The pentagonal prism below has a height of 13 units and a volume of 247 units ^3. Find the area of one of its bases.

The area of the right angled triangle as well as that of the isosceles triangle is calculated as

Area = 1/2 (b * h)

The explanation is logical, observe the right angled triangle (the one on the left) and you'll see that the length covered by the height (labelled as h) is not the entire width covered by the base (labelled as b) unlike what you have in a rectangle or square. Its only logical to multiply the base by half of the height, otherwise you might end up calculating the area of a rectangle.

That applies to all triangles in general, the area is calculated as

Given:

There are given two triangles.

Explanation:

According to the question:

We need to find the tall of Ariadne.

So,

To find the value, we need to use triangle proportion properties.

So,

Suppose the value of tall is x.

So,

We need to find the value of x.

Then,

Final answer:

Hence, the solution is 5 ft tall.

To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.

This equation has 2 solutions which are -5 and -1.

The class interval of the median is 1 ≤ x ≤ 2 and the mean of the distribution is 1.8

From the question, we have

Number of students = 30

This represents the total frequency

So, we have

Total frequency = 30

The median position is then calculated as

Median = (Total frequency + 1)/2

Substitute the known values in the above equation

So, we have

Median = (30 + 1)/2

Evaluate

Median = 15.5th

The 15.5th element is located in the second class

i.e. the class with the interval 1 ≤ x ≤ 2

So, the class interval in this case is 1 ≤ x ≤ 2

To do this, we start by calculating the average of the class interval

This is represented as

0 ≤ x ≤ 1 ⇒ 0.5

1 ≤ x ≤ 2 ⇒ 1.5

2 ≤ x ≤ 3 ⇒ 2.5

3 ≤ x ≤ 4 ⇒ 3.5

So, we have

x        f

0.5   6

1.5    13

2.5    7

3.5    4

The mean is calculated as

Mean = ∑fx/∑f

So, we have

Mean = (0.5 * 6 + 1.5 * 13 + 2.5 * 7 + 3.5 * 4)/30

Evaluate

Mean = 1.8

Hence, the mean value is 1.8

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Figure IJKL is congruent to Figure TUVW because rigid motions can be used to map Figure IJKL onto Figure TUVW

Figure IJKL is similar to Figure TUVW because rigid motions and/or dilations can be used to map Figure IJKL onto Figure TUVW

Since the figures are congruent, the scale factor is 1

SOLUTION

1. From the question the machine stamps 36 caps in 10 seconds

In 5 minutes it will cap

So in 5 minutes, it would stamp 1080 bottle caps

2. Minutes it would take to stamp 24,408 bottle caps?

Hence it would take 113 minutes to stamp 24,408 bottle caps

Given the following question:

Your answer is x = -2.

The ratio of the perimeters of two similar shapes is equal to the ratio of their corresponding sides, then, by taking the top sides of these figures we can express the following ratio

18 : 24

by dividing both numbers by 2, we get:

9 : 12

Dividing by 3:

3 : 4

Then the ratio of their perimeters equals 3 : 4

SOLUTION

The initial points is 1050

The points earned per hour is 350

The total point y earned in x hours is:

Substitute y=2450 into the inequality

Solve for x

Therefore the lease number of hours is 4.

A graph is proportional if the line intersects at the origin (0, 0)

and the y-intercept will always equal to 0

Since y-intercept is the value of y when x =0, and it passes the origin at x = 0, y= 0.

The answer is 0

Answer:

2-×+3-×-4=0

Step-by-step explanation:

×=1\2

0.5,2`1

114 minutes

Explanation

Step 1

find the rate of production of each machine (cans per minute)

so

a)The newer machine:

b)the older machine:

Step 2

Add the rates together to determine their combined

so, the total rate( both machine working ) is 50 cans per minute

Step 3

finally, to find the time to produce 5700 cans, divide the total cans by the rate, so

therefore, the answer is 114 minutes

I hope this helps you

Answer:

45,000

Step-by-step explanation:

Hey! Let's help you with your question here!

So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).

First Digit:

Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.

Second, Third, Fourth Digit:

Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.

Fifth (Last) Digit:

For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.

Answer Explanation:

Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:

[tex]9*10*10*10*5[/tex]

[tex]=45,000[/tex]

Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.

Substitute second expression (x=y) in the first expression.

Substitute the above value of y in the expression number 2.

Thus, the value of x=3 and the value of y=3.

We have the parallel sides of the rectangle are equal, therefore:

The perimeter is the sum of all sides, then:

Substitute the given data:

And solve for x:

Next, we find the length of side RS:

Answer: RS = 51 units

y varies directly as x, y = 7 when x = 21. Determine x when y = 5.

Step 1

Let

y varies directly as x, it is y depends on x, in math terms

f(x)=y

y = 7 when x = 21

f(21)=7

Determine x when y = 5. f(?)=5

Step 2

there is a proportion, this must be equal, make a rule of three to find the value

so

x y

so , when y=5, x=15

We have from the question 1200 liters, and we need to convert it into kiloliters.

To find the equivalent in kiloliters to 1200 liters, we can proceed as follows:

1. Find the equivalent between these two measures:

2. Then we have:

Therefore, in summary, we can conclude that 1200 liters are equivalent to 1.2kiloliters.

The expression (m⁻⁵n⁻³)⁻³ has an equivaent of m⁻¹⁵n⁹

From the question, the expression is represented as

(m−5n−3)−3

Rewrite the expression properly

This is done as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

This gives

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution is (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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The given expression (m⁻⁵n⁻³)⁻³ has an equivalent to the m⁻¹⁵n⁹

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is represented as (m−5n−3)−3

Rewrite the expression as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets , we have

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products, we have;

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution will be; (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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Answer:

st - r = -33

Explanation:

We need to replace r by -31, s by 4 and t by -16, so the expression is equal to

st - r = 4(-16) - (-31)

st - r = - 64 + 31

st - r = -33

So, the answer is

st - r = -33

ticket sale on Saturday night is triple the ticket sale on Friday night.

Therefore

ticket sales on Saturday night = 3 x 12425 = 37275

Then

ticket sales for both nights = 12425 + 37275 = 49700

A ticket costs 35.

Let the number of people that attended the carnival on both nights be n.

Then, we have

Therefore 1420 people attended the carnival on both nights

Answer:

skill issue

Step-by-step explanation:

skill issue

The quadrilateral has diagonals that are both congruent and perpendicular is square.

The correct option is (d)

Answer:

Its A

Step-by-step explanation:

Four more than the product of a number and 8 is equal to

Let

x -----> the number

we have that

the algebraic expression is equal to

the product of a number and 8 ------> 8x

so

Four more than the product of a number and 8 is equal to 3

8x+4=3

solve for x

8x=3-4

8x=-1

x=-1/3

therefore

the number is -1/3

Step 1

Given the triangle, ABC translated to A'B'C'

Required to find the algebraic description that maps triangle ABC and A'B'C'

Step 2

The coordinates of points A, B,C are in the form ( x,y)

Hence

Step 3

Find the algebraic description that maps triangle ABS TO A'B'C'

The algebraic description is found using the following;

Hence,

Hence the answer is option B

Given:

Length of the two adjacent sides = 533 feet and 525 feet

Angle between the two sides = 53 degrees

Let's find the area of park.

Let's make a sketch representing this situation:

Let's first find the length of the third side.

Apply the cosine rule.

We have:

Now, apply the Heron's formula to find the area:

Where:

a = 472.13

b = 533

c = 525

Let's solve for s:

• Therefore, the area will be:

The area in square feet is 111,738.81 square feet.

Now, let's find the area in square yards.

Apply the metrics of measurement.

Where:

1 square yard = 9 square feet

Thus, we have:

111,738.81 square feet =

Therefore, the area of the park in square yards is 12,415 square yards.

ANSWER:

12,415 square yards.

Answer:

-4 +9i

Step-by-step explanation:

complex number in standard form.

(-2+6i)-(2-3i)=

Combine like terms

-2 -2  +6i +3i

Standard form is a+bi

-4 +9i

The external angle formed by the secants equals one-half the difference of the intercepeted arcs. Therefore:

Given:

Percent of participants that used triangles shape = 80% = 0.80

The triangles shaped won their trials 16% of the time = 0.16

The other shaped plane won their trials 36% of the time = 0.36

Thus, we have:

Percent of participants who used other shapes = 100% - 80% = 20% = 0.20

Amount of time the triangle shaped plane lost = 100% - 16% =84% = 0.84

Amount of time the other shaped plane lost = 100% - 36% = 64% = 0.64

Let's solve for the following:

• (a) Create a tree diagram for this situation.

We have the tree diagram below:

• (b) What is the probability that a triangle plane won overall?

To find the probability that a triangle plane won overall, we have:

• (c) Out of 100 planes, which shape has the most winners?

Given that 80% used triangle, the number of planes with triangle shape will be:

0.8 x 100 = 80 planes

Number of planes with other shape:

0.2 x 100 = 20 planes

Number of winners for traingles:

0.16 x 80 = 12.8

Number of winners for other shape:

0.36 x 20 = 7.2

Therefore, the shape with the most winners is the triangle shape.

• (d),. A winning plane is selected at random, what is the chance it is triangle shaped?

To find the probability a winning plane selected at random is triangle shaped, wehave:

ANSWER:

(b) 0.64

(c) Triangle shape

(d) 0.64



For the given functions, we can write the sum as:

(f + g)(x) = 9x + 1

Here we want to find the sum between functions f(x) and g(x), and in this case, we have:

f(x)= x - 8

g(x) = 8x + 9

The sum can be written as:

(f + g)(x) = f(x) + g(x)

Replacing the functions there we get:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (x - 8) + (8x + 9)

(f + g)(x) = x + 8x - 8 + 9

(f + g)(x) = 9x + 1

That is the sum of the functions.

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A.

In order to calculate the area of the trapezoid, we need to calculate its height:

Using the Pythagorean Theorem, we have:

Now, calculating the area:

B.

If each square yard is $35, first let's convert the area from ft² to yd² (1 yard = 3 feet, 1 yd² = 9 ft²):

So the total cost is:

So the cost is approximately $2347.45.