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Elodia [21]
3 years ago
13

(ED. 21) Analytic Geometry Unit Test..... #3 Which point is a solution of x2 + y2 > 49 and y ≤ –x2 – 4?

Mathematics
1 answer:
sdas [7]3 years ago
8 0

Answer:

We want to find a solution of the system:

x^2 + y^2 > 49

y ≤ –x^2 – 4

Here we do not have any options, so let's try to find a general solution.

First, we can remember that the equation of a circle centered in the point (a, b) and of radius R is:

(x - a)^2 + (y - b)^2 = R^2

If we look at our first inequality, we can write it as:

x^2 + y^2 > 7^2

So the solutions of the first inequality are all the points that are outside (because the symbol used is >) of the circle of radius R = 7 centered in the origin.

From the other equation, we would get:

y ≤ –x^2 – 4

This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.

Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.

You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:

by looking at the graph, we can see a lot of points that are solutions, like:

(0, -10)

(0, -15)

(2, -10)

etc.

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KengaRu [80]

Answer:

Square root of 87.35 will be plotted between 9 and 10 as shown below.

Step-by-step explanation:

We are given that, 'The number line is numbered in tenths'

Also, the square root of 87.35 is given by,

\sqrt{87.35}=9.4

That is, we have to plot the point 9.4 on the number line numbered in tenths.

As, 9.4 will lie between the points 9 and 10.

Thus, we get that square root of 87.35 will be plotted between 9 and 10 as shown below.

8 0
3 years ago
3 1/2x +4 1/3=7 2/9 does anyone know how to do this?????
saw5 [17]
I hope this helps you

5 0
3 years ago
Is the number -14 irrational ?
Alenkinab [10]
I think it is irrational
5 0
2 years ago
Read 2 more answers
Adam currently runs about 40 miles per week, and he wants to increase his weekly mileage by 30%. How many miles will Adam run pe
BigorU [14]

Answer:

52 miles/week (12 more miles per week)

Step-by-step explanation:

In order to know the miles per week with this increasement, we'll use the rule of 3, assuming that 40 miles is the 100% innitially so:

If:

40 miles --------->100%

X miles ----------> 30%

Solving for X we have the following:

X = 30 * 40 / 100 = 12 miles

So, if Adam wants to increase his weekly mileage by 30%, he needs to run 12 more miles, and that makes a total of 52 miles/week

6 0
2 years ago
You can upgrade lighting at your factory to LED bulbs that cost $6.95 each and last an average of 5 years. It costs S3 in labor
marshall27 [118]

Answer:

11.95 dollars

Step-by-step explanation:

Cost of one LED bulb = 6.95 dollars

Cost of changing one bulb = 3 dollars

Life of each bulb = 5 years.

In 10 years, only one time after 5 years the bulbs would have been changed

Hence cost of 100 lamps = 695 and

cost of changing once = 500

Total cost = 1195 dollars for 11 years

Divide this by 10 years to get average cost per year

Cost of 100 lamps per year = 1195/100 = 11.95 dollars


8 0
3 years ago
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