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jenyasd209 [6]
3 years ago
8

What are the domain and range of this function

Mathematics
1 answer:
belka [17]3 years ago
3 0
f(x)=\sqrt{x-7}+9\\\\\text{the domain:}\\x-7\geq0\to x\geq7\\\\\text{the range:}\\\sqrt{x-7}\geq0\ \text{therefore}\ \sqrt{x-7}+9\geq9\\\\y\geq9

Answer:\\domain:\ x\geq7\\range:\ y\geq9
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Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). What are the possible coordina
grandymaker [24]

Important question. No menu of choices given so we'll just have to figure it out.

It's not possible in two dimensions for all three vertices of an equilateral triangle to be lattice points, i.e. points with integer coordinates.  

Since A(-2,1) and B(4,1) have integer coordinates, our other point won't. There will be a √3 involved, the algebraic tell that there's a 30/60/90 triangle lurking somewhere in the problem.

Here the given side is parallel to the x axis which makes things easier.  

|AB| = 4 - -2 = 6

The x coordinate of the third vertex will be the same as that of the midpoint of AB, let's call it M,

M = ( (-2 + 4) / 2, (1 + 1)/2 ) = (1, 1)

We're making some progress.  Whatever our height h is our two candidates for the third vertex C are (1, 1 ± h).

Since |AB|=6, we get |AB|=|BC|=|AC|=6 because it's an equilateral triangle.

The altitude CM bisects the triangle into 2 30/60/90 triangles.  Let's take one of them, AMC.  Angle AMC is a right angle, so we have a right triangle with legs |AM|=3 and |CM|=h, and hypotenuse |AC|=6. The Pythagorean Theorem tells us:

3² + h² = 6²

9 + h² = 36

h² = 27

h = 3√3

Answer: C is (1, 1 + 3√3) or (1, 1 - 3√3)

4 0
3 years ago
What is the answer to 8k-4(k-1)+7-k
seropon [69]
8k-4k+4+7-k = 
8k-4k-k+4+7 = 
3k+11
8 0
3 years ago
Read 2 more answers
Complete the comparison: 26 < ? A. 25 B. 54 C. 13 D. 26
Nookie1986 [14]
The answer for that one is B, because 26<54
meaning 26 is less than 54 which is true 
6 0
3 years ago
Read 2 more answers
Help, i'll give a brainliest
Valentin [98]

Answer:

The equation is y=2x + 2

Step-by-step explanation:

4x+2y=7

2y=-4x+7

y=-2x+7/2

Hence, the gradient =-2

Note that: parallel lines share the same gradient

sub m(gradient)=-2 and the point (1,0) into y=mx+c

0=-2(1)+c

c=2

Therefore, the equation in the form of y=mx+c is y=-2x+2

8 0
3 years ago
Is the equation y + 1=7(x+2) in point slope form
olga nikolaevna [1]
No nodcause it has to me in y=mx+b form. so just sub. 1 from each side
8 0
3 years ago
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