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Allisa [31]
3 years ago
12

What is the following simplified product? Assume x greater-than-or-equal-to 0

Mathematics
2 answers:
nlexa [21]3 years ago
5 0

Answer:

  10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}

Step-by-step explanation:

Remove perfect squares from under the radicals.

  (\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\=(\sqrt{10x^4})(2\sqrt{15x^4}) +(\sqrt{10x^4})(\sqrt{3x^3}) -(x\sqrt{5x^2})(2\sqrt{15x^4}) -(x\sqrt{5x^2})(\sqrt{3x^3})\\\\=2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\=\boxed{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}

_____

The applicable rules of exponents are ...

  (x^a)(x^b) = x^(a+b)

  √(a^2) = a . . . . . . . for a > 0

  (√a)(√b) = √(ab)

lapo4ka [179]3 years ago
4 0

Answer:

See attached.

Step-by-step explanation:

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An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles
uranmaximum [27]

Answer:

The airplane flies 95 miles.

Step-by-step explanation:

  1. First we need to find the distance for the first segment using the formula for distance D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}. Let's say (x_{1},y_{1}) is (0, 0) and (x_{2},y_{2}) is (33, 56). This gets us that the length of this segment is 65 miles.
  2. Next, we need to find the distance for the second segment. Using the same formula for distance  D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}, we can say (x_{1},y_{1}) is now (33, 56) and (x_{2},y_{2}) is now (23, 32). This gets us that the length of this segment is 26 miles.
  3. To get the total distance traveled, add the length of these two segments together (65 miles + 26 miles) to get 91 total miles traveled.
7 0
2 years ago
Read 2 more answers
Shop sells bagles for 5 per dozen how much bagles can you buy for 50
spayn [35]
120 Bagels
Explanation:
if you get 12 bagels for 5 dollars, and your wondering how many you’d get for 50 dollars, 5 times 10 is 50 and 10 times 12 is 120. That doesn’t make the most sense but yes
3 0
3 years ago
I don't know to find the answer to 8. Can someone explain to me?
lapo4ka [179]
Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.

A) The midpoint C' of AB is
.. (A +B)/2 = ((0, 0) +(m, n))/2 = ((0 +m)/2, (0 +n)/2) = (m/2, n/2) = C'
The midpoint B' is
.. (A +C)/2 = ((0, 0) +(p, 0))/2 = (p/2, 0) = B'
The midpoint A' is
.. (B +C)/2 = ((m, n) +(p, 0))/2 = ((m+p)/2, n/2) = A'

B) The slope of the line between (x1, y1) and (x2, y2) is given by
.. slope = (y2 -y1)/(x2 -x1)
Using the values for A and A', we have
.. slope = (n/2 -0)/((m+p)/2 -0) = n/(m+p)

C) We know the line goes through A = (0, 0), so we can write the point-slope form of the equation for AA' as
.. y -0 = (n/(m+p))*(x -0)
.. y = n*x/(m+p)

D) To show the point lies on the line, we can substitute its coordinates for x and y and see if we get something that looks true.
.. (x, y) = ((m+p)/3, n/3)
Putting these into our equation, we have
.. n/3 = n*((m+p)/3)/(m+p)
The expression on the right has factors of (m+p) that cancel*, so we end up with
.. n/3 = n/3 . . . . . . . true for any n

_____
* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.

The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
7 0
3 years ago
Is a percent a number?
mars1129 [50]
Yes, percent is a number.
7 0
3 years ago
Read 2 more answers
By visual inspection, determine the best-fitting regression model for the data plot below.
NeX [460]

Answer:

Quadratic

Step-by-step explanation:

It looks like it’s forming a very wide arch so quadratic formulas are arches

7 0
3 years ago
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