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allochka39001 [22]
3 years ago
11

Find the standard equation of a circle that passes through the point (−1, 1) with center (2, 3).

Mathematics
1 answer:
Firlakuza [10]3 years ago
6 0
The equation of a circle is
  (x-h)² + (y-k)² = r²
for center (h, k) and radius r. Of course, the radius can be computed by putting the point in the equation.
  (x-2)² + (y-3)² = (-1-2)² + (1-3)² = 9+4 = 13

The standard equation of the circle is (x-2)² + (y-3)² = 13.

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Gap sells jeans that cost $21.00 for a selling price of $29.95. The percent of markup based on cost is
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If Gap sells jeans that cost $21.00 for selling price of $29.95. The percent of markup based on cost is approximately 43%. The markup in price is exactly $8.95.
3 0
3 years ago
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The sum of 4 consecutive even integers is -12. find the largest integer.
Ipatiy [6.2K]

Answer:

The largest even integer is 0

Step-by-step explanation:

Given as :

The sum of four consecutive even number = - 12

Let The first even number = 2 x

The second even number = (2 x + 2)

The third even number = (2 x + 4)

The fourth even number = (2 x + 6)

<u>According to question</u>

sum of four consecutive even number = - 12

Or, 2 x + (2 x + 2) + (2 x + 4) + (2 x + 6) = - 12

Or, (2 x + 2 x + 2 x + 2 x) + (2 + 4 + 6) = - 12

Or, 8 x + 12 = - 12

Or, 8 x = - 12 - 12

Or, 8 x = - 24

∴  x = \frac{- 24}{8}

i.e  x = - 3

now, putting the value of x

The first even number = 2 × - 3 = - 6

The second even number = (2 × - 3 + 2) = - 6 + 2 = - 4

The third even number = (2 × - 3 + 4) = - 6 + 4 = - 2

The fourth even number = (2 × - 3 + 6) = - 6 + 6 = 0

So, The largest even integer = 0

Hence, The largest even integer is 0  Answer

6 0
3 years ago
Tony Stark is trying to improve his Iron Man suit by increasing its power. One modification will cost $350 million, of which the
statuscvo [17]
69 Nicce elon musk would be proud
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3 years ago
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It will take Adam four hours to drive to Disney Park, and 2.5 times less time if driving 45 mph faster. What is the distance Ada
Mashcka [7]
<h2>Hello!</h2>

The answer is:

The distance to over by Adam to get to the park is 108 miles.

<h2>Why?</h2>

To solve the problem, we need to write two equations using he given information about the times and his speed.

So,

For the first equation we have: Travel to Disney Park

time=4hours

Distance=v*4hours

For the second equation we have: Travel back from Disnery Park

time=4hours-2.5hours=1.5hours

Speed=v+45mph

Distance=(v+45mph)*1.5hours

Then, if Adam covered the same distance going and coming back, we have:

v*4hours=(v+45mph)*1.5hours

v*4hours=v*1.5hours+45mph*1.5hours

v*4hours-v*1.5hours=45mph*1.5hours

v*2.5hours=67.5miles

v=\frac{67.5miles}{2.5hours}=27\frac{miles}{hour}=27mph

We have that the speed when he was going to Disney Park was 27 mph.

Now, to calculate the distance, we need to substitute the obtained speed in any of the two first equations.

Therefore, substituting the speed into the second equation, we have:

Distance=(v+45mph)*1.5hours

Distance=(27mph+45mph)*1.5hours=72mph*1.5hours=108miles

Hence, we have that the distance that Adam should cover to get to the park is 108 miles.

Havea nice day!

8 0
3 years ago
Prove that the median to the hypotenuse of a right triangle is half the hypotenuse,
REY [17]

Answer:

D. 2

Step-by-step explanation:

M(0,2b)

N(2a,0)

Then the midpoint P coordinates are

P\left(\dfrac{2a+0}{2},\dfrac{0+2b}{2}\right)\Rightarrow P(a,b)

Use distance formula to find OP and MN:

OP=\sqrt{(a-0)^2+(b-0)^2}=\sqrt{a^2+b^2}\\ \\MN=\sqrt{(2a-0)^2+(2b-0)^2}=\sqrt{4a^2+4b^2}=2\sqrt{a^2+b^2}

So,

MN=2OP

or

OP=1/2 MN

Click to let others know, how helpful is it

7 0
2 years ago
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