Hi Mehta06 heres my question that i told you​

The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.

The theatre charges $4.50 per student.

Assume the number of students is x, the equation of the theatre's income would be:

I(x) = 4.5x

The theatre expense per student is $1.25, and the operating cost on the staff is $130

The equation of the theatre's expenses would be:

E(x) = 1.25x + 130

Using the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:

Students, x  0       10        20     30      40      50      60    70

Income, I      0      45        90     135     180    225    270   315

Expenses, E 130  142.5   155    167.5   180   192.5   205  217.5

See attachment

The functions I(x) and E(x) are linear functions.

So, the pattern with which the functions increase is a linear pattern.

This means that:

I(x) = E(x)

So, we have:

4.5x = 1.25x + 130

Subtract 1.25 from both sides

3.25x = 130

Divide both sides by 3.25

x = 40

Hence, the number of students is 40

This is the difference between the theatre expenses and their income.

So, we have:

P(x) = E(x) - I(x)

This gives

P(x) = 1.25x + 130 - 4.5x

Simplify

P(x) = 130 - 3.25x

We have:

E(x) < 255

This gives

1.25x + 130 < 255

Subtract 130 from both sides and divide by 1.25

x < 100 students

Also, we have:

I(x) > 675

This gives

4.5x > 657

Solve for x

x > 146 students

Hence, the number of students for the inequalities are less than 100 and greater than 146

Read more about linear equations and inequalities at:

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Answer:

found in a toys store and cost more than 50$

Step-by-step explanation:

it makes the most sense don't you think?

Answer:

Solution. To find the perimeter of \triangle ABC we use the Pythagorean Theorem which tells us that |AB|^2 = |AC|^2 + |BC|^2. Since |AC| = 5 and |BC| = 12 we find that |AB| = \sqrt{169} = 13. The perimeter of \triangle ABC is then 5 + 12 + 13 = 30 units.

Answer:

Your answer would be:
A.) (36 × 6) + (c × 4) = 232

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

Let y = '?'

6(x + y) = 6x + 30

6x +6y = 6x + 30

6x + 6y - 6x = 6x + 30 - 6x

6y = 30

6y / 6 = 30 / 6

y = 5

Answer:

D

Step-by-step explanation:

this is not standard form

Answer:

D

Step-by-step explanation:

The first number should be equal to or greater than one but less than 10

Answer:

i think its 48

since 144384 divided by 48 would be 3008 and 432 divided by 48 would be 9. I believe thats the highest it can go to.

Answer:

  36.24 cm²

Step-by-step explanation:

The shaded region is the inscribed circle in the isosceles triangle. In order to find its area, we need to know the radius of the circle.

__

One way to find the radius of the circle is to make use of the Angle Bisector theorem. It tells us an angle bisector divides the sides of a triangle proportionately. In the attached figure, that means angle bisector CD divides segment AE in proportion to sides CA and CE.

To make use of this theorem, we need to know the length of side CA. That is the hypotenuse of right triangle AEC, so can be found using the Pythagorean theorem. Isosceles triangle ABC is given as having height AE=10 and base BC = 12.

  CA² = CE² +AE²

  CA² = 6² +10² = 136 . . . . . . . CE is half the base length: 12/2 = 6

  CA = √136 = 2√34

__

Now we can write the proportion using the angle bisector theorem.

  DE/CE = DA/CA

  r/6 = (10 -r)/(2√34)

  r√34 = 3(10 -r) . . . . . . . multiply by 6√34

  r(3 +√34) = 30

  r = 30/(3 +√34)

__

From this, we can find the area of the shaded circle to be ...

  A = πr² = (3.14)(30/(3 +√34))²

  = 3.14·900/(43 +6√34) ≈ 36.2374 . . . cm²

The area of the shaded region is about 36.24 cm².

_____

Additional comment

Using area considerations, the formula for the radius of the inscribed circle in an isosceles triangle with base 'b' and sides 'a' can be found to be ...

  [tex]r=\dfrac{b}{2}\sqrt{\dfrac{2a-b}{2a+b}}[/tex]

For a=√136 and b=12, this becomes ...

  [tex]r=\dfrac{12}{2}\sqrt{\dfrac{2\sqrt{136}-12}{2\sqrt{136}+12}}=6\sqrt{\dfrac{(\sqrt{34}-3)^2}{34-9}}=1.2(\sqrt{34}-3)\approx3.39714[/tex]

This is the same value we found above.

Answer:

Squaring a number.

Step-by-step explanation:

The square root is an operation that undoes an exponent of 2, which is the inverse operation of squaring a number.

Answer:

8

Step-by-step explanation:

It has the highest frequency

[tex]5^{7/3} = 42.75[/tex] (approximately)

using the formula [tex]x^{a/b}=\sqrt[b]{x^a}[/tex] we can solve the problem

so we rewrite it as [tex]\sqrt[3]{5^7}[/tex] and get ~42.75

The trigonometry identity sin(x + y) = sinx cosy + cosx siny.

sin(x + y) is one of the identities in trigonometry for compound angles.

The angle (x + y) represents the compound angles.

sin(x + y) = sinx cosy + cosx siny

To prove

sin(x + y) = sinx cosy + cosx siny

Consider OX as a rotating line anti-clockwise. Let angle XOY = a

the making of an acute angle b the rotation in the same direction is

angleYOZ = b , angle XOZ = a + b

From triangle PTR,

∠TPR = 90 - ∠PRT , ∠ROX = a

From the right-angled triangle PQO

sin(a + b) = PQ/OP

= (PT + TQ) / OP

= PT/OP + TQ/OP

= PT/PR × PR/OP + RS/OR × OR/OP

= cos (∠TPR ) sinb + sina cosb

= sina cosb + cosa sinb

if we replace a=x and b=y

Therefore, sin(x + y) = sinx cosy + cosx siny.

Learn more about trigonometry identity;

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Answer: 3.75 is at it's lowest terms. if you mean fractions its 15/4 or 3 & 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Identify the equation in slope-intercept form for the line containing the points

(3,5) and (2,-5)

Choices:

y = 3x − 15

y = 5x − 25

y = 10x − 25

y = 5x + 10

Pls help

Sooo let’s solve this….

Notice the x-axis

Slope Intercept form changes at a constant rate soooo… from (3,5) to (2,-5)

The axis goes left by 1

On A graph the more to the left the smaller number get.

The Y-axis goes down by 10 from the bigger point

But…..

It’s really not going left 1 and 10 down you always start with the smaller point so from

(2,-5) to (3,5) It goes Right 1 and 10 up

Knowing this

Slope Intercept form

Y=mx+b

Where m=slope

b= y-intercept where the line crosses x=0

Our Slope Is 10

Because from -5 to 5 you have to add 10 to get the other value

y=10x+b

But lets just figure out the y-intercept to be sure.

We want the X-axis to be 0 so we will be going left until we get to 0

So We get this point (2,-5)

Knowing that we go up 10 and right 1 to get to the higher value we will do the opposite.

We will go 1 to the left and 10 down

(2,-5)

(1,-15)

(0,-25) As you can see x=0 so the y-intercept will be -25

y=mx+b

m=slope

b= y-intercept

y=10x-25 The Third Option is the Answer….

SonicIsCoool, at your service if you need any help :)

Answer:270

Step-by-step explanation:

Length:

U = 3 inches

W = 7 inches

Y = 8 inches

Add them up: 18 inches all together.

Width:

V = 4 inches

X = 7 inches
Z = 4 inches

Add them up: 15

A= L x W —>  15 x 18 = 270

Answer:

Angle BFC.

Step-by-step explanation:

Because angle BFD is a right angle because angle AFE is equal to BFD because of vertical angles

Answers:

10.) [tex]\displaystyle \pm{5}[/tex]

9.) [tex]\displaystyle 1\frac{1}{2}[/tex]

8.) [tex]\displaystyle \pm{1\frac{1}{2}}[/tex]

7.) [tex]\displaystyle \pm{1\frac{1}{2}}[/tex]

6.) [tex]\displaystyle \pm{\frac{1}{2}}[/tex]

Step-by-step explanations:

10.) [tex]\displaystyle \frac{\sqrt{200}}{\sqrt{8}} \hookrightarrow \sqrt{25} \hookrightarrow \frac{\pm{10\sqrt{2}}}{\pm{2\sqrt{2}}} \\ \\ \boxed{\pm{5}}[/tex]

9.) [tex]\displaystyle \frac{\sqrt[3]{135}}{\sqrt[3]{40}} \hookrightarrow \sqrt[3]{3\frac{3}{8}} \hookrightarrow \frac{3\sqrt[3]{5}}{2\sqrt[3]{5}} \\ \\ \boxed{1\frac{1}{2}}[/tex]

8.) [tex]\displaystyle \frac{\sqrt[4]{162}}{\sqrt[4]{32}} \hookrightarrow \sqrt[4]{5\frac{1}{16}} \hookrightarrow \frac{\pm{3\sqrt[4]{2}}}{\pm{2\sqrt[4]{2}}} \\ \\ \boxed{\pm{1\frac{1}{2}}}[/tex]

7.) [tex]\displaystyle \frac{\sqrt{63}}{\sqrt{28}} \hookrightarrow \sqrt{2\frac{1}{4}} \hookrightarrow \frac{\pm{3\sqrt{7}}}{\pm{2\sqrt{7}}} \\ \\ \boxed{\pm{1\frac{1}{2}}}[/tex]

6.) [tex]\displaystyle \frac{\sqrt{12}}{\sqrt{48}} \hookrightarrow \sqrt{\frac{1}{4}} \hookrightarrow \frac{\pm{2\sqrt{3}}}{\pm{4\sqrt{3}}} \\ \\ \boxed{\pm{\frac{1}{2}}}[/tex]

I am joyous to assist you at any time.

X/6 = 15/18

Cross multiply:

18x = 15 times 6

18x = 90

Divide both sides by 18

X = 5

5/6 = 15/18

Answer:

Step-by-step explanation:

X= 15  x6

     18

I guess it is correct

Trigonometric functions are not only used in cases of an object that has a cyclical behavior.

It should be noted that trigonometric functions are real functions that relate the angle of a right angled triangle to the ratios of the two side lengths.

Trigonometric functions are not only used in cases of an object that has a cyclical behavior. It can be used to obtain unknown angles in geometric figures.

It can also be used to model the fluctuations in temperature data for a particular year.

The movement of a yo-yo can be modeled by a sinusoidal curve since it exhibits a periodic behavior.

Learn more about trigonometry on:

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Answer:

21/2

Step-by-step explanation:

10.5 is correct, but that's a decimal

21/2=10.5

Answer:

21/2

Step-by-step explanation:

10*2 = 20

then 20 + 1 = 21

to get your answer which is 21/2

PLEASE RATE!! I hope this helps!!

If you have any questions let me know

Answer:

12ft

Step-by-step explanation:

A prism is a 3D shape which has the same 2D shape repeated along its length (this is sometimes called the cross section).

The 2D shape at the ends of the prism is the base of the prism, so for this shape, the bases are the triangles.

The height of the prism is actually the length of the prism, so for this prism the height is 12 ft.

A transversal line is a line that crosses through two lines on the same plane.

Example:

I attached a photo below showing the Transversal line (the line in red) crossing two lines located on the same plane. Note: The Transversal line is only the red line, not the whole diagram below.

I am open to corrections if I unintentionally added false information :).

#learnwithbrainly

Answer:4mL

Step-by-step explanation: if you multiply 18 by 2.2 you would get 39.6, you would divide by 10 to get 3.96, then you would round to the nearest whole number so you’d get 4.

By using a change of units, we will see that the dog needs 4 mL of medication.

Here we need to see how many pounds are in 18 kilograms, using the relation:

1kg = 2.2lb

We get:

18 kg = 18*(2.2lb) = 39.6 lb

Now, for each 10 lb, we add 1mL of medication, then we need to divide the mass of the dog by 10lb, we get:

M = (39.6 lb)/(10 lb) = 3.96

Rounding to the next whole number we get 4, so the dog needs 4 mL of medication.

If you want to learn more about changes of units:

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Answer:

D

Step-by-step explanation:

[tex]\frac{x^2-11x+24}{(x-8)(x+2)}[/tex] ← factorise the numerator

= [tex]\frac{(x-8)(x-3)}{(x-8)(x+2)}[/tex] ← cancel the common factor (x - 8) on numerator/ denominator

= [tex]\frac{x-3}{x+2}[/tex]

The quotient of the given division problem is D. (x - 3) / (x + 2).

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given expression is,

(x² - 11x + 24) / (x - 8)(x + 2)

We have to first factor the numerator.

x² - 11x + 24 can be factored as (x - 8) (x - 3).

This is done using the factorization method.

Now the expression becomes,

(x² - 11x + 24) / (x - 8)(x + 2) = (x - 8) (x - 3) / (x - 8)(x + 2)

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

Hence the quotient is option D.

Learn more about Division here :

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Answer:

No

Step-by-step explanation:

Because sqrt 2 is not an integer

Answer:

3root2 is not a rational number

Answer:

there is not enough information to solve

Step-by-step explanation:

You need two ordered pairs to calculate the average rate of change.

Let's say the value of the function at n = 1 is a, and the value of the function at n = 3 is b, then the average rate of change from n = 1 to n = 3 is

(b - a)/(3 - 1) = (b - a)/2

Answer:

2.3 miles

Step-by-step explanation:

Given by the circular pattern as shown in the diagram:

Ranger station to Nature Center = 90°

Nature center to petting zoo= 40°

Petting zoo to Tennis court =120°

Tennis court to Pool = 65°

Pool to Ranger station= 45°

The radius of the circular pattern = 1 mile

Formula:

Arc length = 2πr angle / 360° where r is radius and π=3.14

Solution:

Thus,

Arc length = 2×3.14×1×90°/360°

Arc length=2×3.14×1×1/4 =1.57 miles

Distance from Nature Center to Petting Zoo

Arc length= 2×3.14×1×40°/360°

Arc length= 2×3.14×1×1/9 = 0.70 miles

Total =1.57+0.70 =2.27 miles

Answer to the nearest tenth = 2.3 miles

For more information:

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~lenvy~

Answer:

x = 61

y = 29

Step-by-step explanation:

The angle with the measure of 58 degrees and the angle represented by 2x are supplementary because they form a straight line.

2x + 58 = 180 subtract 58 from both sides

2x = 122 divide both sides by 2

x = 61

The angle represented by 2x and the angle represented by 58 are corresponding and their measure is equal to each other

2y = 58 divide both sides by 2

y = 29