It costs $15 per hour to rent a bike. The additional fee for a helmet is $3 for the entire ride.

Segment FG begins at point F(-2, 4) and ends at point G(-2, -3). The segment is translated 3 units left and 2 units up, then ref

Alexus [3.1K]

Answer:

$F'G' = 7$

Step-by-step explanation:

Given

$F = (-2,4)$

$G = (-2,-3)$

Required

Distance of F'G'

The transformation that give rise to F'G' from FG are:

Translation
Reflection

The above transformations are referred to as rigid transformation, and as such the side lengths remain unchanged.

i.e.

$F'G' = FG$

Calculating FG, we have:

$FG = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

Where:

$F = (-2,4)$ --- $(x_1,y_1)$

$G = (-2,-3)$ --- $(x_2,y_2)$

$FG = \sqrt{(-2 - -2)^2 + (4 - -3)^2}$

$FG = \sqrt{(0)^2 + (7)^2}$

$FG = \sqrt{0 + 49}$

$FG = \sqrt{49}$

Take positive square root

$FG = 7$

Recall that:

$F'G' = FG$

$F'G' = 7$

6 0

2 years ago

Find all solutions of the equation in the interval (0,2π) cot theta +root 3 = 0

Alisiya [41]

Answer:

θ = 5π/6 rad and 11π/6 rad

Step-by-step explanation:

Given the expression cotθ+√3=0

Subtract √3 from both sides

cotθ+√3-√3=0-√3

cotθ = -√3

Since cotθ = 1/tanθ

1/tanθ = -√3

Reciprocate both sides:

tanθ = -1/√3

θ = tan^-1(-1/√3)

θ = -30°

Since the angle is negative, and tanθ is negative in the second and fourth quadrant.

In the second quadrant;

θ = 180-30

θ = 150°

Since 180° = πrad

150° = 150π/180

150° = 5π/6 rad

In the fourth quadrant;

θ = 360-30

θ = 330°

Since 180° = πrad

330° = 330π/180

330° = 11π/6 rad

Hence the solutions are 5π/6 rad and 11π/6 rad.

7 0

3 years ago

What percent of 100 is 25? Show you work.

ANEK [815]

.25 its a quarter of 100!

4 0

3 years ago

Read 2 more answers

A segment has an endpoint at (1,−2). The midpoint is at (−4,−2). What are the coordinates of the other endpoint?

vodka [1.7K]

Answer:

The other midpoint is located at coordinates (-9,-2) (Second option)

Step-by-step explanation:

Midpoints

If P(a,b) and Q(c,d) are points in $\mathbb{R} ^2$ , the midpoint between them is the point exactly in the center of the line that joins P and Q. Its coordinates are given by

$\displaystyle x_m=\frac{a+c}{2}$

$\displaystyle y_m=\frac{b+d}{2}$

We are given one endpoint at P(1,-2) and the midpoint at M(-4,-2). The other endpoint must be at an equal distance from the midpoint as it is from P. We can see both given points have the same value of y=-2. This simplifies the calculations because we only need to deal with the x-coordinate.

The x-distance from P to M is 1-(-4)=5 units. This means the other endpoint must be 5 units to the left of M:

x (other endpoint)= - 4 - 5 = - 9

So the other midpoint is located at (-9,-2) (Second option)

5 0

3 years ago

Which expression is equivalent to (5^-2)(5^-1) A. -1/125 B. -1/5 C. 1/125 D. 1/5

n200080 [17]

Answer:

1/125

Step-by-step explanation:

(5^-2)(5^-1) = 5^-3=1/5^3=1/125

3 0

3 years ago