How do you find the area of a 30 60 90 triangle?

The value of the expression  0.3k - 4m is 14. 14 is a constant term.

What is an expression?

There are numerous branches of mathematics. Arithmetic is the branch of mathematics that deals with numbers and their operations. Arithmetic taught us how to add, subtract, multiply, and divide two or more numbers.

An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4a - 5 is an expression in which the terms 4m and 5 are separated by the arithmetic sign - and a is the variable of the given expression.

Given expression is  0.3k - 4m.

To find the value of  0.3k - 4m, when k =20 and m =-2 put the values in the given expression.

Putting k =20 and m =-2 in  0.3k - 4m

0.3k - 4m

= 0.3 × 20 - 4 × (-2)

=6.0 + 8

= 14

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To determine the separation between two points in a coordinate plane, we analyze the distance formula. We can use this to study the connections between points and resolve mathematical issues.

A mathematical method called the distance formula is used to determine how far apart two points in a coordinate plane are from one another. The Pythagorean Theorem, which states that the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, is the source of the formula. We must first ascertain the coordinates of each point in order to compute the distance between them. The first point's coordinates are (x1, y1), and the second point's coordinates are (x2, y2). then, the separation between The formula d = (((x2-x1)2 + (y2-y1)2) can be used to identify the two points. This formula can be applied to several mathematical issues, including the analysis of point relationships.

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The probability that none of the shoes are black is 51.2%.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given twenty percent of the shoes in a factory are black,

probability of black shoes = 0.2

probability of not getting a black shoe = 1 - 0.2

probability of not getting a black shoe = 0.8

shoes selected three times and each time the shoe is replaced,

probability for each time is 0.8

for three times = 0.8 x 0.8 x 0.8

total probability = 0.512

probability in percent = 0.512 x 100 = 51.2%

Hence the probability is 51.2%

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450 envelopes if Binita decides to purchase them. Binita will have to pay 0.72 pounds (£) in order to purchase the envelopes from Value World.

Calculating the cost of value in the world is the second step.

Cost =  450 / 25 × 3.29

Cost = 59.22

The second step is to calculate the cost of value world

Cost = 450 /30 × (1.95 ×2)

Cost = 58.50

Let's now determine how much it would cost to purchase envelopes from Value World.

Cost = 59.22 - 58.50

Cost = 0.72 pounds

As a result, the price is 0.72 pounds.

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The airplane is  368.6 feet from the base of the tower

as the details stated above,

the angle of elevation from his line of sight is 19 degrees

the air traffic controller observer is located at the top of a  building of height  is 120 feet

let the distance from the plane and the tower be x

to find the value of the distance we have to use the sine rule or sine function.

sin A = opposite side of the triangle by the hypotenuse side of the triangle

where A is 19 degrees

the opposite side is the observer located at a distance of 120 feet

therefore,

sin 19 = 120/x

=> 120 / sin 19 = x

=> x = 368.6 feet

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x + y = 1

2x - y = 4

The answer is: (5/3; -2/3)

The height at which the air pressure equals 65% of the air pressure at the surface of the earth is -ln(0.65P0)/0.0012 meters.

An equation is a mathematical statement that shows the equality of two expressions. It can be written in a variety of forms, including an equation with an equals sign, an inequality with a greater than or less than sign, or a system of equations with multiple variables. Equations can be used to solve problems, model real-world scenarios, and explore relationships between different quantities.

To solve this problem, we can rearrange the equation to find the height h, given the pressure P. The rearranged equation is h=-ln(P/P0)/0.0012. Substituting 65% of the surface pressure for P, we get h=-ln(0.65P0)/0.0012. Therefore, the height at which the air pressure equals 65% of the air pressure at the surface of the earth is -ln(0.65P0)/0.0012 meters.
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Answer:

Surface area = 31.42

Step-by-step explanation:

A=2πrh+2πr²=2·π·1.25·2.75+2·π·1.25²≈31.41593

For a set population, a parameter does not change. A parameter is a numerical value that describes some aspect of a population, such as the mean, median, or standard deviation.

It is a fixed value that represents the entire population and does not change as new data is collected.

If there are three different samples of the same size from a set population, it is possible to get three different values for the same statistic.

Because a sample is a subset of a population, the values of statistics calculated from samples will vary depending on the specific individuals or observations that are included in the sample. Even if the samples are of the same size, they will likely have different values for the statistics because of the randomness of sampling.

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Answer:

write a letter to your friends in another school and direct him or her to visit your school

18 3/4 because 600/32

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

Since the two prisms are similar, the ratios of each of the sides of the larger prism to the corresponding sides of the smaller prism must be the same

[tex]\dfrac{16}{4} = \dfrac{24}{6} = \dfrac{x}{1} = 4[/tex]

So each side of the larger prism is 4 times the corresponding side of the smaller prism

[tex]\dfrac{x}{1} = 4\\\\x = 4[/tex]

As given 4x+y<2 but y>-2, so the only linear inequality are 4x+(-1)<2, 4x+(0)<2 and 4x+(1)<2, graph these three and we have it.

Linear functions are used in mathematical linear inequalities. Because both sides in these functions are not equal, an equal sign cannot be used to denote them. In general, an inequality can be both an algebraic inequality and a generic inequality.

The definition of a linear inequality includes expressions with unequal sides. In this case, the equal sign is replaced by the symbols greater than, less than, greater than or equal to, and less than or equal to. Inequality can take many different forms. These three types of inequality are rational, absolute value, and polynomial.

The graph for the given linear inequality is given below↓↓↓

Every point in the dark purple zone represents

4x + y < 2

y > -2

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Answer:

Step-by-step explanation:

Let's call the number of women in the club "W", the number of men in the club "M", and the number of children in the club "C".

We may deduce from the facts provided that:

The club has a membership of 60 people.

Because women make up half of the club's membership, W = 60 / 2 = 30.

Because there are three times as many women as males in the club, W = 3M.

The remaining members of the club are youngsters, therefore C = 60 - W - M

The male-to-child ratio is n:1.

We know that W=30 from the first equation.

We may use the second equation to replace in the value of W to get 3M = 30. So, M = 30/3 = 10.

We can calculate the number of children in the club by inserting the values of W and M: C = 60 - W - M = 60 - 30 - 10 = 20

Now we may calculate the child-to-male ratio: C:M = 20:10 = 2:1. As a result, the value of n is 2.

Answer:

n=2

Step-by-step explanation:

Total 60 people in the club

Half are women ==> number of women = 60/2 = 30

Rest are are  men and women so rest = 30

This number is 3 times number of men

Number of men = 30/3 = 10

Number of children = 30 -10 = 20

Ratio of children to men: 20:10 or 2:1

So n= 2

Answer:

Shorter leg of triangle: 4cm

Step-by-step explanation:

So, we are told   is the longer leg, let's say this is a. [tex]4\sqrt{15} = \sqrt{240}[/tex], the Pythagorean theorem is [tex]a^2+b^2=c^2[/tex] , we'll say b = shortest leg, which is what we're solving for.

Since the hypotenuse (c), is 4 times b I changed it to 4b in my equation. [tex]\sqrt{240} + b =4b[/tex], square this to get [tex]240 + b^2 = 16b^2[/tex], -b^2 on both sides, [tex]240 = 15b^2[/tex]  then divide by 15. [tex]16=b^2[/tex] , use square root and you get 4 = b. To find hypotenuse, which isn't needed for your answer multiply by 4.

Hypotenuse: 16 cm

Shorter leg: 4 cm

The binomial formula to find the coefficient of the t^17q^2 term in the expansion of (t+2g) ¹⁹ is 32.06.

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a. Graph the system:

The two lines will intersect at the point (2,-5). The first line will cross the y-axis at (0, 1), and the second line will cross the y-axis at (0, -6). The lines will be in different slope-intercept form.

What exactly is a math graph?

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

b. What are the equations of the lines:

To find the equations of the lines, we can use the point-slope form of a line: y - y1 = m(x - x1)

Given the point (0,1) on the first line, the slope of the first line is m = (y2 - y1) / (x2 - x1) = (-5 - 1) / (2 - 0) = -3

so the equation of the first line is y = -3x + 1

Given the point (0,-6) on the second line, the slope of the second line is m = (y2 - y1) / (x2 - x1) = (-5 - (-6)) / (2 - 0) = 1/2

so the equation of the second line is y = 1/2x - 6

c. Check that (2,-5) is the solution of the system of equations you wrote in problem 2b.

To check that (2,-5) is the solution of the system of equations we need to substitute x=2 and y=-5 in both equations

for the first equation:

-5 = -3*2 + 1 = -6 + 1 = -5

for the second equation

-5 = 1/2*2 - 6 = 1 - 6 = -5

as we can see that both equation are true for x=2 and y=-5 so the point (2,-5) is the solution of the system of equations.

The graph will be two lines crossing each other at point (2,-5) and both lines crossing the y-axis at different points (0,1) and (0,-6) respectively.

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The value of x for the triangle is 11 units.

In geometry, the ray, line, or segment that divides a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. It splits one angle into two smaller congruent angles, to put it another way.

Given a Triangle PQR,

QS is the angle bisector

and measure of sides as given in the figure,

QP = 31.2, QR 26, and SR = 5,

let the measure of PS be a

and x = PS + SR

according to angle bisector property,

A triangle's opposite side is split into two segments by an angle bisector that is proportional to the triangle's other two sides.

so QP/PS = QR/SR

31.2/a = 26/5

a = 31.2*5/26

a = 6

x =  PS + SR

x = 6 + 5 = 11

Therefore, a measure of x is 11 units.

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The complete question is in the image,

The factor of the given expression [tex]x^4-5x^2-36=0[/tex] is -2i, 2i, -9 and 9.

In the given question, we have to find the solutions of the equation [tex]x^4-5x^2-36=0[/tex] using factoring to solve.

The given polynomial is [tex]x^4-5x^2-36=0[/tex].

We can write this expression as

[tex](x^2)^2-5x^2-36=0[/tex]

The multiplication of first and third term is 36 and the middle term is 5. So the possible factors are 4 and 9.

So the factor of the given expression is

[tex](x^2)^2-(9-4)x^2-36=0[/tex]

[tex](x^2)^2-9x^2+4x^2-36=0[/tex]

Now taking the common

[tex]x^2(x^2-9)+4(x^2-9)=0[/tex]

[tex](x^2+4)(x^2-9)=0[/tex]

Now taking the factor equal to zero.

[tex]x^2+4=0[/tex]

Subtract 4 on both side, we get

[tex]x^2 = -4[/tex]

Now taking the square root on both side, we get

[tex]x = -2i,+2i[/tex]

The second factor is

[tex]x^2-9=0[/tex]

Add 9 on both side, we get

[tex]x^2=9[/tex]

Taking square root on both side, we get

[tex]x = 9,-9[/tex]

Now the factor of the given expression [tex]x^4-5x^2-36=0[/tex] is -2i, 2i, -9 and 9.

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when two values are multiplied together, the result will be a new value that is the sum of the two original values multiplied by each other. Therefore, the product of XA and X+b is X2 + Xb.

The product of XA and X+b is XA(X+b).

XA(X+b) = X(A)(X+b) = X2 + Xb

The product of XA and X+b can be expressed as XA(X+b). This is the same as X(A)(X+b), which can be further expanded to X2 + Xb. This means that when two values, XA and X+b, are multiplied together, the result is a new value that is the sum of X2 and Xb. In other words, the product of XA and X+b is the sum of X multiplied by itself and X multiplied by b. This means that when two values are multiplied together, the result will be a new value that is the sum of the two original values multiplied by each other. Therefore, the product of XA and X+b is X2 + Xb.

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The diapers of brand B that cost $39.99 for 100 diapers is a better buy that the diapers of brand A that cost $24.94 for 60 diapers.

We must utilize the unitary method in this elementary algebra issue, which is nothing more than figuring out the price per diaper in both of the cases. The cost per diaper from Brand A which has 60 diapers worth $24.94 is to be determined. As a result, since 60 diapers cost $24.94, 1 diaper must cost $24.94/60, or around 42 cents per diaper. When we repeat the job for the Brand B, we see that 100 diapers cost $39.99, making 1 diaper cost $39.99/100, or 40 cents per diaper. Now that each diaper costs less when bought from Brand B, it turns out to be a superior purchase.

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Answer:

m<1=41°

Step-by-step explanation:

m<1 and m<4 are vertically opposite angles, making them equal. We know m<4=41°, so we can say m<1=41° too.

The estimated gradient of the curve at x=3 is given by the value of m.

Tangent is a line or surface that touches a curve or curved surface at one point and is perpendicular to the curve or surface at that point. It is a fundamental concept in geometry and calculus and can be used to calculate the slope of a curve at any given point. It also has many applications in engineering, physics, and other fields.

The gradient of the curve at x=3 can be estimated by the tangent drawn on the graph. In the diagram, the gradient of the tangent is given by the slope of the line, m. This can be determined using the formula, m= $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Plugging in the coordinates of the point of tangency on the graph and the coordinates of a point on the tangent, we get:

m= $\frac{f(3)-f(4)}{4-3}$

Therefore, the estimated gradient of the curve at x=3 is given by the value of m.

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Segment QS is not a radius of Circle P because it is diameter.

The rate of the number of haircuts to the number of days as -

{r} = 15.25.

Given is that the barber cuts 61 haircuts in 4 days.

We can write the rate for the ratio of the number of haircuts to the number of days as mentioned below -

{r} = 61/4

{r} = 15.25

Therefore, the rate of the number of haircuts to the number of days as -

{r} = 15.25.

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The total number of pupils in the class will be 25.

Solution can be found with a simple calculation.

In the question, it has been given that,

In order to find how many pupils are there in the class ( the total )

Calculate by assuming the unknown quantity as a character

Let total number of pupils be 'p'

So,

No. of pupil that swim = (3/5)p

                                      = 3p/5

No. of pupil that dance = (3/5)p

                                       = 3p/5

5 pupils do both swim and dance.

Since both the counting include these 5 pupils, we will take the 5 away. Thus subtracting the 5

The equation will be,

3p/5 + 3p/5 - 5 = p

6p/5 - 5 = p

6p - 25 = 5p

6p - 5p = 25

p = 25

Hence, the total number of pupils in the class is 25.

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The combined rate of the two pipes is 8/30 of the pool per hour.

To find the time it takes for both pipes to fill the pool together, we can use the formula for finding the combined rate of two processes.

Let's call the rate of the large pipe L and the rate of the small pipe S. We know that L can fill the pool in 6 hours and S can fill the pool in 10 hours, so we can set up the following equations:

L = 1/6

S = 1/10

The combined rate of the two pipes is simply the sum of the individual rates:

L + S = 1/6 + 1/10

We can simplify this expression by finding a common denominator:

L + S = (5/30) + (3/30) = 8/30

So, the combined rate of the two pipes is 8/30 of the pool per hour. To find the time it takes for both pipes to fill the pool together, we can use the formula:

Time = Pool size / Combined rate

Since we do not have the pool size, we cannot determine the exact time it takes. However, we can see that the combined rate is greater than either of the individual rates, so it would take less time for both pipes to fill the pool together than for either one alone.

Therefore, The combined rate of the two pipes is 8/30 of the pool per hour.

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The combined rate of the two pipes is 8/30 of the pool per hour.

To find the time it takes for both pipes to fill the pool together, we can use the formula for finding the combined rate of the two processes.

Let's call the rate of the large pipe L and the rate of the small pipe S. We know that L can fill the pool in 6 hours and S can fill the pool in 10 hours, so we can set up the following equations:

L = 1/6

S = 1/10

The combined rate of the two pipes is simply the sum of the individual rates:

L + S = 1/6 + 1/10

We can simplify this expression by finding a common denominator:

L + S = (5/30) + (3/30) = 8/30

So, the combined rate of the two pipes is 8/30 of the pool per hour. To find the time it takes for both pipes to fill the pool together, we can use the formula:

Time = Pool size / Combined rate

Since we do not have the pool size, we cannot determine the exact time it takes. However, we can see that the combined rate is greater than either of the individual rates, so it would take less time for both pipes to fill the pool together than for either one alone.

Therefore, The combined rate of the two pipes is 8/30 of the pool per hour.

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The required value of k will the system of linear equations has infinite number of solutions is 8.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given set of equations is

kx + 4y = k - 4 ...(i)

16x + ky = k ...(ii)

We apply Cramer's rule to find the value of k.

Here,

D = k² - (16 × 4)

= k² - 64

= (k + 8) (k - 8)

D1 = k (k - 4) - 4k

= k² - 4k - 4k

= k² - 8k

= k (k - 8)

D2 = k² - 16 (k - 4)

= k² - 16k + 64

= (k - 8)²

= (k - 8) (k - 8)

For infinite number of solutions, we must have

D = 0 = D1 = D2

⇒ k = 8,

since (k - 8) is the common factor in D, D1 and D2.

∴ the required value of k is 8.

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