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3 years ago

Use the graph below to answer the question that follows:

Mathematics

1 answer:

Strike441 [17]3 years ago

3 0

By graphing the given points, we will get the attached figure
which represents:
f(x) = 3 sin x
but sin x = cos (x - π/2)
∴ f(x) = 3 cos ( x - π/2 )

The correct choice is option ⇒⇒⇒ f(x) = 3 cos(x − pi over 2 )

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Solve the system by substitution

Lina20 [59]

Answer:

(-5, -30)

Step-by-step explanation:

We start with the equation:

y = 6x

y = -4x - 50

Since both of them are equal to y, we can substitute the 6x into y. So:

6x = -4x - 50

Now we can solve for x. Add 4x to both sides...

6x = -4x - 50

+4x +4x

10x = -50

Now, divide both sides by 10.

10x = -50

10 10

x = -5

So, we now know that x is -5. Now we know this, we can substitute -5 where we see x. It works in both equations, so I will do both.

y = 6(-5)

y = -30

And...

y = -4(-5) - 50

y = 20 - 50

y = -30

As you can see, both equations show that y = -30. To check our work, let's plug in the values.

-30 = 6(-5)

-30 = -30

Also:

-30 = -4(-5) - 50

-30 = -20 - 50

-30 = -30

So, we can see that both of the equations gave us the same answer. So, our answer is x = -5 and y = -30, so the ordered pair is: (-5, -30). Hope this helps you!

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3 years ago

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In ΔABC, if AB = 14 and BC = 9, AC may be equal to

Pie

Answer:

AC could be any number of these numbers 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

Step-by-step explanation:

There is a fact in any triangle:

The length of any side of a triangle must be greater than the difference of the lengths of the other two sides and smaller than the sum of the lengths of the other two sides

If the lengths of the three sides of a triangle are a , b and c, then

a - b < c < a + b
b - c < a < b + c
a - c < b < a + c

In Δ ABC:

→ (BC) - (AC) < AB < (BC) + (AC)

→ (AB) - (AC) < BC < (AB) + (AC)

→ (AB) - (BC) < AC < (AB) + (BC)

∵ AB = 14 units

∵ BC = 9 units

- Find the sum and difference of them

∵ AB - BC = 14 - 9

∴ AB - BC = 5

∵ AB + BC = 14 + 9

∴ AB + BC = 23

- That means the length of AC could be any integer greater

than 5 and smaller than 23

∴ 5 < AC < 23

AC could be any number of these numbers 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

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The equation for this is y= -5/6 x +22/6

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