4/10 = 2/5

Answer:

I'm assuming you want to find the slope.

If so, the answer is: m = 4

Hope this helps! <3

Answer:

F(x)=82(2)+il/3

Step-by-step explanation: