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2 years ago

Write the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8).

Mathematics

1 answer:

mina [271]2 years ago

5 0

Notice the picture below

$\bf \textit{equation of a circle}\\\\
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad center\ ({{ h}},{{ k}})\qquad
radius={{ r}}\\\\
-----------------------------\\\\
\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ 4}})\quad 
% (c,d)
&({{ 4}}\quad ,&{{ 8}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\leftarrow r$

you have the center, the h,k, all you really need is the radius "r"

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A company sells its printers to customers in order to make a profit of 25% calculate the price the company paid for a printer wh

ioda

The company paid $2000 for the printer

Step-by-step explanation:

Let x be the price of the printer for which the company bought it.

If x is the price of printer, then 25% of x will be the profit made by the company.

That is:

0.25x

According to the statement,

The cost and profit earned by company are equal to 2500

So,

$x+0.25x = 2500\\1.25x = 2500$

Dividing both sides by 1.25

$\frac{1.25x}{1.25} = \frac{2500}{1.25}\\x = 2000$

Hence,

The company paid $2000 for the printer

Keywords: Percentage, Profit

Learn more about percentage at:

#LearnwithBrainly

7 0

3 years ago

7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

Learn more about quadratic equations:

brainly.com/question/27638369

6 0

2 years ago

Read 2 more answers

I WILL GIVE BRAINLYEST TO RIGHT ANSWER -4w - 4 =8 what is X equal to

Alecsey [184]

Answer:

w = -3

Step-by-step explanation:

-4w - 4 = 8

Combine the constants by adding 4 to both sides.

-4w = 12

Isolate w by dividing by -4.

w = -3

Check your work by plugging w = -3 into the original equation.

-4(-3) - 4 = 8

12 - 4 = 8

8 = 8

Your answer is correct.

8 0

3 years ago

Payton has 2 pizzas. each pizza is cut into 10 equal slices. she and her friends eat 14 slices. what part of the pizzas did they

kakasveta [241]

14 / 20 total slices = 7 / 10, which is 0.7 if you're looking for a decimal.
That's 70% of the pizza, which I would eat by myself.

3 0

3 years ago

Read 2 more answers

A line through the origin and (10,4) is showin in the standard (x,y) coordinate plane below. The acute angle between the line an

Snowcat [4.5K]

Answer:

$\cos\theta=\frac{10}{\sqrt{116}}$

Step-by-step explanation:

To solve this, we can imagine a line drawn directly down from the point (10,4) to the x-axis. This would make a right triangle with length 10 and height 4.

$\cos\theta$ is equal to the length of adjacent leg to the angle divided by the length of the hypotenuse of the triangle. From the picture, we can see the adjacent leg is 10.