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Nonamiya [84]
3 years ago
15

The difference of the square of a number and 16 is equal to 6 times that number. Find the negative solution.

Mathematics
1 answer:
melamori03 [73]3 years ago
4 0

Answer:

The negative solution is -2

Step-by-step explanation:

Let the number be x

x² - 16 = 6x

Equate the equation to zero (0)

x² - 6x -16 = 0

Factorize

x² + 2x -8x - 16 = 0

x(x + 2) -8(x + 2) = 0

Therefore,

(x-8) (x +2) = 0

x -8 = 0         or           x +2 = 0

x = 8             or            x = -2

The negative solution is -2

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mestny [16]
Mabel spends 4 hours editing a 3 minute video. she edits at a constant rate. how long does mabel spend to edit a 9 minute video?

she spends 4 hours on a 3 minute video
so there are 60 minutes in an hour
4 hours with 60 minutes- 4x60=240
so she spent 240 minutes on a 3 minute video
3 divided by 240
3/240= 0.0125
so her constant rate is 0.0125 minutes an hour
so divide 9 minutes by her constant rate
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7 0
3 years ago
Given that 1 x2 dx 0 = 1 3 , use this fact and the properties of integrals to evaluate 1 (4 − 6x2) dx. 0
Debora [2.8K]

So, the definite integral  \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

Given that

\int\limits^1_0 {x^{2} } \, dx = 13

We find

\int\limits^1_0 {(4 - 6x^{2} )} \, dx

<h3>Definite integrals </h3>

Definite integrals are integral values that are obtained by integrating a function between two values.

So, Integral \int\limits^1_0 {(4 - 6x^{2} )} \, dx

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx = \int\limits^1_0 {4} \, dx - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - 6\int\limits^1_0 {x^{2} } \, dx \\= 4[1 - 0]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4[1]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4    - 6\int\limits^1_0 {x^{2} } \, dx

Since

\int\limits^1_0 {x^{2} } \, dx = 13,

Substituting this into the equation the equation, we have

\int\limits^1_0 {(4 - 6x^{2} )} \, dx = 4 - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6 X 13 \\= 4 - 78\\= -74

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

Learn more about definite integrals here:

brainly.com/question/17074932

4 0
2 years ago
Question 29 of 30
frozen [14]

Answer:

7/10

Step-by-step explanation:

this is the simplest form

3 0
2 years ago
From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will ne
Morgarella [4.7K]
For this case, what we must do is solve the following system of equations:
 tan (50) = h / x
 tan (40) = h / (x + 50)
 Solving the system we have:
 (x + 50) * tan (40) = h
 (x) * tan (50) = h
 Matching:
 (x + 50) * tan (40) = (x) * tan (50)
 Rewriting:
 x (tan (50) - tan (40)) = 50 * tan (40)
 x = 50 * tan (40) / (tan (50) - tan (40))
 x = 118.9692621
 Substituting:
 h = (x) * tan (50)
 h = (118.9692621) * tan (50)
 h = 141.7820455
 Answer:
 
The height of the building is:
 
h = 141.7820455 ft
5 0
3 years ago
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uysha [10]
2/3 is the answer to this problem.
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