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Juli2301 [7.4K]
3 years ago
6

#1. Solve for x. Round your answers to the hundredths place x^2+12x- 37 = 0

Mathematics
1 answer:
Natalka [10]3 years ago
3 0

Answer:

-14.54, 2.54

Step-by-step explanation:

Solve by using the quadratic forumla

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For the point P(21,19) and Q(28.24), find the distance d(P,Q) and the coordinates of the
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Answer:

1. √74; 2. (24.5, 21.5)

Step-by-step explanation:

1. Distance

You could use the distance formula to calculate the length of PQ, but I prefer a visual approach, because it requires less memorization.

Draw a horizontal line from P and a vertical line from Q until they intersect at R (28, 19).

Then you have a right triangle PQR, and you can use Pythagoras' theorem to calculate PQ.

\begin{array}{rcl}PQ^{2} & = & PR^{2} + QR^{2}\\& = & 7^{2} + 5^{2}\\ & = & 49 + 25\\& = & 74\\PQ& = & \mathbf{\sqrt{74}}\\\end{array}\\\text{d(P,Q) = $\large \boxed{\mathbf{\sqrt{74}}}$}

2. Midpoint of line

The coordinates of the midpoint are half-way between the x- and y-coordinates of the end points.

For the x-coordinate, the half-way point is

(21 + 28)/2 = 49/2 = 24.5

For the y-coordinate,  the half-way point is

(19 +24)/2 = 43/2 = 21.5

The coordinates of the midpoint M are (24.5, 21.5).

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