Answer:
x=21
Step-by-step explanation:
subtract 6 from both sides get -1/3x=-7
multiply -1/3 or -1/3 as decimal times -7
and get x=21
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Answer:
2520cm²
Step-by-step explanation:
Surface area = sum of the area of all the bases.
Area of bottom base = 28 * 30 = 840
Area of right base = 25 * 30 = 750
Area of left base = 17 * 30 = 510
Area of two triangles = ( 15 * 28 ) / 2 = 210 * 2 = 420
Then add all the areas together to find surface area
Surface area = 840 + 750 + 510 + 420 = 2520cm²
Relevant Formulas:
Area of a rectangle = length * width. This formula was used to find the area of the bottom base, the right base and the left base
Area of a triangle = ( height * base length ) / 2 . This formula was used to find the area of the sides which are triangles.
Answer:
Since this is a right triangle with one angle and hypotenuse given and opposite side unknown, we can use the definition of sine to find the unknown side.
sin 17 = x/hypotenuse = x/19
x = 19sin17 = 5.6
<span>x^2 + 15x + 56.25 = 105.25
"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.
Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?"
Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25
Now take the square root of each side
(x+7.5) = sqrt(105.25)
And let's use both the positive and negative square roots.
So
x+7.5 = 10.25914226
and
x+7.5 = -10.25914226
And let's find X.
x+7.5 = 10.25914226
x = 2.759142264
x+7.5 = -10.25914226
x = -17.75914226
So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
