Answer:
a) (x/2 +3)^2
b) (5a -3b)^2
c) (x/3 +y/5)^2
d) (10b -3c)^2
e) (a/4 -2b)^2
Step-by-step explanation:
Assuming you can do that, write the terms of the quadratic in lexicographical order. (The square terms will be first and last.) Then the binomial is the "sum" of the square roots of the first and last terms with the sign of the middle term.
Using (e) as an example, the term are already in order. (In (d), they need to be rearranged.) The first term is 1/16a^2, and its square root is 1/4a = a/4. The last term is 4b^2 and its square root is 2b. The sign of the middle term is negative, so these two roots will be separated by a minus sign:
(a/4 - 2b)^2
The expression you want is the square of the binomial.
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As a check, you can make sure that double the product of these terms is the middle term of the trinomial you started with.
In this example, that double product is 2·a/4·(-2b) = -ab, which exactly matches the middle term you started with.
Answer:
Step-by-step explanation:
Given that Ten fish from each species were randomly selected from each of three lakes and their respective lengths were recorded
a) Experimental unit is the length of two species of fish of lake trout.
b) Population is the set of all species in the lake
c) Sample is the twenty taken for testing
d) Response variable is the length of the fish
e) This is an observational study as already existing is recorded without any external control to change.
Circumference of a circle: 2 * Pi * R
1. Calculate radius from diameter.
Radius = Diameter/2
Radius = 15/2
Radius = 7.5cm
Formula to calculate the circumference:
2 * Pi * R
= 2 * Pi * 7.5
= 15 * Pi
= About 47.10 cm in terms of Pi.
So, in conclusion, the circumference if this circle is about: 47.10cm.
I hope this helps you
--29+30
+1
Answer: 11x
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Explanation:
Let L be the length of rectangle B
There are two copies of L (along the top and bottom of the rectangle). The vertical pairs of sides are both 7x each.
For the triangle, we have three sides of 12x since this is an equilateral triangle. All three sides are congruent for any equilateral triangle.
The perimeter of the triangle is
P = s1+s2+s3
P = 12x+12x+12x
P = 36x
The perimeter of the rectangle is
P = 2*L+2*W
P = 2L+2*7x
P = 2L+14x
Since both perimeters are the same, this means
perimeter of triangle = perimeter of rectangle
36x = 2L+14x
36x-14x = 2L+14x-14x
22x = 2L
2L = 22x
2L/2 = 22x/2
L = 11x
So the length of the rectangle, in terms of x, is 11x. This is the final answer.
Note: if we knew the value of x, then we could find the numeric value of the length for the rectangle. But since we don't know x, we leave it as 11x.