2. An aerial mast is supported by four wires attached to points on the

20 Points! Which ordered pair is the best estimate for the solution of the system of equations?

yan [13]

Answer:

The best estimate for the solution is the ordered pair $(-6.5,-3.5)$

Step-by-step explanation:

we have

$y=\frac{3}{2}x+6$ ------> equation A

$y=\frac{1}{4}x-2$ ------> equation B

we know that

using a graphing tool, the solution of the system of equations is the intersection point both graphs

The intersection point is $(-6.4,-3.6)$

therefore

The best estimate for the solution is the ordered pair $(-6.5,-3.5)$

3 0

2 years ago

If a = √3-√11 and b = 1 /a, then find a² - b²

Serga [27]

If $b=\frac1a$ , then by rationalizing the denominator we can rewrite

$b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8$

Now,

$a^2 - b^2 = (a-b) (a+b)$

and

$a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8$

$a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8$

$\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}$

5 0

1 year ago

Find the midpoint of X (26,56) and Y (26,1)

Svetradugi [14.3K]

Answer:

(26, $\frac{57}{2}$ )

Step-by-step explanation:

Hi there!

We are given the coordinates (26, 56) and (26, 1)

We want to find the midpoint of these two points

The midpoint can be found using the formula $(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2})$ , where $(x_1, y_1)$ & $(x_2, y_2)$ are points

We have 2 points, which is what we need to find the midpoint, but let's label the values of the points to avoid confusion and mistakes when actually calculating

$x_1=26\\y_1=56\\x_2=26\\y_2=1$