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goldfiish [28.3K]
3 years ago
9

40 points + brainliest. Please solve using deductive geometry step by step.

Mathematics
1 answer:
Amanda [17]3 years ago
8 0

Answer:

Step-by-step explanation:

Tri WYV is a right triangle

WYV ~ SVU Reflective property

Angle YVW = Right angle, Right Triangle property

SVY ~ WVU by reflective property

VW = VU by perpendicular property

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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
saveliy_v [14]

Answer: Choice B

12.5 < x < 18.9

================================================

Explanation:

We have a triangle with these side lengths:

  • a = 10
  • b = 16
  • c = x = unknown

Let's assume that b = 16 is the largest side of this triangle.

By the converse of the pythagorean theorem, we need b^2 < a^2+c^2 to be true in order for an acute triangle to happen.

So,

b^2 < a^2 + c^2\\\\c^2 > b^2 - a^2\\\\c > \sqrt{b^2-a^2}\\\\x > \sqrt{16^2-10^2}\\\\x > \sqrt{156}\\\\x > 12.4899959967968 \ \text{(approximate)}\\\\x > 12.5

Now let's consider the possibility that the missing side x is actually the longest side.

Using the same theorem as before, we would say,

c^2 < a^2 + b^2\\\\c < \sqrt{a^2 + b^2}\\\\x < \sqrt{10^2 + 16^2}\\\\x < \sqrt{356}\\\\x < 18.8679622641132 \ \text{(approximate)}\\\\x < 18.9\\\\

We found that x > 12.5 and x < 18.9

This is the same as saying 12.5 < x and x < 18.9

Put together, they form the approximate answer of 12.5 < x < 18.9

6 0
2 years ago
Suppose that the batting averages or AVG (hits per at-bat) of all players in the AAA baseball league are normally distributed wi
bulgar [2K]

Answer:

0.1

Step-by-step explanation:

Solving using empirical rule formula

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Hence, the lower bound 95% =

μ - 2σ

Mean = 0.2

Standard deviation of 0.05

= μ - 2σ

= 0.2 - 2(0.05)

= 0.2 - 0.1

= 0.1

The lower bound is 0.1

6 0
3 years ago
Noel has rowing lessons every 5 days and guitar lessons every 6 days. If he had both lessons on the last day of the previous mon
bixtya [17]

Answer:

Since every 30 days  he  wil have both lessons on the same day , and  he already  had both lessons on the last day of the previous month, that means that the day 30  the current month   he  wil have both lessons on the same day (It may be the last day if the month has 30 days or it may not be the last day if the month has 31 days)

Step-by-step explanation:

Lets find the least common factor of 5 and 6

Multiples of 5

5  10  15  20  35  30  35  40......

Multiples of 6

6  12  18  24  30 36  

LCF of 5 and 6 = 30

Every 30 days  he  wil have both lessons on the same day

3 0
3 years ago
The following equation is being multiplied by the LCD. Complete the multiplication to eliminate the denominators
frosja888 [35]

Answer:

(x+2)(x-2) -1(3x)=(x-3)(x-2)

Step-by-step explanation:

x+2/3x - 1/x-2 = x-3/3x

\frac{x+2}{3x}-\frac{1}{x-2}=\frac{x-3}{3x}

LCD is (3x)(x-2). so we multiply the whole equation by LCD

(3x)(x-2)(\frac{x+2}{3x}-\frac{1}{x-2}=\frac{x-3}{3x})

We multiply each term by LCD

(3x)(x-2)(\frac{x+2}{3x})-(3x)(x-2)(\frac{1}{x-2})=(3x)(x-2)(\frac{x-3}{3x})

(x+2)(x-2) -1(3x)=(x-3)(x-2)

4 0
3 years ago
Read 2 more answers
We can use special triangles to solve for x in triangle A<br>true or false​
KIM [24]
I believe the answer is false.

explanation: a special triangle has side lengths of 3-4-5 or 6-8-10. In this case since you have 10 one of the other sides would have to be 6 or 8. You can use pythagorean theorem.
8 0
2 years ago
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