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3 years ago

Is the given point interior, exterior, or on the circle (x + 2)2 + (y - 3)2 = 81? Q(3, 0)

1 answer:

8 0

Answer: interior

From the given equation you know that the center of the circle is (-2,3) and the radius is √81 = 9

You know that all the points that are at a distance smaller than 9 from the center (-2,3) are interior. This results pretty obvious to me but I will make the calculations for you.

Use the distance formula for the points (3,0) and (-2,3):

d = √[ (x1 -x2)^2 + (y1 -y2)^2 ] = √[ (3-(-2))^2 + (0 - 3)^2 ] =√[25 + 9] = √36 = 6

Given that 6 < 9, the point is interior to the circle.

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6 3/4 min = seconds?

Leokris [45]

60x6=360
360+45=405 hope this helps

4 0

3 years ago

Read 2 more answers

A manufacturing plant earned \$80$80dollar sign, 80 per man-hour of labor when it opened. Each year, the plant earns an addition

vagabundo [1.1K]

Answer:

$A(t)=80(1.05)^t$

Step-by-step explanation:

The manufacturing plant earned $80 per man-hour of labor when it opened

The plant earns an additional 5% for every additional man-hour t.

This can be modeled using the function:

$A(t)=P(1+r)^t$

where Initial Amount Earned, P=80

Rate of Increase, r=5%=0.05

Therefore, the function that models the amount earned at any time t is:

$A(t)=80(1+0.05)^t\\A(t)=80(1.05)^t$

3 0

4 years ago

Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Lostsunrise [7]

Answer:

The correct options, rearranged, are:

Options:

$A)(a^2+ab+b^2)/(a-b)\\\\B)(a^2-ab+b^2)/(a+b)\\\\C)(a^3+0a^2+0ab^2-b^3)/(a+b))\\\\ D)(a^3+0a^2+0ab^2-b^3)/(a-b)$

And the asnwer is the last option (D).

Explanation:

You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.

The difference of two perfect cubes may be represented by:

$a^3-b^3$

And it is, as a very well known special case:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Then, to prove, it you must divide the left side, $a^3-b^3$ , by the first factor of the right side, $a-b$

Note that, to preserve the places of each term, you can write:

$(a^3-b^3)=(a^3+0a^2+0ab^2-b^3)$

Then, you have:

$(a^3+0a^2+0ab^2-b^3)=(a-b)(a^2+ab+b^2)$

By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:

$(a^3+0a^2+0ab^2-b^3)/(a-b)=(a^2+ab+b^2)$

That is the last option (D).

3 0

3 years ago

Read 2 more answers

Solve the system of equationsy=6x^2-5x+1,y=-2x+4

lubasha [3.4K]

Answer:

Solutions are (1,2) and (-1/2,5)

Don't forget to like rate and mark brainliest!

Step-by-step explanation:

y=6x^2-5x+1

y=-2x+4

Substitute

-2x+4=6x^2-5x+1

Simplify

0=6x^2-3x-3

Solve by factoring

(x-6/6)(x+3/6)=0

x-1=0, x+1/2=0

x=1, x=-1/2

Plug x's into oringinal equation

y=-2(1)+4, y=-2(-1/2)+4

y=-2+4, y=1+4

y=2, y=5

Write out solutions

(1,2) and (-1/2,5)

7 0

3 years ago

The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the func

Hunter-Best [27]

Answer:

A) (-5,7)

Step-by-step explanation:

Functions and Relations

A set of values A can have a relation with another set B as long as at least one element of A has at least one image in B. Functions are special relations where each element of A (the domain of the function) has one and only one image on B (the range of the function).

By looking at the options, we can see that x=9, x=-8, and x=-1 already have defined values in Y, so if we define another value for any of them the relation will stop being a function. The only possible choice to preserve the function is the option

$\boxed{A)\ (-5,7)}$

8 0

4 years ago