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Vikentia [17]
3 years ago
13

How do you solve this?

Mathematics
2 answers:
Lemur [1.5K]3 years ago
8 0

The equation of a circle is:

(x - h)² + (y - k)² = radius²

Note:

h = x coordinate for the centre of the circle

k = y coordinate for the centre of the circle

The equation for the circle in the question is:

(x - 6)² + (y - 5)² = 16

So the coordinates for the centre of the circle is:

(6, 5)

------------------------

Since PQ is the diameter of the circle, that means the coordinates for the  midpoint of PQ would also be the coordinates for the centre of the circle

That  means:

( (x coords of P and Q) / 2 , (y coords of P and Q) / 2 )= (6 , 5)

So x-coords of Q:

\frac{10 + x}{2} = 6

10 + x = 12

<u>x = 2</u>

y-coords of Q

\frac{-5+ x}{2} = -5

-5 + x = - 10

<u>x = 5</u>

So the coordinates for Q are:

(2, -5)

---------------------------------------------

Answer:

Option A) (2, - 5)

Katarina [22]3 years ago
6 0

\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-6)^2+(y+5)^2=16\implies [x-\stackrel{h}{6}]^2+[y-(\stackrel{k}{-5})]^2=\stackrel{r}{4^2}~\hfill \begin{cases} \stackrel{center}{(6,-5)}\\ \stackrel{radius}{4} \end{cases}

Check the picture below.

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The height and base dimensions of a pyramid are shown in the diagram.
marusya05 [52]

Volume of the pyramid = 40 cubic units

Solution:

Let us find the volume of the pyramid.

Area of the base = \frac{1}{2}\ bh

                            $=\frac{1}{2}\times4\times5

                            = 10 square units

Area of the base (B) = 20 square units

Height of the pyramid = 12

Volume of the pyramid = \frac{1}{3}\times \text{Base}\times \text{Height}

                                       $=\frac{1}{3}\times 10\times12

                                       = 40 cubic units

Volume of the pyramid = 40 cubic units

5 0
2 years ago
If y is directly proportional to x and y is 12 when x = 10, what is the function rule that describes the variation?
azamat

Answer: y=1.2x

Step-by-step explanation:

Given

Y is directly proportional to x

and y=12 for x=10

\Rightarrow y\propto x\\\Rightarrow y=kx\\\text{Substitute x and y}

\Rightarrow 12=k(10)\\\Rightarrow k=1.2

\therefore \text{The function becomes}\\\Rightarrow y=1.2x

8 0
3 years ago
Read 2 more answers
A countertop is 16ft long &amp; 3ft wide what is the area in square meters
astra-53 [7]

ANSWER

Find out the area of the  countertop in square meters .

To proof

As given

A countertop is 16ft long & 3ft wide.

A countertop is in the shape of the rectangle.

FORMULA

Area of a rectangle = length × breadth

long = 16ft

wide = 3ft

put the value

we get

Area of a countertop = 16 ×3

                                   = 48 feet²

1 meter = 3.281 feet

1feet = \frac{1}{3.281} meter

convert Area of a countertop in  square meters

= \frac{48\times1\times1}{3.281\times3.281}

=  4.461 m² ( approx )

Hence proved

8 0
3 years ago
a box in the shapr of s rectangular prism has a length of 3 5/8 inches, a width of 2 1/2 inches and a height of 4 inches. what i
Sergeeva-Olga [200]

Answer:

V = 36 1/4 in.^3

Step-by-step explanation:

V = LWH

L = 3 5/8 in.

W = 2 1/2 in.

H = 4 in.

V = (3 5/8)(2 1/2)(4) in.^3

Change the mixed numerals to fractions.

<em>To change the mixed numeral a b/c to a fraction, do this: </em>

<em>a b/c = (ac + b)/c</em>

V = (3 * 8 + 5)/8 * (2 * 2 + 1)/2 * 4/1

V = (24 + 5)/8 * (4 + 1)/2 * 4/1

V = 29/8 * 5/2 * 4/1 in.^3

V = 580/16 in.^3

V = 145/4 in.^3

V = 36 1/4 in.^3

4 0
3 years ago
If a 45 degree 45 degree 90 degree triangle has a hypotenuse length of 12 find the leg length
AURORKA [14]

Answer:

<h2>Leg length = 8.5</h2><h2 />

Step-by-step explanation:

let x represent the leg length

if we use the Pythagorean theorem we get:

x² + x² = 12²

then

2x² = 12²

Then

x² = 144/2 = 72

then

x = √(72)

 =8,485281374239

7 0
2 years ago
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