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3 years ago

14

When I run up a staircase, my stride can carry me up 1, 2, or 3 steps at a time. In how many ways can I run up a 9-step staircas

e (given that my last stride lands me on the 9th step)?

1 answer:

Romashka [77]3 years ago

6 0

1+1+1+1+1+1+1+1+1
3+3+3
2+1+2+1+2+1
2+1+3+1+2

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Determine whether the triangles are congruent by AA., SSS, SAS, or not similar.

klemol [59]

Step-by-step explanation:

they are similar by AA .

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2 years ago

What is the perimeter of a square which has the same area as a circle with circumference of 4π?

Contact [7]

The circumference of a circle is given by: 2πr, where r is the radius of the circle. Equating 4π, we have 2πr = 4π so the radius of the circle is: r = 4/2 = 2. Then, the area of the circle is given by πr ^ 2 = π * (2 ^ 2) = 4π.Since the square and the circle have the same area, then: Let L be the side of the square, we have: L ^ 2 = 4π, clearing L = 2 * (π ^ (1/2))The perimeter of a square is the sum of its sides: P = L + L + L + L = 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π) ^ (1/2)) P = 8 * (π ^ (1/2))

6 0

3 years ago

Does anyone know the minim value of the function f(x) =2x^2 -4x -6?. I’m online due to my quarantine and am looking for extra he

navik [9.2K]

Answer:

f(x) = - 8

Explanation:

The given function is

f(x) =2x^2 -4x -6

The first step is to find the derivative of the function. Recall, if

y = ax^b

y' = abx^(b - 1)

Thus,

f'(x) = 4x - 4

We would equate f'(x) to zero and solve for x. We have

4x - 4 = 0

4x = 4

x = 4/4

x = 1

We would substitute x = 1 into the original function and solve for f(x) or y. It becomes

f(1) =2(1)^2 -4(1) - 6 = 2 - 4 - 6

f(1) = - 8

Thus, the minimum value is f(x) = - 8

4 0

11 months ago

Factor: x2 - 11x + 30

Nonamiya [84]

Ask which two numbers add up to -11 and multiply to 30?

That would be; -6 and -5

Rewrite the expression using what you have above;

<u>(x - 6)(x - 5)</u>

8 0

3 years ago

Read 2 more answers

Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x

egoroff_w [7]

Answer:

$y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where <em>m</em> is the slope and <em>b</em> is the y-intercept.

Perpendicular lines always have slopes that are negative reciprocals (ex. 1/2 and -2, 3/4 and -4/3)

<u>Determine the slope (</u><em><u>m</u></em><u>):</u>

$y = 1 -2x$

Rearrange into slope-intercept form:

$y = -2x+1$

Now, we can identify clearly that the slope is -2. Because perpendicular lines always have slopes that are negative reciprocals, a perpendicular line would have a slope of $\displaystyle\frac{1}{2}$ . Plug this into $y=mx+b$ :

$y=\displaystyle\frac{1}{2} x+b$

<u>Determine the y-intercept (</u><em><u>b</u></em><u>):</u>

$y=\displaystyle\frac{1}{2} x+b$

Plug in the given point (1,3) and solve for <em>b</em>:

$3=\displaystyle\frac{1}{2} *1+b\\\\b=\displaystyle \frac{5}{2}$

Therefore, the y-intercept is $\displaystyle \frac{5}{2}$ . Plug this back into $y=\displaystyle\frac{1}{2} x+b$ :

$y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}$

I hope this helps!

8 0

2 years ago