A drain must be installed with a grade of 1/10 in. of vertical drop per foot of horizontal run. How much of a drop will there be for 58 ft of run?​

3.- Notice that:

Therefore, we can rewrite the given equation as follows:

Adding like terms we get:

Subtracting 5 from the above equation we get:

Dividing the above equation by -√3 we get:

Finally, recall that:

Therefore:

Answer: Option C.

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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Answer:

y'=|x-5|-1

Step-by-step explanation:

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Answer:

∠ MON = 51°

Step-by-step explanation:

∠ LON is composed of the 2 angles LOM and MON , that is

∠ LOM + ∠ MON = ∠ LON

42° + ∠ MON = 93° ( subtract 42° from both sides )

∠ MON = 51°

Answer:

<MON= 51°

Step-by-step explanation:

Look at the diagram and locate LON. You can see that LON is the angle of the complete line. Now LOM is given which is the angle of a part of the lines. So that means that to find MON we can minus LON with LOM.

<MON= <LON - <LOM

= 93-42

<MON= 51°

Feel free to ask any doubt you have!

Answer:

x = 3

Step-by-step explanation:

the diagonals bisect each other so:

6x + 2 = 20

subtract 2 from both sides of the equation:

6x = 18

x = 18/6

x = 3

Answer:

14 and 37

Step-by-step explanation:

\(x-y =23\\xy=518\)

x= mother's age

y= Monique's Age

\(y=\frac{518}{x}\)

\(x=23+y\)

\((23+y)y=518\)

\(23y+y^{2} =518\)

\(y^{2} +23y-518=0\)

\((y-14)(y+37)=0\)

\(y=14\)  monica is 14 years old

The mother: \(x-y=23\\x-14=23\\x=23+14 = 37\)

Hope this helps

Answer:

rational

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

A radius is a part of a circle that doubles to form its diameter. The radius of each sphere is 3.34 cm.

A circle is a shape bounded by curved line known as circumference. some of its parts of a circle are; diameter, radius, arc, chord etc.

A radius is that part of the circle that is half of its diameter. This implies that;

   radius = \(\frac{diameter}{2}\)

Such that;

diameter = 2*radius

A sphere is an object that can be derived from the volume of a circle.

Given that the height of the cylindrical can is 20 cm, and three identical spherical balls would fit entirely within the can.

Then;

diameter of each spherical balls = \(\frac{20}{3}\)

                                                      = 6.67 cm

Thus;

the radius of each of the spherical balls =  \(\frac{diameter}{2}\)

                                                   =  \(\frac{6.67}{2}\)

radius of each of the spherical balls = 3.335 cm

Therefore, the maximum radius of each ball is 3.34 cm.

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer:

f(x) = -3/2 x - 2

Step-by-step explanation:

The line rises to the left so the slope is negative, also:

the slope of the line is -3/2 and the y-intercept is at (0, -2)

2 1/2 as an improper fraction is 5/2

First, split the mixed fraction into the sum of a whole number and a fraction:

2 1/2 =>2+ 1/2

Then, rewrite the whole number as an equivalent fraction:  2 => 4/2

Lastly, add together the two fractions to get the answer:

4/2 + 1/2 = 5/2

Answer:

The graph of g(x) has a lesser y intercept

Step-by-step explanation:

Given

f(x) = 100(-x + 4)

Required

Determine the relationship between f(x) and g(x)

First, we need to get the equation of g(x).

From the question, we have that:

Initial Value = 360

Rate = -90 yearly

[It is negative because the rate shows decrement]

Hence, the equation of g(x) is:

g(x) = Initial Value + Rate * x

Where x represents number of years

g(x) = 360 + (-90 * x)

g(x) = 360 - 90x

g(x) = -90x + 360

Recall that

f(x) = 100(-x + 4)

f(x) = -100x + 400

To solve y intercept, we set x = 0.

f(0) = -100 * 0 + 400 = 0 + 400 = 400

g(0) = -90 * 0 + 360 = 0 + 360 = 360

By comparison, the graph of g(x) has a lesser y intercept

To solve x intercept, we set y = 0

For f(x)

0 = -100x + 400

100x = 400

x = 4

For g(x)

0 = -90x + 360

90x = 360

x = 4

By comparison, they have the same x intercepts.

From the list of given options, option A answers the question.

Answer:

301.59 units or 301.6 after rounding

Answer:

Domain: 0, 1, 2, 3, 4,

Range: 1, 2, 3, 4, 5,

Step-by-step explanation:

Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5,  therefore, the answer is:

Answer:

(m? - 5 m +6 )  ÷ (m - 2)​ = \(\frac{m}{-5m+6} / (m - 2)\)

Step-by-step explanation:

Divide the first expression by the second expression.

\(\frac{m}{-5m+6} / (m - 2)\)

I hope this helps.

The slope intercept form of the given equation is,

y = 5x - 1/4

Given an equation of a line as,

5x - y = 1/4

We have to write the equation of the line in slope intercept form.

Equation of the line in slope intercept form is,

y = mx + c

Here m is the slope and c is the y intercept.

Rearranging the given equation,

5x = y + 1/4

5x - 1/4 = y

or,

y = 5x - 1/4

Hence the slope intercept form is y = 5x - 1/4.

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Answer:

I think it is 18(A)

Step-by-step explanation:

I multiplied 8x3 then I did 6x3 and got 18

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

y = - 3

Step-by-step explanation:

the midline is a horizontal line positioned midway between the maximum and minimum values of the graph.

maximum = - 1 and minimum = - 5

then

(- 1 + (- 5)) ÷ 2 = (- 1 - 5) ÷ 2 = - 6 ÷ 2 = - 3 so equation of midline is

y = - 3

Answer:

Step-by-step explanation:

Given the expression (–5a)(2a – 1)

Open the bracket

(–5a)(2a – 1)

= -5a(2a) -5a(-1)

= -10a² + 5a

hence the equivalent expression is -10a² + 5a

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = \(x^2+7\)

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = \(x^2+7\)

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

None of the three points (A, B, C) lies on the circumference of the unit circle.

Unit circles are circles centered at the origin and with a radius of 1. A point is on the circumference if and only if the distance of the point respect to the origin is equal to 1. The distance of each point is determine by Pythagorean theorem:

Point A

\(d = \sqrt{4^{2}+3^{2}}\)

d = 5

Point B

\(d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{1}{5}\right)^{2} }\)

d = √29 /10

d ≈ 0.539

Point C

\(d = \sqrt{\left(\frac{3}{4} \right)^{2}+\left(\frac{7}{4} \right)^{2}}\)

d = √58 /4

d ≈ 1.904

None of the three points (A, B, C) lies on the circumference of the unit circle.

The statement presents a typing mistake, correct form is shown below:

A(x, y) = (4, 3), B(x, y) = (1/2, 1/5), C(x, y) = (3/4, 7/4). Which point lies on the circumference of the unit circle?

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Answer:

The length is 15 inches squared

Step-by-step explanation:

total area / height = length

120 / 8 = 15

The value of ||3u - 2v|| for the given  initial point  and the final points of the vectors u and v are : ||3u - 2v|| = 39.4588.

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation.

Velocity, force,  momentum, electromagnetic fields, and weight are a few examples of vectors in nature.

Vector u:  initial point at (17, 5) and terminal point at (9, -12).

Vector u written in terms of the initial points as origin:

u = (9 - 17, -12 - 5)

u = (-8, -17)

For vector v:

Vector u:  initial point at (12, 4) and terminal point at (3,-2).

v = (3 -12, -2-4)

v = (-9, -6)

Then, the value of 3u - 2v:

3u - 2v = 3(-8, - 17) -(-9,-6)

3u - 2v = (-6, -39)

Find norms by Pythagorean theorem.

||3u - 2v|| = ||-6, -39||

||3u - 2v|| = √(-6)²+(-39)²

||3u - 2v|| = 39.4588

Thus, the value of ||3u - 2v|| for the given  initial point  and the final points of the vectors u and v are : ||3u - 2v|| = 39.4588.

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Answer:

C

Step-by-step explanation:

Tyler, because his money is increasing exponentially.

I finished taking the test and got it right :)

The person who will have more money by year 20 is given by: Option C: Tyler, because his money is increasing exponentially

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

For example, \(y = a.b^x\) , where a is a and b are constants is an exponential function.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

\(I = \dfrac{P \times R \times T}{100}\)

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

\(CI = P(1 +\dfrac{R}{100})^T - P\)

The final amount becomes:

\(A = CI + P\\A = P(1 +\dfrac{R}{100})^T\)

Usually these two rates are used on money. The compound interest is exponential as it has power T as a variable, but for simple interest, there is no variable exponent.

Both are positive, and growth of exponential function is always going to surpass the growth of linear function (can be proven by derivatives).

Since we are not given the function's equation, we cannot correctly calculate the value just from graph, but as in 14 years, the blue line is already close to red line so it will likely cross it after 6 more years (thus total 20 years) because of good growth.

Thus, the person who will have more money by year 20 is given by: Option C: Tyler, because his money is increasing exponentially

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Answer: \(y=-\frac{4}{3}x+2\)

Step-by-step explanation:

The slope of \(AB\) is \(-4/3\). Thus, the slope of \(CD\) is also \(-4/3\).

Thus, the equation of \(CD\) can be found as follows:

\(y-10=-\frac{4}{3}(x+6)\\\\y-10=-\frac{4}{3}x-8\\\\y=-\frac{4}{3}x+2\)

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Answer: Choice E

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

Explanation:

Each item A through D is false because one set may be infinite while the other is finite, or vice versa. One set being finite doesn't automatically make the other finite as well.

---------

Here's an example of why choice B is false.

A = set of nonzero real numbers

B = {-1, 1}

f(x) = |x|/x

This function is surjective because we target everything in the range B = {-1,1}. Positive x values map to 1, negative x values map to -1. Notice how set A is infinitely large, and B is finite.

The other answer choices can be ruled out through similar logic.

An injective function and A is finite, then B is finite as well and the Cardinality, a surjective function and B is finite, then A is finite as well and the cardinality of A is at most the cardinality of B. True statements: A and C.

Let's analyze each statement:

A. If f:A→B is an injective function and A is finite, then B is finite as well and the cardinality of B is at most the cardinality of A.

True. An injective function preserves the cardinality, and if A is finite, then B must also be finite. The cardinality of B is at most the cardinality of A.

B. If f:A→B is a surjective function and B is finite, then A is finite as well and the cardinality of A is at least the cardinality of B.

False. A surjective function does not necessarily imply a relationship between the cardinalities of the domain and codomain. A could be finite or infinite.

C. If f:A→B is a surjective function and B is finite, then A is finite as well and the cardinality of A is at most the cardinality of B.

True. A surjective function implies that every element in B is mapped from an element in A. If B is finite, then A must also be finite, and the cardinality of A is at most the cardinality of B.

D. If f:A→B is an injective function and A is finite, then B is finite as well and the cardinality of B is at least the cardinality of A.

False. An injective function does not guarantee that the cardinality of the codomain is related to the cardinality of the domain. B could be finite or infinite.

E. None of the above

False. As analyzed above, there are true statements among the given options.

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We have a system of linear equations:

We have to solve by substitution. This is the most appropiate method a s we already have one of the variables in function of the other.

Then, we can replace x in the second equation as:

With the value of y, we can calculate x from the first equation:

Answer: x=-16 and y=2