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3 years ago

The circle below is centered at (2, 3) and has a radius of 4. What is its equation?

Mathematics

1 answer:

disa [49]3 years ago

4 0

Answer:

Step-by-step explanation:

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$ where h and k are the center of the circle and r is the radius. Filling in:

$(x-2)^2+(y-3)^2=16$

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Solve the system of linear equations by substitution.<br> 3x + y = -9<br> y=5x+7

11Alexandr11 [23.1K]

Answer:

The solution is x = -2, y = -3

Step-by-step explanation:

Let's start with the equation 3x + y = -9

Substitute the y for 5x+7 seen in the second equation

Now you have 3x + (5x+7) = -9

Lets solve:

Let's add the x's

Now we have 8x + 7 = -9

Substracy seven from each side

Now we have 8x = -16

Now let's divide 8 on each side

Now we have x = -2

Now lets plug in -2 to the second equation

The second equation is y = 5x+7

When we plug in -2 we get y=5(-2)+7

We multiply

We now have y = -10+7

Add

y = -3

The solution is x = -2, y = -3

8 0

3 years ago

What is the value of x? show work

Alona [7]

2x+38=180
2x=142 (or x+x=142 from which 2x=142)
x=71

The unknown angles are each 71

You know this answer is logical as, since two sides are 21 it hints that we are looking at an equilateral triangle, which means two of its angles will be the same

7 0

3 years ago

22. Use your model to determine when the volume of oil will get down to 500 gallons.

Helen [10]

Answer:

21. y = 75000·0.935^t

22. after 74.6 days

23. y = 27.8112·1.18832^t

24. 18.8% per month

25. 1748

Step-by-step explanation:

22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)

23. y = 27.8112·1.18832^t (see the second attachment)

24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.

(1.18832 -1) × 100% ≈ 18.8% . . . . per month

25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.

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<em>Comment on graphing calculator</em>

A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.