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Papessa [141]
2 years ago
10

During a figure skating routine, Jackie and Peter skate apart with an angle of 15° between them. Jackie skates for 5 meters and

Peter skates for 7 meters. How far apart are the skaters? Round to the nearest hundredth of a meter.
Mathematics
1 answer:
Fantom [35]2 years ago
7 0

Answer:

Ans = 2.53m

Step-by-step explanation:

It is a simple law of Cosine, on a right-angle triangle draw the length as 5 and the base as 7 the angle is 15°. Find x.

So x = 5² +7² - 2 (5) (7)cos 15°

Solve this and you get your answer.

Hope this was helpful :)

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Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6
Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. 2x-4y=12

-3x+6y=-15

b. 2x-4y=12

-5x+3y=10

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0

1. One solution:

There will be one solution to the system of equations,  If we have:

\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}

2. Infinitely Many Solutions: (Identical lines in the system)

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}

3. No Solution:(Parallel lines)

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}

Now, let us discuss the system of equations one by one:

a. 2x-4y=12 OR 2x-4y-12=0

-3x+6y=-15 OR -3x+6y+15=0

A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15

Here, the ratio:

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}

Therefore, no solution i.e. parallel lines.

b. 2x-4y=12 OR 2x-4y-12=0

-5x+3y=10 OR -5x+3y-10=0

A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10

\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}

\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0
3 years ago
Can someone help please?
Alekssandra [29.7K]

Answer:

y=1X

Step-by-step explanation:

This is because the distance over the money made over the days worked is 2/2 which simplifies to 1 so that would be the one x. then the y intercept is found on the y axis where does the line cross the y axis? this would be at zero so you do not need to put that in the equation

8 0
3 years ago
What is the value of x in the equation 2x + 9 = 21?<br> O2<br> 06<br> 09<br> O 15
Taya2010 [7]

Answer:

the answer is 6

Step-by-step explanation:

2x + 9 = 21

2x = 21 - 9

2x = 12

x = 6

4 0
2 years ago
A 6 sided die was rolled 9 times. What is the mode of these rolls?
yuradex [85]
That 1,2,3,4,5,6 is one the die and it has a chance to at least get all the numbers at least once but u dont have enough data so i can help u more.
6 0
3 years ago
If , n^-3 = 1/8 then n would be which of the following? -1/2 -2 2 1/2
lions [1.4K]

Answer:

2

Step-by-step explanation:

{n}^{ - 3}  =  \frac{1}{8}  \\  \\  {n}^{ - 3}  =  \frac{1}{ {2}^{3} }  \\  \\  {n}^{ - 3}  = {2}^{ - 3}.. (\because \frac{1}{a^n} = a^{-n}) \\  \\ n = 2 \\(\because exponents \: are \: same\: hence\: \\bases\: will \: also\: be\: equal)

4 0
3 years ago
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