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2 years ago

15

Lee marks sixths on a number line. He

1 answer:

tigry1 [53]2 years ago

4 0

Okay wait what how i do this mark me brainless 0

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If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find

Evgesh-ka [11]

Answer:

The equation of the circle is $(x+3)^2+(y-5)^2 = 17$

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is the distance from the center to either endpoint of the diameter. Finally use the center-radius form to find the equation.

Find the center-radius form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

$(\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5)$ .

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by $\sqrt[]{(a-c)^2+(b-d)^2}$ . So, let us use (1,4) to calculate the radius.

$r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}$ .

REcall that given a point $(x_0,y_0)$ . The equation of a circle centered at the point $(x_0,y_0)$ is

$(x-x_0)^2+(y-y_0)^2 = r^2$

In our case, $(x_0,y_0)=(-3,5)$ and $r=\sqrt[]{17}$ . Then, the equation is

$(x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17$

4 0

3 years ago

A drink is made by mixing 650 ml of water with 150 ml of fruit juice.

Luda [366]

<h2>○=> <u>Correct answer</u> :</h2>

$\boxed{\color{hotpink}\tt18.75\%}$ of the drink is fruit juice

<h3>○=> <u>Steps to derive correct answer</u> :</h3>

Quantity of water in a drink = 650 ml

Quantity of fruit juice in a drink = 150 ml

Total quantity of both items in the drink :

$=\tt 650 + 150$

$\color{plum}=\tt 800 \: ml$

Thus, the total quantity of both items in the drink = 800 ml

Let the percentage of of fruit juice in the drink be x%.

Which means :

$= \tt\frac{x}{100} \times 800 = 150$

$= \tt \frac{x \times 800}{100} = 150$

$=\tt \frac{800x}{100} = 150$

$=\tt 8x = 150$

$=\tt x = \frac{150}{8}$

$\hookrightarrow\color{plum} \bold{x = 18.75\%}$

Then, the percentage of water in the drink :

$= \tt100 - 18.75$

$\color{plum}= \tt81.25\%$

Thus, the percentage of water in the drink = 81.25%

<h3>○=> <u>Therefore</u> :</h3>

▪︎Percentage of fruit juice in the drink = 18.75%

▪︎Percentage of water in the drink = 81.75%

8 0

3 years ago

Read 2 more answers

What is the next step to10x-4(2x-9)

bezimeni [28]

10x= -8x + 36
-8x -8x
———————-
2x= 36
— —
2 2

X=18

6 0

3 years ago

F(x) = -7x2 + 9x - 15 and g(x) = -12x2 – 15x + 7

djyliett [7]

Answer:

${5x}^{2} + 6x = - 8$

Step-by-step explanation:

This question is asking you to insert two equations, f(x) and g(x), into the equation g(x) - f(x). This will lead to the equation below.

${ - 12x}^{2} - 15x + 7 - ({ - 7)x}^{2} + 9x - 15$

Now we can solve for the equation.

${ - 5x}^{2} - 6x - 8 = 0 \\ {5x}^{2} + 6x = - 8$

3 0

2 years ago

The formula for the perimeter of a rectangle with the length and the width is given above. If a rectangle has perimeter 24, what

NARA [144]

Answer: Length could be 5 and width 2

Explanation:
Perimeter = 2l + 2w = 2x5 + 2x2 = 14 units

7 0

3 years ago