up the hill. If the hill slopes at 23◦ from the horizontal, how deep does the rescue shaft
need to be to meet the horizontal tunnel? Answer to one decimal place.
Explanation
The diagram is shown below.
We have a right triangle with an unknown vertical leg (which I'll call x) and a known hypotenuse that is 200 meters long.
We use the sine ratio to connect the opposite and hypotenuse.
sin(angle) = opposite/hypotenuse
sin(23) = x/200
x = 200*sin(23)
x = 78.1462256978548 approximately
x = 78.1
Make sure your calculator is in degree mode.
Bill has 4 letter blocks: A, B, C and D. In how many different ways can Bill arrange the blocks in a row? 6, 12, 18 or 24?
The number of different ways can Bill arrange the blocks in a row will be 24. Then the correct option is D.
A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
Bill has 4 letter blocks: A, B, C, and D.
The number of different ways can Bill arrange the blocks in a row will be
⇒ 4!
⇒ 4 x 3 x 2 x 1
⇒ 24
The number of different ways can Bill arrange the blocks in a row will be 24. Then the correct option is D.
More about the permutation and the combination link is given below.
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The slope of any line parallel to y = 3x - 4 is also 3.
The given equation is y = 3x - 4 , I will assume you meant to write:
y = 3x - 4
To find the slope of a line parallel to this line, we can observe that parallel lines have the same slope. The equation of the given line is in the slope-intercept form y = mx + b, where "m" represents the slope. In this case, the slope (m) of the line is 3.
So, the slope of any line parallel to y = 3x - 4 is also 3.
To know more about slope click here :
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Answer: If the original equation is y = 3x -4, the slope is 3.
Any equation of a line parallel to the line y = 3x -4 will have a slope of 3.
Step-by-step explanation:
In slope-intercept form, y =mx + b the coefficient of x, m is the slope.
Here 3 is that value.
It is very unusual to have two equal signs in a question about slope.
I am not sure what to do with the =8y + 1
Is this supposed to be another equation in the system, missing a term?
Answer:
y=3x+18
Step-by-step explanation:
Since slope-intercept form is y=mx+b, we first need to find the slope.
m=y2-y1/x2-x1
m=0-(-9)/-6-(-9)
m=9/3=3
Next we need to find b, or the y-intercept
to do that we plug in numbers to what we already have.
y=3x+b
0=-18+b
b=18
Now we put it all together.