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Step2247 [10]
2 years ago
13

6y+12=-2x x+3y=-6 In y form

Mathematics
1 answer:
Vlada [557]2 years ago
4 0

Answer:

  both equations reduce to y = -1/3x -2

Step-by-step explanation:

In each case, subtract the term not containing y and divide by the coefficient of y.

1.  6y = -2x -12 . . . . 12 was subtracted from both sides

  y = -1/3x -2 . . . . . . the equation was divided by 6

__

2. 3y = -x -6 . . . . . . x was subtracted from both sides

  y = -1/3x -2 . . . . . the equation was divided by 3

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A ½in diameter rod of 5in length is being considered as part of a mechanical linkagein which it can experience a tensile loading
Evgesh-ka [11]

Answer:

a. Maximum Load = Force = 27085.09 N

b. Maximum Energy = 3.440 Joules

Step-by-step explanation:

Given

Rod diameter = ½in = 0.5in

Length = 5in

Young's modulus = 15.5Msi

By applying the 0.2% offset rule,

The maximum load the rod can hold before it gets to breaking point is given as follows by taking the strain as 0.2%

Young Modulus = Stress/Strain ------- Make Stress the Subject of Formula

Stress = Strain * Young Modulus

Stress = 0.2% * 15.5

Stress = 0.002 * 15.5

Stress = 0.031Msi

Calculating the area of the rod

Area = πr² or πd²/4

Area, A = 22/7 * 0.5^4 / 4

A = 22/7 * 0.25 / 4

A = 5.5/28

A = 0.1964in²

The maximum load that the rod would take before it starts to permanently elongate is given by

Force = Stress * Atea

Force = 0.031Msi * 0.1964in²

Force = 31Ksi * 0.1964in²

Force = 6.089Ksi in²

Force = 6.089 * 1000lbf

Force = 6089 lbf

1 lbf = 4.4482N

So, Force = 6089 * 4.4482N

Force = 27085.09 N

b.

Using Strain to Energy Formula

U = V×σ²/2·E

Where V = Volume

V = Length * Area

V = 5 in * 0.1964in²

V = 0.982in³

σ = Stress = 0.031Msi

= 0.031 * 1000Ksi

= 31Ksi

= 31 * 1000psi

= 31000psi

E = Young Modulus = 15.5Msi

= 15.5 * 1000Ksi

= 15.5 * 1000 * 1000psi

= 15500000psi

So,

Energy = 0.982 * 31000²/ ( 2 * 15500000)

Energy = 943,702,000/31000000

Energy = 30.442in³psi

------- Converted to ftlbf

Energy = 2.537 ftlbf

-------- Converted to Joules

Energy = 3.440 Joules

7 0
3 years ago
ASK YOUR TEACHER Two streets meet at an 84° angle. At the corner, a park is being built in the shape of a triangle. Find the are
Alla [95]

Answer:

22,203 ft^2

Step-by-step explanation:

The area of a triangle with angle ∅ and two sides a and b is;

Area A = 1/2 × absin∅ ......1

The park is in the shape of a triangle, with two sides and an angle given;

Given;

a = 190 ft

b = 235 ft

∅ = 84°

Substituting the values into equation 1;

Area of the park;

A = 1/2 × 190 × 235 × sin84°

A = 22,202.70131409 ft^2

A = 22,203 ft^2 (to the nearest whole number)

Area of the park is 22,203 ft^2

3 0
2 years ago
3 (4x + 7) = 43; 12x + 21 = 43
777dan777 [17]

Answer:

Distributive property

Explanation:

You are distributing the 3 to the parenthesis to get 12x+21 =43

6 0
3 years ago
Read 2 more answers
Which fraction is equivalent to 4/-9 ?<br><br> A) -4/9 <br> B) 4/9 <br> C) -4/-9 <br> D) 9/4
Art [367]
The answer is A  hope this helps

4 0
3 years ago
Read 2 more answers
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found t
Wittaler [7]

Answer:

a=30 +1.04*8=38.32

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.  

C) 38.32

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Solution to the problem

Let X the random variable that represent the waiting time in minutes of a population, and for this case we know the distribution for X is given by:

X \sim N(30,8)  

Where \mu=30 and \sigma=8

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

We want to find a value a, such that we satisfy this condition:

P(X>a)=0.15   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.04

And if we solve for a we got

a=30 +1.04*8=38.32

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.  

C) 38.32

7 0
3 years ago
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