6. The Grand Theater has 13,451 seats. If 15,340 people need to be seated in the theater for a music concert, write and solve
an equation to find the number of seats that need to be added to the theater to accommodate all the people.

13 because each diagonal in a rectangle are the same

Answer:

I did this question just the other day. The answer you are looking for is B or the second one.

Step-by-step explanation:

Answer:

The correct answer option is B. [tex] a _ 1 = -4[/tex], [tex] r = \frac{1}{2} [/tex], [tex] n = 6 [/tex], [tex] S_n = -\frac{63}{8} [/tex].

Step-by-step explanation:

We are given the following:

[tex]6_\sum_{n=1}[/tex] [tex]-4(\frac{1}{2} )^{n-1}[/tex]

and we are to identify the first term ( [tex] a _ 1 [/tex] ), common ratio ( [tex] r [/tex] ), number of terms ( [tex] n [/tex] ) and the sum of n terms ( [tex] S_n [/tex] ).

Here, [tex] a _ 1 = -4[/tex],

[tex] r = \frac{1}{2} [/tex],

[tex] n = 6 [/tex]; and

[tex]S_n = \frac{a_1(1-r^n)}{(1-r)} = \frac{-4(1-0.5^6)}{(1-0.5)} = -\frac{63}{8}[/tex]

Answer: OPTION B

Step-by-step explanation:

The like term of the given monomial [tex]5m^2n[/tex] must have the following characteristics:

- The exponent of "m" must be "2".

- The exponent of "n" must be "1".

Then, you can observe that the option that shows a monomial with this characteristics is the option B.

Therefore, the like term with the given monomial [tex]5m^2n[/tex] is:

[tex]-m^2n[/tex]

Answer:

B

Step-by-step explanation:

ANSWER

D. 4 minutes 40 seconds

EXPLANATION

The given data set showing the number of seconds of each song the playlist is:

283,204,198,229,173,230,168,236,215,204

Let the length of the 11th song be x.

Because he wants the mean to be 3 minutes 40 seconds, which is equal to 220 seconds, we write and solve the following equation for x.

[tex] \frac{283 + 204 + 198 + 229 + 173 + 230 + 168 + 236 + 215 + 204 + x}{11} = 220[/tex]

[tex] \frac{2140 + x}{11} = 220[/tex]

[tex]2140 + x = 2420[/tex]

[tex]x = 2420 - 2140[/tex]

[tex]x = 280[/tex]

We convert 280 seconds to minutes.

[tex] \frac{280}{60} = 4 \frac{2}{3} = 4mins : 40 sec[/tex]

The correct choice is D

Answer:

d???

Step-by-step explanation:

16-7a=-33

-16 | -16

____________

-7a/-7a| -49/-7a

a=7

16- (7•7)= 33

Expand

5x + 5x - 15y + 12 (4x - 6y)

Expand

5x + 5x - 15y + 48x - 72y

Collect like terms

(5x + 5x + 48x) + (-15y - 72y)

Simplify

= 58x - 87y

Answer: 88.5

Step-by-step explanation:

First you need to order the data set from least to greatest:

So,

77,83,83,85,87,90,90,93,94,99

Then you find the middle number, in this case it's 87 and 90.

Because there is two middle numbers in the data set, you need to find the average between those numbers.

The average between 87 and 90 is 88.5.

Hope this helps :)

The median of the Data set B: {87, 90, 77, 83, 99, 94, 93, 90, 85, 83} is 88.5.

Median is the mid-value of the given data set when the set of the data is properly arranged.

The value of the data set is {87, 90, 77, 83, 99, 94, 93, 90, 85, 83}, now rearranging the set we will get,

77, 83, 83, 85, 87, 90, 90, 93, 94, 99

As we can see that the number of data points in the set is 10, therefore, the value of the median is the arithmetic average of the 5th and the 6th term,

[tex]\text{The average of the 5^{th} and the 6^{th} value}=\dfrac{87 + 90}{2} = 88.5[/tex]The average of the 5th and 6th = (87+90)/2 = 88.5

hence, the median of the Data set B: {87, 90, 77, 83, 99, 94, 93, 90, 85, 83} is 88.5.

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The value of [tex]\(\tan^{-1}\left(\frac{100}{41}\right)\)[/tex] is approximately [tex]\(65.386^\circ\)[/tex] or [tex]\(1.141\)[/tex] radians.

To find the value of [tex]\(\tan^{-1}\left(\frac{100}{41}\right)\)[/tex], you can use a calculator or trigonometric tables. However, if you want to understand how to solve it step by step, here's how you can do it:

1. First, calculate the ratio [tex]\( \frac{100}{41} \)[/tex]. This gives you approximately [tex]\(2.439\)[/tex].

2. Now, you need to find the angle whose tangent is [tex]\(2.439\)[/tex]. You can do this using a calculator or by using trigonometric identities.

  Typically, this is done using an inverse tangent function, often denoted as [tex]\(\tan^{-1}\)[/tex], [tex]\(\arctan\)[/tex], or [tex]\(\text{atan}\)[/tex] depending on the notation of your calculator or programming language.

So, [tex]\(\tan^{-1}\left(\frac{100}{41}\right) \approx 65.386^\circ\)[/tex].

Therefore, the value of [tex]\(\tan^{-1}\left(\frac{100}{41}\right)\)[/tex] is approximately [tex]\(65.386^\circ\)[/tex].

k=hj

do u mean to make subject of k

The formula after substitution of indicated variable, k is k = h*j .

The given formula in the question is h = k/j .

We have to substitute the formula to find the required parameter variable k .

Thus we have ,

⇒ h = k/j

∴  k = h*j .

Therefore, the formula after substitution of indicated variable, k is k = h*j .

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The new equation is

Y = (x-8)² .

The other way to write it is like this:  (you might not recognize it in this form)

Y = x² - 16x + 64

The vertex of parabola [tex]y=x^{2}[/tex] is [tex](0,0)[/tex]

After shifting [tex]8[/tex] units towards the right, it will become [tex](8,0)[/tex].

Therefore, the equation of the new parabola will be [tex]y=(x-8)^{2}[/tex].

Hence, the answer is [tex]y=(x-8)^{2}[/tex].

The equation to the new parabola is [tex]y=(x-8)^{2}[/tex].

What is the equation of a parabola?

The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.

A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.

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Answer:

[tex]x =12.08\ in[/tex]

Step-by-step explanation:

The Pythagorean theorem says that the sum of the side adjacent to the square and side opposite to the square, in a right triangle, is equal to the hypotenuse squared.

This is:

[tex]c ^ 2 = a ^ 2 + b ^ 2[/tex]

[tex]x ^ 2 = 11 ^ 2 + 5 ^ 2[/tex]

Now we solve the equation for the variable x

[tex]x=\sqrt{11^2 +5^2}\\\\x =12.08\ in[/tex]

Finally the hypotenuse is 12.08 in

Answer:

D) 0.97

Step-by-step explanation:

P(blue | yellow) = P(blue and yellow) / P(yellow)

P(blue | yellow) = 0.73 / 0.75

P(blue | yellow) = 0.97

D

See the attached picture:

Answer:

22.62

Step-by-step explanation:

Given:

Side of square = 16

Length of diagonal= x

If the sides of square are 16, then by using pythagora theorem we can calculte length of diagonal:

x=[tex]\sqrt{16^{2} +16^{2} }[/tex]

  =[tex]16\sqrt{2}[/tex]

  =22.62 !

Answer: The parabola does not intercept the x-axis.

Step-by-step explanation:

The parabola intercepts the x-axis when [tex]y=0[/tex], then, you need to substitute [tex]y=0[/tex] into the equation:

[tex]y=4x^2 -4x+9\\0=4x^2 -4x+9[/tex]

Now, use the Quadratic formula:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case:

[tex]a=4\\b=-4\\c=9[/tex]

Substituting these values and evaluating, you get:

[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(4)(9)}}{2(4)}\\\\x=\frac{4\±\sqrt{-128}}{8}[/tex]

Remeber that:

[tex]\sqrt{-1}=i[/tex]

Then, rewriting:

[tex]x=\frac{4\±8i\sqrt{2}}{8}[/tex]

Simplifying:

 [tex]x=\frac{4(1\±2i\sqrt{2}}{4(2)}\\\\x=\frac{1\±2i\sqrt{2}}{2}\\\\x=\frac{1}{2}\±\frac{2i\sqrt{2}}{2}\\\\x=\frac{1}{2}\±i\sqrt{2}[/tex]

Then:

[tex]x_1=\frac{1}{2}+i\sqrt{2}[/tex]

[tex]x_2=\frac{1}{2}-i\sqrt{2}[/tex]

The roots are complex, therefore, the parabola does not intercept the x-axis.

ANSWER

a)The x-intercepts are:

(-4,0) and (2,0)

b) The axis of symmetry is x=-1

c) The vertex of this function is (-1,-9)

d)Domain: { [tex]x|x \in \: R[/tex]}

e) Range : {[tex]y |y \geqslant - 9[/tex]}

EXPLANATION

The given function is:

[tex]f(x) = {x}^{2} + 2x - 8[/tex]

We complete the square to write this function in the form:

[tex]f(x)=a{(x - h)}^{2} + k[/tex]

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 2x + {1}^{2} - {1}^{2} - 8[/tex]

[tex]f(x) = {(x + 1)}^{2} - 9[/tex]

The vertex of this function is (h,k) which is (-1,-9)

The equation of axis of symmetry is x=h

But h=-1, hence the axis of symmetry isx=-1

To find the x-intercepts, we put f(x)=0

[tex]{(x + 1)}^{2} - 9 = 0[/tex]

[tex]{(x + 1)}^{2} = 9[/tex]

[tex]x + 1= \pm \sqrt{9} [/tex]

[tex]x= - 1 \pm3[/tex]

x=-4, 2

The x-intercepts are:

(-4,0) and (2,0)

The given function is a polynomial function, the domain is all real numbers.

[tex]x|x \in \: R[/tex]

e) The function has a minimum value of y=-9.

Therefore the range is

[tex]y |y \geqslant - 9[/tex]

Using the intercepts and vertex we can now draw this graph easily.

The graph of this function is shown in the attachment.

Final answer:

To address the student's question about the quadratic function, x-intercepts are found by setting the equation to zero, the axis of symmetry is calculated using -b/(2a), and the vertex is derived from these elements. The domain is all real numbers, and the range is all y-values greater than or equal to the y-value of the vertex. Finally, the function is graphically represented by plotting key points and drawing a parabola.

Explanation:

The student has inquired about the quadratic function f(x) = x2 + 2x - 8.

The x-intercepts of a quadratic function are the values of x where f(x) = 0. To find the x-intercepts, we set the equation to zero and solve for x: x2 + 2x - 8 = 0. In this case, the x-intercepts can be found using factorization or the quadratic formula.

The axis of symmetry is a vertical line that divides the parabola into two mirror images. For a quadratic function in the form of f(x) = ax2 + bx + c, the axis of symmetry equation is x = -b/(2a). We can use this formula to find the axis of symmetry for the given function.

The vertex of the function is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. To find the vertex, we use the axis of symmetry and plug that x-value into the function to find the corresponding y-value.

The domain of any quadratic function is all real numbers, which is denoted as {x | x is a real number}.

The range of a quadratic function depends on whether the parabola opens upwards or downwards. For the given function f(x) = x2 + 2x - 8, which opens upwards, the range is {y | y is greater than or equal to the y-value of the vertex}.

To graph the function, plot the vertex, axis of symmetry, and x-intercepts on a coordinate plane, then draw a smooth curve through these points to complete the parabola.

If we assume that she was walking in a straight line then turned 90 degrees, we would say that it was a right angle of a 90 degree angle.

Hope this helps:)

Madeline made a right angle by turning 90° to the left, which exactly measures 90 degrees and is one of the fundamental angle types in geometry.

Madeline made a 90° turn to the left, which is described as a right angle. A right angle is an angle that measures exactly 90 degrees. This is a common type of angle found in many different contexts, such as the corner of a square or rectangle. In geometry, right angles are significant because they have unique properties that distinguish them from other types of angles, such as acute angles (less than 90°), obtuse angles (more than 90° and less than 180°), and straight angles (180°).

Answer:

10 friends.

Step-by-step explanation:

Givens

Sum = 275

a1 = 5

d = 5

n = ?

Formula

Sum = (  (2*a1) + (n - 1)*d) * n / 2   Substitute the knows.

Solution

Sum = ( 2 * 5 + (n - 1)*5 ) * n/2      Combine on the right

275 = (10 + (n - 1)5 ) n/2                Multiply by 2 and remove the brackets.

550 = (10 + 5n - 5) * n                  Combine

550 = (5 + 5n ) * n                        Remove the brackets

550 = 5n + 5n^2                          Subtract 550 from both sides.

5n^2 + 5n - 550 = 0                     Divide by 5 (all terms are divisible by 5)

n^2 + n - 110 = 0                           Factor  

(n + 11)(n - 10) = 0

The only root that has any meaning is n - 10 = 0

n + 11 means Jane has - 11 friends. That has no meaning at all.

n - 10 = 0

n = 10

She had 10 friends who got stickers.

Answer:

-3.

Step-by-step explanation:

Final answer:

The correct answer is D. 0, since the question involves a positive elevation (3 feet above the painting) and does not appropriately call for the use of negative numbers to describe the position of the ceiling relative to the painting.

Explanation:

The question asks about the location of the ceiling in the room relative to the top of the painting, given that the ceiling is 3 feet above the top of the painting and the wall height is 10 feet. To determine this, we can use the information provided without needing to consider mathematical concepts such as negative numbers in a non-standard context.

Since the ceiling is 3 feet above the top of the painting, and this measurement is given in a direct, positive manner, the idea of using negative numbers to describe this position is not applicable. Choices A (-10), B (-7), and C (-3) suggest a misunderstanding of the question's context. The correct answer is D. 0, as it is the only option that does not assign a negative value to describe a position that is above the painting, thereby avoiding the inappropriate assignment of negative numbers to a scenario where they are not contextually relevant.

Thus, the number 3 describes the location of the ceiling in the room relative to the top of the painting as a positive elevation, not as a negative value or a ill-suited attempt to describe spatial positions in a non-intuitive manner.

1/3 times 3.14 (can’t use pi button) times 8 times 21

Answer:

The volume of cone = 448π m³

Step-by-step explanation:

Points to remember

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the volume of given cone

From the figure we can see,

Radius r = 8 m and Height h = 21 m

Volume = (πr²h)/3

 = (π * 8² * 21)/3

 = π * 64 * 7 = 448π

Therefore volume of cone = 448π m³

Answer:

Step-by-step explanation:

The line is tangent. Therefore, the angle between the tangent and the radius is the right angle.

We know: the sum of the angles measures in a triangle is 180°.

Therefore we have the equation:

[tex]x+36+90=180[/tex]          combine like terms

[tex]x+126=180[/tex]            subtract 126 from both sides

[tex]x=54[/tex]

The value of x is [tex]54^{0}[/tex].

A line that touches the circle at a single point is known as a tangent to a circle.

As by theorem:

The tangent is always perpendicular to the radius of the circle.

Also, The sum of the angles measures in a triangle is 180°.

By, Using Angle Sum property, we have

90 + x + 36 = 180

x+ 126= 180

x= 180-126

x= 54[tex]^{0}[/tex]

Hence, the value of x is [tex]54^{0}[/tex].

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Answer:

3,150.

Step-by-step explanation:

These are all of the steps to completely and correctly solve this question.

Hope this helps.

Kyle.

Answer:

110˚

Step-by-step explanation: angles 3 4 and six equal 180 together because it is a straight line and angle 3 is 70˚ because angle 1 is 70˚  so if angle 3 is 70˚ then the other 2 angles together have to be 110

ANSWER

D.

[tex]f(x) = - {x}^{4} + {x}^{3} + 3 {x}^{2} [/tex]

EXPLANATION

The given graph rises on the left and falls on the right.

This implies that the degree of the function is even.

Since the graph opens downward, the coefficient of the leading term must be negative.

The graph graph of the function also has 3 intercepts with one of them having an even multiplicity.

This means that the degree must be 4.

Therefore the last choice is correct.

Answer:

D

Step-by-step explanation:

Answer:

[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

We are given that the measure of angle θ is 600° and we are to fin the point (x, y) corresponding to angle θ on the unit circle,

We know that the x,y coordinates in the unit circle are the cosine and sine ratios, respectively.

θ = 600

1 unit circle= 360°

It means that 600° corresponds to 600° - 360° = 240°.

So, θ =  360° + 240°

180° < 240° < 270° (this tells that the point is in the third quadrant and its coordinates are negative)

240° - 180° = 60° (using the supplementary angles to find the sin and cos)[tex]\sin 60^\circ = \frac{\sqrt{3}}{2}\\\\\cos 60^\circ= \frac{1}{2}[/tex]

Therefore, the x-coordinate is the cos of the given angle while y-coordinate is the sine of the given angle and the coordinates are:

[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]

The answer is:

The answer is the fourth option,

[tex]f(-3)=-\frac{1}{3}[/tex]

Piecewise functions are functions that are composed by two or more expressions, the expression to use will depend of the domain or input that we need to evaluate.

We are given the piecewise function:

[tex]\left \{ {{\frac{1}{x}, if x<-2} \atop{x^{2}, ifx\geq 2}} \right.[/tex]

There, we know that:

We should use the first expression if the value to evaluate is less than -2.

So, for this case, the function will be:

[tex]f(x)=\frac{1}{x}[/tex]

We should use the second expression if the value to evaluate is greater or equal than 2.

So, for this case, the function will be:

[tex]f(x)=x^{2}[/tex]

Now, since we are given that the value to evaluate is -3, and its less than -2, we need to use the first expression, and evaluate it.

[tex]-3<-2[/tex]

So, evaluating the function we have:

[tex]f(x)=\frac{1}{x}[/tex]

[tex]f(-3)=\frac{1}{-3}[/tex]

[tex]f(-3)=-\frac{1}{3}[/tex]

Hence, we have that the answer is the fourth option,

[tex]f(-3)=-\frac{1}{3}[/tex]

Have a nice day!

Answer:

C

Step-by-step explanation:

The problen asks for 5 more than two times n. 2 times n suggests multiplication. So we start out with 2n. When it says 5 more it suggests addition. So we end up with 2n+5

ANSWER

+49/4

EXPLANATION

The given expression is

[tex] {y}^{2} - 7y[/tex]

For this to be a perfect square we must add the square of half the coefficient of y.

[tex]( { \frac{ - 7}{2} })^{2} = \frac{49}{4} [/tex]

The correct choice is the third option.

+49/4

Answer:  The correct option is (C) [tex]+\dfrac{49}{4}.[/tex]

Step-by-step explanation:  We are given to choose the constant term that completes the following perfect square trinomial :

[tex]T=y^2-7y.[/tex]

Let the required constant term be c.

Then, we have

[tex]y^2-7y+c\\\\\\=y^2-2\times y\times\dfrac{7}{2}+\left(\dfrac{7}{2}\right)^2+c-\left(\dfrac{7}{2}\right)^2\\\\\\=\left(y-\dfrac{7}{2}\right)^2+c-\dfrac{49}{4}.[/tex]

Therefore, to complete the perfect square trinomial, we must have

[tex]c-\dfrac{49}{4}=0\\\\\\\Rightarrow c=+\dfrac{49}{4}.[/tex]

Thus, the required constant term is [tex]+\dfrac{49}{4}.[/tex]

Option (C) is CORRECT.

To build a scale model, the student's school height is first converted to centimeters using the scale factor (50.4 cm), then divided by the length of a toothpick and a cotton swab respectively to determine how many of each would be needed to reach the scaled height. The model will be 8 toothpicks tall and approximately 7 cotton swabs tall.

To solve the problem of building a scale model of the student's school, we need to apply the scale factor provided and the measurements of the materials at hand. The school is 30 feet tall, and the scale is 1 ft:1.68 cm.

To calculate the height of the model in toothpicks, we'll convert the height of the school from feet to centimeters, and then divide by the length of a toothpick:

For the model in cotton swabs, we'll also convert the height to centimeters and then divide by the length of a cotton swab:

Complete Question is :

"You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.68 cm. If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be? The model will be toothpicks tall. Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.2 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number. The model will be approximately cotton swabs tall."

Answer:

-4 units per unit

Step-by-step explanation:

As x increases from a = -2 to b = 2 (a change of 4 units), f(x) changes from f(-2) = 25 to f(2) = 9, a decrease of 16.  Thus, the average rate of change of f(x) on the interval [-2, 2] is:

    -16

---------- = -4 units per unit.

     4