How do you use the substitution method with three variables?.

On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

θ = 30 °

terminal point = cos 30° , sin30°

= (underroot 2 , 1/2 )

tan30° = 1/ underroot 3 = underroot3/3

On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.

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When Richter scale magnitude is less 3. 0 to 3. 9, the frequency of occurrence in the whole world will be over 100,000 per year.

The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the change in distance between different seismographs and the epicenter of the earthquake). The original formula is: [tex]Mₗ = log_{10}(A) - log_{10}(A₀ ) = log_{10}( \frac{A}{ A₀}) \\ [/tex]. The classification starts with "small" for magnitudes between 3.0 and 3.9, where earthquakes generally begin to be felt, and ends with "major" for magnitudes greater than 8.0, where significant damage is expected. The National Earthquake Information Center now locates about 20,000 earthquakes worldwide each year, or about 55 per day.

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To calculate my grade in class 10 divide your total points by the total points possible.

Total points earned divided by total points possible

The maximum amount of points you may have obtained in the course is referred to as total points possible.

The total number of available points in a class with 50 participation points, 50 homework points, 100 essay points, and 200 test points is 400. If you received 330 points in this class, divide that number by 400 to get a quotient of 0.825, This is equivalent to an 82.5% grade, or a low B.

Divide the total by the number of entries to get a percentage. Divide the total by 30, for instance, if you have % grades for 30 activities. Your final grade is expressed as a percentage by the quotient.

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There was 1200 men and 800 women at the funfair in the morning

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let x represent the number of men and y represent the number of women in the morning.

There are 400 more men than women at a funfair in the morning. Hence:

x = y + 400

x - y = 400     (1)

In the afternoon 2/5 of the men and 1/4 of the women left the funfair. hence:

number of men remaining = x - (2/5)x = (3/5)x

number of women remaining = y - (1/4)y = (3/4)y

There were 120 more men than women remaining at the funfair. therefore:

(3/5)x - (3/4)y = 120     (2)

From both equations:

x = 1200, y = 800

There was 1200 men in the morning

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Answer:

They are perpendicular!

Step-by-step explanation:

Get 7x-3y=-21 into y=mx+b format.

7x-3y=-21           Bring 7x to the other side

-3y=7x-21          Divide -3 by both sides, it cancels out on the y's side.

y=-7/3x+7       Two negatives equal a positive, that it why 7 is positive.

y=-7/3x+7 is the line, the other is y=-3/7x+5

The slope of this line is -7/3 , the slope of the given line is -3/7.

Lines are perpendicular if the slopes are opposite reciprocals, such as this.

So, while they intercept at different points on the y-axis, they will intersect at some point! This makes them perpendicular.

The following triangles are congruent.

Yes AAA

Answer:

7

Step-by-step explanation:

La tasa unitaria de salvamentos por juego es de 7 salvamentos por juego. Esto se puede calcular dividiendo el número total de guardados (35) por el número de juegos (5): 35 guardados / 5 juegos = 7 guardados por juego.

The expression $(4 - 5i) - (-2i - 8) + (-1 + 8i) is simplified to $5i -11

Algebraic expressions are defined as expressions that are  composed of variables, coefficients, factors, constants and terms.

These expressions are likely to consist of some arithmetic operations, such as;

From the information given, we have that;

$(4 - 5i) - (-2i - 8) + (-1 + 8i)

expand the bracket

$4 - 5i + 2i +8 - 1 + 8i

Now, collect like terms

$-5i +2i + 8i +4 +8 - 1

Add or subtract the like terms

$5i -11

Hence, the expression is $5i -11

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Answer:

One ft2 of sod costs $10.14 and one pot of ivy costs $0.24

Step-by-step explanation:

We can use the information provided to find the cost of one ft2 of sod and the cost of one pot of ivy.

To find the cost of one ft2 of sod, we can divide the total cost of sod by the total area of sod:

Cost of 1 ft2 of sod = (71 / 7) = $10.14/ft2

To find the cost of one pot of ivy, we can divide the total cost of ivy by the total number of pots:

Cost of 1 pot of ivy = (76 - 71) / (11 + 10) = $5 / 21 = $0.24/pot

So one ft2 of sod costs $10.14 and one pot of ivy costs $0.24

Keep in mind that these calculations only give approximate prices since it's not specified that the cost of ivy and sod is the same, but it's just an estimation based on the information that you provided.

Answer: 4,000 people live in condominiums.

Step-by-step explanation:

First add 55%+25%=80%

Then subtract 100%-80%=20%

Then turn 20% to 0.2.

Last, multiply 0.2x20,000= 4,000

The average cost of the given question is $115.11.

Average Cost:

The average cost is the total cost of goods divided by the number of units produced or sold. It is used to determine the cost of each unit produced or sold. Without more information about your costs and the number of products you have produced or sold, it is not possible to determine the average cost.

To calculate the average cost of the product, you will need to subtract the gross margin percentage from 100% and then divide the result into the selling price.

First, convert the gross margin percentage to a decimal: 3% = 0.03

Then, subtract the gross margin from 1: 1 - 0.03 = 0.97

Finally, divide the selling price by the result: 111.55 / 0.97 = 115.11

So your average cost is $115.11

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The expression which represents the amount Gabe spent at the mall will be 18.58k + 52.

The amount that Gabe spent if he bought 3 items will be $107.74.

From the information, Gabe goes to the mall. If k is the number of items he bought, the expression 18.58k+30 gives the amount he spent in dollars at one store and he spent 22 dollars at another store.

The expression which represents the amount Gabe spent at the mall will be:

= 18.58k + 30 + 22

= 18.58k + 52

The amount that Gabe spent if he bought 3 items will be:

= 18.58k + 52

= 18.58(3) + 52

= $107.74

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Time-series Plot graph is the best choice for determining the change in the stock market over time.

The term stock exchange refers to several exchanges where shares of publicly traded companies are bought and sold. Such financial activities are conducted through formal stock exchanges and over-the-counter (OTC) markets that operate under a specific set of regulations.

Other major stock exchanges in the world are Tokyo Stock Exchange (Japan), Shanghai Stock Exchange (China) and London Stock Exchange (UK). Stock exchanges are considered capital markets as they provide long-term financing for companies.

A time series chart, also known as a time series chart or time series graph, is a data visualization tool that plots data points at successive time intervals. Each point on the chart corresponds to both time and quantity being measured.

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You can draw a 100 degree angle with the help of Protractor.

A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.

Each of the 360 equal segments that make up a rotation is referred to as a degree. We use a circle ° to represent a degree. 180°, for instance, denotes 180 degrees. An angle in degrees is an angle whose measure is expressed in degrees.

Follow the given steps to construct a 100-degree angle with the help of a protractor.

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Answer:The steps in solving the quadratic function 7x – 9 = 7x^2 – 49x by completing the square are as follows:

Add and subtract (49/2)^2 = (36) to the right-hand side of the equation to complete the square. This gives us:

7x - 9 = 7x^2 - 49x + 36

Factor out the coefficient of the x^2 term, which is 7, on the right-hand side of the equation. This gives us:

7x - 9 = 7(x^2 - 7x + 6)

Take the square root of the number inside the parenthesis and add and subtract it, to get:

7x - 9 = 7(x - 3.5)^2 - 2.25

Now we can add 9 to both sides of the equation to get:

7x = 7(x - 3.5)^2 + 0.75

Now we can divide both sides by 7 to get:

x = (x - 3.5)^2 + 0.75/7

Now we can solve the equation by taking the square root of both sides and adding and subtracting 3.5 to get:

x = 3.5 ± √(x^2 - 7x + 6)

Now we have our solutions, x = 3.5 + √(x^2 - 7x + 6) and x = 3.5 - √(x^2 - 7x + 6) which are the solutions of the quadratic equation.

Step-by-step explanation:

Answer:

56, 112, 16

Step-by-step explanation:

I just know

Aditi and Kavita had 40 coins in total. the coin share b/w them is

x=25, y=15

Generally, Aditi and Kavita's original coin total is 40.

x+y=40

Aditi gave 10 coins to Kavita.

(x-10)*(y+10)=375

Now solving a system of equations using a calculator

x=25, y=15

x=35, y=5

Since Aditi had fewer than 30 coins when she started.

The correct proportion is

x=25, y=15

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CQ

Aditi and Kavita had 40 coins in total. Aditi gave 10 coins to Kavita. The product of the coins they now have is 375. Aditi had fewer than 30 coins when she started.

How much coin did dey both have

Answer:

$0.40

Step-by-step explanation:

4% = 0.04

10 times 0.04 = $0.40

So, sale tax is $0.40

1) Triangle Midsegment Theorem will be used to solve the given problem.

2) The value of x would be 10.

What is Triangle Midsegment Theorem?

A triangle midsegment is a segment that links the midpoints of two triangle sides. A midsegment joining two triangle sides is parallel to the third side and half the length.

1) Triangle Midsegment Theorem will be used to solve the given problem.

2) Here M is the midpoint of AB, and P is the midpoint of BC. So, PM is a midsegment.

Therefore by the Triangle Midsegment Theorem,

      [tex]PM=\frac{1}{2} AC\\\\(x+5)=\frac{1}{2} 3x\\\\x=10[/tex]

 Hence, The value of x would be 10.

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The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

From the given expression ,

y = 2.5 x + 10

So, we have to find the length of line segment from x = 0 to x = 16.

so when x = 0 ,

y = 0+10

y = 10

and when x=1

y = 2.5*1+10

y=12.5

and similarly

when x = 2

y = 2.5* 2 + 10

y = 15

So, like this the sequence will be goin on y = 10 , 12.5 , 15 , 17.5 and etc .

Hence, The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.

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The ladder will now reach 21.7 ft.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is that a 45-foot ladder is placed against the side of a house so that it reaches 27 feet in height. Cooper grabs the ladder by its base and pulls it 4 feet farther away from the house.

Refer to the image attached. We can write in ΔCEB as -

EB² = 45² - 27²

EB² = (45 + 27)(45 - 27)

EB² = 72 X 18

EB² = 1296

EB = √1296

EB = 36 ft

Now -

AB = AE + EB = 36 + 4 = 40

From ΔDAB, we can write -

BD² = 45² - 40²

BD² = (45 + 40)(45 - 40)

BD² = 95 X 5

BD² = 475

BD = 21.7 ft

Therefore, the ladder will now reach 21.7 ft.

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To write 3 more than 5, we use the mathematical operation of addition and the notation 5 + 3 = 8.

To write 3 more than 5, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 5 + 3 = 8.

This notation means that we are adding 3 to 5, which results in 8. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is 8.

Another way to write 3 more than 5 is to use the phrase "5 plus 3". This phrase indicates that we are adding 3 to 5 to get 8.

Therefore, In short, to write 3 more than 5, we use the mathematical operation of addition and the notation 5 + 3 = 8. This means that we are adding 3 to 5, resulting in 8. It can also be written as "5 plus 3", indicating the same operation.

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Different types of multiplication method is given by :

a. Addition method

b. Vertical method

c. Box method

d. Partial multiplication method

As given in the question,

Different types of the multiplication method are as follow :

a. Addition method :

In addition method if 4 × 3 it means add 4 three times.

4 + 4 + 4 = 12

b. Vertical method :

It is traditional way of multiplying the given numbers . Example : 12 × 4

1 2

×4

48

c. Box method :

In this box was formed as per the given numbers . Example 42 × 13

           10          3

40     400         120

2       20           6

Add : 400 + 120 + 20 + 6 = 546

d. Partial multiplication method :

This method is based on distributive property to make the calculation easy.

45 × 6

= ( 40 + 5 ) × 6

= 40 × 6 + 5 × 6

= 240 + 30

= 270

Therefore, the different types of multiplication methods are:

a. Addition method

b. Vertical method

c. Box method

d. Partial multiplication method

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10 is the least 2-digit number having 0 on one's place and 1 on ten's place.

There are just two place values in 2-digit numbers: the units place and the tens place. Every number with more than one digit has various digits, each of which is described by its place value. 2-digit numbers range in value from 10 to 99. In other words, the smallest and largest 2-digit numbers are 10 and 99, respectively. When a number has two digits, it is called a 2-digit number. 2-digit numbers have two digits and range from 10 to 99.

Any number between 1 and 9 can be used as the digit in the tens place. The placement of each digit in a number is known as place value. There is just one place value that matters when discussing 1-digit numbers, and that is the ones place.

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Answer:

24 inches.

Step-by-step explanation:

In order for a triangle to be obtuse, one of its angles must be greater than 90 degrees. In a right triangle, the angle opposite the hypotenuse is always 90 degrees, so in order for the triangle to be obtuse, the hypotenuse must be the longest side.

To find the lowest whole number side length in inches that would ensure that the triangle is obtuse, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

a^2 + b^2 < c^2

If we take the base 48cm and convert it to inches, 48cm = 48*0.393701 = 18.897638 inches

So the base is 18.897638 inches.

Now we have to find the lowest whole number side length of c so that:

18.897638^2 + b^2 < c^2

358.565744 + b^2 < c^2

We can see that the lowest whole number of c is 24 inches.

So, the lowest whole number side length in inches that would ensure that the triangle is obtuse is 24 inches.

Step-by-step explanation:

0.22222222222222222222222222

The product of numbers , 3× 3×3×3 is equals to the eighty-one.

In mathematics, a product is a number or result that is obtained by multiplying two or more numbers together. So, 12 is the product of 3 and 4. For example product of 5 and 4 is represented by 5 × 4 = 20 , it is a multiplication expression. A multiplication expression has three parts, a multiplier ( i.e., 4) , a multiplicand ( i.e., 5), and the product ( i.e., 20). We have, a multiplication expression as 3×3×3×3. We can rewrite it in form 3¹× 3¹ ×3¹× 3¹ = 3¹⁺¹⁺¹⁺¹ = 3⁴ , it is an exponential form number. Therefore, results is equals to 81. So, the required product value is 81.

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For each 45-45-90 triangle, the period of the hypotenuse equals the length of the leg expanded via the square root of 2. That is the 45-45-90 Triangle Theorem.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is greater than thousand years vintage, having been described at the very first web page of Euclid's elements.

In Euclidean geometry, any 3 elements, at the same time as non-collinear, determine a very precise triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean area). In special words, there's exceptional one plane that includes that triangle, and each triangle is contained in some plane. If the complete geometry is best the Euclidean plane, there is the fine one aircraft and all triangles are contained in it; however, in better-dimensional Euclidean areas, this isn't actual. this text is prepared triangles in Euclidean geometry, and specifically, the Euclidean plane, besides in which otherwise said.

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On Solving we get that the zero of the polynomial "3x -9" is x = 3 .

The polynomial function is a type of function which involves only non negative integer powers or involves only positive integer exponents of a variable in an equation .

the polynomial function is given as : 3x-9 ;

to find the zeros of the polynomial we equate the given polynomial to zero(0) .

we get ; 3x - 9 = 0 ;

⇒ 3x = 9 ;

dividing both sides by 3 ,

we get ;

⇒ x = 3 .

Therefore , the zero is x = 3 .

The given question is incomplete , the complete question is

What is the zero of the polynomial "3x - 9" ?

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There are seven types of fractions.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part is denominator.

consider a fraction 1/8.

Here, numerator is 1, denominator is 8

When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8

The types of fractions are:

1) Proper fraction -  the numerator is always less than the denominator

2) Unit Fractions - the numerator of fraction is always 1

3) Improper fraction -  the numerator is greater than the denominator

4) Mixed fraction - it is a combination of a natural number and fraction

5) Like fractions - the fractions have the same denominators

6) Unlike fractions - the fractions have the different denominators

7) Equivalent fractions - the fractions have the same value when simplified.

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Step-by-step explanation:

answer is 567