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2 years ago

A hiker begins a trip by first walking 22.2 km

Mathematics

1 answer:

Dominik [7]2 years ago

4 0

9514 1404 393

Answer:

20.6 km

Step-by-step explanation:

Using (East, North) coordinates, the hiker's position ends up being ...

22.2(cos(-45°), sin(-45°)) +40.1(cos(65°), sin(65°))

We're only interested in the second coordinate of this total, which is ...

22.2sin(-45°) +40.1sin(65°) ≈ -15.698 +36.343 = 20.645 . . . km

The y-component of the hiker's position at the end of the second day is 20.6 km north of her starting location.

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Solve the system of equations by using substitution.<br> x+8y=-2<br> x-3y=20

zysi [14]

Answer:

(14, -2)

Step-by-step explanation:

To solve by using substitution, begin by solving for a variable in the first equation. Let's solve for x:

$x+8y=-2\\x=-2-8y$

Now we know what <em>x</em> equals. Let's substitute this into the second equation:

$x-3y=20\\(-2-8y)-3y=20$

We can then simplify:

$-2-8y-3y=20$ Given equation

$-2-11y=20$ Combine y terms

$-11y=22$ Add 2

$y=-2$ Divide by -11

So, we now know the value of y = -2.

To find the value of X, we can substitute the value of Y into one of the equations. Let's use the first one:

$x+8y=-2$

$x+8(-2)=-2$ Substitute for y

$x-16=-2$ Distribute 8

$x=14$ Add 16

So, we now know the value of x = 14.

Therefore, we know a solution to the system of equations is (14, -2).

4 0

3 years ago

PLEASE HELP ASAP 30 POINTS ):

ladessa [460]

Answer:

c (0,-4)

Step-by-step explanation:

-5x+y = -4

4x - 4y =16

Solve the first equation for y since we are using substitution.

-5x+y = -4

Add 5x to each side

-5x+5x+y = -4+5x

y = 5x-4

Substitute this equation y = 5x-4 into the second equation.

4x -4(5x-4) = 16

Distribute the -4

4x - 4(5x) -4(-4) = 16

4x-20x +16 = 16

Combine like terms

-16x +16 =16

Subtract 16 from each side

-16x+16-16 = 16-16

-16x =0

Divide by -16

x=0

But we still need to find y

y = 5x-4

y = 5(0) -4

y = -4

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3 years ago

Add the product of (-16) and (-9) to the quotient of (-132) by 6.

alukav5142 [94]

9*16-132/6=122...........

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2 years ago

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zaharov [31]

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3 years ago

Pls answer the question attached

barxatty [35]

$\huge\mathfrak{\underline{answer:}}$

$\large\bf{\angle ACD = 105°}$

__________________________________________

$\large\bf{\underline{Here:}}$

BCD is an isosceles right triangle , right angled at D
ABC is an equilateral triangle

$\large\bf{\underline{To\:find:}}$

∠ ACD

$\large\bf{In\: triangle\:ABC:}$

❒ Sum of all angles is 180° , since it is an equilateral triangle all the three angles would be same

$\large\bf{\underline{So}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼\angle ACB = \frac{180}{3}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼\angle ACB = 60°}$

$\large\bf{In\: triangle\:BDC}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼\angle D = 90°}$

$\bf{⟼\angle DBC =\angle DCB }$ (Isosceles triangle)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼\angle DBC + \angle BDC + \angle DCB = 180° }$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼2\angle DCB + 90° = 180°}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼2\angle DCB = 180 -90}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼\angle DCB = \frac{90}{2}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟼\angle DCB = 45°}$

$\large\bf{\underline{Therefore,}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟹\angle ACD = \angle ACB + \angle DCB}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\bf{⟹\angle ACD = 60+45}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹\angle ACD = 105°}$

6 0

3 years ago