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belka [17]
3 years ago
5

If a number is increased by its square, the result is 72 find the number

Mathematics
1 answer:
gregori [183]3 years ago
8 0
Translating into a mathematical equation:

n + n^2 = 72

Rewriting,    n^2 + n - 72 = 0
Factoring,    (n+9)(n-8) = 0
Solving for n:  n = -9 or n = 8

You must check both answers before accepting one, the other or both.

Example:  suppose we check out n = 8.  Then  8 + 8^2 = 72 is true, and n = 8 is a solution.  Is n = -9 a solution?  Try it.
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alexandr402 [8]

15. is your answer. have a good day

3 0
2 years ago
Read 2 more answers
Need help plz!!!!? Help would be appreciated
kolbaska11 [484]

Answer:

118•

Step-by-step explanation:

The interior side lengths are:

90

180-34

180-x

180-x

The sum of these are 360º

90 + 180-34 + 180-x + 180-x = 360

-2x = -236

x = 118º

3 0
3 years ago
In the given figure find the value of the unknown interior angle x in the following figure.​
Leto [7]

Answer:

Therefore, the measure of angles x is 55°.

Step-by-step explanation:

From the given figure ,

105° is the exterior angle

x° and 50° are the two interior opposite angles to 105°

We know that

An exterior angle formed by extending the side of a triangle is equal to the sum of the two interior opposite angles

⇛ x° + 50° = 105°

⇛ x° = 105°-50°

⇛ x° = 55°

Therefore , x = 55°

<u>Exterior</u><u> </u><u>Angle:</u><u>↓</u>

An exterior angle formed by extending the side of a triangle is equal to the sum of the two interior opposite angles.

Hope this helps!!

5 0
2 years ago
1-cot^2a+cot^4a=sin^2a(1+cot^6a) prove it.​
aliina [53]

Step-by-step explanation:

We have

1-cot²a + cot⁴a = sin²a(1+cot⁶a)

First, we can take a look at the right side. It expands to sin²a + cot⁶(a)sin²(a) = sin²a + cos⁶a/sin⁴a (this is the expanded right side) as cot(a) = cos(a)/sin(a), so cos⁶a = cos⁶a/sin⁶a. Therefore, it might be helpful to put everything in terms of sine and cosine to solve this.

We know 1 = sin²a+cos²a and cot(a) = cos(a)/sin(a), so we have

1-cot²a + cot⁴a = sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

Next, we know that in the expanded right side, we have sin²a + something. We can use that to isolate the sin²a. The rest of the expanded right side has a denominator of sin⁴a, so we can make everything else have that denominator.

sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

= sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

We can then factor cos²a out of the numerator

sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

= sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

Then, in the expanded right side, we can notice that the fraction has a numerator with only cos in it. We can therefore write sin⁴a in terms of cos (we don't want to write the sin²a term in terms of cos because it can easily add with cos²a to become 1, so we can hold that off for later) , so

sin²a = (1-cos²a)

sin⁴a = (1-cos²a)² = cos⁴a - 2cos²a + 1

sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-2cos²a+1-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

factor our the -cos²a-sin²a as -1(cos²a+sin²a) = -1(1) = -1

sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

=  sin²a + cos²a (cos⁴a-1 + 1)/sin⁴a

= sin²a + cos⁶a/sin⁴a

= sin²a(1+cos⁶a/sin⁶a)

= sin²a(1+cot⁶a)

8 0
2 years ago
Shawn is conducting an experiment where he is flipping a fair coin (where the probability of the coin landing heads up is 50%).
Serhud [2]
I believe the answer is d
8 0
3 years ago
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