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JulijaS [17]
11 months ago
10

Need help with homework

Mathematics
1 answer:
motikmotik11 months ago
4 0

We have two points describing the diameter of a circumference, these are:

\begin{gathered} A=(-12,-4) \\ B=(-4,-10) \end{gathered}

Recall that the equation for the standard form of a circle is:

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

Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.

For this we use the following equation:

M=(\frac{x_1+x_2_{}_{}}{2},\frac{y_1+y_2}{2})

Now, we replace and solve:

\begin{gathered} M=(\frac{-12+(-4)}{2},\frac{-4+(-10)}{2} \\ M=(\frac{-12-4}{2},\frac{-4-10}{2}) \\ M=(\frac{-16}{2},\frac{-14}{2}) \\ M=(-8,-7) \end{gathered}

The center of the circle is (-8,-7), so:

\begin{gathered} h=-8 \\ k=-7 \end{gathered}

On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation:

r^2=\Delta x^2+\Delta y^2

In this case, we will solve the delta with the center coordinate and the B coordinate.

\begin{gathered} r^2=((-4)-(-8))^2+((-10)-(-7)) \\ r^2=(-4+8)^2+(-10+7)^2 \\ r^2=4^2+(-3)^2 \\ r^2=16+9 \\ r^2=25 \\ r=5 \end{gathered}

Therefore, the equation for the standard form of a circle is:

\begin{gathered} (x-(-8))^2+(y-(-7))^2=25 \\ (x+8)^2+(y+7)^2=25 \end{gathered}

In conclusion, the equation is the following:

(x+8)^2+(y+7)^2=25

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LOM and KOL are equivalent, so the equation is 43=6x+25 :)
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Please solve this question on rationalising denominators showing all working <3
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Step-by-step explanation:

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What is the slope of (-1,6) and (2,3)?
LenKa [72]

Answer:

-1

Step-by-step explanation:

For a line joining two points (x1, y1) and (x2, y2), it's slope is given as:

\boxed{ \mathsf{slope =  \frac{ y_{2} -y  _{1}}{ x_{2} - x _{1}} }}

Here, the two points are (-1, 6) and (2, 3) in place of (x1, y1) and (x2, y2).

Solving for slope:

\implies \mathsf{ \frac{3 - 6}{2 - ( -1 )} }

\implies \mathsf{ \frac{ - 3}{2  + 1 } }

\implies \mathsf{ \frac{ - 3}{3 } }

\implies \mathsf{  - 1 }

Hence, the slope of the line joining the given points is <u>-1.</u>

4 0
3 years ago
The ratio of boys to girls in Coach Sheppard's class is 3 to 5. There are 20 girls in the
kondaur [170]

Answer:

32 Students

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3/5 = 12/20

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8 0
2 years ago
Read 2 more answers
Is -¼ + 2 ¼y + 2 - y equivalent to y + 2 ?
Juliette [100K]

Answer: No

Step-by-step explanation:

-\frac{1}{4}+2\frac{1}{4}y+2-y=y+2

(-\frac{1}{4}+2)+(2\frac{1}{4}y-y)=y+2\\

(\frac{(-1)+(4)(2)}{4})+(\frac{9}{4}y-y)=y+2

(\frac{-1+8}{4})+(\frac{(9)(1)-(4)(1)}{4} )y=y+2

(\frac{7}{4})+(\frac{9-4}{4} )y=y+2

(\frac{7}{4})+(\frac{5}{4})y=y+2

5 0
3 years ago
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