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Find the total area of the given figure.

996 sq in


576 sq in


12 sq in


240 sq in

Answer:

Step-by-step explanation:

There is no answer because this is a formula

We need an equation — something that equals something else

Assuming you mean

[tex]8x^2 + 25y = 0\\25y = -8x^2\\y = -\frac{8}{25}x^2[/tex]

Answer:

2/3 of a year is 8 months.

Step-by-step explanation:

Since there is 12 months in a year, divide 12 by 3.

12÷3= 4

Now, multiply 4 by 2.

4×2= 8

This gives you the answer of 8 months.

Answer: 8 months

Step-by-step explanation: multiply denominator and numerator by 4 so it can be equivalent to 12 months.

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

For test point x = 2, the inequality is false.

Solution:

Given expression is the inequality.

[tex]$\frac{5 x-3}{(x-1)(x+1)} \leq 0[/tex]

Substitute x = –2 in the inequality.

[tex]$\frac{5 (-2)-3}{(-2-1)(-2+1) }=\frac{-13}{(-3)(-1) }[/tex]

                            [tex]$=\frac{-13}{3 }[/tex]

                            < 0

For test point x = –2, the inequality is true.

Substitute x = 0 in the inequality.

[tex]$\frac{5 (0)-3}{(0-1)(0+1) }=\frac{-3}{(-1)(1) }[/tex]

                      [tex]$=3[/tex]

                      > 0

For test point x = 0, the inequality is false.

Substitute [tex]x=\frac{4}{5}[/tex] in the inequality.

[tex]$\frac{5 (\frac{4}{5} )-3}{((\frac{4}{5} )-1)((\frac{4}{5} )+1) }=\frac{1}{(-\frac{1}{5} )(\frac{9}{5} ) }[/tex]

                            [tex]$=\frac{-25}{9 }[/tex]

                            < 0

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

Substitute x = 2 in the inequality.

[tex]$\frac{5 (2)-3}{(2-1)(2+1) }=\frac{7}{(1)(3) }[/tex]

                      [tex]$=\frac{7}{3 }[/tex]

                      > 0

For test point x = 2, the inequality is false.

Hence,

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

For test point x = 2, the inequality is false.

Answer:

In the picture below

Step-by-step explanation:

Edge 2021

Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.

Solution:

Given system of equations:

8x + 5y = –7 – – – – (1)

–7x + 6y = –4 – – – – (2)

Multiply top equation by 6 and and bottom equation by –5

(1) × 6 ⇒ 48x + 30y = –42

(2) × –5 ⇒ 35x – 30y = 20

Now add these two equations, we get

(48x + 30y) + (35x – 30y) = –42 + 20

48x + 35x + 30y  – 30y = –42 + 20

83x = –20

The variable y is eliminated.

Therefore Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.

Answer:

Multiply the top equation by −5, then add the equations.

Step-by-step explanation:

Did it on Khan Academy

The total length of the three longest bulletin boards when placed side by side would be 180 inches.

To calculate the total length of the three longest bulletin boards when placed side by side, we first need to determine the average length of a bulletin board and then multiply it by three.

The length of bulletin boards can vary widely depending on their purpose, but let's assume a standard size commonly found in schools or offices.

A typical bulletin board might measure around 4 feet (48 inches) in length.

However, some bulletin boards can be longer, reaching up to 6 or 8 feet.

Let's take a conservative estimate of 5 feet (60 inches) for our calculations.

So, if we have three bulletin boards each measuring 5 feet (60 inches) in length, the total length when placed side by side would be:

Total length = Length of one bulletin board × Number of bulletin boards

Total length = 60 inches × 3

Total length = 180 inches

Therefore, the total length of the three longest bulletin boards when placed side by side would be 180 inches.

Answer:

volume is 432 cubic inches

Step-by-step explanation:

A box measures 1 ft. long, 1/2 ftwide, and  1/2 ft high.

we need to find the volume of the box

Volume of the box formula is

[tex]volume = length \cdot width \cdot height\\[/tex]

convert all the measurement into inches

1 feet = 12 inches

1/2 feet = 6 inches

length = 12 inches, width = 6 inches , height = 6 inches

now we plug in the values in volume

[tex]volume = 12 \cdot 6 \cdot 6= 432 in^3[/tex]

Percentage change in perimeter is 100%.

Step-by-step explanation:

Calculate perimeter of R1 = 2 (length + breadth) = 2 (5 + 3)  = 16 ft

Calculate perimeter of R2 = 2 (10 + 6) = 32 ft

= (32 - 16/16) [tex]\times[/tex] 100 = 100%

Answer:

x=1

Step-by-step explanation:

1-2x=-3x+2

-1=-x

1=x

Answer:

8

Step-by-step explanation:

plus 6 plus 3 look iam just trying to cheat I got stuff to do

Answer: 47

Step-by-step explanation:

Just add 27 and 20 then you get f

Just use inverse operations

Answer:

  5·7

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

  5×7 = 35

Both 5 and 7 are prime numbers, so that is the prime factorization.

Number of adult tickets = 75

Number of student tickets = 175

Solution:

Let x represents the number of adult tickets and

y represents the number of student tickets.

Total number of tickets sold = 250

⇒ x + y = 250 – – – – (1)

Cost of adult ticket = $15

Cost of student ticket = $5

Total cost of collection = $2000

15x + 5y = 2000 – – – – (2)

Multiply equation (1) by 5

⇒ (1) × 5  5x + 5y = 1250 – – – – (3)

Subtract equation (3) from equation (2), we get

15x + 5y – 5x – 5y = 2000 – 1250

⇒ 10x = 750

⇒ x = 75

Substitute x = 75 in equation (1), we get

⇒ 75 + y = 250

⇒ y = 250 – 75

⇒ y = 175

Number of adult tickets = 75

Number of student tickets = 175

Test corner points for maximum revenue. The optimal solution is 250 adult tickets and 0 student tickets, yielding $3750.

To solve this problem, let's set up the equations based on the given information:

1. The total number of tickets sold cannot exceed 250:

[tex]\[ x + y \leq 250 \][/tex]

2. The total revenue must be at least $2000:

[tex]\[ 15x + 5y \geq 2000 \][/tex]

Now, let's solve this system of inequalities step by step:

Step 1: Graph the constraints:

Let's graph the lines corresponding to the equations:

x + y = 250 and  15x + 5y = 2000

Step 2: Find the feasible region:

The feasible region is the area that satisfies all the given constraints. In this case, it will be the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.

Step 3: Identify the corner points:

The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.

Step 4: Test the corner points:

Substitute the coordinates of each corner point into the objective function (the total revenue) to find which one yields the maximum revenue.

Let's start with the calculations:

1. **Graph the constraints:**

We'll need to find the intercepts of each line and draw them on the graph.

For ( x + y = 250 ):

When ( x = 0 ), ( y = 250 )

When ( y = 0 ), ( x = 250 )

For ( 15x + 5y = 2000 ):

When ( x = 0 ), ( y = 400 )

When ( y = 0 ),[tex]x = \frac{2000}{15} = \frac{400}{3} \)[/tex]

Now, let's plot these points and draw the lines.

2. **Find the feasible region:**

Shade the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.

3. **Identify the corner points:**

The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.

4. **Test the corner points:**

Substitute the coordinates of each corner point into the objective function ( R = 15x + 5y ) to find which one yields the maximum revenue.

Let's calculate the corner points:

Corner Point 1: (0, 0)

[ R = 15(0) + 5(0) = 0 ]

Corner Point 2: (250, 0)

[ R = 15(250) + 5(0) = 3750 ]

Corner Point 3: (0, 400)

[ R = 15(0) + 5(400) = 2000 ]

Now, let's compare the revenues:

- Corner Point 1: $0

- Corner Point 2: $3750

- Corner Point 3: $2000

The maximum revenue is $3750, which occurs at the corner point (250, 0).

Therefore, to maximize revenue while satisfying the given constraints, the Arlington Drama Club should sell 250 adult tickets and 0 student tickets.

To simplify a fraction by division you must have common factors between the denominator and the neominator to divide (or cancel) them

Answer:

(4,5)

Step-by-step explanation:

We are to find the circumcenter of triangle EFG with vertices

E(2,6), F(2,4), and G(6,4)

Let S(x,y) be the circum center.  Then this point is equidistance from E, F and

G

i.e. [tex]ES=FS=GS\\ES^2 =FS^2 =GS^2[/tex]

[tex](x-2)^2+(y-6)^2 =(x-2)^2+(y-4)^2 =(x-6)^2+(y-4)^2 \\i.e. x^2-4x+4+y^2-12y+36 = x^2-4x+4+y^2-8y+16 = x^2-12x+36+y^2-8y+16 \\4y = 20: y =5\\8x=32\\x=4[/tex]

Thus circumcenter is (4,5)

Answer:

11 feet

Step-by-step explanation:

Area of rectangle (170.5cm) = length (15.5) x width

170.5/15.5=width

Width = 11

Hope this helps! :)

Answer:

OF course!Dividing by 100 just means move the decimal two places to the left, so the answer is 9.652

Step-by-step explanation:

Answer:

=9.852

Step-by-step explanation:

985.2/100

=9.852

Answer:

The new principal after the first payment is $ 1,380.65

Step-by-step explanation:

1. We calculate the amount of interest to pay in the first payment, this way:

Interest = Amount of loan * (interest rate/months in a year)

Replacing with the real values we know:

Interest = 1,500 * (0.1/12)

Interest = 1500 * 0.0083 = $ 12.50

2. Now we subtract the Interest from the monthly payment, as follows:

Payment to principal = 131.85 - 12.50

Payment to principal = $ 119.35

3. Finally we subtract that 1st payment to principal from the initial principal to get the new principal, this way:

New Principal = 1,500 - 119.35

New Principal = $ 1,380.65

The new principal after the first payment is $ 1,380.65

This is pretty much half the volume of a rectangular prism, so we multiply 4.8*2.5*3.4 to get 40.8 mm^3

Then we take half of that to get 20.4 mm^3

Hope that helped you to understand!

Answer:

[tex]f(x) = {x}^{2} - 15x + 26[/tex]

Step-by-step explanation:

Assuming we want to write a quadratic function with intercepts x=13 and x=2.

Then we can work backwards.

This means that:

x-13=0 and x-2=0

The factored form of this quadratic function becomes:

[tex]f(x) = (x - 13)(x - 2)[/tex]

We expand to get:

[tex]f(x) = {x}^{2} - 2x - 13x + 26[/tex]

We simplify to obtain:

[tex]f(x) = {x}^{2} - 15x + 26[/tex]

The simplified ratio that correctly compares 27 feet to 36 feet is 3:4

Step-by-step explanation:

Step 1: Simplify the ratio by finding common factor

Step 2: Here, in this case the lowest common factor is 3. Divide both numerator and denominator by 3.

⇒ 27/36 = 9/12 (on dividing by 3)

⇒ 9/12 = 3/4 (again on dividing by 3)

Answer:

35/12

Step-by-step explanation:

1 1/2+1 5/12

=3/2+17/12

=3*6+17*1/12

=18+17/12

=35/12

Tom read a total of 11/12 of the two books combined by reading 1/2 of the first book and 5/12 of the second book, after finding a common denominator to add the fractions.

To calculate the total fraction of the two books that Tom has read, we need to add the fractions of each book he has read together. Tom read 1/2 of the first book and 5/12 of the second book.

To add these fractions, they need to have a common denominator. The lowest common denominator between 2 and 12 is 12.

Therefore, we convert 1/2 into 6/12 so that both fractions have the same denominator.

Now, the fractions to be added are 6/12 (from the first book) and 5/12 (from the second book).

Adding these fractions, we get:

6/12 + 5/12 = 11/12

So, Tom has read a total of 11/12 of the two books combined. This method of finding a common denominator and then adding the numerators is an effective strategy to add fractions with different denominators, providing a clear, step-by-step approach to solving such problems in mathematics.

Answer:

exact form is 5/12

decimal form is 0.416666

Step-by-step explanation:

Equivalent fractions are fractions that have the same value or proportion. To find an equivalent fraction to a given fraction, you multiply or divide both the numerator and the denominator by the same number. Therefore, 10/24 and 15/36 are equivalent fractions to 5/12.

To find an equivalent fraction to 5/12, you simply multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number. An equivalent fraction will have a different numerator and denominator, but it will represent the same value or proportion. For example, if we multiply both the numerator and the denominator of 5/12 by 2, we get 10/24. Therefore, 10/24 is an equivalent fraction to 5/12.

Similarly, if we multiply 5 (the numerator) and 12 (the denominator) by 3, we get the equivalent fraction 15/36.

So, 5/12 = 10/24 = 15/36 in terms of value or proportion.

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The break even point for this book store is 10

Solution:

Given that, book store cost $80 a day to keep open, and it spends $15 for each book that it sells

Cost to open the book store = $ 80

The formula for solving the break even point (BEP) is:

[tex]BEP = \frac{\text{Fixed cost}}{\text{Selling price - variable cost}}[/tex]

Fixed Cost is the cost that remains constant whether the services provided or products sold increases or decreases

Variable Cost is the cost that varies or differs in proportion to the products or services produced, whether they increased or decreased

In this problem,

Fixed cost = $ 80

Selling price = $ 23

Variable cost = $ 15

Therefore,

[tex]BEP = \frac{80}{23-15}\\\\BEP = \frac{80}{8}\\\\BEP = 10[/tex]

Thus break even point for this book store is 10

In order for the bookstore to continue its business, it should sell at least 10 books to meet its $80 cost

Answer:p=10

Step-by-step explanation:

Answer:

F(3) = 2 * 3 - 1, which is 6 - 1 equaling 5.

Step-by-step explanation:

3 times 2 is six since you have to follow PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction). Multiplication is before Subtraction, and that is why we multiply 2 and 3 first, since 3 replaces the variable x. After multiplying 2 and 3 to get 6, subtract by 1 to get 5.

Answer: 5

Answer:

216

Step-by-step explanation:

1. √{6^6}

2. √(6^3)^2}

3.6^3

4.216

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Hope this helps!

-ShadyK

The value of the given expression is 216.

The given expression is,

[tex]\sqrt{2\cdot 6^5 + 2\cdot 6^5 + 2\cdot 6^5[/tex]

Square Root Computations:

The square root of a number is the number that we require to multiply by itself to obtain the original number

Now, solving the given expression as,

[tex]\sqrt{2\cdot 6^5 + 2\cdot 6^5 + 2\cdot 6^5}=\sqrt{2\cdot6\cdot6^4+2\cdot6\cdot6^4+2\cdot6\cdot^4}\\ =6^2\sqrt{12+12+12}\\ =36\sqrt{36}\\ =36\sqrt{4\cdot9}\\ =36\cdot2\cdot3\\=216[/tex]

Learn More information about the simplification:

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Option B: 5.25 is the length of XZ

Explanation:

The triangles PQR and XYZ are similar.

To determine the length of XZ, let us use the similarity theorem.

The theorem states that, "if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar".

Thus,

[tex]\frac{QR}{YZ} =\frac{PR}{XZ}[/tex]

Let us substitute the values from the diagram, we have,

[tex]\frac{4}{3} =\frac{7}{XZ}[/tex]

Multiplying both sides by 3, we get,

[tex]4 =\frac{21}{XZ}[/tex]

Thus,

[tex]XZ =\frac{21}{4}=5.25[/tex]

Thus, the length of XZ is 5.25

Hence, Option B is the correct answer.

Answer:

x = - 2

Step-by-step explanation:

– 2(– 3х + 4) + 3x — 3 = — 29

6x - 8 + 3x - 3 = - 29

9x = - 29 + 8 + 3

9x = - 18

x = - 18 : 9

x = - 2

Answer:

x = -2

Step-by-step explanation:

– 2(– 3х + 4) + 3x — 3 = — 29 multiply -2 with inside the parenthesis remember negative sign multiplied by negative sign is positive

6x - 8 + 3x - 3 = - 29 add the like terms

9x - 11 = -29

9x = -29 + 11

9x = -18

x = -2

Answer: r = 12.1cm, d = 24.2cm, Area = 460.0cm²

Step-by-step explanation:

From the formula,

Circumference of a circle = πd or 2πr.

To find the radius, we have to equate 76 cm to πd or 2πr and make r or d the subject of the formula. Now

76 = 2πr, don't forget that

π = 22/7 or 3.142

Now make r the subject of the formula

r = 76/2π

= 76/2 x 3.142

= 76/6.284

= 12.1 cm

d = 2r

= 2 x 12.1

= 24.2cm.

Area of the circle is πr²

= 3.142 x (12.1)²

= 3.142 x 146.41

= 460.0 cm²