With the process and explanation in details

Answer:

Final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].

Step-by-step explanation:

Given rational expressions are [tex]\frac{x+2}{x-4}[/tex] and [tex]\frac{3x}{x+4}[/tex].

Now we need to find about what is the product of given rational expressions.

to multiply the rational expressions, we simply multiply numerator with numerator. Then multiply denominator with denominator.

[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}[/tex]

[tex]=\frac{\left(x+2\right)\cdot3x}{\left(x-4\right)\cdot\left(x+4\right)}[/tex]

[tex]=\frac{3x^2+6x}{x^2+4x-4x-16}[/tex]

[tex]=\frac{3x^2+6x}{x^2-16}[/tex]

Hence final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].

Answer:

Part A : |x-2.5| ≤ 0.75  , x ∈ [1.75,3.5]

Part B : yes, the lifeguard should add more chlorine.

Step-by-step explanation:

Part A:

Let  C is the variation of the level of chlorine in a hot tub.

Level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.

To find absolute value inequality, need to find the standard level of chlorine 1.75 + C or 3.25 - C

1.75 + C = 3.25 - C

2C = 5

C = 2.5

So, the standard level would be 2.5 ppm,

If x represents the present level of chlorine,

Then it would be lie within 1.75 ppm of 3.25 ppm.

1.75 ≤ x ≤ 3.25

Subtract 2.5 from all sides

1.75 - 2.5 ≤ x -2.5 ≤ 3.25 - 2.5

-0.75 ≤ (x-2.5) ≤ 0.75

which is equivalent to the following absolute value inequality.

|x-2.5| ≤ 0.75

And the solve of the inequality : x ∈ [1.75,3.5]

Part B:  If x = 1.0 ppm,

∴ |1.0-2.5| = 1.5 which is not less than equal to 0.75.

Another explanation:

the minimum safe level of chlorine in a hot tub is 1.75 ppm

Since 1 < 1.75

Therefore, lifeguard should add more chlorine.

They form a proportion when both of the ratios are equivalent.

An example: 3/15 and 1/5 is a proportion because the are equivalent.

The reason why they are equivalent is because if you cross multiply meaning doing 3*5 which equals 15 and 15*1 which equals 15 so basically you multiply the numerator by the other fractions denominator and do the same for the other side and see if the numbers are the same if they are not the same they are not a proportion if they are the same they are a proportion.

Hope this helps!

Answer:

yes

Step-by-step explanation:

because you can set them up as a fraction too. example;

2/3 is the same as 2:3, with which you can set equal to another thing and solve

Answer:

2 2/3 inches cubed

Step-by-step explanation:

volume is length x width x height. 3 x 2 2/3 x 1/3 = 2 2/3.

Answer:

2 2/3 in cubed

Step-by-step explanation:

Answer:

Option 3 (angle WXY + angle YXZ = 180) is the answer.

Answer:

x = -1

Step-by-step explanation:

We are given the following two points from which the line passes and has a slope of [tex]\frac{2}{3}[/tex].

We are to find the value of x.

Slope = [tex] \frac { y _ 2 - y _ 1 } { x _ 2 - x _ 1 } [/tex]

[tex]\frac{2}{3}[/tex] = [tex]\frac{10-8}{x-(-4)}[/tex]

[tex]\frac{2}{3}[/tex] = [tex]\frac{2}{x+4}[/tex]

By cross multiplication:

[tex]2(x+4)=3 \times 2[/tex]

[tex]2x+8=6[/tex]

[tex]2x=-2[/tex]

x = -1

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with ele axis and

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

How we have:

[tex]\frac {2} {3} = \frac {8-10} {- 4-x}\\\frac {8-10} {- 4-x} = \frac {2} {3}\\\frac {-2} {- 4-x} = \frac {2} {3}[/tex]

We clear the value of "x"

[tex]2 (-4-x) = - 6\\-8-2x = -6\\-2x = -6 + 8\\-2x = 2\\x = \frac {2} {- 2}\\x = -1[/tex]

Answer:

[tex]x = -1[/tex]

Answer:

2u

Step-by-step explanation:

Convert the percentage into a decimal

[tex]50 * .20 = 10[/tex]

[tex]50 - 10 = 40[/tex]

20% of 50 is 40

Answer:

x = 18

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x+x+3}{x+3}[/tex] = [tex]\frac{14+12}{14}[/tex]

[tex]\frac{2x+3}{x+3}[/tex] = [tex]\frac{26}{14}[/tex] ( cross- multiply )

14(2x+3) = 26(x + 3) ← distribute both sides

28x + 42 = 26x + 78 ( subtract 26x from both sides )

2x + 42 = 78 ( subtract 42 from both sides )

2x = 36 ( divide both sides by 2 )

x = 18

Answer:

n = -5, 3.

Step-by-step explanation:

n^2 + 2n - 15 = 0

Let's check if we can factor this quadratic:

We need 2 numbers whose product is -15 and whose sum is +2.

There are 2 such numbers and they are +5 and -3, so the factors are:

(n + 5)(n - 3) = 0.

n + 5 = 0 or n - 3 = 0

therefore the zeroes are -5 and 3.

Answer:

12.)a>/=-4

15.)b</=2/3

cant graph sorry

Step-by-step explanation:

ANSWER:

The 100 one is 10 and the 1,728 one is 12!

I think this is right and I hope I helped!

Tell me if it was right!

Answer:

3240°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 20, hence

sum = 180° × 18 = 3240°

The answer would be 20

You multiply 62.5% by 32

32*0.625=20

They are correct it is 20.

Answer: The graph is shifted 2 units to the right.

Step-by-step explanation:

Given a function f(x), we know that one transformation rule is:

If [tex]f(x-k)[/tex] then the function is shifted "k" units to the right.

 Therefore, for the function [tex]f(x)=x^{2}[/tex], when we subtract 2 from the input, then we get the function g(x) in the form:

 [tex]g(x)=(x-2)^{2}[/tex]

We can conclude that subtracting 2 from the input of the function [tex]f(x)=x^{2}[/tex], then the graph is shifted 2 units to the right.

The answer is right graph shifted 2 units to the right

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

[tex]m1*m2=-1[/tex]

we have

[tex]y=3x+5[/tex] -----> equation of line q

the slope of line q is

[tex]m1=3[/tex]

Find the slope of line p

[tex]m1*m2=-1[/tex]

[tex]3*m2=-1[/tex]

[tex]m2=-1/3[/tex] ----> slope of line p

Find the equation of the line p

The equation into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]point(6,-5)[/tex]

[tex]m=-1/3[/tex]

substitute

[tex]y+5=-(1/3)(x-6)[/tex]

[tex]y=-(1/3)x+2-5[/tex]

[tex]y=-(1/3)x-3[/tex] ----> equation of the line p

see the attached figure to better understand the problem

The slope of line q is 3, so the slope of line p, which is perpendicular to line q, is -1/3. Substituting the given point (6, -5) and this calculated slope into the point-slope form of a linear equation, we find the equation of line p to be y = -1/3x + 3. The reciprocal of the slope -1/3 is -3.

The equation of line q given is y=3x+5. The slope of this line is 3. Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of line p, which is perpendicular to line q, should be the negative reciprocal of 3, which is -1/3. To find the equation of line p, use the point-slope form of a linear equation, which is y-y₁ = m(x-x₁), where m is the slope, and (x₁, y₁) is a point on the line. Substituting the given point (6, -5) and the calculated slope -1/3 into that formula, the equation for line p becomes: y - (-5) = -1/3 (x - 6), or simplifying further, y = -1/3x + 3. The reciprocal of the slope -1/3 is -3.

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If your asking whats 86.4 divided by 36 its 2.4

12÷4

=3

because theres 12 gallons n theres four qts in each so you divide

The answer is the 12 multiplied by 4

Answer:

PD = 30

Step-by-step explanation:

2 secants intersect inside a circle the product of their parts are equal, that is

20(2x + 3) = 18(2x + 6) ← distribute both sides

40x + 60 = 36x + 108 ( subtract 36x from both sides )

4x + 60 = 108 ( subtract 60 from both sides )

4x = 48 ( divide both sides by 4 )

x = 12

Hence

PD = 2x + 6 = (2 × 12 ) + 6 = 24 + 6 = 30

Answer:

Here is the answer with the steps

Step-by-step explanation:

Hope you liked it!!

Answer:

Step-by-step explanation:

Interesting question. Perhaps an inverse relationship.

y = k/x where k is a constant like 10.

The problem begins to become a problem when  x approaches 0 and that happens quite frequently.

I would say as a class of numbers, 0 is the most problematic. 0 was developed about 1100 years after the death of Christ so the concept is pretty subtle. The Romans had no value for 0 as a place holder. 2019 for them was not written with anything that resembled a zero. (MMXIX is how they would write it). That's got to be very awkward when giving parts of an inch in their engineering drawings.

The second group that probably causes some trouble would be the irrationals. pi for one. sqrt(3) for another.  That took a while to develop as well.

Final answer:

The type of number that often gets mathematicians in trouble when using functions to model real-world situations is irrational numbers.

Explanation:

The type of number that often gets mathematicians in trouble when trying to use functions to model real-world situations is irrational numbers. Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. They consist of an infinite decimal expansion without a repeating pattern. Examples of irrational numbers include π (pi) and √2 (the square root of 2).

Mathematicians may encounter irrational numbers when dealing with measurements, calculations, or any situation that requires precise numerical representations. Irrational numbers can cause difficulties because they cannot be represented exactly and must be approximated for practical use.

For example, if a mathematician is trying to model the distance a car travels in a given time, they may encounter irrational values when dealing with measurements involving π or √2. These values may need to be rounded or approximated to fit the model, introducing potential errors in the calculations.

Answer:

[tex]\large\boxed{a.\ -3x^5y^6}[/tex]

Step-by-step explanation:

[tex]-3x^2y^2\cdot y^4x^3=(-3)(x^2x^3)(y^2y^4)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-3x^{2+3}y^{2+4}=-3x^5y^6[/tex]

Answer:

Surface area of original cube:

6(12²) = 6(144) = 864 cm²

Surface area of new cube:

6(24²) = 6(576) = 3,456 cm²

If the edge length of the cube is doubled, the surface area of the cube will be quadrupled.

Doubling the edge length of a cube from 12 cm to 24 cm increases the surface area by a factor of four, from 864 cm^2 to 3456 cm^2, because surface area is a two-dimensional measure and each dimension has been doubled.

If a cube has an edge length of 12 cm, its surface area is calculated by the formula 6s^2, where s is the length of a side. So the surface area of the original cube is 6  imes 122 cm^2 = 864 cm^2.

When the edge length of the cube is doubled to 24 cm, to find the new surface area, we also apply the formula 6s^2. Therefore, the new surface area is 6  imes 242 cm^2 = 3456 cm^2.

Comparing the new surface area to the original, we see that it has increased by a factor of 4, which is the square of the factor by which the edge length was multiplied (22 = 4). This occurs because surface area is a two-dimensional measure (involving length by width), so when each dimension is doubled, the overall area increases by a factor of four (2  imes 2).

Answer:

There is a 2.275% chance that more than 250 books were borrowed in a week.

Step-by-step explanation:

Let the random variable X denote the number of books borrowed from the library each week. Then from the information given;

X is normally distributed with a mean of 190 and a standard deviation of 30.

We are required to determine the probability that more than 250 books were borrowed in a week;

This can be written symbolically as;

Pr(X > 250)

The first step is to determine the z-score associated with the value 250. This is obtained via standardizing X;

Pr(X > 250) = [tex]Pr(Z>\frac{250-190}{30})=Pr(Z>2)[/tex]

This is simply the area to the right of 2 in a standard normal curve. From the standard normal table, this area is; 0.02275

As a percentage this is equivalent to 2.275%

To find the probability of borrowing more than 250 books, calculate the Z-score and use a standard normal distribution table to find the corresponding percentile. Subtract this percentile from 1 to obtain the desired probability.

The question involves using the properties of a normal distribution to find the probability that more than 250 books were borrowed in a week, given that the mean number of books borrowed is 190 and the standard deviation is 30. To determine this probability, one would calculate the Z-score for 250 books and then refer to a standard normal distribution table or use a calculator with normal distribution functions to find the area under the curve to the right of this Z-score.

To calculate the Z-score, we use the formula:

Where X is the value of interest (250 books), μ is the mean (190 books), and σ is the standard deviation (30 books).

Calculating it gives:

The Z-score of 2 corresponds to a certain percentile in the standard normal distribution, which indicates the probability that a sample has a value less than 250. To find the probability of a value being more than 250, one would subtract this percentile from 1.

Answer:

The coordinates of A'' are (-2 , -5) ⇒ answer A

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

* Now lets solve the problem

- The vertices of triangle ABC are:

 A is (2 , -5) , B is (1 , -3) , C is (5 , -3)

∵ The triangle is reflected across the y-axis

∴ The x- coordinates of the three point are changed to opposite sign

∵ A is (2 , -5)

∴ its image A" is (-2 , -5)

* The coordinates of A'' are (-2 , -5)

Answer:

(-2, -5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The volume of a box with dimensions length x, width (x+1), and height (x+2), is given by the formula x^3 + 3x^2 + 2x cubic units.

The volume of the box can be calculated by multiplying its length, width, and height together. Given that the length is x, width is (x+1), and height is (x+2), the volume would be x*(x+1)*(x+2).

To further expand this, apply the distributive law which first multiplies x*(x+1), resulting in x^2 + x. Then multiply this result by (x+2), giving the final volume V = x^3 + 3x^2 + 2x.

Therefore, the volume of the box given the stated dimensions is x^3 + 3x^2 + 2x cubic units.

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Answer:

Option B

Step-by-step explanation:

It is always wise to ask who or what the organization is asking. Always be safe.

Answer:

I would 100% go with

"Option B. Ask for the name of their organization and look for information about them to make sure they're authentic before he donates"

Step-by-step explanation:

That was the only logical decision, because for D. you can't just hope for the best and donate "blindfolded". A. was really not a smart decision because if you give someone your credit card number, they could easily take all the money they wanted off of it and put you in loads of debt. And then for C., it was the same with D., you can't just donate to an organization or charity fund when you have no idea if it's a probable cause or not. So, in conclusion "Option B." is your best and most logical answer.

tan 24 = x/12

0.4452 · 12 = X

5.34 = X

93.75h. Mr. Demir must work 93.75h at his part-time job to make sure that he and his wife have met their monthly budget.

This problem can be solved by simply  arithmetic, The montly budget is $5,500, Mrs. Demir takes home $4,000 each month.  Then what remains to achieve the budget is:

$5,500 - $4,000 = $1,500

Mr. Demir works part time and earns $16 per hour, In order to achieve the monthly budget, Mr. Demir need to take home $1,500. Then, to take home $1,500 Mr. Demir has to work:

1500/16 = 93.75

Mr. Demir has to work 93.75 hours per month in order to achieve the monthly budget

Answer:

[tex]A=2\ m^{2}[/tex]

Step-by-step explanation:

we know that

The resulting two-dimensional cross-section is a rectangle 1 m x 2 m

so

the area of this rectangle is equal to

[tex]A=2*1=2\ m^{2}[/tex]