MATHEMATICS COLLEGE

Find the area of the composite figure below.

Answers

Answer 1

Answer:

Answer:

702 ft²

Step-by-step explanation:

24x27=648

(30-24)x(27-18)=6x9=54

648+54=702 ft²

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Help me out please and thank you

A theater has a seating capacity of 750 and charges $3 for children, s5 for students, and $7 for adults. At a certain screening with fll ttendance, there were combined. The receipts totaled $3450. How many children attended the show?

Answers

Answer:

Between 150 and 450

Step-by-step explanation:

We are going to find the number by resolving a system of linear equations.

First we write the system equations :

$C+S+A=750$

Where C : children, S : students and A : adults

The equation represents the ''full attendance''

The second equation :

$3C+5S+7A=3450$

This equation represents the totaled receipts.

The system :

$C+S+A=750\n3C+5S+7A=3450$

has the following associated matrix :

$\left[\begin{array}{cccc}1&1&1&750\n3&5&7&3450\end{array}\right]$

By performing elementary matrix operations we find that the matrix is equivalent to

$\left[\begin{array}{cccc}1&0&-1&150\n0&1&2&600\n\end{array}\right]$

The new system :

$C-A=150\nS+2A=600$

Working with the equations :

$C = 150 + A\nS = 600-2A$

Our solution vector is :

$\left[\begin{array}{c}C&S&A\end{array}\right] =\left[\begin{array}{c}150+A&600-2A&A\end{array}\right]$

For example :

If 0 adults attended ⇒ A = 0

$C = 150 + 0 \nC = 150\nS = 600 - 2A\nS = 600$

This verify the totaled receipts equation :

150($3)+600($5) = $ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

$S = 600 -2A$

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

Please helpppp!!! it’s timed!!!! thank u for helping!!!!!

Answers

Answer:

ADMC

Step-by-step explanation:

The secant of a circle is a line that cuts the cuts two points of the circumference with one end point external to the circle;

Fro the given diagram, the two lines that cuts the circumference of the circle at two points are AEB and ADMC

Hence the one that contains diameter with point M is line ADMC

8 POINTS WILL BE GIVEN!!

Answers

24° because it says x=24° have a nice day :)

Answer:

x=39 degrees

Step-by-step explanation:

How to convert from point slope form to slope intercept form

Answers

Answer:

$y=mx+(y_1-mx_1), b=y_1-mx_1$

Step-by-step explanation:

The point slope form of the equation of a line is given as:

$y-y_1=m(x-x_1)$

The slope-intercept form of the equation of a line is given as:

$y=mx+b$

where: m=slope, b=y-intercept.

To convert from the point slope form to slope intercept form, follow these steps:

Step 1: Distribute the right hand side

$y-y_1=m(x-x_1)\ny-y_1=mx-mx_1$

Step 2: Isolate the y variable

$y=mx-mx_1+y_1\ny=mx+(y_1-mx_1)$

This is the slope-intercept form. We can evaluate $y_1-mx_1 $ given values for $(x_1,y_1)$ and slope, m$

Which statements are true? Select three options. ∠F corresponds to ∠F'. Segment EE' is parallel to segment FF'. The distance from point D' to the origin is One-third the distance of point D to the origin. The measure of ∠E' is One-third the measure of ∠E. △DEF △D'E'F'