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2 years ago

14. Twelve more than seven times a number equals the number less six

Mathematics

2 answers:

kotegsom [21]2 years ago

3 0

Answer:

The number is -3.

Step-by-step explanation:

Set up an equation:

Variable n = number

12 + 7n = n - 6

Assuming the question is solve for n, isolate the variable:

Subtract n from both sides:

12 + 6n = -6

Subtract 12 from both sides:

6n = -18

Divide by 6 on both sides:

n = -3

Check your work:

12 + 7(-3) = -3 - 6

12 - 21 = -3 - 6

-9 = -9

Correct

Zina [86]2 years ago

3 0

12+7n=n-6
12+6n=-6
6n=-18
n=-3

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Big Ben, the famous clock tower in London, has a minute hand that is 14 feet long. How far does the tip of the minute hand of Bi

ycow [4]

Answer:

36.65 ft (2 dp)

Step-by-step explanation:

Angles around a point sum to 360°
1 hour = 60 minutes

Therefore, the minute hand of a clock travels 360° in 60 minutes

Number of degrees the minute hand will travel in 25 minutes:

$\sf =\dfrac{360}{60} \times 25=150^{\circ}$

To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:

$\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)$

$\textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}$

Given:

r = length of minute hand = 14 ft
$\theta$ = 150°

$\begin{aligned}\implies \textsf{Arc length} &=2 \pi (14)\left(\dfrac{150^{\circ}}{360^{\circ}}\right)\\ & = 28\pi \left(\dfrac{5}{12}\right)\\ & = \dfrac{35}{3} \pi \\ & = 36.65\: \sf ft\:(2\:dp)\end{aligned}$

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2 years ago

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

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

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2 years ago