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1 year ago

The slope of the line below is -1/7.

Mathematics

1 answer:

KatRina [158]1 year ago

3 0

Answer:

y = (-1/7)x + (24/7)

Step-by-step explanation:

The general structure of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

You have been given the value of the slope (m = -1/7). You have also been given values for "x" and "y" from the point (3,3). Therefore, you can substitute these values in for their variables and simplify to find the value of the y-intercept.

y = mx + b <----- Slope-intercept form

y = (-1/7)x + b <----- Plug -1/7 into "m"

3 = (-1/7)(3) + b <----- Plug in "x" and "y" values from point (3,3)

3 = -3/7 + b <----- Multiply -1/7 and 3

24/7 = b <----- Add 3/7 to both sides

Now that you know that m = -1/7 and b = 24/7, you can determine the formula satisfying the given information.

y = (-1/7)x + (24/7)

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a. $24\sqrt{3}$ and 41.6

b. 52.1

Step-by-step explanation:

Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.

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Thus, we can write $Tan(60)=\frac{y}{24}\\y=24*Tan(60)\\y=24*\sqrt{3} \\y=24\sqrt{3}$

Approximate value (rounded to nearest tenth): $24\sqrt{3} =41.6$

Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.

Thus we can write and solve:

$Sin(53)=\frac{41.6}{x}\\x=\frac{41.6}{Sin(53)}=52.1$