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3 years ago

What is the equation of the circle passing through the point (6,5) and centered at (3.-4)?

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

3 0

Answer:

(x - 3)² + (y + 4)² = 90 or [3√10)²

Step-by-step explanation:

We need to calculate the radius of this circle. To do this we calculate the distance from the center (3, -4) to the point (6, 5).

As we move from (3, -4) to (6, 5), x (the run) increases by 3 and y (the run) increases by 9. Thus, the distance between these points, according to the Pythagorean Theorem, is

r = √[3² + 9²], or r = √90, or r = 3√10.

Using the standard equation of the circle, (x - h)² + (y - k)² = r², we obtain

(x - 3)² + (y + 4)² = 90 or [3√10)²

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271+425 use rounding or compatible numbers to estimate the sum

Irina-Kira [14]

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3 years ago

PLEASE ANSWER RN!! Which statement can be represented by the equation Two-fifths x + 9 = 9? Two-fifths of nine is a number. Two-

nadezda [96]

Answer:

Step-by-step explanation:

(2/5)x + 9 = 9 is equivalent to (2/5)x = 0

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3 years ago

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Wilton collected $8.50 in dimes and quarters while cleaning his father's truck. If the number of quarters is 3 times the number

dusya [7]

Answer:

Wilton found 10 dimes while cleaning his father's truck.

Step-by-step explanation:

Given that:

Total amount collected = $8.50 = 8.50*100 = 850 cents

Let,

x be the number of dimes

y be the number of quarters

According to given statement,

10x+25y=850 Eqn 1

y = 3x Eqn 2

Putting y=3x in Eqn 1

$10x+25(3x)=850\\10x+75x=850\\85x=850$

Dividing both sides by 85

$\frac{85x}{85}=\frac{850}{85}\\x=10$

As x represents dimes, therefore, number of dimes is 10.

Hence,

Wilton found 10 dimes while cleaning his father's truck.

8 0

3 years ago

Please use statemnet reasoning!

dlinn [17]

Answer:

lineHO parallel lineEN - Given

lineHW = lineNW - Given

angle HWO congruent angle EWN Vertical Angles

angle OHW congruent angle ENW Alternate interior angles

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2 years ago

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Find an upper limit for the zeroes 2x^4 -7x^3 + 4x^2 + 7x - 6 = 0

erik [133]

Answer-

2 is the upper limit for the zeros.

Solution-

The given function f(x) is,

$2x^4 -7x^3 + 4x^2 + 7x - 6 = 0$

For calculating the zeros,

$\Rightarrow f(x)=0$

$\Rightarrow 2x^4 -7x^3 + 4x^2 + 7x - 6 = 0$

$\Rightarrow 2x^4-4x^3-3x^3+6x^2-2x^2+ 4x+3x-6=0$

$\Rightarrow 2x^3(x-2)-3x^2(x-2)-2x(x-2)+3(x-2)=0$

$\Rightarrow (x-2)(2x^3-3x^2-2x+3)=0$

$\Rightarrow (x-2)(x^2(2x-3)-1(2x-3))=0$

$\Rightarrow (x-2)(x^2-1)(2x-3)=0$

$\Rightarrow (x-2)(x+1)(x-1)(2x-3)=0$

$\Rightarrow x-2=0,\ x+1=0,\ x-1=0,\ 2x-3=0$

$\Rightarrow x=2,\ x=-1,\ x=1,\ x=\frac{3}{2}$

From all the 4 roots, it can be obtained that 2 is the greatest zero.

7 0

2 years ago