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Natalka [10]
2 years ago
15

**PLEASE HELP** What is the length of the altitude of the equilateral triangle below?

Mathematics
1 answer:
charle [14.2K]2 years ago
5 0
For any 30-60-90 triangle:
Let the length of hypotenuse = x
∴ The leg which faces the angle 30 = (1/2) x 
And the leg which faces the angle 60 = (√3/2) x 
So, The ratio between two legs will be 
= (1/2) x : (√3/2) x     ⇒⇒⇒⇒ divide over x
= 1/2  :  √3/2             ⇒⇒⇒⇒ multiply by 2
= 1  :  √3

Or the ratio will be

= (√3/2) x  :  (1/2) x    ⇒⇒⇒⇒ divide over x
= √3/2  :  1/2             ⇒⇒⇒⇒ multiply by 2
=  √3  :  1
==============================

The correct answer will be option B only

B.  1 : √3







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Write the slope intercept ​
mrs_skeptik [129]

Answer:

b = 4,

m = 4/3,

y = 4x/3 + 4

Step-by-step explanation:

We can see the line intercepts the x-axis in (-3,0) and the y-axis in (0,4). So, using the fact that the line equation in the slope-intercept form is:

y = mx+b

We can substitute the points we know:

→ (0,4):

y = mx+b\\\\4 = m\cdot0+b\\\\4 = 0+b\\\\\boxed{b=4}

→ (-3,0):

y = mx+b\\\\0 = -3m + 4\\\\3m = 4\\\\\boxed{m = \dfrac{4}{3}}

So, the line equation in form requested is:

\boxed{y=\dfrac{4}{3}x+4}

7 0
2 years ago
Which graph represents the piecewise-defined function?
Valentin [98]

Answer: The below figure shows the graph of f(x).

Explanation: Given function, f(x)=\begin{cases}5 & \text{ if } x6 \end{cases}

Since, here three conditions are given,

In first case for values x<-5 , f(x)=5, so we get a line y=5 parallel to x-axis which passes through point (0,5).

In second case, for values  -5\leq x\leq 6, f(x) =-2, so we get a line y=-2 parallel to x-axis which passes through point  (0,-2).

In third case, for values x>6, f(x)=1, so we get a line y=1 parallel to x-axis which passes through point (0,1).

Thus, these three lines make the piecewise-defined function f(x).

7 0
3 years ago
Read 2 more answers
What is the maximum number of possible extreme values for the function,<br> f(x) = х2 -7x – 6?
timama [110]

Answer:

Only one extreme value of f(x) is possible.

Step-by-step explanation:

We are given the quadratic function of independent variable x which is f(x) = x² - 7x - 6 ......(1)

Now. the condition for extreme values of f(x) is \frac{df(x)}{dx} =0

Hence, differentiating both sides of equation (1) with respect to x, we get

\frac{df(x)}{dx} = 2x -7 = 0

⇒ x = 3.5.

So there is only one value of x for which f(x) has extreme value which is x = 3.5.

Therefore, only one extreme value of the given function is possible. (Answer)

3 0
3 years ago
7y - 8y - 28 = -14
Pachacha [2.7K]

Answer:

y = -14

Step-by-step explanation:

7y - 8y - 28 = -14

- y = -14 + 28

- y = 14

y = -14

hope it helps!

3 0
2 years ago
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Grace [21]

Answer:

24.56

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x is roughly equal to 24.56.

Hope this helps!

7 0
3 years ago
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