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Mathematics

1 answer:

AnnZ [28]3 years ago

7 0

Answer:

$\huge\boxed{x=59}$

$\texttt{Read the explanation for the equation.}$

Step-by-step explanation:

Given that lines $l$ and $m$ are parallel, that means that we can establish some basic angle relationships here.

Since both lines are cut by a transversal, that means all angles formed by that line will be equivalent.

$(3x-33)\textdegree$ and $(2x+26)\textdegree$ are going to be equivalent because they are alternate exterior angles. These are formed by two parallel lines being cut by a transversal, and they will always be equal.

Since we know that both angles are equivalent to each other, we can set the expressions equal to each other to find x.

$(3x-33) = (2x+26)$

Here's your equation, by the way.

We can now solve for x.

$3x-33=2x+26$

Add 33 to both sides:

$3x=2x+59$

Subtract 2x from both sides:

$x=59$

Therefore, x = 59.

Hope this helped!

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M44b

viktelen [127]

Answer:

84.85 feet or 60 $\sqrt2$ feet.

Step-by-step explanation:

Given that:

Distance of paths between each pair of consecutive bases is 60 ft.

To find:

Distance that the ball needs to travel if it is thrown directly from home plate to second base?

Solution:

Actually the given problem can be mapped to a right angled triangle in which base and height are given to be equal to 60 ft (because each pair of consecutive bases are 60 ft apart), Plus, they are at right angles to each other.

So, kindly refer to the image attached.

AB and BC are the distance of paths between consecutive bases.

And we have to find AC.

We can use Pythagorean theorem to find out the Hypotenuse of the triangle.

According to Pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AC^{2} = AB^{2} + BC^{2} \\\Rightarrow AC^{2} = 60^{2} + 60^{2} \\\Rightarrow AC = \sqrt{2 \times 60^2}\\\Rightarrow AC = \bold{60\sqrt{2}\ ft = 84.85\ ft}$