Write the equation of a line parallel to the line y = 3x+5 and passes through the point (-7, 2)

Answer:

the answer is x=12√2

hope it helps

Answer: 1) 36 m and 60 m^2     2) 15π/2 + 10 m and 75π/4 m^2

Step-by-step explanation:

Using the pythagorean theorem in the first question, we get that the slope is 10 m so the perimeter = 10 + 14 + 6 + 6 = 36 m and the area is

(14 + 6)*6/2 = 60 m^2

So in the next question, the arc of the circle has a length of

2π*5*3/4 = 15π/2

So the perimeter is 15π/2 + 5 + 5 = 15π/2 + 10 m

And the area is 3/4*π*5*5=75π/4 m^2

Hope it helps

Answers:

16 chickens

35 pigs

========================================================

Explanation:

x = number of chickens

y = number of pigs

There are 51 heads, so x+y = 51 which solves to y = 51-x

2x = number of legs just from the chickens (2 legs per chicken)

4y = number of legs just from the pigs (4 legs per pig)

2x+4y = 172 legs total

----------

Plug in y = 51-x and solve for x.

2x+4y = 172

2x+4(51-x) = 172

2x+204-4x = 172

-2x+204 = 172

-2x = 172-204

-2x = -32

x = -32/(-2)

x = 16

Now use this to find y

y = 51-x

y = 51-16

y = 35

Since x = 16 and y = 35, this means there are 16 chickens and 35 pigs.

----------

Check:

x+y = 16+35 = 51 which works

2x+4y = 2*16+4*35 = 172 and that also works.

Both equations are confirmed.

The correlation coefficient of the number of employees and the number of products is 0.1.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

A result of zero indicates no relationship at all, therefore, independent variable.

A.) In order to find the correlation between the two quantities we need to know the mean of the two values, therefore, the mean of the number of employees can be written as,

The mean of the  number of employees

[tex]\text{Mean of the number of employees} = \dfrac{0+50+100+150+200+250+300+350+400}{9}[/tex]

[tex]\text{Mean of the number of employees} = 200[/tex]

The mean of the  number of products

Mean of the number of Products [tex]= \dfrac{100+1100+2100 +3100+ 4100 +5100+ 6100+ 7100+ 8100}{9}\\\\\\=4100[/tex]

Now, the table can be written in the following manner as shown below, using the formula of the correlation,

[tex]r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

[tex]r =\dfrac{(30 \times 10^4)}{\sqrt{(15 \times 10^4)\times (60 \times 10^6)}}\\\\r = 0.1[/tex]

B.) The given data follows the linear relationship, therefore, the function of the given data will follow the general equation of a line.

y = mx + C

If we look at the value of y when the value of x was 0,

[tex]y = mx +C \\\\100 = m(0) + C\\\\C = 100[/tex]

Substitute the value of C in any other data point we will get,

[tex]y = mx+C\\\\1100 = m(50) +100\\\\m = 20[/tex]

Hence, the function that best fits the data is y=20x+100.

C.)  The slope and y-intercept of the plot indicate that as the number of employees in the organization increases the number of products increases as well. The y-intercept shows us that if there are no employees in the company at that point the company will be able to produce 100 products on its own.

Learn more about Correlation Coefficients:

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Answer:

10 miles

Step-by-step explanation:

Distance walked in 1 hour = 4 miles

So, distance walked in 2.5 hours

= 4 miles × 2.5

= 10 miles

Answer:

last one "kiki" is true...

Answer:

Option 2 and 4

Step-by-step explanation:

2) Number of science questions = (3/4) of total questions

                              = [tex]\dfrac{3}{4}*24[/tex]

4) Number of marbles in the jar = (3/4) of the total marbles

                  [tex]=\dfrac{3}{4}*24[/tex]

Answer:

The 4th term is geometric

Step-by-step explanation:

For geometry series we use Tn = a•r^n-1

r = -3

a = 3

Use the equation Tn = 3(-3)^n-1 and you'll see that it's geometric.

Answer:

e= 2.15

Step-by-step explanation:

Subtract both sides by 6

2.15=e

Thus e is 2.15

Hope this helps!

Step-by-step explanation:

8x+ 14y= 4

-6×-7y= -10

For elimination method we can decide to eliminate either the y or x variable I'm going to eliminate the x variable so either of the one am eliminating we multiply the first equation by the coefficient of the variable we are eliminating in other words

8x +14y=4.....*-6

-6×-7y= -10......*8

-48x-84y= -24

-48x-56y= 80

then we multiply the second equation all through by -1

-48x-84y= -24

48x+ 56y= -80

28y=-104

y= 26/7

x= 8/3

Answer:

Step-by-step explanation:

Let the width is x, then the length is 2x.

Area of rectangle:

Dimensions are:

Perimeter is:

Let dimensions be x and 2x

Now

Now

Breadth=3

Length=2(3)=6

Perimeter

Answer:

Step-by-step explanation:

sin 44° = [tex]\frac{63}{ST}[/tex]

ST = [tex]\frac{63}{sin44}[/tex]

ST ≈ 90.7

Answer:

7 X = 30 + 2(x + 5)

7x = 30 + 2x + 10

7x = 40 + 2x

7x - 2x = 40 + 2x -2x

5x = 40

x=8

Answer:

x=8

Step-by-step explanation:

7 X = 30 + 2(x + 5)

7x = 30 + 2x + 10

7x = 40 + 2x

7x - 2x = 40 + 2x -2x

5x = 40

x=8

Answer:

can you make it look better

Step-by-step explanation:

The quality

Answer:

When a radius meets a tangent the angle is always 90° and the length of the radius stays constant

So you can do pythagoras theorem

A2+b2=c2

9^2+14^2=C^2

C= 16.64

C~17

Answer:

37

Step-by-step explanation:

（x+10)+x+(3x-5)=180

5x=185

x=37

The sum of angles in the triangle is 180 degrees. Therefore, the value of x in the triangle is 35

The sum of angles of a triangle is 180 degrees. This simply implies the sum of the three angles in a triangle is equals to 180 degrees.

Therefore,

x + 10 + 3x - 5 + x = 180

combine like terms

x + x + 3x + 10 - 5 = 180

5x + 5 = 180

subtract 5 from both sides of the equation

5x + 5 - 5 = 180 - 5

5x = 175

divide both sides by 5

5x / 5 = 175 / 5

x = 35

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Answer:

a) 7 in

b) 72 steps

Step-by-step explanation:

Angle of elevation formula:  [tex]tan(\theta)=\dfrac{y}{x}[/tex]

where [tex]\theta[/tex] is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.

a)  Given:

[tex]\implies tan(32)=\dfrac{y}{12}[/tex]

[tex]\implies y=12tan(32)[/tex]

[tex]\implies y=7 \ \textsf{in (nearest inch)}[/tex]

b)  Given:

⇒ Total height = 21 + 21 = 42 feet

1 foot = 12 inches

⇒ 42 feet = 42 x 12 = 504 inches

Using vertical rise of 7 in per step found in part (a):

Number of steps = 504 ÷ 7 = 72

Increased accuracy

Using unrounded vertical rise of 12tan(32):

Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step

Chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology.

Chaos theory is a branch of mathematics that studies the behavior of systems that are highly sensitive to initial conditions. The "butterfly effect" is a popular term used to describe the idea that small variations in initial conditions can lead to vastly different outcomes over time. This theory has many real-world applications in various fields.

One of the fields that makes use of chaos theory is weather prediction. Meteorologists use chaos theory to understand how small variations in atmospheric conditions can lead to large-scale weather patterns. They use computer simulations to model how different initial conditions can lead to different weather outcomes. This helps them make more accurate weather predictions and plan for extreme weather events.

Another field that uses chaos theory is finance. Financial analysts use chaos theory to understand how small fluctuations in financial markets can have a significant impact on the economy. They use mathematical models to analyze stock prices and interest rates and determine how small changes can lead to large market movements. This helps them make informed investment decisions and minimize risk.

Chaos theory is also used in biology to study the behavior of populations of animals, plants, and microorganisms. Biologists use chaos theory to understand how small changes in the environment can have a major impact on the growth and survival of populations. This helps them make informed decisions about the conservation and management of natural resources.

In conclusion, chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology. The idea that small variations in initial conditions can lead to vastly different outcomes over time is a powerful tool for understanding complex systems and making informed decisions.

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#SPJ1

x = 2

y = -1/2

multiply 1st equation by 2 to get common coefficient

6x + 4y = 10

2x + 4y = 2

‐-------------- subtract equation

4x = 8

x = 2

substitute

3×2 + 2y = 5

6 + 2y = 5

2y = -1

y = -1/2

It should cut into

2 ne t is accurate

Answer:

A)  net A

B) AB = 3 in    BC = 5 in    CD = 8.6 in

C) 106.6 in²

Step-by-step explanation:

Part A:  

Part B:

From inspection of the diagram:

Part C:

Area of a rectangle = width x length

Area of a triangle = 1/2 x base x height

Surface area = 2(4 x 8.6) + (3 x 8.6) + 2(1/2 x 4 x 3)

                     = 68.8 + 25.8 + 12

                     = 106.6 in²

Answer:

B. nonlinear

Step-by-step explanation:

Difference                        Difference

   in x                x     y            in y

                         0   -2

       1                                         1

                         1     -1

       1                                         7

                        2      6

       1                                         19

                       3     25

The difference between any two consecutive x-coordinates is 1. Each difference between any two consecutive y-coordinates is different. This means it is a nonlinear function.

Answer:

-28, -20, -12, 4, 4

Step-by-step explanation:

I really dont know how to explain this but yeah pretty much thats the answer.

Answer:

Yo hope you do not get in trouble for plagiarism

Step-by-step explanation:

The number of days for which the money is left to reach the 20,400$ mark is; 21.28 days

The final amount to be reached is; $20400

The principal amount is; $8,000 and at. rate of 4.75 % compounded.

Hence, it follows that;

Divide both sides of the equation by 8000; we have;

Take log of both sides;

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Answer:

Question 1 is A  (7/10) Question 2 is b (39/56)

Step-by-step explanation:

Answer:

11/61

Step-by-step explanation:

cos b = adj side/hypotenuse

=11/61

Answer:

CosB = B/H

Base(B)= 11

Perpendicular (P)=60.

Hypotenuse (H)= 61

CosB = B/H

CosB= 11/61

Answer:

= B

[tex]\frac{16}{40} +\frac{15}{40} = \frac{31}{40} \\\\\frac{2}{5} +\frac{3}{8} =\frac{31}{40}[/tex]

Answer:

Story

Jane is 1.7 m tall.  She stands 250 m away from the base of the Eiffel tower and looks up at the top of the building.  The angle of elevation from her eyeline to the top of the building is 45°.

Question

Calculate an estimate of the height of the building. Give your answer to the nearest meter.

Calculation

Label the sides of the triangle O, A and H (where O is the side opposite to the angle, A is the side adjacent to the angle and H is the hypotenuse).

In the triangle, the angle and side A is known, and O must be calculated.

Therefore, use the trig ratio tan(x) = O/A:

⇒ tan(40) = O/250

⇒ 250tan(40) = O

⇒ O = 209.7749078...

Assume Jane's eye-level is approximately 1.5 m above the ground.

Therefore, the Eiffel tower is approximately:

209.7749078... + 1.5 = 211.2749078.. meters tall

Rounding to the nearest meter ⇒ 211 m