Arlington High School recently installed a new black-box theatre for local productions. They only had
room for 14 rows of seats, where the number of seats in each row constitutes an arithmetic sequence starting
with eight seats and increasing by two seats per row thereafter. How many seats are in the new black-box
theatre? Show the calculations that lead to your answer.

Answer:

20%

the above was solved using set

Answer:

(-4, -17), (-3, -10), (-2,5), (-1,2)

Step-by-step explanation:

All the coordinates are represent linear function.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The coordinates are,

⇒ (-4, -12), (-3,-10), (-2, -8), (-1,-6)

⇒ (-4, -17), (-3, -10), (-2,5), (-1,2)

⇒ (1, -7), (2, -10), (3, -13), (4, -16)

⇒ (1, 1), (2, 4), (3, 7), (4, 10)

Now,

We know that;

A relation between a set of inputs having exactly one output each is called a linear function.

Clearly, All the coordinate have exactly one output for every input.

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Answer:

The college student can get 5 concert tickets

Step-by-step explanation:

$367.50÷(70+$3.50)

Answer:

Given:

1 mile = 1.6 km

So, to find how many miles are in 100 km, we need to divide 100km by 1.6km because one single mile contains 1.6km.

100km/1.6km = 62.5 miles

Answer:

Step-by-step explanation:

So,

We'll solve this using the Pythagorean Theorem.

Let

We know that,

[tex]{ \longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} }[/tex]

[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = (7) {}^{2} +( 6) {}^{2} }[/tex]

[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = 49 +36 }[/tex]

[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = 85 }[/tex]

[tex]{ \longrightarrow \sf \qquad AC = \sqrt{85} }[/tex]

[tex]{ \longrightarrow \sf \qquad AC \approx 9.21 }[/tex]

⠀

Therefore,

The solution for the linear inequality, in interval notation, is [tex]\:(-\infty \:,\:-\frac{7}{6}][/tex].

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use of follow symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than) and > (greater than).

The solutions for inequalities can be given by: graph in a number line or numbers.

For solving this exercise, it is necessary to find a number solution for  the given inequality.

                                 12x-8≤6x-15

                                12x-6x≤ -15+8

                                   6x≤-7

                                    x≤ -7/6

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Answer:

A)

Step-by-step explanation:

Starting point is at o and ending point at 2.

So, 2 in

Answer:

a - 2b

Step-by-step explanation:

❖ Step 1: Distributive negative sign.

❖ Step 2: Combine like terms.

Therefore, the answer is a - 2b.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

a-2b

Step-by-step explanation:

(a-b+c)-(c+b)

Distribute the minus sign to the terms in the second parenthesis

a-b+c-c-b

Combine like terms

a-b+c-c-b

a-b-b+c-c

Cancel like terms

a-2b

Answer:

Angles H, J, M, N

Step-by-step explanation:

Since m<p is 90 degrees it must be the largest angle so both triangles have angle 45-45-90. m<P is equal to m<K. This means that angle h, j, m, and n are equal.

angles M, N, and J.

try drawing diagrams to help you figure out the problem :)

Point :

Parallel lines have same slopes.

_________________________________

[tex]6x + 5y = 11[/tex]

Subtract sides -6x

[tex] - 6x + 6x + 5y = - 6x + 11[/tex]

[tex]5y = - 6x + 11[/tex]

Divided sides by 5

[tex] \frac{5}{5}y = \frac{ - 6}{5}x + \frac{11}{5} \\ [/tex]

[tex]y = - \frac{6}{5}x + \frac{11}{5} \\ [/tex]

Look :

This is the slope-intercept of the given line. We know that the coefficient of x is the slope of the linear functions in slope-intercept form.

Thus the slope of the line which we want is :

[tex]slope = - \frac{6}{5} \\ [/tex]

_________________________________

We have following equation to find the point-slope form of the linear functions.

[tex]y - y(given \: point) = (slope) \times (x - x(g \: p) \: ) \\ [/tex]

Now just need to put the slope and the coordinates in the above equation.

[tex]y - ( - 8) = - \frac{6}{5} \times (x - ( - 2) \: ) \\ [/tex]

[tex]y + 8 = - \frac{6}{5}(x + 2) \\ [/tex]

To find the slope-intercept form of the above equation we need to take the y alone and then simplifies the equation.

Look :

[tex]y + 8 = - \frac{6}{5}x - \frac{12}{5} \\ [/tex]

Subtract sides by -8

[tex]y + 8 - 8 = - \frac{6}{5}x - \frac{12}{5} - 8 \\ [/tex]

[tex]y = - \frac{6}{5}x - \frac{12}{5} - \frac{40}{5} \\ [/tex]

[tex]y = - \frac{6}{5}x - \frac{52}{5} \\ [/tex]

This is what we want...

_________________________________

Now we must Check the equation by using the given point :

[tex]( - 8) = - \frac{6}{5}( - 2) - \frac{52}{5} \\ [/tex]

[tex] - 8 = \frac{12}{5} - \frac{52}{5} \\ [/tex]

[tex] - 8 = \frac{ - 52 + 12}{5} \\ [/tex]

[tex] - 8 = \frac{ - 40}{5} \\ [/tex]

[tex] - 8 = - 8[/tex]

So the equation is right.

_________________________________

And we're done.♥️♥️♥️♥️♥️

A little square marked on angle means that the angle is 90 degrees.

By the vertical angle theorem, angles opposite each other are equal thus the angle opposite the angle with the little square is also 90 degrees.

That angle is split into two angles that is off measure 22 degrees and x degrees

  -- x + 22 = 90 --> x = 68.

Hope that helps!

Answer:

68

Step-by-step explanation:

[tex] \hookrightarrow \: x + 22 = 90(complementary \: angles) \\ [/tex]

[tex] \hookrightarrow \: x + 22 = 90 \\ \hookrightarrow \: x = 90 - 22 \\ \hookrightarrow \: x = 68[/tex]

Answer:

If you're multiplying then the answer would be  B.

Step-by-step explanation:

If you multiply two negative numbers, your product would be positive.

If you multiply 1 positive and 1 negative then your product will be negative.

Answer:

12

Step-by-step explanation:

For this question, simply plug in -2 for x:

[tex]g(-2)=2(-2)^2-4(-2)-4\\g(-2)=2(4)+8-4\\g(-2)=8+8-4\\g(-2)=12[/tex]

Hope this helps!!

Answer:

[tex]\frac{4}7[/tex]

Step-by-step explanation:

Just as a reminder, to find the ratio of 2 numbers, you divide the first by the second, and to divide 2 fractions, you multiply the dividend by the reciprocal of the divisor.

In this case, that would be:

[tex]\frac{\frac{4}{5}}{\frac{7}{5}}[/tex]

[tex]= \frac{4}{5} \cdot\frac{5}{7}[/tex]

=[tex]\frac{4}7[/tex]

I hope this helped you.

Answer:

The explicit formula is [tex]a_n=15(\frac{4}{5})^{n-1}[/tex].

Step-by-step explanation:

First, we need to find the common ratio. We know this is a geometric sequence because the decrease from one term to the next is not a constant number.

To find the constant ratio, we can take the [tex]2^{nd}[/tex] term and divide by the [tex]1^{st}[/tex] term:

[tex]\frac{2nd}{1st}=\frac{12}{15}=\frac{4}{5}[/tex]

So, our common ratio is [tex]r=\frac{4}{5}[/tex].

We already know our initial term, [tex]a_0[/tex] is 15, so we get:

[tex]a_n=a_0(r)^{n-1}\\a_n=15(\frac{4}{5})^{n-1}[/tex]

Answer:

u = 7\/10

Step-by-step explanation:

Answer:

[tex]\displaystyle \boxed{y = -3} \\ \boxed{\pi} \\ \boxed{N/A} \\ f(x) = \boxed{-2cot\:(x + \frac{\pi}{2}) - 3}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x) = Acot(Bx - C) + D \\ \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ \\ Vertical\:Shift \hookrightarrow -3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]

OR

[tex]\displaystyle f(x) = \boxed{2tan\:x - 3} \\ \\ f(x) = Atan(Bx - C) + D \\ \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ \\ Vertical\:Shift \hookrightarrow -3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]

Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS a tangent graph, if you plan on writing your equation as a function of cotangent, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle f(x) = 2cot\:x - 3,[/tex]in which you need to replase "tangent" with "cotangent", then figure the appropriate C-term out that will make the graph horisontally shift and map onto the tangent graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two graphs, we can tell that the cotangent graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]to the right, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{2}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1},[/tex]but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is [tex]\displaystyle f(x) = -2cot\:(x + \frac{\pi}{2}) - 3.[/tex]Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are at [tex]\displaystyle -\frac{\pi}{2} = x\:and\:\frac{\pi}{2} = x.[/tex]From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{\pi} = \frac{\pi}{2} + \frac{\pi}{2}.[/tex]So, the period of this function is [tex]\displaystyle \pi.[/tex]Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = -3.[/tex]

Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.

I am delighted to assist you at any time.

Answer:

x=20

Step-by-step explanation:

Answer:

A) H you have to run before you can climb is what my teacher told me when looking at a graph so when reading the problem you have to run left for negative then climb for positive leaving the answer being a) h

Answer:

minimum

Step-by-step explanation:

Because of the negative infront of 52. The graph opens downward which makes it minimum. Hope this helps

The volume of the rectangular prism is the amount of space in the prism

The volume of the rectangular prism is x^3+8x^2+19x+12 cubic inches

The given parameters are:

Base area = x^2+5x+4

Height = x + 3

The volume is then calculated as:

Volume = Base area * Height

So, we have:

Volume = (x^2+5x+4) * (x + 3)

Expand

Volume = x^3+5x^2+4x + 3x^2+15x+12

Collect like terms

Volume = x^3+5x^2+ 3x^2+4x +15x+12

Evaluate the sum

Volume = x^3+8x^2+19x+12

Hence, the volume of the rectangular prism is x^3+8x^2+19x+12 cubic inches

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Answer:

24

Step-by-step explanation:

Hope this helps and please mark me brainliest :D

Answer:

192 SQUARE FEET

Step-by-step explanation:

Area of a triangle= 1/2 ×base×height

1/2 of the base =32/2 ft

=16 ft

Let the height be A ft and another side(16 ft) be B ft

We know that, A^2 + B^2 =Hypotenuse^2

OR, A^2 + 16^2 = 20^2

OR, A^2= 400-256

OR, A^2 =144

OR, A= Square root of 144

OR, A=12 ft

By the problem,

1/2 ×Base×Height =Area of half of the triangle

1/2 ×16×12= Area of half of the triangle

96=Area of half of the triangle

AREA OF THE TRIANGLE=96 ×2

AREA OF THE TRIANGLE=192 SQUARE FEET.

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The area of the floor the carpet needs to cover is 20 1/8 cm².

The floor has the shape of a rectangle. A rectangle is a 2-dimensional quadrilateral with four right angles.

Area of a rectangle = length x width

5 3/4 x 3 1/2

23/4 x 7/2 = 161/8 = 20 1/8 cm²

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Answer:

8

Step-by-step explanation:

2 ÷ 1/4 = 8
You can draw 2 squares and make them into quarters for your diagram. Hope this helped!

Answer:  There are 8 1/4 inches in 2 inches.

Step-by-step explanation:

1/4 x 4 = 1, so 1/4 x 8 = 2

Diagram can be made to look as splitting 2 inches into 8 parts.

Step-by-step explanation:

89 multiplied by negative 34 gives a negative answer, since positive multiplied by negative is negative hence,

(89) × (-34) = -3026

Answer:

I'm sure it's 1/52

Step-by-step explanation:

because if there is 52 cards and one 7 of spades then it would be a 1 out of 52 chance

Answer:

C. 128 in²

Step-by-step explanation:

We know that the opposite sides of rectangles are congruent, so 8 = 2x. If we divide 8 by 2 and 2x by 2, we get x = 4.

Now, the area of a rectangle is l × w, where l = length and w = width. The dimensions of this rectangle are 8 and 16, so 8 × 16 = 128 in².