2. What is the solution to the equation? If necessary, round your answer to the nearest tenth. A. 3x^2 = 48 B. x^2 – 2 = 12

Answers

Answer 1

Answer: The first one is 4, and the second one is 3.7

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Can someone please show how to solve this ln(5x-1)+ln(x-6)=ln6 ???

Answers

when you add ln, you multiply
ln((5x-1)(x-6)=ln6 do now FOIL
ln(5x^2-30x-x+6)=ln6
therefore
5x^2-31x+6=6 and
5x^2-31x=0 furthermore
x(5x-31)=0
one solution is 0, which we will reject
the other solution is 5x=31
x=31/5

ln(5x - 1) + ln(x - 6) = ln(6)
ln((5x - 1)(x - 6)) = ln(6)
      ln(5x(x - 6) - 1(x - 6) = ln(6)
ln(5x(x) - 5x(6) - 1(x) - 1(-6)) = ln(6)
ln(5x² - 30x - x + 6) = lm(6)
ln(5x² - 31x + 6) = ln(6)
   5x² - 31x + 6 = 6
5x² - 31x + 6 - 6 = 6 - 6
   5x² - 31x + 0 = 0
x = -(-31) +/- √((-31)² - 4(5)(0))
   2(5)
x = 31 +/- √(961 - 0)
   10
x = 31 +/- √(961)
10
x = 31 +/- 31
   10
x = 31 + 31 x = 31 - 31
10 10
x = 62    x = 0
10 10
x = 6²/₅ x = 0

For the coordinates of P and M (the midpoint) are given. Find the coordinates for Q.P(3, 11) and M (0, 0)

Answers

Given an endpoint of a segment and a midpoint, the other endpoint can be obtained by manipulation of the midpoint formula. The said formula is shown below:

Let: (a,b) = coordinates of point 1 ; (c,d) = coordinates of point 2; (e,f) = coordinates of the midpoint

Midpoint = ( (a+c)/2 , (b + d)/2 )

From the formula: (a+c)/2 = e ; (b + d)/2 = f

Since we are already given an endpoint and the midpoint, we can solve for the other endpoint using the obtained equations. This is shown below:

(a+c)/2 = e
(3 + c)/2 = 0
c = -3

(b + d)/2 = f
(11 + d)/2 = 0
d = -11

Therefore, the coordinates of the other point is Q(-3,-11)

The length of a rectangle is three times longer than its width. The perimeter of the rectangle is 16 feet. If x represents the width of the rectangle, which equation can be used to find its value?

Answers

l = 3x
perimeter = 2(l + w) = 2(3x + x) = 2(4x) = 8x = 16
x = 16/8 = 2 feet
l = 3x = 3 * 2 = 6 feet

Jacob has a piece of toast that has butter on one side, and he dropped it twice. Both times it landed with the butter side up. If he drops it two more times, what is the probability that it will have landed butter side up a total of three times? one over four one over two one over three two over three

Answers

P(total of 3) = 2C1 * (0.5) * (0.5) = 2 * 0.25 = 0.5 = 1/2

Quick question!!!!!!!

Answers

Answer:

72.5

Step-by-step explanation:

Find the volume of a cube whose diagonal measures 36√3 cm.

Answers

Answer:

$46656 cm^3$

Step-by-step explanation:

If a cubes diagonal measures you can solve for its sidelength by creating a triangle. Visualize the diagonal as the hypotenuse of our triangle inside the cube. Then, one of the legs would be the side of the cube itself, and the other leg would be the diagonal of the bottom side of the cube. Knowing this is a cube, we can call each side s. If each side is s, then the diagonal of the bottom face is $s√(2)$ ( this is a special triangle property, $45-45-90$ triangle.) Then we know our triangle is a right triangle, so we can use the Pythagorean theorem to solve for s.