MATHEMATICS HIGH SCHOOL

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

Answers

Answer 1

Answer:

Answer: The co-ordinates of the center are (-7, -1) and length of the radius is 6 units.

Step-by-step explanation: The given equation of a circle is as follows :

$x^2+y^2+14x+2y+14=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the co-ordinates of the center and the length of the radius of the circle.

We know that

the standard equation of a circle with center at the point (h, k) and radius r units is given by

$(x-h)^2+(y-k)^2=r^2.$

From equation (i), we have

$x^2+y^2+14x+2y+14=0\n\n\Rightarrow (x^2+14x+49)+(y^2+2y+1)+14-49-1=0\n\n\Rightarrow (x+7)^2+(y+1)^2-36=0\n\n\Rightarrow (x+7)^2+(y+1)^2=36\n\n\Rightarrow (x-(-7))^2+(y-(-1))^2=6^2.$

Comparing with the standard equation, we get

the co-ordinates of the center, (h, k) = (-7, -1)

and

length of the radius, r = 6 units.

Thus, the co-ordinates of the center are (-7, -1) and length of the radius is 6 units.

Answer 2

Answer: (-7, -1), 6 units Is The Answer

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Three added to 8 times a number is the same as 3 times the value of 2 times the number minus 1. what is the number?

Answers

Let the number be y;
3+8y=3(2y-1)
8y+3=6y-3
Putting like terms together;
8y-6y=-3-3
2y=-6
y=-3
The number is -3

Answer: The required number is -3.

Step-by-step explanation: Given that three added to 8 times a number is the same as 3 times the value of 2 times the number minus 1.

We are to find the number.

Let x represents the given number.

Then, according to the given information, we have

$8x+3=3(2x-1)\n\n\Rightarrow 8x+3=6x-3\n\n\Rightarrow 8x-6x=-3-3\n\n\Rightarrow 2x=-6\n\n\Rightarrow x=-(6)/(2)\n\n\Rightarrow x=-3.$

Thus, the required number is -3.

Can anyone help me out with this

Answers

Answer:

X = 62.4

Step-by-step explanation:

To find x or the weight of water per one cubic foot we take the 12.48 and divide it by two

12.48 = 6.24

Then multiply 6.24 by ten because 6.24 is the weight of .1 cubic feet

6.24 * 10 = 62.4

To check and make sure we calculated it correctly we can do 6.24 * 17 to find the weight of the larger tank

6.24 * 17 = 106.08

And 6.24 * 15 to find the weight of the smaller tank

6.24 * 15 = 93.6

The subtract 93.6 from 106.08

106.08 - 93.6 = 12.48 which was the difference in weight between the two tanks.

The function f(x) = −x2 − 9x + 10 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does it represent?A: x = 1; the diver jumps in the pool at 1 foot per second
B: x = 10; the diver jumps in the pool at 10 feet per second
C: x = 1; the diver hits the water 1 foot away horizontally from the board
D: x = 10; the diver hits the water 10 feet away horizontally from the board

Answers

Answer
C: x = 1; the diver hits the water 1 foot away horizontally from the board

Explanation
The question requires you to solve for x.
f(x) = −x² − 9x + 10

When f(x)=0

−x² − 9x + 10 = 0
= x²+9x-10 = 0
The product in this expression is -10
The factors of this expression is 9
Factors are 10 and -1.

x²+9x-10 = x²-1x+10x-10 = 0
=x(x-1)+10(x-1) = 0
=(x+10)(x-1) = 0
This means that;
x+10=0 or x-1=0
x = -10 x = 1.
Since distance can not be negative, x =1.

Answer:

x = 1; the diver hits the water 1 foot away horizontally from the board

Step-by-step explanation:

took the test :)

Factor completely 49x2 − 81

Answers

49x2 - 81
(7x - 9)(7x + 9)

Answer:

(7x + 9)(7x -9)

Step-by-step explanation:

3. Suppose you invest $5,000 in a continuously compounded interest account. After four years,your account balance was $6,230. What interest rate were you earning on this account?
Convert your answer to percent and round your answer to the nearest tenth(one decimal
place).

Answers

Step-by-step explanation:

FV = PV e^(rt)

6230 = 5000 e^(4 r) <====solve for 'r' = 5.5 %

A group of students is taking a CPR course. The total cost for the course is $275. The room in which the course will be held can hold a maximum of 25 people, including the instructor. What is the minimum number of students needed to take the course so that the cost per student will be less than $15? A. 11 B. 17 C. 18 D. 19