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VARVARA [1.3K]
3 years ago
15

Simplify. x+7/x^2+4x-21

Mathematics
1 answer:
mr_godi [17]3 years ago
7 0
To silpify the expression we proceed as follows:
(x+7)/(x^2+4x-21)
Factorizing the given the denominator:
x^2+4x-21
x^2-3x+7x-21
=x(x-3)+7(x-3)
=(x-3)(x+7)
thus plugging back in our expression we have:
(x+7)/[(x-3)(x+7)]
simplifying this we obtain:
1/(x+3) 

Answer: 1/(x+3) 

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Which best describes the triangle
sukhopar [10]

Answer:

B.

Step-by-step explanation:

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3 years ago
A towns population went from 25800 to 42600 in 15 years. What was the percent of change
Novay_Z [31]
42600-25800=16800
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4 0
4 years ago
GIVING BRAINLIEST PLEASE HELP How many triangles can you make with side lengths of 3mm, 7mm, and 4.69mm? (explain in words or nu
DanielleElmas [232]

Answer:

  1

Step-by-step explanation:

Three side lengths that meet the requirements of the triangle inequality will form exactly one triangle.

_____

The triangle inequality requires the sum of the short sides be at least as long as the long side. Here, we have 3 + 4.69 = 7.69 > 7, so we satisfy the triangle inequality.

The side lengths can be arranged in clockwise or counterclockwise order, least to greatest. Each triangle is a reflection of the other, so they are considered to be the same triangle (congruent).

3 0
3 years ago
Can please someone help me? The question is in the picture. Thank you
maxonik [38]

Answer:

C. 9\pi

Step-by-step explanation:

We proceed to solve for x by the Pythagorean Theorem:

(x+1)^{2} = (x-1)^{2} + (2\cdot x - 4)^{2} (1)

x^{2} + 2\cdot x + 1 = (x^{2}-2\cdot x + 1) + (4\cdot x^{2}-16\cdot x + 16)

x^{2} + 2\cdot x + 1 = 5\cdot x^{2}-18\cdot x  + 17

4\cdot x^{2} -20\cdot x + 16 = 0

(2\cdot x)^{2} -10\cdot (2\cdot x) + 16 = 0

(2\cdot x -8)\cdot (2\cdot x -2) = 0

There are two different solutions:

x_{1} = 4, x_{2} = 1

A solution of x is considered realistic when the length of every side of the triangle is a not negative number.

x_{1} = 4

UV = 2\cdot (4) - 4

UV = 4

WU = 4 - 1

WU = 3

WV = 4 + 1

WV = 5

x_{2} = 1

UV = 2\cdot (1) - 4

UV = -2

WU = 1 - 1

WU = 0

WV = 1 + 1

WV = 2

The only realistic set of solutions is for x = 4, and the radius of the circle is represented by the line segment WU: r = 3

And the area of the circle (A) is calculated from the following formula:

A = \pi\cdot r^{2}

A = \pi\cdot (9)

A = 9\pi

The correct answer is C.

6 0
3 years ago
If the side lengths of a cube are 15 feet, what is the correct way to write the expression to represent the volume of the cube i
Oksi-84 [34.3K]

Answer:

D

Step-by-step explanation:

A cube is something that has the same length on all sides, so therefore, multiplying one of the side lengths by 3 gets you the answer.

5 0
3 years ago
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