area of a sector with 150° and 6ft

Answer: -3

Step-by-step explanation:

To solve the system of equations y=4x-3 and y=-2x+9, we can set the two equations equal to each other and solve for x:

4x - 3 = -2x + 9

Adding 2x and 3 to both sides, we get:

6x = 12

Dividing both sides by 6, we get:

x = 2

Now that we have the value of x, we can substitute it into either of the original equations to find the corresponding value of y. Let's use the first equation:

y = 4x - 3

y = 4(2) - 3

y = 8 - 3

y = 5

Therefore, the solution to the system of equations is x = 2 and y = 5. The solution is the ordered pair (2, 5).

Answer:

Step-by-step explanation:

SSS" is when we know three sides of the triangle, and want to find the missing angles

The main step to add rational expressions with unlike denominators is to take least common multiple of denominator and make them like before applying the required operation.

Therefore, the addition of rational expressions with unlike denominators is simplified by taking least common multiple.

The above question is incomplete, the complete question is:

Write steps for adding rational expressions with unlike denominators with example ?

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The points are plotted and labeled in the graph.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

A graph of the coordinate plane.

The points are (0, 2), (-3, 4), (4, -6), (6, -2), (5, 5), (-3, -5), (0, -4), (4, 0), (5, 0), and (3, -6).

The points are plotted and labeled in the graph.

The required graph is given in the image below.

Therefore, all the coordinates are plotted in the graph.

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Answer:

Step-by-step explanation:

To find the diagonal of a rectangular lot, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side, also known as the diagonal of the rectangle) is equal to the sum of the squares of the lengths of the other two sides.

So, for a rectangular lot 165 feet long and 90 feet wide, the length of the diagonal can be calculated as follows:

d = √(165^2 + 90^2) = √(27225 + 8100) = √35325 = 189 feet

The diagonal fence for the lot would require 189 feet of fencing. To round this to the nearest foot, we would round up to 190 feet, since 189.5 is closer to 190 than 189.

Therefore, 190 feet of fencing are needed to make a diagonal fence for the lot.

Answer:

Step-by-step explanation:

a

The simplified answer in improper fraction is -3 ¹/₅.

To simplify the equation we will solve the equation and obtain the value of x as shown below.

7 ( x + 1 ) = 1 - 2( 5 - x )

open the bracket by multiplying by 7 and 2

7x  +  7  = 1 - 10 + 2x

collect similar terms as shown below;

7x - 2x = 1 - 10 - 7

5x = -16

x = -16 / 5

x = -3 ¹/₅

Thus, the simplified answer in improper fraction is obtained by finding the value of x.

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a) Height of section A is 15.21 m, b) the length of the wire structure from the point O to the top of section A is 51 units and the length of the wire structure from the point O to the top of section B is 41.56 units

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that an arrangement of wires and tower, making it as two right triangles, Let us consider the foot of the tower be C (refer to image attached)

Using the concept of height and distance, we will find the asked measurements,

a) What is the height of the section A?

CA = tan 45° × CO [tan 45° = 1]

CA = 36 m

Similarly,

CB = tan 30° × CO [tan 30° = 0.577]

CB = 20.78

Height of section A = CA - CB

= 15.21 m

b) What is the length of the wire structure from the point O to the top of section A?

OA = AC / sin 45°

OA = 36 / 0.707

OA = 51

Therefore, the length of the wire structure from the point O to the top of section A is 51 units

c) What is the length of the wire structure from the point O to the top of section B?

OB = BC / sin 30°

OB = 41.56

Therefore, the length of the wire structure from the point O to the top of section B is 41.56 units

Hence, the answers are a) Height of section A is 15.21 m, b) the length of the wire structure from the point O to the top of section A is 51 units and the length of the wire structure from the point O to the top of section B is 41.56 units

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The complete question is :-

Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure, including microwave dishes. They are among the tallest human-made structures. There are 2 main types: guyed and self-supporting structures.

On a similar concept, a radio station tower was built in two sections A and 6. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 m. From point O, the angle of elevation of the top of section B is and the angle of elevation of the top of section A is

On the basis of the above information, answer any three of the following questions

*(i) What is the height of the section A?*

*(ii)What is the length of the wire structure from the point O to the top of section A?*

*(iii) What is the length of the wire structure from the point O to the top of section B ?*​

The total area for the parallelogram-shaped tiles Felix needs to buy exists 80cm² at the price of $40.

In calculating the area of a parallelogram, the base exists multiplied by the height, in an exact way as computing the area of a rectangle.

here, we have,

Given that, the base of one parallelogram-shaped tile exists 4cm with a height of 2 cm.

Area of one parallelogram shaped tile = 4cm × 2cm

Area of one parallelogram-shaped tile = 8cm²

Total area for the 5black and 5white tiles = 10 × 8cm²

Total area for the 5black and 5white tiles = 80cm²

Therefore, Felix must buy a total area of 80cm² of 10 parallelogram-shaped tiles.

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Answer:

2/5 bottle of juice

2/15L of juice

Step-by-step explanation:

We originally have 2 bottle of juice and each bottle contains 1/3 liter. From this, we can find that there are 2/3L of juice in total. Since five friends equally drink the juice, each of them drank 2/5 bottle of juice and 2/15L of juice.

I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!

Answer:

It should be = 20/68 = 0.294117647

Answer:

The secant function is undefined for angles where the cosine function equals zero, because dividing by zero is undefined. Therefore, we need to find the values of Θ where cos Θ = 0.

The cosine function equals zero at 90° and 270° (or π/2 and 3π/2 in radians), so we have:

cos 90° = 0, cos 270° = 0

Therefore, the angles that satisfy sec Θ = undefined are:

Θ = 90° + 360°k, Θ = 270° + 360°k

where k is an integer (positive, negative, or zero) that allows us to generate all possible angles in the range 0° ≤ Θ ≤ 360°.

So, the solutions for Θ are:

Θ = 90° + 360°k, Θ = 270° + 360°k

where k is an integer.

Step-by-step explanation:

We can determine the radius of the container using the formula for a sphere's surface area because it resembles an orange and has a surface area of roughly 50.3 square inches:

A sphere's surface area equals [tex]4 r^2[/tex].

where r denotes the sphere's radius.

50.3 sq. = 4πr²

By multiplying both sides by 4, we obtain:

r² = 50.3 sq. / (4π)

r² ≈ 4

When we square the two sides, we obtain:

r ≈ 2

Hence, the spherical container has a radius of around 2 inches.

The volume of the container can now be calculated using the following formula:

A sphere's volume equals [tex](4/3)r^3[/tex].

Container volume = (4/3) X(23)

The container's volume is 33.5 cubic inches.

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Answer: y=6x^2 opens downward. y=11x^2 opens upward

Step-by-step explanation:

-6 is a negative so it opens downward. 11 is a positive number so it will open upward.

Answer: answer to 2nd mcq

Step-by-step explanation:

For (-6, 0): -6 + 3(0) = -6 + 0 = -6 ≥ -8         [true]

For (-1, -2): -1 + 3(-2) = -1 - 6 = -7 ≥ -8       [true]

For (-5, -1): -5 + 3(-1) = -5 - 3 = -8 ≥ -8       [true]

Using Distributive Property, the two expressions that is equal to 72 are

3(10+14) and 4(5+13).

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. The operations includes sum, Difference, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

Now,

The expressions using distributive property can be

3(10+14)=3*10+3*14

            =30+42

            =72

4(5+13)=4*5+4*13

            =20+52

           =72

Hence,

            the two expressions that is equal to 72 are 3(10+14) and 4(5+13).

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The steps to calculate standard deviation using a TI-84 calculator:

1.Enter the data into a list

2.Calculate the mean

3.Calculate the standard deviation

Here are the steps to calculate standard deviation using a TI-84 calculator:

1.Enter the data into a list: Press STAT, then ENTER, and then use the arrow keys to move to a list (e.g., L1, L2, etc.) and press ENTER. Enter the data into the list by typing each value followed by ENTER.

2.Calculate the mean: Press STAT, then RIGHT ARROW to select the CALC menu, and then select 1: 1-Var Stats. This will display a list of variables. Type the list name that contains the data and press ENTER. The calculator will display the mean value.

3.Calculate the standard deviation: From the same list in step 2, look for "Sx" or "σx" in the output. Sx stands for the sample standard deviation, and σx stands for the population standard deviation.

That's it! Now you know how to calculate standard deviation using a TI-84 calculator.

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The measure of angle B is given as follows:

<B = 295º.

Angles A and B in the context of this problem are reflex angles, meaning that the sum of their measures is of 360º.

The measures are given as follows:

Hence the measure of angle B is obtained as follows:

65 + <B = 360

<B = 360 - 65

<B = 295º.

The diagram modeling the situation is given by the image presented at the end of the answer.

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Note that using relationship 1 where

A = 50°; and

Y = 110°

Angle b = 70°; and

Angle c = 60°

This means that the triangle is a scalene triangle.

Since a = 50° - Given; and

y = 110° - Given

to determine the m∠b, you must use the concept of sum of angles on a straight line. Sum of angles on a straight line must always equal 180°

Thus,

b = 180 - y

b = 180 - 110

b = 70°

To determine the m∠c, we used the sum of angles in a Δ theorem. This states that all angles in Δ must equal 180°

Since

a = 50° - Given; and

b = 70° - as derived above,

c = 180 - (a + b)

c = 180 - (50 + 70)

c = 180 - 120

c = 60°

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One needs to connect the points where these arcs intersect the circle to form the desired shape. Finally, the angles need to be labeled to complete the unit circle.

A unit circle is a circle with a radius of 1. It is a tool used in trigonometry to measure angles and lengths of arcs. To calculate the length of an arc, one needs to know the angle it subtends at the center of the circle. The formula for finding this length is L = rθ, where L is the length of the arc, r is the radius, and θ is the angle subtended at the center. To fill in a unit circle, one needs to first calculate the lengths of the arcs subtended by the angles in the circle. Then, one needs to connect the points where these arcs intersect the circle to form the desired shape. Finally, the angles need to be labeled to complete the unit circle.

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The value of each of the following:

(a) 0.0837 ml

(b) 460.68 m

(c) 84 L

(d) 100￠

The denominator of a percentage (also known as a ratio or fraction) is always 100. Ram, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test.

For 6 1/5 % of 1.35 ml

⇒ 6 1/5 % = 31/5 %

⇒ 31/5 % of 1.35 ml

= 31/(5×100) × 1.35 ml

= 0.0837 ml

For 56 7/8 % of 810 m

⇒ 56 7/8 % = 455/8 %

⇒ 455/8 % of 810 m

= 455/(8×100) × 810 m

= 460.68 m

For 0.56% of 15 000 L

⇒ 0.56% of 15 000 L

= 0.56/100 × 15 000 L

= 84 L

For 2000% of 5￠​

⇒ 2000% of 5￠​

= 2000/100 × 5￠​

= 100￠​

Hence, the answers are as follows:

(a) 0.0837 ml

(b) 460.68 m

(c) 84 L

(d) 100￠

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The metric system of measurement is based on the number 10.

This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.

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The circumference of the circle is 30 cm.

Any unit for measuring length can be used to calculate the circumference, including feet, miles, metres, millimetres, etc.

By substituting 3 for, we can use the following formula to determine the circle's circumference:

C = 2πr

where r is the radius and C is the circumference.

We can observe from the provided diagram that the circle's radius is 5 cm. Thus, by changing r = 5 cm and = 3 in the formula, we obtain:

C = 2(3)(5) = 30

The circle's circumference is 30 cm as a result.

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Answer:

D)  229.05

Step-by-step explanation:

f(75) = 0.81(75) + 168.3 = 229.05

Answer: 23.56 in

Step-by-step explanation:

The perimeter of the 30-60-90 triangle with a shorter leg of 3.4 inches is 16.08 inches.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In a 30-60-90 triangle, the lengths of the sides are in the ratio of 1:√3:2, where the shortest side is opposite the 30-degree angle,

the medium side is opposite the 60-degree angle, and

the longest side is opposite the 90-degree angle.

So if the shorter leg of the triangle is 3.4 inches long, the other two sides can be found as follows:

Medium side =√3× shorter leg

= 1.732 × 3.4

= 5.88 inches

Longest side = (2 × shorter leg)

= (2 × 3.4)

= 6.8 inches

The perimeter of the triangle is simply the sum of the lengths of all three sides:

Perimeter = Shorter leg + Medium side + Longest side

= 3.4 + 5.88 + 6.8

= 16.08 inches

Therefore, the perimeter of the 30-60-90 triangle with a shorter leg of 3.4 inches is 16.08 inches.

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The amount that Ayaan will have in his tax-free savings account after 6 months of depositing $746 at 2.15% interest is $754.02.

The future value refers to the present value plus the interest.

The future value for this savings account can be computed using the simple interest system since there is no compounding of interest.

The initial deposit (present value) = $746

Interest rate = 2.15%

Savings period = 6 months

Future value = $754.02 ($746 + ($746 x 2.15% x 6/12)

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A time complexity cheat sheet is a reference guide that provides an overview of the time complexity of common algorithms and operations in computer science.

Time complexity is a measure of the amount of time an algorithm takes to solve a problem, expressed in terms of the input size of the problem. It is typically denoted using Big O notation, which provides an upper bound on the amount of time an algorithm takes.

A time complexity cheat sheet can be useful for quickly determining the time complexity of an algorithm or operation, as well as for comparing the time complexity of different algorithms. Some common time complexities that may be included in a time complexity cheat sheet are:

O(1): Constant time complexity. An algorithm with O(1) time complexity takes a fixed amount of time, regardless of the input size.

O(log n): Logarithmic time complexity. An algorithm with O(log n) time complexity takes time proportional to the logarithm of the input size.

O(n): Linear time complexity. An algorithm with O(n) time complexity takes time proportional to the input size.

O(n log n): Log-linear time complexity. An algorithm with O(n log n) time complexity takes time proportional to the input size multiplied by the logarithm of the input size.

O(n^2): Quadratic time complexity. An algorithm with O(n^2) time complexity takes time proportional to the square of the input size.

O(2^n): Exponential time complexity. An algorithm with O(2^n) time complexity takes time proportional to two raised to the power of the input size.

Other time complexities may also be included, depending on the complexity of the algorithm or operation. A time complexity cheat sheet can be a helpful tool for understanding and analyzing algorithms, but it is important to remember that time complexity is not the only factor to consider when evaluating the performance of an algorithm.

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