What happens at an end of a function?

Answers:

Team A = 175 people

Team B = 150 people

This is before the 45 students transfer from A to B.

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

Explanation:

x = number of people in team A

y = number of people in team B

These counts are before the 45 pupils transfer from A to B.

The counts are in ratio 7:6, which means,

x/y = 7/6

6x = 7y

x = 7y/6

If we subtract 45 people from team A, we have x-45 people left. Those 45 people go to team B to have y+45 pupils there.

The quantities x-45 and y+45 are in ratio 2:3, so,

(x-45)/(y+45) = 2/3

3(x-45) = 2(y+45)

3x-135 = 2y+90

3(7y/6)-135 = 2y+90 .... plug in x = 7y/6

21y/6 - 135 = 2y+90

6*( 21y/6 - 135 ) = 6*(2y+90)

21y-810 = 12y+540

21y-12y = 540+810

9y = 1350

y = 1350/9

y = 150

x = 7y/6

x = 7(150)/6

x = 175

We have 175 people on team A, and 150 people on team B.

This is before the 45 students transfer from A to B.

-------------------

Check:

x/y = 175/150 = (7*25)/(6*50) = 7/6

This shows x and y are in ratio 7:6 to match the instructions.

x-45 = 175-45 = 130

y+45 = 150+45 = 195

(x-45)/(y+45) = 130/195 = (2*65)/(3*65) = 2/3

And we have the updated counts in the ratio 2:3, which matches the stated info in the instructions. The answers are fully confirmed.

Equivalent rational expressions with Denominator = (5q + 6)(q-3)(9-8)

The portion of a fraction that lies below the fractional bar is known as the denominator. The denominator displays the total number of constituent elements. A horizontal bar between two integers and occasionally the sign "/" are indicators of a fraction.

The "fractional bar" is a name for this bar or symbol. The "numerator" is the number at the top, while the "denominator" is the number that comes after the fractional bar.

The numerator and denominator of any fraction a/b are 'a' and 'b,' respectively. Part of a whole is represented by a fraction. It can be demonstrated mathematically by dividing two numbers.1)

[tex]2/5q^2 -9q -185q^2-9q -18 = 0\\\\5q^2 + 6q -15q -18 =0\\\\5q^2 -15q + 6q-18 = 0\\\\5q(q-3) + 6(q-3) = 0\\\\(q-3)(5q+6) = 0\\\\ q-3=0 \\\\5q+6=0\\\\ q=3 \\\\ q= -6/5\\\\[/tex]

therefore,

[tex]2/(q-3)(5q+6)\\\\2/(q-3)(5q+6) * q-8/q-8\\\\= 2(q-8)/(q-3)(5q+6)(q-8)[/tex]

equivalent rational expressions with denominator

[tex](5q+6)(q-3)(q-8): 110q/5q^2 -34q -48\\\\5q^2-34q +48= 0\\\\5q^2-40q + 6q-48=0\\\\5q(q-8) + 6(q-8)= 0\\\\(q-8)(5q+6) =0\\\\[/tex]

Therefore,

[tex]10q/(q-8)(5q+6)\\\\Therefore, 10q/(q-8)(5q+6) * q-3/q-3\\\\= 10q(q-3)/(q-8)(5q+6)(q-3)\\\\[/tex]

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Answer:

6 ≤ x ≤ ∞

Step-by-step explanation:

The domain is the "allowable inputs" or x-values. We know that there cannot be a negative number under a radical, so that means "x-6" must be greater than or equal to zero. Thus, we can set up the equation:

x - 6 ≥ 0

x ≥ 6                  This is the domain

There aren't restrictions on positive x-values, so we can also write the domain as:

6 ≤ x ≤ ∞

The function of piecewise graph shown in the figure is,

f(x) = {y = 6   for x < -5

        { [tex]y = -\frac{19}{9}x-\frac{5}{9}[/tex]    for -5 ≤x < 5

        { y = 8/5x -14   for x ≥ 5

What is piecewise function?

A piecewise-defined function in mathematics is a function with several sub functions, each of which has a certain interval in the domain for which it is applicable. Piecewise definition is a method of expressing the function, not a property of the function.

From graph we can see that the first function is a line y = 6

Hence, f(x) = {y = 6    for x < -5}

Now to find the equation of second function.

From graph we get two points (-5, 10) and (4, -9).

First to find the slope

[tex]m = \frac{-9-10}{4+5} = \frac{-19}{9}[/tex]

Now to find the equation of line, using slope point form

[tex]y - 10 = \frac{-19}{9} (x-(-5))\\y-10=-\frac{19}{9}x-\frac{95}{9} \\ y=-\frac{19}{9}x-\frac{95}{9} + 10\\y = -\frac{19}{9}x -\frac{5}{9}[/tex]

So, f(x) = { [tex]y= -\frac{19}{9}x-\frac{9}{5}[/tex],    for -5 ≤ x < 5}

Now to find the equation of third line.

From graph we get two points (5, -6) and (10, 2).

First to find the slope of the line

[tex]m = \frac{2-(-6)}{10-5} = \frac{8}{5}[/tex]

Now to find the  equation of line, using slope point form

[tex]y-(-6)=\frac{8}{5}(x-5)\\ y+6=\frac{8}{5}x-8\\ y = \frac{8}{5}x - 14[/tex]

So, f(x) = {[tex]y = \frac{8}{5}x-14[/tex],   for x ≥ 5}.

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this is technically a 7 page essay, if you put this on 10000000000000x text size, 2+2=4 for bcs thats law of math, 1+1=2 bcs thats law of math.

Count with your fingers,

2 + 2 =4

1+1 = 2

The exponential growth from the exponential function has a growth rate of 28.5%

In mathematics, an exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Data;

Using the formula of exponential function;

A = A₀(1 + r)ˣ

450 = 100(1 + r)⁶

r = 0.2849 * 100 = 28.5%

The growth rate is 28.5%

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Answer: A

Step-by-step explanation:

The quotient is the result of the division between two numbers.

Answer:

n/3

Step-by-step explanation:

When you divide you get a quotient.

n divided by 3 will equal a quotient.

We can use a double strategy to find the value of the given expression, which is 32.

Mathematical expressions are combinations of numerical variables and operations denoted by subtraction, addition, multiplication, and division signs.

Doubles' strategy is adding two same single-digit numbers or two-digit numbers so we can get the result equal to a number multiplied by 2.

Given 4 x 8, we can evaluate this expression by using the double strategy as follows:

4 x 8 = 2 x 8 + 2 x 8

        = 16 + 16

        = 32.

Therefore, the value of the expression 4 x 8 is 32.

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Answer:

According to the SAS ( Side Angle Side ) rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the equivalent two sides and angle between the sides of the other triangle.  

Step-by-step explanation:

Two figures are said to be "congruent" if they can be placed exactly over one another.

According to the SAS ( Side Angle Side ) rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the equivalent two sides and angle between the sides of the other triangle.  

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We write proof because it teaches us to use deductive and inductive reasoning. We apply this reasoning and logic to a variety of jobs, professions, and everyday happenings

One part of math that understudies frequently battle with, especially in calculation (which generally has been where confirmation is presented), is composing evidences.

We want confirmations in math, first, since we need to be certain that what we truly do is correct. There are an adequate number of wellsprings of blunder in our estimations, from loose estimation to misconception of the equations we ought to utilize, that it's critical to ensure that our reasoning doesn't add more mistake. Verification simply implies actually taking a look at our thinking.

Proving things is a perspective, and at last the benefit of learning different approaches to demonstrating things (two-segment confirmations, yet evidence by enlistment, verification by logical inconsistency, epsilon-delta verifications, etc) is that it ought to assist you with grasping the distinction between knowing something and not exactly knowing it by any means.

Thats why we write proof.

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The lowest temperature with a z score of of -2.49 is 24.0 ˚F

Z scores, measures the amount of standard deviation sample X is from mean. the formula is below

z = (X - μ) / σ

Definition of variables

mean, μ = 4.4˚F

standard deviation, σ = 12.2 ˚F

X = lowest temperature

z = -2.49

substituting into the formula

-2.49 =  (X - μ) / σ

-2.49 = (X - 64.4) / 12.2

-2.49 * 12.2 = X - 64.4

-30.378 + 64.4 = X

X = 34.022

X = 34.0  (to one decimal place)

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The four types of functions are one one function , Onto function , Many One function and Into function ,

In the question ,

we have been asked about the four different types of functions ,

the four types of functions are defined as ,

(1) One - to - One Function

A function defined as f: A → B , is said to be one one if every element of set A is connected to a distinct element in set B.

The one one  function is also called as injective function.

(2) Onto Function

A function defined as f: A → B , is said to be onto if  every element in set B has a pre-image in set A.

The onto function are also called as subjective function.

(3) Many One function

A function defined as f: A → B , is said to be Many One if more than one element of the set A are connected to same element in set B .

(4) Into functions

A function defined as f: A → B , is said to be Into if the elements in the set B are excess and are not connected to any elements in the set A.

Therefore , the four types of Functions are defined above .

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1) The estimated probability of patrick flipping a head with his coin is; 0.45

2) The margin of error for Patrick's estimated probability is; 0.218

3) The confidence interval for the chance of flipping a head with his coin is; CI = (0.232, 0.668)

No, the 95% confidence interval does not contain 50% as a probability, so it will be illogical to think that Patrick's lucky coin has a probability different from 0.5

We are given;

Number of trials; n = 20

Number of successful outcomes; x = 9

Thus; Proportion; p^ = x/n = 0.45

Now, the formula for the confidence interval of proportions is;

CI = p^ ± z√(p^(1 - p^)/n)

where;

z√(p^(1 - p^)/n) is margin of error

1) Probability of Patrick flipping a head with his lucky coin is;

p^ = x/n = 9/20 = 0.45

2) The margin of error is from the formula;

z√(p^(1 - p^)/n)

z for 95% confidence level is 1.96. Thus'

E = 1.96√(0.45(1 - 0.45)/20)

E = 0.218

3) Confidence interval is;

CI = 0.45 ± 0.218

CI = (0.232, 0.668)

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Answer: [tex]11\sqrt{3}-7\sqrt{6}[/tex]

Step-by-step explanation:

[tex]7\sqrt{3}-4\sqrt{6}+\sqrt{48}-\sqrt{54}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16 \cdot 3}-\sqrt{9 \cdot 6}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16}\sqrt{3}-\sqrt{9}\sqrt{6}\\\\=7\sqrt{3}-4\sqrt{6}+4\sqrt{3}-3\sqrt{6}\\\\=11\sqrt{3}-7\sqrt{6}[/tex]

Answer: See attached.

Step-by-step explanation:

        This slope-intercept form equation shows us that there is a y-intercept of -7. This means that (0, -7) will be a point on the line. Next, we have a slope of positive 3. This means we will count up three units, right one unit, plot a point. Then we repeat.

Answer:

start at the y-intercept, plot some points using the slope, then connect them using a straight line.

Step-by-step explanation:

Generally you'll have an equation in slope-intercept form, which is denoted as: [tex]y=mx+b[/tex]

This is a really useful form for a couple of reasons, and it has two key features. Firstly, the "m" represents the slope of the linear equation.

This makes sense the definition of slope is: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]

and we can generally define the points:

[tex]\text{at x = 1, y = }m(1)+b\implies m+b\\\text{at x = 2, y = } m(2)+b\implies m + m + b\\\text{at x = 3, y = }m(3) + b\implies m + m + m +b\\\text{and so on...}[/tex]

as the x value increases by 1, the change in y is the "m" value, we have one more "m" than the previous x-value, so the slope is the "m" value, which is the coefficient of the x variable.

The second key feature of slope-intercept form is the y-intercept, which is represented as "b" in this form. This also makes sense because the y-intercept is simply when the x-value is zero, and if you plug in x=0 into the equation, you're only left with the "b" value

Knowing these two things we can analyze the equation given:

[tex]y = 3x-7[/tex]

since it's given in slope-intercept form, we know that slope = 3, and y-intercept = -7. We immediately know one point, which is the y-intercept, since the x-value is going to be zero at the y-intercept, so one point on the graph is: (0, -7)

now from this point we can draw the graph by going to the right one, and up three, by definition of a slope (as x increases by 1, the y-value increases by 3).

We can do something similar on the left side, except instead of right one and up three, we go left one, and down three. You may be asking why down three? Well as you go right one, you go up three, this means if you compare the previous point to the new point, the previous point is down three compared to the new point (which is to the right one), so if you were to go back, you would be going left one and down three.

Now from these points you can do the same thing to extend the line a bit, and since it's a linear equation you can connect them using a straight line.

I also attached a graph from desmos to illustrate what I was saying a bit and also show the graph.

Answer: Equivalent fractions are two or more fractions that are all equal even though they have different numerators and denominators. For example, the fraction 1/2 is equivalent to (or the same as) 25/50 or 500/1000.

*(This is not my work)*

Step-by-step explanation:

Side-Angle-Side (SAS) Rule prove the congruency of the triangle

What is a triangle ?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Triangles can be divided into three sorts based on the lengths of their sides, and they are: Scalene. Isosceles. Equilateral.

The Side-Angle-Side rule is used to demonstrate whether a set of triangles is congruent. According to the SAS rule, two sides and the included angle of one triangle must equal two sides and the included angle of another triangle in order for the two triangles to be considered congruent.

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yes

Step-by-step explanation:

5

Prices of two ratios in the ratio is 4 : 1.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.

For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole.

For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.

Let us assume price of radios are x and y

According to the question

[tex]\frac{x + 20}{y+20} =\frac{5}{2}\\2x+40=5y+100\\2x-5y=60[/tex]-------------------------- eq(1)

and

[tex]\frac{x-5}{y-5} =\frac{5}{1}\\5y-x = 20[/tex]

5y-x = 20

multiplying this equation by 2

we get

10y-2x = 40 ------------------ eq(2)

adding eq 1 and 2

we get

5y=100

y=20

solving further we get x=80

Thus the ratio is 4 : 1.

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For the path, we'll need 25 gallons of coating.

We know that the area of the path is given by the formula

A = πr₁² - πr₂²

Where r₁ is the outer radius, and r₂ is the inner radius

As per the question, we have

r₁ = 12 yd, and r₂ = 9 yd

Substitute the values in the formula, and we get

A = π(12)² - π(9)²

A = π(144) - π(81)

A = 63π = 63(3.14)

A = 197.92 sq yd

Since one gallon of coating can cover 8 sq yd.

The gallons of coating needed :

Divide the area of the path by 8

So, 197.92/8

⇒ 24.74 ≈ 25 gallons

Thus, we'll need 25 gallons of coating for the path.

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The 3 medians of triangle are the line segments that connects a vertex to the midpoint of the opposite side.

A triangle is a three-sided polygon with three vertices and three sides that enclose three angles.It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the angles measured. The sum of a triangle's interior angles is 180 degrees.

Median of a Triangle:-

Thus, the median of triangle line segment that connects a vertex to the midpoint of the opposite side.

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The degree of a polynomial in factored form is the number of zeros or roots of that polynomial.

Given:

Degree of a polynomial:

Degree is the highest or the greatest power of a variable in a polynomial equation.

ex : 2x^2 + 2xy^2

Degree = 3

Degree of a polynomial in factored form:

Degree of a polynomial in factored form is the number of zeros or roots of that polynomial.

Example:

= (x-1) (x-2) (x-3)

number of roots = 3

Degree = 3

= (y-5)(y+3/2)(y-4)(y+1)

number of roots = 4

Degree = 4

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The selling price of the radio with a cost price of 550 and sold at a profit of 35 is 585.

The selling price is how much a buyer pays for a product or service.

To calculate the selling price of the radio, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the selling price of the radio is 585.

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The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

What is the hypotenuse leg theorem?

The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

Hence, if the hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

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The two whole numbers that lie between -1 and 3 is 0 and 1.

Given:

Whole numbers:

The whole numbers are defined as positive integers including zero. The whole number does not contain any decimal or fractional part. It means that it represents the entire thing without pieces or Whole numbers is a collection of all the basic counting numbers and 0.

The whole numbers are all the natural number along with zero or 0.

whole number between -1 and 3:

0 , 1, 2

we can take any two.

so whole numbers lie = 0,1,2

Therefore the two whole numbers that lie between -1 and 3 is 0 and 1.

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Full question:

What are the 2 whole numbers that lie between -1 and 3?

Answer:

17 years old

Step-by-step explanation:

cathleen- C

Brody- B

b+6=c

c+b=1/2(56)

b+6+b=1/2(56)

2b+6=28

   -6  -6

2b=22

/2. /2

b=11

11+6=c

17=c

cathleen is 17 years old

hopes this helps please mark brainliest

Answer:

is

Step-by-step explanation:

The domain of g is identical to the domain of f.

They both have the same slope which means they have the same domain.

Answer:

is NOT

Step-by-step explanation:

the equation of g(x) is not the same as f(x)

so, g(x) and f(x) are NOT identical (aka not the same)

*domain is different by looking at b-value

The graph of exponential function y = 5.2^x

exponential function in the form y = ab^x + c

Exponential function:

An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is also a variable, and a is a constant called the base of the function.

where

a is the initial y - intercept.

b is the constant ratio.

c is the horizontal asymptote.

So, in this problem, we have:

constant ratio = 2

y-intercept at y = 5

horizontal asymptote at y = 0

The graph is in the image uploaded.

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