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salantis [7]
3 years ago
11

Solve each system of equations below by the substitution method. And show your work.

Mathematics
1 answer:
Simora [160]3 years ago
7 0
Instead of typing it all on here, I included my explanations with the work.

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Find the obtuse angle the line y-2x=7 makes with the x- axis
Kazeer [188]
In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to

tan θ =m, where m is the slope of the equation

In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.

<span>y-2x=7
y = 2x+7
dy/dx = 2 =m

So,

tan </span>θ = 2
θ = tan⁻¹(2)
θ = 63.43°
5 0
3 years ago
-4n+3&gt;23<br> A. -5<br> B. 5<br> C. -9<br> D. -20<br> E. 20
Pani-rosa [81]
It will be 20 after u subtract
6 0
3 years ago
NEED HELP!!<br><br> Complete the sentence. <br> 60% of _______ peaches is 15 peaches.
goblinko [34]
25 ! i hope this helps :)
7 0
3 years ago
A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company prod
tekilochka [14]

Answer:

C) 515 hours.

D) 500 hours

c) sample 3

Step-by-step explanation:

1. Sample 2 mean = x2`= ∑x2/n2= 2060/4= 515 hours

Sample Service Life (hours)

1                2              3

495      525            470

500         515           480

505        505            460

<u>500         515             470        </u>

<u>∑2000     2060         1880</u>

x1`= ∑x1/n1= 2000/4= 500 hours

x2`= ∑x2/n2= 2060/4= 515 hours

x3`= ∑x3/n3= 1880/4=  470 hours

2. The mean of the sampling distribution of sample means for whenever service life is in control is 500 hours . It is the given mean in the question and the limits are determined by using  μ ± σ , μ±2 σ  or μ ± 3 σ.

In this question the limits are determined by using  μ ± σ .

3. Upper control limit = UCL = 520 hours

Lower Control Limit= LCL = 480 Hours

Sample 1 mean = x1`= ∑x1/n1= 2000/4= 500 hours

Sample 2 mean = x2`= ∑x2/n2= 2060/4= 515 hours

Sample 3 mean = x3`= ∑x3/n3= 1880/4=  470 hours

This means that the sample mean must lie within the range 480-520 hours but sample 3 has a mean of 470 which is out of the given limit.

We see that the sample 3 mean is lower than the LCL. The other  two means are within the given UCL and LCL.

This can be shown by the diagram.

8 0
2 years ago
The algebraic rule for a reflection over the x-axis is one for the following:
ludmilkaskok [199]

Answer:

C

Step-by-step explanation:

When reflecting around the x axis, the x value stays the same and the y- will change.

5 0
3 years ago
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