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Maslowich
3 years ago
15

What is the perimeter of a rectangle with sides 2/3x+10 and 1/3x+5

Mathematics
1 answer:
gogolik [260]3 years ago
8 0

Answer:

The perimeter of the rectangle  is 2x+ 30

Step-by-step explanation:

Sides of the rectangle are 2/3x+10 and 1/3x+5

Now, Perimeter of the Rectangle = 2(Length + Breadth)

Here, sum of the sides = (\frac{2}{3}x + 10 )  + (\frac{1}{3}x + 5 )  = (\frac{2}{3}x +\frac{1}{3}x  )  + ( 10+ 5 )

adding like terms with like terms, we get

(\frac{2x + x}{3})  + 15 = \frac{3x}{3}  + 15

Hence, Sum = (x + 15)

Now,  2(Length + Breadth)  = 2(x+15) = 2x + 30

hence, the perimeter of the rectangle  = 2x+ 30

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The shape of the distribution of the time required to get an oil change at a 10 minute oil change facility is unknown. However,
lyudmila [28]

Answer:

The answer is below

Step-by-step explanation:

a) For a normal model the sample size has to be equal or greater than 30 so that it can be a normal distribution.

b) Given that:

μ = 11.2 minutes, σ = 4.8 minutes, n = 45

The z score determines how many standard deviations the raw score is above or below the mean. It is given by:

z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }

For x < 10 minutes

z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.8/\sqrt{45} }= -1.68

Therefore from the normal distribution table, P(x < 10) = P(z < -1.68) =  0.0465

7 0
3 years ago
MODELING A WATER WHEEL
kvasek [131]

Answer:

The true statements include

- This is the pattern for a sine function.

- The amplitude is 1

- The vertical shift is 0

- An equation for this graph is y = sin(x)

The only untrue statement is

- The graph follows the zero-max-zero-min-zero pattern.

Step-by-step explanation:

Observing the graph of the function presented, one can examine the options and pick the true options from them all.

Statement 1

The graph follows the zero-max-zero-min-zero pattern.

From the graph, it is obvious that this is a false claim as the graph doesn't follow a zero-max-zero-min-zero pattern, rather, its values range from 0 to 1 to 0 to -1, then it goes back to zero to repeat the cycle all over.

Statement 2

This is the pattern for a sine function.

This is true. A sine wave follows the exact pattern that this plot follows; its values range from 0 to 1 to 0 to -1, then it goes back to zero to repeat the cycle all over.

Statement 3

The amplitude is 1

This is true. The amplitude of a motion of a body refers to the maximum displacement of that body from the equilibrium position. From this plot, it is evident that that amplitude is 1 for the vertical motion of this barnacle.

Statement 4

The vertical shift is 0

The vertical shift of the plot refers to how far the equilibrium position of the motion is from the origin line (x-axis line). And for this motion and plot, the equilibrium position for the vertical motion, is placed on the x-axis, indicating a vertical shift of 0.

Statement 5

An equation for this graph is y = sin(x)

This is true. As described under statement 2 and as evident from the corresponding values of x and y from the plot; with x in radians, the values of y can be obtained by taking the sin of the value of x, indicating that this plot is a plot of y = sin x

Hope this Helps!!!

7 0
3 years ago
Read 2 more answers
PLEASE HELP 20 POINTS<br> solve the system of equations y=-5x-7 and -4x-3y=-1 by substitution.
Ainat [17]

Answer:

Solution: x = -2; y = 3 or (-2, 3)

Step-by-step explanation:

<u>Equation 1:</u>  y = -5x - 7  

<u>Equation 2:</u> -4x - 3y = -1

Substitute the value of y in Equation 1 into the Equation 2:

-4x - 3(-5x - 7)  = -1

-4x +15x + 21 = -1

Combine like terms:

11x + 21 =  - 1

Subtract 21 from both sides:

11x + 21 - 21 =  - 1 - 21

11x = -22

Divide both sides by 11 to solve for x:

11x/11 = -22/11

x = -2

Now that we have the value for x, substitute x = 2 into Equation 2 to solve for y:

-4x - 3y = -1

-4(-2) - 3y = -1

8 - 3y = -1

Subtract 8 from both sides:

8 - 8 - 3y = -1 - 8

-3y = -9

Divide both sides by -3 to solve for y:

-3y/-3 = -9/-3

y = 3

Therefore, the solution to the given systems of linear equations is:

x = -2; y = 3 or (-2, 3)

Please mark my answers as the Brainliest if you find this helpful :)

7 0
3 years ago
Please help me! Given (x+a)(x+b) = x^2+x-12, what is the value of a^2+b^2
Sonja [21]
(x + 4) (x - 3)
a = 4
b = -3

a^2 + b^2 = ...
= 4^2 + (-3)^2
= 16 + 9
= 25
4 0
3 years ago
Suppose you are given two angles A and B in which angle a is equal to angle b. If the measure of a compliment of angle a is equa
zepelin [54]
5x + 20 = 90 - a = 90 - (3x + 40)
5x + 20 = 90 - 3x - 40 = 50 - 3x
5x + 3x = 50 - 20
8x = 30
x = 30/8 = 15/4

b = 3(15/4) + 40 = 45/4 + 40 = 51.25
The measure of a supplementary angle is 180 - 51.25 = 128.75
 
4 0
3 years ago
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