Answer:
Domain: (-∞, ∞)
Range: [0, ∞)
Step-by-step explanation:
The domain represents what x can be. In this scenario, we do not have x as a denominator, and there is nothing limiting x, so its domain is (-∞, ∞)
The range represents what f(x) can be, Because |x-4| is in absolute value, the lowest |x-4| can be is 0, and as a result, the lowest value of 2|x-4| is 2*0=0. The maximum value of f(x) is ∞ as an absolute value does not limit the maximum, making the range [0, ∞)
Answer:
The length of the rectangle is 12cm and the area of the rectangle is 60cm2.
Explanation:
By definition, the angles of a rectangle are right. Therefore, drawing a diagonal creates two congruent right triangles. The diagonal of the rectangle is the hypotenuse of the right triangle. The sides of the rectangle are the legs of the right triangle. We can use the Pythagorean Theorem to find the unknown side of the right triangle, which is also the unknown length of the rectangle.
Recall that the Pythagorean Theorem states that the sun of the squares of the legs of a right triangle is equal to the square of the hypotenuse. a2+b2=c2
52+b2=132
25+b2=169
25−25+b2=169−25
b2=144
√b2=√144
b=±12
Since the length of the side is a measured distance, the negative root is not a reasonable result. So the length of the rectangle is 12 cm.
The area of a rectangle is given by multiplying the width by the length.
A=(5cm)(12cm)
A=60cm2
Answer:
yes
Step-by-step explanation:
-8x-2y<6
put in x and y and see if it is less than 6
-8(3) -2(2) <6
-24 -4 <6
-28 <6
yes
it is a solution
<span>Simplifying
x2 + 8x + y2 + -2y = 64
Reorder the terms:
8x + x2 + -2y + y2 = 64
Solving
8x + x2 + -2y + y2 = 64
Solving for variable 'x'.
Reorder the terms:
-64 + 8x + x2 + -2y + y2 = 64 + -64
Combine like terms: 64 + -64 = 0
-64 + 8x + x2 + -2y + y2 = 0
The solution to this equation could not be determined.</span>
Well, kid all you have to do is add like terms and place the subjected terms in alphabetical order.
1. (6y-2c+2)+(-3y+4c)
2. 6y + - 3y = 3y
3. -2c+4c =2c
4. the positive in the first set of parenthesis has to term other than its number by itself. (so it remains alone and only positive 2)
5. take all the separate term answers and add them into a complete expression- 3y + 2c + 2: and that is all
