2q-r=p, r=q-s, p=q+2r prove s=2r

Bearing is a topic that deals with angles and distance. Thus, the required answers to the given question are:

i. Distance of 1034.2 miles

ii. Bearing of \(158^{o}\)

The speed of an object is the rate of movement of the object with time.

speed = \(\frac{distance}{time}\)

So that:

distance = speed x time

i. In the given question; let the initial distance covered be represented by d, so that:

d = 250 x 2

  = 500 miles

ii. Let the second distance covered by the pilot be represented by D, so that:

D = 300 x 2

   = 600 miles

iii. Thus let the distance to the starting point be represented by x. From Cosine rule, we have:

\(c^{2}\) = \(a^{2}\) + \(b^{2}\) - 2abCos C

\(x^{2}\) = \(500^{2}\) + \(600^{2}\) - 2(500 x 600)Cos \(140^{o}\)

   = 250000 + 360000 - 600000(-0,7660)

   = 610000 + 459600

   = 1069600

x = \(\sqrt{1069600}\)

  = 1034.22

x = 1034.2 miles

Using the Sine rule to determine the required internal angle, we have:

\(\frac{a}{Sin A}\) = \(\frac{c}{Sin C}\)

\(\frac{500}{Sin A}\) = \(\frac{1034.22}{Sin 140}\)

Sin A = \(\frac{500*0.6428}{1034.22}\)

         = 0.3108

A = \(Sin^{-1}\) 0.3108

   = 18.11

A = \(18^{o}\)

To determine angle B, we have:

140 + 18 + B = 180 (sum of angles in a triangle)

158 + B = 180

B = 180 - 158

  = 22

B = \(22^{o}\)

Thus, the required bearing is 180 - 22 = 158

Therefore the distance and bearing required to fly to starting point are 1034.2 miles and \(158^{o}\) respectively.

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Answer:

x=−17

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

1) 2 (5x+9) = 6x+26 --> 10x + 18 = 6x + 26

This is because you would multiply 2 by the numbers inside the parentheses.

2)  10x + 18 = 6x + 26  --> 4x +18 = 26

You would subtract the 6x from each side so it would cancel out the 6 on the right and you would get 4x on the left.

3) 4x +18 = 26 --> 4x = 8

Subtract 18 from both sides canceling out the 18 on the left and giving you 8 on the right.

4) 4x = 8 --> x = 2

Divide both sides by 4.

Answer: The answer is 2:3 4:6.

Step-by-step explanation: 2 x 4 = 8. 3 x 4 = 12.

4 x 2 = 8. 6 x 2 = 12. Hope this works! :) If not I am sorry :(

some possible equations equivalent to 2x+3y=12 would be:

1)

y=−2x+12/3

written form:

y= negative 2x plus 12 over/divided by 3

2)

y=−2/3x+4

written form:

y= negative 2 over/divided by 3x plus 4

3)

y=4−2/3x

written form:

y= 4 minus 2 over/divided by 3x

4)

y=12−2x/3

written form:

y= 12 minus 2x over/divided by 3

those are all i could think of! Hope this helped :)

If its too complicated comment and ill try to simplify it. remember ITS NEVER WRONG TO ASK QUESTIONS!!!

The equivalent expression for the equation 2x + 3y = 12 are:

x = 6 - 3y/2

y = 4 - 2x/3

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

2x + 3y = 12

We need to find an equivalent expression for this equation.

We can have many forms:

Case 1.

2x + 3y = 12

Subtracting 3y on both sides.

2x + 3y - 3y = 12 - 3y

2x = 12 - 3y

Dividing 2 into both sides.

x = 12/2 - 3y/2

x = 6 - 3y/2

Case 2.

2x + 3y = 12

Subtracting 2x on both sides.

2x + 3y - 2x = 12 - 2x

3y = 12 - 2x

Dividing 3 into both sides.

y = 12/3 - 2x/3

y = 4 - 2x/3

Thus the equivalent expression for the equation 2x + 3y = 12 are:

x = 6 - 3y/2

y = 4 - 2x/3

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The missing values are 8 and 23.

Missing x : 8

Missing y : 23

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

x      y

4     17

6     19

__   21

10   __

The missing values are 8 and 23.

The table has linear relationships.

This means,

There is an increase of 2 with the x values.

There is also an increase of 2 with the y values.

Thus,

The missing values are 8 and 23.

Missing x : 8

Missing y : 23

Option A is the correct answer.

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Answer:

534.07cm² * 0.35=186.9245 dollar

Answer:714,000

Step-by-step explanation:

Answer:

714000

Step-by-step explanation:

The ordered pair which s included in the solution to this system of inequality y ≥ 2/3x + 2, y < - 1/3x + 1 is (-6, -2) and (-6, 3).

The correct answer option is option B and C

y ≥ 2/3x + 2

y < - 1/3x + 1

Check all that applies:

(x, y) = (−6, −3)

(x, y) = (−6, −2)

(x, y) = (−6, 3)

(x, y) = (−6, 4)

y ≥ 2/3x + 2

substitute x = -6 into the inequality

y ≥ 2/3(-6) + 2

y ≥ -12/3 + 2

y ≥ - 4 + 2

y ≥ - 2

(x, y) = (-6, -2)

y < - 1/3x + 1

substitute x = -6 into the inequality

y < -1/3(-6) + 1

y < 6/3 + 1

y < 2 + 1

y < 3

(x, y) = (-6, 3)

So therefore, the solution to the system of inequality is (-6, -2) and (-6, 3).

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Answer:

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
0.0755 * 100 = 7.55%

Step-by-step explanation:

To find the percentage of 1 - 3√(5/35), we need to first evaluate the expression.

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755

To convert this decimal to a percentage, we simply multiply by 100:

0.0755 * 100 = 7.55%

The derivative of the function is dy/dx = 20x⁴ - 2

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative.

Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

y = 4x⁵ - 2x + 3   be equation (1)

Now , the derivative of the function is

dy / dx ( 4x⁵ ) = 20x⁴

dy / dx ( -2x ) = -2

dy / dx ( 3 ) = 0

So , on further simplification , we get

dy / dx ( 4x⁵ - 2x + 3 ) = 20x⁴ - 2

Hence , the derivative of the function is 20x⁴ - 2

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The answer is C. There is a positive linear relationship between player height and number of points scored for basketball players in the coach's state.

A confidence interval is a range of values that is calculated from the data and is believed to contain the true population parameter with a certain level of confidence, in this case 96%. The slope of the regression line is the average change in y for a one unit change in x, which represents the direction and strength of the relationship between x and y.

The confidence interval for the slope is (−0.432,1.844), which does not include 0, which means that the slope is not equal to 0. If the slope were 0, there would be no relationship between player height and points scored. The fact that the confidence interval is positive means that the slope is positive, which indicates a positive linear relationship between player height and number of points scored.

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So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros

Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.

Here,

To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:

120 + 72 + 68 = 260

The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:

0.4615 x 1600 = 738.40 euros

Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:

0.2769 x 1600 = 443.04 euros

The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:

0.2615 x 1600 = 418.56 euros

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Complete question:

The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?

Answer:

it took Goran 1 hour longer to clean the bathroom than it took him to clean the den.

Step-by-step explanation:

Answer:

To convert 3 1/2 hours to an improper fraction:

3 1/2 = 7/2

So, Goran took a total of:

1/8 + 7/2 = 8/8 + 28/8 = 36/8 = 4 1/2 hours

Thus, it took Goran:

4 1/2 - 3 1/2 = 1 hour longer to clean the bathroom.

Explanation:

To solve the problem, we first need to convert the mixed number 3 1/2 to an improper fraction. We can do this by multiplying the whole number (3) by the denominator of the fraction (2) and adding the numerator (1):

3 x 2 + 1 = 7

So, 3 1/2 is equal to 7/2.

Next, we can add the time it took Goran to clean the den (1/8 hours) to the time it took him to clean the bathroom (7/2 hours):

1/8 + 7/2 = 8/8 + 28/8 = 36/8 = 4 1/2 hours

Therefore, it took Goran a total of 4 1/2 hours to clean both the den and the bathroom.

To find out how much longer it took Goran to clean the bathroom, we can subtract the time it took him to clean the den (1/8 hours) from the time it took him to clean both the den and the bathroom (4 1/2 hours):

4 1/2 - 3 1/2 = 1 hour

Therefore, it took Goran 1 hour longer to clean the bathroom than it took him to clean the den.

Answer:

The answer is 40.

Step-by-step explanation:

Calculate within the parenthesis. After calculate the outside by the inside.

4.352 rounded to the nearest tenth

Is 4.4

Answer:

4.4

Step-by-step explanation:

The nearest tenTH is the number right after the decimal point. To identify, look at the next digit see if its greater than half way or exactly halfway then you will know when to add an extra tenth.

Answer:

1 5/8

Step-by-step explanation:

Answer:

1 and 5/8

Step-by-step explanation:

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Answer:

13/40

Step-by-step explanation:

Answer

Yes, zero is contained in the interval

Answer:

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Step-by-step explanation:

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Answer:

The size of the investment after 40 years is of $74,872.

Step-by-step explanation:

Continuous compounding:

The amount of money, in continuous compounding, after t years, is given by:

\(y(t) = y(0)(1+r)^t\)

In which y(0) is the initial investment and r is the interest rate, as a decimal.

You decide to continuously invest $5000 of your income each year in a risk-free investment with a 7% yearly interest rate compounded continuously.

This means that \(y(0) = 5000, r = 0.07\). So

\(y(t) = y(0)(1+r)^t\)

\(y(t) = 5000(1+0.07)^t\)

\(y(t) = 5000(1.07)^t\)

What is the size of your investment after 40 years?

This is y(40), that is, y when t = 40. So

\(y(t) = 5000(1.07)^t\)

\(y(40) = 5000(1.07)^{40}\)

\(y(40) = 74872\)

The size of the investment after 40 years is of $74,872.

To make lines u and v parallel, the indicated angle must be 108°.

So, if two parallel lines n and m intersect, then all the angles generated in line m must be exactly the same as the angles generated in line n.

According to the second (and previously used) criterion, we must have:

When we solve that, we get:

Therefore, to make lines u and v parallel, the indicated angle must be 108°.

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The probability that at most 2 of the next 10 callers have to wait more than 8 minutes is the sum of the probabilities of 0, 1, or 2 callers having to wait for more than 8 minutes which is 0.810

The probability that at most 2 of the next 10 callers having to wait can be defined using the expression :

P(X ≤ 2) = P(0) + P(1) + P(2)

Using the individual probabilities given by the histogram attached :

P(X ≤ 2) = 0.181 + 0.345 + 0.284

P(X ≤ 2) = 0.810

Therefore, the probability that at most 2 callers have to wait more than 8 minutes is 0.810

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Answer:

Option (B)

Step-by-step explanation:

x² + x - 1) x³ + 6x² + 0x + 5 ( x + 5

           - (x³ +   x²  -  x)

                      5x² + x + 5

                    -(5x² + 5x - 5)

                             -4x + 10

Result : \(x+5+\frac{-4x+10}{(x^{2}+x-1)}\)

By the comparing the result with the Lorie's solution,

She made a mistake in the last step in which she combined the constant incorrectly.

Therefore, Option (B) will be the answer.

Answer:

False

Step-by-step explanation:

3 out of 2 can be represented as 3/2 which simplified is 1.5, This statement is saying that out of 1 person, 1.5 of them have trouble with fractions which isn't possible because 2/2 is the whole amount, so anything above 2/2 is simply not possible in this scenario

The equation of the line is: y = -3/5x + 1.

The slope (m) of two lines that lie perpendicular to each other are negative reciprocals.

Given, y = 5/3x - 3, the slope (m) of the line is 5/3. The negative reciprocal of 5/3 is -3/5.

Thus, the line that is perpendicular to it will have a slope (m) of -3/5.

Substitute m = -3/5 and (a, b) = (5, -2) into y - b = m(x - a):

y - (-2) = -3/5(x - 5)

y + 2 = -3/5x + 3

y + 2 - 2 = -3/5x + 3 - 2

y = -3/5x + 1

Thus, the equation of the line is: y = -3/5x + 1.

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Answer: A a aa a a a a a

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

A=2πrh+2πr2=2·π·3·20+2·π·32≈433.53979

Answer:

Hey! so the answer is $750

Step-by-step explanation:

Here is why: $550 is how much money someone already has in their account. After that you have 3% simple interest each year. 3% of 550 is 16.5. Do 16.5x10 and you will get 165. 165 plus the money already in someones account would equal $750.

Hoped this helped Im Eve btw. Hope you have a great day and consider marking this brainliest Thank you so much if you do! ✨