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3 years ago

Eight times the reciprocal of a number equals 4 times the reciprocal of 10.

Mathematics

1 answer:

saveliy_v [14]3 years ago

8 0

Answer:

8(1/x) = 4(1/10)

Step-by-step explanation:

lets say the number is x

eight times the reciprocal of a number equals 4 times the reciprocal of 10

8 * 1//x = 4 * 1/10

8/x = 4/10 , cross multiply

4x =8*10, divide both sides by 4

x= 80/4

x= 20

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12) The school that Danielle goes to is selling tickets to a choral performance. On the first day of

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Answer:

Senior citizen tickets = $9

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Step-by-step explanation:

We begin by converting these into simultaneous linear equation;

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Student tickets = b

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5a = 144 - 9b

a = 144/5 - 9b/5

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We now substitute this into the first equation

14(28.8 - 1.8b) + 6b = 192

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6 0

3 years ago

The diameter of a circle has length 12. The center is at*(-5, 2). Give the equation

labwork [276]

Answer:

Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

Step-by-step explanation:

Let us consider the image attached in the answer area.

The center O has the co-ordinates i.e. (-5,2) and the diameter given is 12 units.

We know that radius is half of diameter.

$\text{Radius = }\dfrac{\text{Diameter}}{2}$

$\text{Radius = }\dfrac{12}{2}\\\Rightarrow \text{Radius = 6units}$

The equation for circle given the center and radius, can be represented as:

$(x-a)^{2}+ (y-b)^{2} = r^{2}$

Where (a,b) is the co-ordinate of center and r is the radius.

Let us consider the following formula:

$(p+q)^2 = p^{2}+ q^{2} +2pq\\(p-q)^2 = p^{2}+ q^{2} -2pq$

$(x-(-5))^{2}+ (y-2)^{2} = 6^{2}\\\Rightarrow (x+5)^{2}+ (y-2)^{2} = 36\\\Rightarrow x^{2} + 25 + 10x +y^{2} + 4-4y=36\\\Rightarrow x^{2} + 10x +y^{2} -4y-7=0$

Hence, Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

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3 years ago