Calculating Areas of Multiple Polygons

Each unit on the coordinate grid represents
1 yard.
The rectangular pool and triangular hot tub shown are both in need of covers.
How much total material is needed to cover both?
square yards

Answer:

3

Step-by-step explanation:

8 x 5 = 40

43 - 40 = 3

The number of students who cannot sit at tables based on the given conditions in a classroom setting are 3.

The number of students who cannot sit at tables can be calculated as follows:

Number of students per table = 8

Total number of students = 43

Total number of students that can be accommodated by tables = 5 tables x 8 students = 40 students

Number of students who cannot sit at tables = Total number of students - Total number accommodated by tables = 43 - 40 = 3 students

Answer:

C. 45.82

Step-by-step explanation:

We know the circumference is given by

C = 2 * pi *r

24 = 2 * 3.14 * r

24 = 6.28r

Divide each side by 6.28

24/6.28 = r

r = 3.821656051

We want to find the area

A = pi r^2

A =3.14 * (3.821656051) ^2

   =45.85987261

To find the new price of the jeans after using a 30% off coupon, multiply the original price by the discount percentage and subtract that amount from the original price.

To find the new price of the jeans after using the 30% off coupon, you need to multiply the original price by the discount percentage and subtract that amount from the original price. Here's how:

Therefore, the new price of the jeans after using the coupon is $23.80.

Final answer:

The equivalent expression to 16a + 24b is 8(2a + 3b) by factoring out the greatest common factor of 8 from both terms.

Explanation:

The expression equivalent to 16a + 24b is 8(2a + 3b). To find this, we can factor out the greatest common factor from the terms in the original expression. Both 16a and 24b have a common factor of 8, which when factored out leaves us with 2a and 3b, respectively, yielding the expression 8(2a + 3b).

Check the attached picture for the diagram attached to the question

Answer: VOLUME A = VOLUME B

Step-by-step explanation:

The volume of a prism = cross-sectional area × length

PRISM A:

Rectangular prism

Cross-section, as given above, equals 3units by 2units

Therefore, the Area of the cross-section equals

Area of rectangle= Length × Width

Area of rectangle( 3×2) = 6

Length = 3.61

The volume is 6 × 3.61 = 21.66 unit^3

PRISM B:

Triangular prism:

Cross-section, as given above, equals 4units by 3units

Therefore, the Area of the cross-section equals

Area of triangle = (1/2) × base × height

Area of triangle 0.5 × 4 × 3= 6

Length = 3.61

The volume is 6 × 3.61 = 21.66unit^3

Answer: D) Volume A = Volume B

Answer:

2.44

Step-by-step explanation:

Given: x³ + 2x² - 5ax - 7      and  x³ + ax² - 12x + 6

Also, R1 + R2 = 6

in order to find the value of a:

Let p(x) = x³ + 2x² - 5ax - 7 and q(x) = x³ + ax² - 12x + 6

Using remainder theorem i.e if a polynomial p(x) is divisible by polynomial of form x - a then remainder is given by p(a).

Then,

R1 = p( -1 ) = (-1)³ + 2(-1)² - 5a(-1) - 7 = -1 + 2 + 5a - 7 = 5a - 6

R2 = q( 2 ) = 2³ + a(2)² - 12(2) + 6 = 8 + 4a - 24 + 6 = 4a - 10

Now,

R1 + R2 = 6

5a - 6 + 4a - 10 = 6

9a = 22

a=2.44

Therefore, Value of a is 2.44

Answer:

515

Step-by-step explanation:

Answer:

the correct answer would be 3030000000

Step-by-step explanation:

2500000000+530000000=3030000000

= Cube root of -27 = -3 (because the factors of 27 = 3×3×3)

= Cube root of 125 = 5 ( because the factors of 125 = 5×5×5)

Thus, cube root of -27/125 = -3/5

Answer:

-3/5

Step-by-step explanation:

hello :

- 27 =(-3)^3  and  125= 5^3

-27/125 ​ = (-3)^3 / 5^3 = (-3/5)^3  

so : ∛((-3/5)^3 )= -3/5

Answer:

B. 81 cubic inches

Step-by-step explanation:

Since this is an irregular 3 dimensional object, I will cut it into a 3 by 3 by 3 cube and a 6 by 3 by 3 rectangular prism.

Solving for the cube:

3*3*3=

9*3=

27 units or in this case inches³

Solving for the rectangular prism:

6*3*3=

18*3=

54 units or in this case inches³

To get the total volume, we need to add the cube and rectangular prism's volume together:

54+27=81 inches³

Our answer is B. 81 cubic inches.

Answer:

y = 5x

Step-by-step explanation:

The standard equation for directly proportional equations is y = kx. We can see that y is directionally proportional to x when y = 30 and x = 6 and we need to work out an equation connecting x and y.

→ First step is to substitute in the values

y = k × x

30 = k × 6

→ Divide both sides by 6 to isolate k and find the value of k

5 = k

k = 5

→ Now we substitute k = 5 back into y = kx

y = 5x

Answer:

y=5x

Step-by-step explanation:

The answer is y=5x hope you have a nice day!

Answer:

6.

Step-by-step explanation:

To solve this, you can set up an equation as such:

x²-18= 3x

Now, rearrange this to make it an equation in standard form:

x²-3x-18=0.

Simply turn this equation into factored form:

(x-6)(x+3)= 0.

The only positive solution here is x=6.

The problem is about a quadratic equation where a number's square, minus 18 equals 3 times the number. This equation is solved by factoring to get two potential solutions, -3 and 6. The positive solution is 6.

The subject matter of this question is quadratic equations in Mathematics. We are to find a number where the difference between the square of the number and 18 is equal to 3 times the number.

We first turn this into a quadratic equation:x2 - 3x - 18 = 0. Then we solve using a technique such as factoring which results to (x - 6)(x + 3) = 0. Giving the solutions x = 6 and x = -3.

Since you asked for the positive solution, x = 6 is the correct answer.

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Answer:

photo please!

Step-by-step explanation:

Answer:

34 + 35 + 36 = 105

Step-by-step explanation:

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 105

3X + 3 = 105

3X + 3 - 3 = 105 - 3

3X = 102

3X/3 = 102/3

X = 34

Which means that the first number is 34, the second number is 34 + 1 and the third number is 34 + 2. Therefore, three consecutive integers that add up to 105 are 34, 35, and 36.

34 + 35 + 36 = 105

We know our answer is correct because 34 + 35 + 36 equals 105 as displayed above.

Answer:

1 2/3b + 6 2/3

Step-by-step explanation:

[tex]12\frac{1}{3}b+6\frac{2}{3}-10\frac{2}{3}b[/tex]

Combine like terms:

[tex]1\frac{2}{3}b+6\frac{2}{3}[/tex]

Since you cannot do any more combination or simplification, you are done. Hope this helps!

The simplified form of the given expression is (26-b)/3.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is [tex]12\frac{1}{3}b+6\frac{2}{3}-10\frac{2}{3}b[/tex].

Here, [tex]12\frac{1}{3}b-10\frac{2}{3}b+6\frac{2}{3}[/tex]

= (36+b)/3 - (30+2b)/3 +20/3

= (36-30+b-2b)/3 +20/3

= (6-b)/3+20/3

= (6-b+20)/3

= (26-b)/3

Therefore, the simplified form of the given expression is (26-b)/3.

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Answer:

Long story short its C)

Step-by-step explanation:

Option B is correct, (-3 + 5i) (1) = -3 + 5i equation demonstrates the multiplicative identity property

A number system is defined as a system of writing to express numbers.

The multiplicative identity property is a multiplicative property in mathematics where each number multiplied by 1 will produce the original number or can be stated simply  :

"The product of any number and one is that number"

So The Multiplicative Identity is 1 can be stated in the formula:

a×1=1×a=a

(-3 + 5i) (1) = -3 + 5i

This is a multiplication operation and 1 is a Multiplicative Identity of multiplication, so the statement is true

Hence, option B is correct, (-3 + 5i) (1) = -3 + 5i equation demonstrates the multiplicative identity property

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Answer:

Around 55.9

Step-by-step explanation:

The first step is to find the area of segment of the circle. Since the segment is a 90 degree angle and a total circle is 360, it is a quarter of the area of a circle. Therefore, you can find its area with the formula [tex]\frac{1}{4}\pi r^2=49\pi[/tex]. Now, you can find the area of the triangle inside. Since all of the radii in a circle are the same length, the triangle has two sides of length 14. Using the triangle area formula, you get an area of 14*14/2=98 square centimeters. [tex]49\pi-98\approx 55.9[/tex] square centimeters. Hope this helps!

Answer:

Height of the building is 32.67 meters.

Step-by-step explanation:

Volume of a Pyramid = [tex]\frac{1}{3}(\text{Area of the rectangular base})(\text{Height})[/tex]

Side of the square base of the Memphis pyramid = 180 m

Height of the pyramid = 98 meters

Volume = [tex][\frac{1}{3}(180)^2](98)[/tex]

             = 1058400 cubic meters

Another building having the same base and volume, is in the shape of a prism.

Therefore, Volume of the pyramid = volume of the building(prism) = 1058400 cubic meters

Volume of the prism = (Area of the base) × height

1058400 = (180)²h

h = [tex]\frac{1058400}{180\times 180}[/tex]

h = 32.67 meters

Therefore, height of the building in the prism shape is 32.67 meters.  

Answer:

$50

Step-by-step explanation:

Sale on sweater = 40% .

Money saved = $20 .

Let original price be x then ,

=> 40% of x = $20

=> 40x/100 = $20

=> x = $20 *100/40

=> x = $ 50

Answer:

630

Step-by-step explanation:

Let the number of adult tickets be a.

Let the number of children tickets be c.

For that day's performance, they have sold a total of 1180 tickets. That means that:

a + c = 1180 _____________ (1)

Also, they have sold 80 more adult tickets than children’s tickets.

This means that:

a = c + 80 ______________(2)

Putting (2) in (1):

c + 80 + c = 1180

2c + 80 = 1180

Collecting like terms:

2c = 1180 - 80

2c = 1100

c = 1100 / 2 = 550

From (2):

a = 550 + 80

a = 630

They sold 630 adult tickets.

Final answer:

The theatre has sold 630 adult tickets after solving a system of equations based on the given conditions of total tickets sold and the difference between adult and children's tickets.

Explanation:

The student is presented with a problem where a theatre sells two types of tickets: children's and adult's tickets. For a particular performance, a total of 1180 tickets were sold, and there are 80 more adult tickets sold than children's tickets. We can let 'x' represent the number of children's tickets sold, and thus 'x + 80' will represent the number of adult tickets sold. According to the information given:

x + (x + 80) = 1180

Solving for 'x' we get:

2x + 80 = 1180

2x = 1100

x = 550

Now, to find the number of adult tickets sold, we add 80 to the number of children's tickets.

x + 80 = 550 + 80

x + 80 = 630

Therefore, the theatre has sold 630 adult tickets.

Answer:

0.16

Step-by-step explanation:

This probability is the area under the standard normal curve to the right of 82.  Note that 82 is ONE standard deviation above the mean:  75 + 7 = 82.

According to the Empirical Rule, 68% of data lies within one standard deviation of the mean.  In other words, 34% lies between the mean and one standard deviation above the mean.  The remaining area under the standard normal curve is thus (100% - 68%), or 32%.  Half of that is 16%.  

The probability that the temperature is above 82, or above 1 standard deviation above the mean, is 16%, which we can also express as 0.16.

Alternatively, use a calculator with built-in statistical functions.  In this case the desired result is found by executing the following command:

normcdf(82, 10000, 75, 7).  The desired result is 0.1587, or approximately 0.16.

Answer:3

Step-by-step explanation:

Answer: 280

To find the total number of 6th grade students at Dutchtown Middle, we can set up a proportion based on the information given:

- 45% of the 6th graders went to the Valentine's Dance.

- 126 students attended the dance.

Let us denote the total number of 6th grade students as N.

Given that 45% of the 6th graders is equal to 126 students, we can write the equation as:

(45/100)N = 126

[tex]\[ 0.45N = 126 \][/tex]

[tex]\[ N = \frac{126}{0.45} \][/tex]

[tex]\[ N = \frac{126}{0.45} \]\[ N = 280 \][/tex]

Therefore, the total number of 6th grade students at Dutchtown Middle is 280.

Answer:

i think the answer is 3.3

Step-by-step explanation:

Final answer:

Quita paid $6.60 in sales tax for an $88 jacket.

Explanation:

To calculate the sales tax Quita had to pay for her jacket, we need to follow a simple two-step process.

First, we will calculate the amount of tax by converting the percentage to a decimal and then multiplying it by the price of the jacket.

Since the tax rate is 7.5%, we convert this to a decimal which gives us 0.075.

Then, we multiply this decimal by the price of the jacket:

Amount of sales tax = price × rate of sales tax

$88.00 × 0.075 = $6.60

So, the sales tax on the jacket priced at $88 is $6.60.

Answer:

24 units ²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases

Counting the squares in the diagram gives

h = 4, a = 4, b = 8, thus

A = [tex]\frac{1}{2}[/tex] × 4 × (4 + 8) = 2 × 12 = 24 units²

Answer: 6

Step-by-step explanation:

Given Data:

Number of people = 6

Amount of Gold to be shared = 40lbs

Subtract 2/3 from your answer.

Therefore

If six people are to share 40lbs of gold evenly

= 40lbs / 6

Divide through by 2

= 20lbs / 3

= 20lbs / 3 - 2/3

= 18/3

= 6

Each person would get approximately 6lbs of gold

Answer:

1. Each individual gets [tex]6\frac{2}{3}lb[/tex] of gold

2. After subtracting by [tex]1\frac{2}{3}[/tex] , the result is 5

Step-by-step explanation:

Given

Size of Gold = 40 lbs

Number of people = 6

Required

1. Proportion of each individual

2. Subtract [tex]1\frac{2}{3}[/tex] from each proportion

1. Proportion of each individual

To calculate how many each individuals get (in other words, the proportion of each individual), we simply divide the total size of gold by the number of people

Mathematically,

[tex]Proportion = \frac{Total}{People}[/tex]

[tex]Proportion = \frac{40}{6}[/tex]

Reduce fraction to lowest term by dividing numerator and denominator by 2

[tex]Proportion = \frac{20}{3}[/tex]

Convert to mixed fraction

[tex]Proportion = 6\frac{2}{3}[/tex]

Hence each individual gets [tex]6\frac{2}{3}lb[/tex] of gold

2. Subtract [tex]1\frac{2}{3}[/tex] from each proportion

This is represented by

[tex]6\frac{2}{3} - 1\frac{2}{3}[/tex]

Convert both fractions to improper fractions

= [tex]\frac{20}{3} - \frac{5}{3}[/tex]

Find LCM of both fractions

= [tex]\frac{20 - 5}{3}[/tex]

Subtract

= [tex]\frac{15}{3}[/tex]

= 5

Hence, after subtracting by [tex]1\frac{2}{3}[/tex] , the result is 5

Answer:

see explanation

Step-by-step explanation:

Calculate the length using the distance formula

AB = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(4,3) and (x₂, y₂ ) = B(- 2, 1)

AB = [tex]\sqrt{(-2-4)^2+(1-3)^2}[/tex]

     = [tex]\sqrt{(-6)^2+(-2)^2}[/tex]

     = [tex]\sqrt{36+4}[/tex]

     = [tex]\sqrt{40}[/tex]

     = [tex]\sqrt{4(10)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex] = 2[tex]\sqrt{10}[/tex] ← exact length