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konstantin123 [22]
4 years ago
14

2.√3x + 7 + √x + 1 =2​

Mathematics
1 answer:
taurus [48]4 years ago
5 0

Answer:

  x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

  \displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

_____

Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

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Rickey has been commissioned to paint a mutual that is allowed to have an area 60 square meters to make the rectangulr shape of
Svet_ta [14]

Answer:

Length of the mural should be 20.78 m

Step-by-step explanation:

Let the length of the mural be L and the width W

Area = L × W = 60 m²

Ticket wants the L = 15 + 2W

Substitute for L in the Area eqn

(15 + 2W) × W = 60

15W + 2W² = 60

2W² + 15W - 60 = 0

Solving the quadratic equation

W = 2.89 m or - 10.39 m

Obviously, the width cannot be negative,

So, W = 2.89 m

L = 15 + 2W = 15 + 2(2.89) = 20.78 m

Check - L × W = 20.78 × 2.89 = 60 m²

Hope this Helps!!!

5 0
3 years ago
Round all the way 2689
Ratling [72]
2689

rounded to the nearest tens = 2690
rounded to the nearest hundreds = 2700
rounded to the nearest thousands = 3000

If the number before the place it needs to be round off is 5 and above, then it is rounded up. If the number is 4 and below, it is rounded down.

For example: 
2444 

rounded to the nearest tens = 2440
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rounded to the nearest thousands = 2000
4 0
4 years ago
How would you explain to someone the rules of a horizontal translation where we are subtracting from the inputs(within the paren
chubhunter [2.5K]

Answer:

Ok, we know that we can write a horizontal translation as:

y' = f(x - A)

where if A is positive, this moves the graph of f(x) A units to the right.

Why is this?

Ok, let's compare:

y = f(x)

and

y' = f(x - A)

in y, when x = 0 we have f(0).

While to have this same point in y', we need to evaluate in x = A.

f(A - A) = f(0).

Then the value f(0) is now at x = A, this means that the point moved A units to the right.

And you can do this for all the values, so you will find that the entire graph of f(x) has ben moved A units to the right.

5 0
3 years ago
A tessellation has 2 pairs of congruent angles around the point of intersection. The measure of each of one pair of congruent an
Over [174]

9514 1404 393

Answer:

  152°

Step-by-step explanation:

If two pairs of congruent angles total 360°, then the different angles must total 180°. The other angle measure is 180° -28° = 152°.

The measure of each angle in the other congruent pair is 152°.

8 0
3 years ago
Solve the one step equation: x-7=13
topjm [15]
The answer is:
X=20
This is because 20-7=13 and makes a true statement
Hope this helps have a good day! :)
6 0
3 years ago
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