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3 years ago

What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. (4 points)

1 answer:

6 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-4)]^2+[5-0]^2}\implies d=\sqrt{(2+4)^2+(5-0)^2} \\\\\\ d=\sqrt{36+25}\implies d=\sqrt{61}\implies d\approx 7.81$

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How to square imaginary numbers

dalvyx [7]

An imaginary number " i " is the squared root of -1, so whenever you square i it's like squaring a squared root. The squared root would cancel and you would be left with just the number under it, that is, the -1.
i ^ 2 = -1

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3 years ago

Consider the equation y = –3(x – 3) Which equation, when graphed with the given equation, will form a system with lines that ove

pentagon [3]

Answer:

y=-3x+9 (D)

Step-by-step explanation:

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3 years ago

What is the surface area of a rectangular prism that is 12cm by 3cm by 5cm?

Cerrena [4.2K]

A = 2lw + 2lh + 2hw
A = 2(12)(3) + 2(12)(5) + 2(5)(3)
A = 72 + 120 + 30
A = 222 cm squared

Hope this helps!! :)

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3 years ago

Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3).

shusha [124]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x + 5y = 10 into this form

Subtract x from both sides

5y = - x + 10 ( divide all terms by 5 )

y = - $\frac{1}{5}$ x +2 ← in slope- intercept form

with slope m = - $\frac{1}{5}$

• Parallel lines have equal slopes, hence

y = - $\frac{1}{5}$ x + c ← is the partial equation of the parallel line

To find c substitute (1, 3) into the partial equation

3 = - $\frac{1}{5}$ + c ⇒ c = $\frac{16}{5}$

y = - $\frac{1}{5}$ x + $\frac{16}{5}$ ← equation of parallel line

3 0

3 years ago

Read 2 more answers

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°

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

4 0

2 years ago