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UNO [17]
2 years ago
14

How many solutions does the system of equations x − y = 7 and y equals the square root of the quantity 3 times x plus 3 end quan

tity minus 2 have?
Mathematics
1 answer:
Alla [95]2 years ago
8 0

9514 1404 393

Answer:

  one solution (11, 4)

Step-by-step explanation:

Both equations describe curves with positive slope. The y-intercept of the line (-7) is less than that of the root function (-2), so the line must intersect the root function in exactly one place. There is one solution.

__

Solved in the conventional way, the equation would become a quadratic, with two solutions. One of them is extraneous. (That is why I prefer a graphical solution.)

Given ...

  x -y = 7

  y = √(3x +3) -2

We can substitute for y to get ...

  x -7 = √(3x +3) -2

  x -5 = √(3x +3)

  x^2 -10x +25 = 3x +3 . . . . . . square both sides

  x^2 -13x +22 = 0 = (x -11)(x -2) . . . . . gives solutions x=11, x=2

The value x=2 does not satisfy the equation ...

  x -7 = √(3x +3) -2   ⇒   2 -7 = √(3·2 +3) -2   ⇒   -5 = 1 (false)

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stiv31 [10]

Answer:

45 square units.

Step-by-step explanation:

Applying the pythagoras theorem:

Base of the bigger triangle = \sqrt{15^2 - 9^2} = \sqrt{144} = 12 units

Area of a triangle is given by \frac{1}{2} × base × height

The area of the bigger triangle is  \frac{1}{2} × 12 × 9 = 54 square units.

The area of the smallest triangle is  \frac{1}{2} × (12 - 10) × 9 = 9 square units.

The area of the figure( required triangle) is 54 - 9 = 45 square units.

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2 years ago
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iVinArrow [24]

Answer:

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Step-by-step explanation:

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3 0
2 years ago
An Equilateral Triangle has sides that all measure 10 inches. What is
densk [106]

Answer:

easy peasy lemon squeasy

Step-by-step explanation:

1. base of triangle: it is an equilateral triangle, so any side of the triangle you take is the base, (usually the largest side of the triangle is the base)

so that would be => 10 inches,

2. a property of an equilateral triangle is that , the median of the triangle coincides with the height of the triangle,

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4 0
3 years ago
The Walt Disney Company paid a $0.35 annual dividend on a day it closed at a price of
Dennis_Churaev [7]

Answer:\

hey check out the attachment i found them online hope it help and thank you!

I looked for them like for 20 min I finnaly found them

Have a nice day/night! LOL

Step-by-step explanation:

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2 years ago
Method for converting an angle in radians to degrees
vladimir1956 [14]

Answer:

Step-by-step explanation:

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