Work out the area of this shape. Give your answer
in cm².



4 cm
4 cm
10 cm

Answer:

ED = AB = 25√3

Step-by-step explanation:

Let ED = AB = X

DC = 100 - BC

Tan 60 = [tex]\frac{\sqrt{3} }{1} = \frac{ED}{DC}[/tex] = [tex]\frac{X}{100-BC}[/tex]

[tex]\sqrt{3} (100-BC) = X[/tex]

Tan 30 = [tex]\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}[/tex]

[tex]\frac{BC}{\sqrt{3} } = X[/tex]

[tex]\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC[/tex]

X = [tex]\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\[/tex]

X = 25√3

Answer:

  (a)  (5, 9)

Step-by-step explanation:

You want the solution to the system ...

The value of x is already given, so no work is required to find that.

The value of y is found by using that value of x in the equation for y:

  y = 2x -1

  y = 2·5 -1 = 10 -1 = 9

The solution is (x, y) = (5, 9).

The measures of the angles of the triangles are

The measure of ∠B = 80.3°

The measure of ∠C = 59.7°

The length of side AB = 20.2 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AC = 23

The measure of side BC = 15

The measure of ∠A = 40°

From the law of sines , we get

( sin A ) / a = ( sin B ) / b = ( sin C ) / c

Substitute the value of A and a in the equation , we get

sin ( 40 )° / 15 = sin B / 23

On simplifying the equation , we get

sin B = ( 23/15 ) x sin ( 40 )°

Now , m∠B = 80.27°

So , the measure of angle ∠B = 80.3°

And ,

The interior angles of a triangle is 180°

So , The measure of angle ∠C = 180° - ( 80.3° + 40° )

On simplifying the equation , we get

The measure of angle ∠C = 59.7°

Now ,

From the law of cosines , c² = a² + b² - 2ab ( cos C )

Substitute the value of a , b and cos C in the equation , we get

c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°

On simplifying the equation , we get

c² = 225 + 529 - 348.12363

c² = 405.87

Taking square roots on both sides of the equation , we get

c = 20.156

c = 20.2 units

Therefore, the measure of side AB = 20.2 units

Hence , the measures angles of triangle is solved

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Answer:

SaS

Step-by-step explanation:

With an accuracy of within $0.01, the student will be able to recognize

and determine the total worth of a given assortment of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills.

TEKS stands for Texas Essential Knowledge and Skills. It is a set of state standards for public schools in Texas, that outline what students should know and be able to do in each grade level and subject area. The standards cover subjects such as English language arts, mathematics, science, social studies, and languages other than English.

The TEKS are used to guide the development of curriculum and instruction in Texas schools.

The clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill of determining the value of a collection of coins and bills could be: "The student will be able to accurately identify and calculate the total value of a given collection of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills, to within $0.01."

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Answer:

  18 tickets at $7

Step-by-step explanation:

You want a "Singapore Math" model solution to the number of $7 tickets Mrs. Hana bought if she got $14 change from $200, and she received a total of 30 tickets, some of which cost $5 each.

The attachment shows the model we decided upon. Starting from $200, we subtract $14 in change, then divide the remainder into tickets costing $7 each and tickets costing $5 each. The point where the total number of tickets is 30 is the point that identifies the solution.

Mrs. Hana bought 12 tickets at $5 each, and 18 tickets at $7 each.

__

Additional comment

Most illustrations of Singapore Math models are solving for a single variable. Here, we must choose values for two variables (the numbers of $5 and $7 tickets) so the intended model isn't clear.

The model we have used is adequate for the purpose, but tedious to construct. It requires us to identify the point at which the count of $7 tickets (top bar) and the count of $5 tickets (bottom bar) has a sum of 30.

As per the given probability, the flipped coin is Coin A.

Probability in math is know as the entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment.

Here we have given that you have two biased coins. Coin A comes up heads with probability 0. 1 and Coin B comes up heads with probability 0. 6.

Here we know that you are not sure which is which, so you choose a coin randomly and flip it.

As per the given situation here we have to know that if the flip is heads, then you guess that the flipped coin is B.  

Which is defined that if the the flip is tails, then you guess that the flipped coin is A.  

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Answer:

Intial money=Rs 3300

final money=3300-(70×5)-(2×125)-2500

=3300-350-250-2500

=3300-3100=RS 200

Now,

share of each of them= 200/2=Rs100

*mark me brainliest

Answer:

8.66 years

Step-by-step explanation:

F = Pe^(rt)

2 = e^(0.08t)

ln 2 = ln [e^(0.08t)]

ln 2 = 0.08t

t = (ln 2)/0.08

t = 8.66

Answer: 8.66 years

Answer:

Hope the picture helps you draw.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The simple explanation is that the hypotenuse and sides of a right triangle are always shorter than one another. Therefore, any side's to any hypotenuse's ratio will never be greater than 1. The figure is no longer a triangle when the angle is 0 or 90 degrees because one of the sides vanishes and the other side lines up with the hypotenuse. For this reason, sin and cosine have values of 0 or 1 in these extreme situations.

The university accepts 6000 students out of the 10000 that applied.

Enrolled, in the context of education, is the process of registering a student with a school. The process typically requires a student to complete an application form and submit it to the school, along with any other required documents or fees. Once the student has been accepted and enrolled, they will be given a student ID number and will be able to access all the school's resources, such as classes and activities. In addition, the school may assign an advisor to the student to help them adjust to the school and plan out their academic path.

Of those 6000 accepted students, 45% will actually enroll, which is 2700 students. Therefore, of the 10000 students that applied, 2700 will actually enroll into the university.

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Answer:

[tex]x = \sqrt{87}[/tex]

Step-by-step explanation:

So, we need to use a bit of an unorthodox method here. We will use the Pythagorean theorem to find x. We will first start by finding out what all of our sides are. In the theorem, it's  [tex]a^{2} + b^{2} = c^{2}[/tex] . We know that the b is x, and the c is 16, but we need to know what a is. a is not 18. We need to find the distance starting at the right triangle. To do that, we must subtract 5 from 18, giving us 13. So, we have:

[tex]13^{2} + x^{2} = 16^{2}[/tex]

Now, we will simplify the equations:

[tex]169 + x^{2} = 256[/tex]

Then, we will subtract 169 from both sides, giving us:

[tex]x^{2} = 87[/tex]

Square rooting both sides gives us:

[tex]x = \sqrt{87}[/tex]

And we cannot simplify further because 87's prime factorization doesn't let it have any ways to get out of the square root.  

Hope this helped

The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

Option (D) is correct.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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We can plot in the coordinate plane if an ordered pair is known to us.

The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.

let we have some pair of numerical terms such as A (4, 9) and B (6, 10)

that is needed to plot in the coordinate plane.

At first, we will plot the point A (4, 9)

we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.

By the same way, we can plot the point B.

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The linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

and the solution would be x = 8, y = 6.

What is a system of linear equations?

A system of linear equations is a set of two or more linear equations that describe a relationship between multiple variables. The variables in each equation are related to each other, and the solution of a system of linear equations is the set of values that satisfy all of the equations in the system.

In this case, since Kent and Rew each bought the same amount of boondins and hopts, we can use the same variable names (x for boondins and y for hopts) for both of them. We can use this information to write two equations to model the relationship between the amounts of boondins and hopts that Kent and Rew bought:

4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

This system of linear equations is called a system of two equations in two variables.

Hence, the linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

and the solution would be x = 8, y = 6.

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Answer:

24.90 pound

1 dollar equivalent to 0.8301 pound

so 30 dollar will be 30 multiply by 0.8301

which equals 24.903 pounds

When a polynomial has four or more terms, the easiest way to factor it is to use grouping.

Grouping can be understand more better with an example:

for eg:  factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:

However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).

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The integer number that represents the submarine's depth is given as follows:

-460.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

The concepts of height and depth are given as follows:

A submarine in the middle of the ocean at a depth of 115 feet, hence the integer that represents the initial depth is given as follows:

-115.

The submarine dived to a depth that is four times the initial depth, hence the integer that represents the final depth is given as follows:

4 x -115 = -460.

(meaning that the final depth of the submarine is of 460 feet).

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Answer: 54 inches squared

Step-by-step explanation:

Since it is a scale drawing, when we scale one variable up or down, we have to scale the other value the same amount because they are proportional. For example, if we divide one value by 3, we have to divide the other value by 3 also.

In this case, the real length is 30 feet, and the scale drawing length is 15 in. We divided by 2, so we have to divide the width by the same amount. 24/2 = 12 inches, so the width would be 12 inches or 1 foot.

The value of the shortest of the four side lengths of the quadrilateral is 30 cm

The perimeter of a quadrilateral is the sum of all the sides.

Perimeter of the Quadrilateral = 132 centimeters

Let

The shortest side = x

Since, the sides are consecutive even integers;

Second side = (x + 2)

Third side = (x + 4)

Fourth side = (x + 6)

Perimeter of the Quadrilateral = shortest side + Second side + Third side + Fourth side

132 = x + (x + 2) + (x + 4) + (x + 6)

132 = x + x + 2 + x + 4 + x + 6

132 = 4x + 12

132 - 12 = 4x

120 = 4x

divide both sides by 4

x = 120/4

x = 30 centimeters

Therefore,

Second side = (x + 2)

= 30 + 2

= 32 cm

Third side = (x + 4)

= 30 + 4

= 34 cm

Fourth side = (x + 6)

= 30 + 6

=36 cm

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A triangular number succession is the representation of numbers as just an ordered set of equilateral triangles. The order of these numbers is 1, 3, and 6.

A triangular number is one that may be written as the sum of a initial n positive integers.

The first 3 triangular numbers are therefore 1, 3, and 6.

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Answer:

5/3

Step-by-step explanation:

4 4/9 * 3/8 = 40/9 * 3/8 = 120/72 = 10/6 = 5/3

On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

U/5 = 17/11

U = 17/11 X 5

U = 7.72

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Answer:

Step-by-step explanation: You can add all of these numbers with a calculator. but be sure what are the numbers telling you what to do. So always focus on the words that are going to mention about the numbers.

Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables

If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.

When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.

To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:

Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)

So if tt represents the number of tables Zachary waits on, then he can expect to earn:

Earnings = $40 + $7 x tt

For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.

Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.

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Answer:

144

I wish you luck in your assignments.

Answer: 144 articles

Step-by-step explanation:

If it makes 12 in half-hour, then 24 in an hour because 12*2 is 24.

then 24*6=144.