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Lady bird [3.3K]
3 years ago
7

Complete each statement in the steps to solve x2 – 4x + 3 = 0 using the process of completing the square.

Mathematics
1 answer:
My name is Ann [436]3 years ago
8 0
(x - 3)(x - 1)

x = 3 
or 
x = 1
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A town has a population of 13,000 and grows at 5% every year. What will be the population after 11 years to the nearest whole nu
timofeeve [1]

Answer:

So all you need to do is find 5% of 13000 which is 650.

Now 650 times 11= 7150

13000+ 7150=

20,150

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PLEASE HELP ASAP! NO SCAMS!
pshichka [43]

Answer:

Step-by-step explanation:

Perpendicular means that the slopes of the "old" line and the "new" line are opposite reciprocals; bisector means that the "new" line goes directly through the center of the "old" line. This perpendicular bisector, then, will go directly through the center of the "old" line, cutting it directly in half and leaving in its wake a 90 degree angle. To write this equation, then, of the perpendicular bisector, we need the slope of the old line and the midpoint of the old line. Let's work on the midpoint first:

M=(\frac{3+6}{2},\frac{5-7}{2})\\M=(\frac{9}{2},\frac{-2}{2})\\M=(\frac{9}{2},-1) So the "new" line will go through this point.

Onto the slope:

m=\frac{-7-5}{6-3}\\m=\frac{-12}{3}so the slope is

m = -4. That means that the perpendicular slope is

m=\frac{1}{4} Now we're ready to write the equation:

y-5=\frac{1}{4}(x-3) and

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Answer:

If the given lengths of 7 cm, 24 cm, and 25 cm for the sides of a triangle satisfy the equation of the Pythagorean Theorem, then, yes, the given side lengths are those of a right triangle. Let's see if they are:

The well-known equation of the famous Pythagorean Theorem is:

a² + b² = c², which says that for a right triangle, the sum of the squares of the lengths of the two shorter sides of the triangle is equal to the square of the length of the longest side called the hypotenuse, where a and b are the lengths of the two shorter sides (also called the "legs") and c is the length of the hypotenuse (the side opposite the right angle).

We're given that a = 7 cm and b = 24 cm and that c = 25 cm. Substituting these values into the equation of the Pythagorean Theorem, we get:

a² + b² = c²

(7 cm)² + (24 cm)² = (25 cm)²

(7 cm)(7 cm) + (24 cm)(24 cm) = (25 cm)(25 cm)

49 cm² + 576 cm² = 625 cm²

625 cm² = 625 cm²

As we can see, the equation of the Pythagorean Theorem is satisfied, i.e., made a true statement, by the given lengths; therefore, if these three lengths, 7 cm, 24 cm, and 25 cm, are the lengths of the sides of a triangle, then the triangle is indeed a right triangle.

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