The solution is -3.

Which multiplication equation has the given solution?

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

\(\tan \dfrac{\theta}2 = \dfrac{1}2\)

Step by step Explanation:

\(\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]\)

         \(=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2\)

Answer:*

Step-by-step explanation:

Answer:250, percentage decreased by 35% (percent) of its value = 162.5

Answer:

x=1

Step-by-step explanation:

y=3x so just add 1+3=4 then add veriable y=4x

Answer:

The correct answer is x = 12.

Step-by-step explanation:

To solve this problem, we must remember that an angle bisector divides the angle into two smaller, equal angles.  This means that we can set the values for each of these smaller angles equal to one another, given that the angle is bisected.  This is modeled below:

9x - 54 = 4x + 6

Now, we can solve this equation like any other.  The first step is to subtract 4x from both sides.

9x - 4x - 54 = 4x - 4x + 6

5x - 54 = 6

Then, we should add 54 to both sides.

5x - 54 + 54 = 6 + 54

5x = 60

Finally, we can divide both sides by 5.

5x/5 = 60/5

x = 12

Therefore, the correct answer is x = 12.

Hope this helps!

Answer:

The value of x is 12°.

Step-by-step explanation:

Given that AC is the angle bisector of ∠BAD which means that AC cuts exactly the center of ∠BAD so ∠BAC and ∠CAD must be the same.

In order to find the value of x, you have to make ∠BAC = ∠CAD

\(∠BAC = ∠CAD\)

\(9x - 54 = 4x + 6\)

\(9x - 4x = 6 + 54\)

\(5x = 60\)

\(x = 60 \div 5\)

\(x = 12\)

Answer:

S A S

Step-by-step explanation:

Corresponding sides are in same ratio

\(\dfrac{21}{15}=\dfrac{14}{10}\\\\\dfrac{7}{5}=\dfrac{7}{5}\)

And the in between angle  of the corresponding sides are common.

So, S A S similarity

could you finish the question? we cannot help you if we don't get the full question!

Answer:

x + 7 and x + 5 are possible dimensions

Step-by-step explanation:

x² + 12x + 35 ← factor the quadratic

consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

the factors are + 7 and + 5 , since

7 × 5 = + 35 and 7 + 5 = + 12 , then

x² + 12x + 35 = (x + 7)(x + 5) ← in factored form

now the area A = length × breadth , that is

A = x² + 12x + 35 = (x + 7)(x + 5) , then

length = x + 7 or x + 5

breadth = x + 5 or x + 7

Solution

Given the equilateral triangle ABC;

The following are the numbers of right triangles:

There are 12 right triangles in the diagram.

Answer:

a³b

Step-by-step explanation:

(ab²)³/b⁵

= a³b⁶/b⁵

= a³b

Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

If I helped, please make this answer brainliest! ;)

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The required equation for how many hours I have to work mowing lawns is f(x) = 10x + 200 and the required no. of hours is 30 hours.

A function can be thought of as an output for the given set of inputs.

According to the given question I work for 25 hours per week at the twist ice-cream shop and earn 8.00 dollars per hour.

∴ My total earning in a week will be (25×8) = 200 dollars.

But i want to earn 500 per week so need (500 - 200) = 300 dollars to reach my goal.

I also mow lawns in my neighbourhood for 10 dollars per hour.

∴  I need (300/10)  = 30 hours to earn the amount i need which is 500 dollars.

An equation can be written as

f(x) = 10x + 200, where x is the no. of hours and f(x) = 500.

500 = 10x + 200.

10x = 500 - 200.

10x = 300.

x = 300/10.

x = 30.

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The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..

Based on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.

The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.

In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.

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Answer:

1.6 or 8/5.

Step-by-step explanation:

(-2/5)/(-1/4)

(-2/5)(-4)

=1.6 or 8/5.

Answer:

It's A

Step-by-step explanation:

The y-intercept is 6, as seen on the chart.

To get the slope it is y2 - y1 / x2 - x1

Use the x and y intercepts

0 - 6 / 3 - 0

-6 / 3

-2

There you have your slope, just put it together!

y = -2x + 6

Answer:

(3.0)/(0.6)

m=6-0/0-3=-2

a

Step-by-step explanation:

An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

We have been given a rational function:

\(f(x)=\frac{x^{2} -81}{x^{2} -11x+18}\)

And we are required to determine an appropriate viewing rectangle for the graphing calculator.

Hence, An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

For the given function, an appropriate viewing rectangle will be [-20,20,2]  by [-20,20,2].

This function, when graphed using a graphing calculator on the said viewing rectangle, it appears as attached.

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Answer:

\( Area \: of \: rhombus =96\: cm^2 \)

Step-by-step explanation:

\( d_1= 2\times 8 = 16\: cm\)

\( d_2= 2\times 6 = 12\: cm\)

\( Area \: of \: rhombus =\frac{1}{2} d_1d_2\)

\( Area \: of \: rhombus =\frac{1}{2}\times 16 \times 12\)

\( Area \: of \: rhombus =8 \times 12\)

\( Area \: of \: rhombus =96\: cm^2 \)

The Fill ups for the Volume Concept is matched below.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

given:

Cone:

R= r

h= 3r

So, Volume of Cone = 1/3πr²h

                                  = 1/3 π r² (3r)

                                  = 1/3 π 3r³

                                  = πr³

As, Volume of Cone = 25n

Cylinder:

R= r

h= 3r

So, Volume of Cylinder = πr²h

                                  = π r² (3r)

                                  = π 3r³

                                  = 3πr³

So, Volume of Cylinder = 3(25n) = 75n

Sphere:

R= r

So, Volume of Sphere = 4/3πr³

 Volume of Sphere = 4/3(25n)= 100/3 n

Now, Volume of sphere + Volume of Cone= Volume of Cylinder

4/3πr³ + 1/3πr²h = πr²h

4/3πr³ = πr²h- 1/3πr²h

4/3πr³ = πr²h(1 - 1/3)

4/3πr³ = πr²h(2/3)

4/3r = 2h/3

h= 4r/3 x 3/2

h= 2r

So, for Volume of sphere + Volume of Cone= Volume of Cylinder the height should be 2r not 3r.

Now, The Volume of Cylinder is 3 times larger than Volume of Cone.

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Answer:

  5

Step-by-step explanation:

If x is the middle number of the 5 consecutive odd numbers, their product is ...

  x(x -2)(x +2)(x -4)(x +4) = x(x² -4)(x² -16)  = x⁵ -20x³ +64x

The first 3-digit prime is 101, so the product of that with this is ...

  101(x⁵ -20x³ +64x) = 101x⁵ -2020x³ +6464x

Since we're only interested in the units digit, we can find the mod 10 value of this to be ...

  (x⁵ +4x) mod 10

Possible units digits of x are 1, 3, 5, 7, 9, so possible units digits of this product are ...

  x(x⁴ +4) = 1(1⁴ +4) = 5

  3(3⁴ +4) = 3(1 +4) = 5 . . . . mod 10

  5(5⁴ +4) = 5(5 +4) = 5 . . . . mod 10

  7(7⁴ +4) = 7(1 +4) = 5 . . . . mod 10

  9(9⁴ +4) = 9(1 +4) = 5 . . . . mod 10

In every case, the units digit of 101z will be 5.

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

6 miles per hour

Step-by-step explanation:

Answer:

6 miles per hour

Step-by-step explanation:

The choice of auto insurance plan depends on the value of the vehicle and financial situation. Plan 2 with higher coverage and deductibles is better for expensive vehicles and those with higher financial stability.

Insurance is a contract between an individual or an entity and an insurance company. The individual or entity pays a premium, and in return, the insurance company agrees to pay for losses or damages that occur, as per the terms of the policy.

Financial stability refers to a situation where an individual, household, company, or economy can manage their financial resources and obligations in a sustainable manner, without facing significant risks or uncertainty.

According to the given information:

Based on my vehicle's value and my financial situation, I have decided to choose Plan 1.

Bodily injury liability coverage provides protection if I were to injure someone while driving, and the amount of coverage in Plan 1 ($25,000 per person up to $50,000 per accident) is adequate for my needs. Property damage liability coverage provides protection for any damage I might cause to someone else's property while driving, and the $25,000 coverage in Plan 1 is also sufficient.

Collision insurance provides coverage for any damage to my own vehicle in the event of an accident, regardless of who is at fault. The $100 deductible in Plan 1 means that I would have to pay the first $100 of any repair costs, but the lower annual premium makes this plan more affordable for me.

Comprehensive insurance provides coverage for non-collision events, such as theft, fire, and natural disasters. Again, the lower annual premium of Plan 1 with a $50 deductible makes it more cost-effective for me.

Uninsured/underinsured motorist coverage is not included in either plan, so I would need to decide if I want to add this coverage as an additional policy or not.

Overall, based on the value of my vehicle and my financial situation, Plan 1 provides adequate coverage at a more affordable price. However, it is important to note that everyone's situation is unique and insurance needs may vary. It is always a good idea to shop around and compare different policies before making a final decision.

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Answer:

3x^2 -20x-32

Step-by-step explanation:

(3x + 4)(x − 8)

Foil

First: 3x*x = 3x^2

outer: -8*3x = -24x

inner: 4x

last: -8*4 =-32

Add them together

3x^2 -24x+4x -32

Combine like terms

3x^2 -20x-32

Standard form is ax^2 +bx+c

Answer:

\(3 {x}^{2} + 20x - 32\)

Step-by-step explanation:

\((3x + 4)(x - 8) \\ 3x(x - 8) + 4(x - 8) \\ 3 {x}^{2} - 24x + 4x - 32 \\ = 3 {x}^{2} + 20x - 32\)

Answer:

yes

Step-by-step explanation:

Answer:

Yes, it is.

Step-by-step explanation:

6,904 - 4,111 = 2,793

Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  \(\boxed{y=\dfrac{-5}{2}x+1}\)

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John William is entitled to purchase 15,000 shares before the offering is made to the public.

a. To calculate the percentage of the total vote John William will control, we need to find the proportion of shares he owns out of the total shares represented at the meeting.

John William owns 6,000 shares out of the 20,000 shares offered so far. Therefore, the proportion of shares he owns is 6,000/20,000, which simplifies to 3/10 or 0.3.

To convert this proportion to a percentage, we multiply by 100:

Percentage of the total vote = 0.3 * 100 = 30%

Thus, John William will control 30% of the total vote at the.         shareholder meeting.    

b. Preemptive rights allow existing shareholders to purchase new shares before they are offered to the public. To determine the number of shares John William is entitled to purchase, we need to calculate the proportion of his current ownership.

John William owns 6,000 shares out of the total shares offered so far, which is 20,000. Therefore, his ownership proportion is 6,000/20,000, or 3/10.

If Peixotto Media plans to issue 50,000 new shares, John William's entitlement would be:

Entitlement = (3/10) * 50,000 = 15,000 shares.

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