40 points with explanation please​

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2+3x-12\qquad \begin{cases} x_1=3\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(3)}{5-3} \\\\\\ \cfrac{[(5)^2+3(5)-12]~~-~~[(3)^2+3(3)-12]}{2}\implies \cfrac{[25+3]~~-~~[9-3]}{2} \\\\\\ \cfrac{28-6}{2}\implies \cfrac{22}{2}\implies 11[/tex]

Answer:

B. By simplifying 9 to [tex]3^{2}[/tex] to make both powers base three and subtracting the exponents

Step-by-step explanation:

When you have a division the quotient of powers property states that the exponents should be substracted, and by simplifying 9 to [tex]3^{2}[/tex] you end up with an equation like this:

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

Then you just have to substract the exponent from the denominator from the numerator´s exponent, which would be:

4-2=2

and the resultant equation would be:

[tex]3^{2} =3^{2}[/tex]

The Quotient of Powers Property allows you to subtract exponents when dividing expressions with the same base. The expression 3^4/9 simplifies to 3^2 because 9 can be expressed as 3^2, therefore their exponents are subtracted (4-2=2).

In this question, the Quotient of Powers Property is used. This property states that to divide where the base remains the same, you subtract the exponents. In the expression 3^4/9 = 3^2, we know that 9 can be expressed as 3^2.

Therefore, it becomes 3^4/3^2. According to the Quotient of Powers Property, we subtract the exponent of the denominator from the exponent of the numerator (4-2=2). Hence the expression simplifies to 3^2. The correct choice is B: By simplifying 9 to 3^2 to make both powers base three and subtracting the exponents.

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Answer: 0.167 is the part of the hall that was not occupied. Or 16.7 %

Step-by-step explanation:

300-250=50 this is the number of seats not occupied since 250 is the amount occupied.

So, 50/300=5/30 which can be converted to a number which is 0.1666666667. It says to round to the thousandths place, which is the 3rd number. That is 0.167

Answer:

0.167 part of the hall was not occupied

Step-by-step explanation:

Given :In a concert hall, 250 seats out of 300 were occupied.

To Find :To the nearest thousand, what part of the hall was not occupied?

Solution:

Total seats = 300

Occupied seats = 250

Unoccupied seats = 300-250 = 50

So, The part of the hall was not occupied = [tex]\frac{\text{unoccupied seats}}{\text{total seats}}[/tex]

                                                                     = [tex]\frac{50}{300}[/tex]

                                                                     = [tex]0.167[/tex]

Hence 0.167 part of the hall was not occupied

Answer:

D. Acute

Step-by-step explanation:

This is an acute angle because the angle is less then 90 degrees.

<FOA is an Acute angle (D).

How I know...

Acute angles are angles are below 90 degrees (aka LESS then a right angle)

Hope this helped!

~Just a girl in love with Shawn Mendes

ANSWER

[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]

EXPLANATION

Coterminal angles are angles that have the same terminal side in standard position.

We want find all angles that are coterminal with

[tex] \frac{5\pi}{3} \: \: radians[/tex]

We add or subtract multiples of 2π radians to this angle to obtain all angles that are coterminal with this angle.

The coterminal angles are:

[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]

where n is an integer.

Answer:

-7 Pi/3, -Pi/3, 11 Pi/3

Step-by-step explanation:

Answer:

(2.4 , -1)

Step-by-step explanation:

Too many commas in second ordered pair but this is how I will interpret the question:

Find the midpoint of (3.2,2.5) and (1.6,-4.5)

So just average x's  : (3.2+1.6)/2 =4.8/2=2.4

And

    just average y's : (2.5+-4.5)/2=-2/2=-1

The midpoint is (average x's , average y's)

Your midpoint is (2.4             ,     -1             )

answer (2.4 , -1)

Answer:

A. The answer is our unit prices when our profit is 0

Step-by-step explanation:

The zeros are the x-intercepts, when the curve passes through the x-axis.

I'm going to call our function P

P(x)=-0.5x^2+221x-224 is equal to 0 (our profit is equal to 0) when x (the unit price is such and such)

The answer is our unit prices when our profit is 0

The expression represents the monthly profit from sales of a product at a given unit price. The zero(s) of the expression represent the unit price(s) when the profit is equal to 0.

The expression -0.5x^2 + 221x - 224 represents the monthly profit, in thousands of dollars, from sales of a product when it is sold at a unit price of x dollars.

The zero(s) of the expression are the unit price(s) when the profit is equal to 0. To find the zero(s), we need to set the expression equal to 0 and solve for x.

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Answer:

27

Step-by-step explanation:

Aloha! My name is Zalgo and I am here to be of assistance to you today. The GCF (Greatest Common Factor) of 14 and 60 would be 12. To the GCF of 24, you need to multiply 2^3 by 3. In order to get the GCF of 60, you need to multiply 2^2 by 3 times 5.

I hope that this info helps! :P

"Stay Brainly and stay proud!" - Zalgo

(By the way, do you think you could mark me as Brainliest? I'd greatly appreciate it! Mahalo! XT)

The greatest common factor of 24 and 60 is 12.

To get the greatest common factor, we will list the factors of each number and find the largest one that they have in common.

The factors of 24 are:

1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

The largest factor that 24 and 60 have in common is 12.

Read more about common factor

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Final answer:

By repeating the perpendicular line segment construction twice using paper folding, one can effectively find the midpoint of a line segment, demonstrating the application of geometric principles and theorems related to perpendicular constructions.

Explanation:

If you repeat the perpendicular line segment construction twice using paper folding, you can construct the midpoint of a line segment. This is based on the principle that constructing perpendiculars at the ends of a given line segment and then erecting a third perpendicular midway between them will intercept the line segment at its midpoint. This is affirmed by the theorems that explain the geometrical properties and relationships of constructing perpendicular lines and their midpoints.

To elucidate, let's take a line segment AB of a certain length, and fold the paper to construct a perpendicular line at point A. Next, repeat the same action at point B. Now, fold the paper to find the midpoint of AB, and erect a perpendicular line at this midpoint. This results in the third perpendicular intersecting AB exactly at its midpoint, demonstrating that this method is effective for finding the midpoint of a line segment, thereby validating option A.

You can construct: The midpoint of a line segment.

The correct option is (A).

Paper folding constructions can be used to create geometric shapes and lines based on certain properties. Let's break down each of the given options and see if they can be achieved by repeating the perpendicular line segment construction twice:

A. The midpoint of a line segment: Yes, this can be achieved. Folding a line segment in half will give you its midpoint. By repeating the perpendicular line segment construction twice, you fold the line segment once to find a point equidistant from both endpoints (which is the midpoint), and folding it again should confirm that the resulting point is indeed the midpoint.

B. An angle congruent to a given angle: No, this cannot be achieved. The perpendicular line segment construction does not involve creating or manipulating angles, so it cannot be used to construct an angle congruent to a given angle.

C. A parallel to a line through a point not on the line: No, this cannot be achieved. The perpendicular line segment construction does not involve creating parallel lines.

D. An angle bisector: No, this cannot be achieved. Again, the perpendicular line segment construction does not involve manipulating angles, so it cannot be used to construct an angle bisector.

Therefore, the correct option is:

A. The midpoint of a line segment.

Answer:

45

Step-by-step explanation:

The 4 part of the ratio represents 30 red ribbons

Divide 30 by 4 to find the value of one part of the ratio

30 ÷ 4 = 7.5, hence

6 × 7.5 = 45 ← number of green ribbons

Answer:

It is (2, 2).

Step-by-step explanation:

Answer:

720/1681

Step-by-step explanation:

First quadrant so everything is positive for a trig function of just the angle.  I would suggest just drawing a right triangle using tan(x)=40/9 (opp/adj). Find the hypotenuse which is sqrt(40^2+9^2)=sqrt(1600+81)=sqrt(1681)=41.  So sin(x)=40/41 and cos(x)=9/41.

Therefore sin(2x)=2sin(x)cos(x)=2(40/41)(9/41)=720/1681

Answer:

Option B is correct.

Step-by-step explanation:

A proportional relationship is a relationship between two variables where the ratio between the two variables is always the same.

Divide b/a for each option, the option having same ratio for the complete tables have proportional relationship

a)

9/3 = 3

12/4 = 3

20/5 = 4

b)

25/20 = 5/4

30/24 = 5/4

40/32 = 5/4

c)

12/4 = 3

15/5 = 3

24/6 = 4

d)

4/3 = 4/3

9/6 = 3/2

12/16 = 3/4

So, Option B is correct.

Answer: Second Option

Step-by-step explanation:

It is said that two variables a and b are propocionales if when b increases then a increases in a constant rate.

That is, a and b are proportional if the quotient between b and a is always equal to a constant k.

[tex]\frac{b}{a}=k[/tex]

To know which of the tables shows a proportional relationship identify in which of the tables the division of b between a always is constant

You can verify that the table where the quotient of b enters a is always constant is in the second table

[tex]\frac{b}{a}=\frac{5}{4}[/tex]

Multiply the two brackets together

(x+2)(3x-3)

x(3x)*(-3)(x)+2(3x)(2*-3)

3x^2-3x+6x-6

3x^2+3x-6

Answer is : 3x^2+3x-6

Answer

A. x5y3

Step-by-step explanation:

Answer:

150(.40)^n is your equation

Step-by-step explanation:

Answer:

[tex]=150\cdot{0.4^n}[/tex]

Step-by-step explanation:

Let n be the number of rounds. Lets look at n=1 which is round one. Therefore if 40% of the contestants are eliminated then we can write an expression of the number of contestants eliminated:

[tex]=150\cdot{0.4}[/tex]

For round two, n=2:

[tex]=150\cdot{0.4)\cdot{0.4}=150\cdot{0.4^2}[/tex]

Therefore for the n number of rounds:

[tex]=150\cdot{0.4^n}[/tex]

Answer:

The second alternative is correct

Step-by-step explanation:

We have been given the expression;

[tex](x^{27}y)^{\frac{1}{3}}[/tex]

The above expression can be re-written as;

[tex](x^{27})^{\frac{1}{3}}*y^{\frac{1}{3}}\\\\(x^{27})^{\frac{1}{3}}=x^{27*\frac{1}{3}}=x^{9}[/tex]

On the other hand;

[tex]y^{\frac{1}{3}}=\sqrt[3]{y}[/tex]

Therefore, we have;

[tex]x^{9}\sqrt[3]{y}[/tex]

Answer:

Option 2: [tex]x^{9}(\sqrt[3]{y})[/tex]

Step-by-step explanation:

Given

[tex](x^{27}y )^{\frac{1}{3} }[/tex]

The exponent power will be multiplied with the powers inside the bracket

So,

[tex](x^{27 * \frac{1}{3}} y^{\frac{1}{3}})[/tex]

[tex]= x^{\frac{27}{3}} y^{\frac{1}{3} }[/tex]

[tex]= x^{9} y^{\frac{1}{3}}[/tex]

Writing in radical form will give us:

[tex]x^{9}(\sqrt[3]{y})[/tex]

So,

Option 2 is the correct answer ..

Answer:

[tex]\frac{\sqrt[3]{100x}}{5}[/tex]

Step-by-step explanation:

we have

[tex]\sqrt[3]{\frac{4x}{5}}[/tex]

Multiply inside by [tex]\frac{25}{25}[/tex]

so

[tex]\sqrt[3]{\frac{4x*25}{5*25}}[/tex]

[tex]\sqrt[3]{\frac{100x}{125}}[/tex]

Remember that

[tex]\sqrt[3]{125}=5[/tex]

substitute

[tex]\sqrt[3]{\frac{100x}{125}}=\frac{\sqrt[3]{100x}}{\sqrt[3]{125}}=\frac{\sqrt[3]{100x}}{5}[/tex]

Hello There!

The answer would be the first one.

This is saying that Tom can not save exactly 50.25 but he must save more than that

Answer:

the answer is B

Step-by-step explanation:

75 is a one time payment. 25 is the amount that you will pay permonth

Answer:

C=25m+75

Step-by-step explanation:

I am not sure but I think the probability of a circle being chosen first is 4/13

because 13 is the amount of shapes in total, and 4 is the amount of circles. I hope you found this helpful.

Answer:

The answer is [tex]\frac{4}{13}[/tex].

Step-by-step explanation:

There are five squares, two triangles, two ovals, and four circles.

So, total shapes are = [tex]5+2+2+4=13[/tex]

The probability that the first chosen shape will be a circle is given by :

[tex]\frac{possible outcomes}{total number of outcomes}[/tex]

= [tex]\frac{4}{13}[/tex]

Note: 4 because any 1 out of 4 can be selected.

[tex]125 = \frac{1}{125} {}^{y - 1} \\ 125 = ( {5}^{ - 2} ) {}^{y - 1} \\ \\ {5}^{3} = {5}^{2 - 2y} \\ 3 = 2 - 2y \\ - 0.5 = y[/tex]

Answer:

The answer is [tex]y=-0.5[/tex]

Step-by-step explanation:

In order to determine the "y" value, we have to change the way of we see the equation.

In these cases, when the variable is in the exponent and  it is possible to make two exponents in each side of the equation, we have to equal bases and then we have to make other equation between the exponents of both sides.

So,

[tex]125=(\frac{1}{25})^y^-^1\\(5)^3=(5^-^2)^y^-^1\\(5)^3=(5)^-^2^*^y^+^2\\[/tex]

Then, we have to make an equation between the exponents of both sides:

[tex]3=-2*y+2\\2*y=2-3\\2*y=-1\\y=\frac{-1}{2}=-0.5\\ y=-0.5[/tex]

Finally, the value of "y" is -0.5

Answer:

A

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 3x² - 2x + 4 - (5x² + 6x - 8) ← distribute parenthesis by - 1

= 3x² - 2x + 4 - 5x² - 6x + 8 ← collect like terms

= - 2x² - 8x + 12 → A

Answer:

{-5,-4,2}

Step-by-step explanation:

The domain is the inputs and the range is the outputs

The outputs are the y values

{ -5,2,-4,2}

We only list them once and in order from smallest to largest

{-5,-4,2}

Answer:

x = -2 or x = -3/2 thus B. & D. are the answer  

Step-by-step explanation:

Solve for x:

2 x^2 + 7 x + 6 = 0

Hint: | Factor the left hand side.

The left hand side factors into a product with two terms:

(x + 2) (2 x + 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x + 2 = 0 or 2 x + 3 = 0

Hint: | Look at the first equation: Solve for x.

Subtract 2 from both sides:

x = -2 or 2 x + 3 = 0

Hint: | Look at the second equation: Isolate terms with x to the left hand side.

Subtract 3 from both sides:

x = -2 or 2 x = -3

Hint: | Solve for x.

Divide both sides by 2:

Answer:  x = -2 or x = -3/2

Answer:

B and D

Step-by-step explanation:

Given

2x² + 7x + 6 = 0

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 6 = 12 and sum = + 7

The factors are + 4 and + 3

Use these factors to split the x- term

2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 → x = - 2 → D

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] → B

Answer:

B

Step-by-step explanation:

Noting the following rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]

Given

([tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex])( [tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex] )

Each term in the second factor is multiplied by each term in the first factor

= [tex]\sqrt{2}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) + [tex]\sqrt{3}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) ← distribute parenthesis

= [tex]\sqrt{10}[/tex] - [tex]\sqrt{14}[/tex] + [tex]\sqrt{15}[/tex] - [tex]\sqrt{21}[/tex]

Answer: Option D

D. 41​

Step-by-step explanation:

A value [tex]x_i[/tex] is considered an outlier if

[tex]x_i> Q_3 + 1.5IQR[/tex]

or

[tex]x_i <Q_1 - 1.5IQR[/tex]

Where

[tex]Q_3[/tex] is the third quartile

[tex]Q_1[/tex] is the first quartile

IQR is the interquartile range.

[tex]IQR = Q_3-Q_1[/tex]

In this case:

[tex]Q_3=92\\Q_1=72[/tex]

So

[tex]IQR = 92-72 =20[/tex]

[tex]Q_3 + 1.5IQR = 92 + 1.5*20 = 122[/tex]

[tex]Q_1 - 1.5IQR=72-1.5*20=42[/tex]

Then the outlier values will be all those greater than 122 or less than 42

Therefore the answer is the option D.

Answer:

[tex]4\pi[/tex] or 12.56

Step-by-step explanation:

[tex]\pi r^{2}[/tex] is the formula to find the area of a circle.

if we plug '2' in... [tex]\pi2^{2}[/tex]

which equals to [tex]4\pi[/tex]

if we multiply 4 with pi, it equals to 12.56

Answer:

Area of circle = 12.56 sq. units

Step-by-step explanation:

radius =  2

Area of circle = π r² sq. units

                       = 3.14 * 2 * 2 = 12.56 sq. units

Answer:

16

Step-by-step explanation:

4 groups of 4 is 16:

[tex]\left\begin{array}{cccc}*&*&*&*\*&*&*&*&*\*&*&*&*&*\*&*&*&*&*\end{array}\right[/tex]