Answer:
<h3>Q1</h3>
<u>Use slope formula</u>
- m = (y2 - y1)/(x2 - x1)
- m = (-2 - 6)/(3 - 7) = -8 / -4 = 2
- m = 2
<h3>Q2</h3>
Angles 2 and 6 are on the corresponding sides of the parallel lines, hence are corresponding angle
<u>Correct option is </u>
<h3>Q3</h3>
Congruent triangles have congruent corresponding parts
- ΔABC ≅ Δ GHI
- AB≅GH
- AB = GH = 13
<u>Correct choice is</u>
<h3>Q4</h3>
Option b is correct for any line and doesn't make the lines parallel. The rest of the options are correct for parallel lines.
<u>Correct option is the last one:</u>
Answer:
<h2><em>
Three to the three fifths power.</em></h2>
Step-by-step explanation:
The given expression is
![\sqrt{3\sqrt[5]{3} }](https://tex.z-dn.net/?f=%5Csqrt%7B3%5Csqrt%5B5%5D%7B3%7D%20%7D)
To simplify this expression, we have to use a specific power property which allow us to transform a root into a power with a fractional exponent, the property states:
![\sqrt[n]{x^{m}}=x^{\frac{m}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D%3Dx%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D)
Applying the property, we have:
![\sqrt{3\sqrt[5]{3}}=\sqrt{3(3)^{\frac{1}{5}}}=(3(3)^{\frac{1}{5}})^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B3%5Csqrt%5B5%5D%7B3%7D%7D%3D%5Csqrt%7B3%283%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%7D%3D%283%283%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
Now, we multiply exponents:

Then, we sum exponents to get the simplest form:
![3^{\frac{1}{2}}3^{\frac{1}{10}}=3^{\frac{1}{2}+\frac{1}{10}} =3^{\frac{10+2}{20}}=3^{\frac{12}{20}} \\\therefore \sqrt{3\sqrt[5]{3}}=3^{\frac{3}{5} }](https://tex.z-dn.net/?f=3%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D3%5E%7B%5Cfrac%7B1%7D%7B10%7D%7D%3D3%5E%7B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B10%7D%7D%20%3D3%5E%7B%5Cfrac%7B10%2B2%7D%7B20%7D%7D%3D3%5E%7B%5Cfrac%7B12%7D%7B20%7D%7D%20%20%5C%5C%5Ctherefore%20%5Csqrt%7B3%5Csqrt%5B5%5D%7B3%7D%7D%3D3%5E%7B%5Cfrac%7B3%7D%7B5%7D%20%7D)
Therefore, the right answer is <em>three to the three fifths power.</em>
Answer:
85 units^2 = Area of Blue Square
and
x = 5 units
Step-by-step explanation:
To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.
Since we know the area of a square is the side length multiplied by itself (or the side length squared),
is the side length of the pink square and
is the side length of the green square.
That means a =
and b =
, so...

35 + 50 = c^2
85 = c^2

Now we need to square the square root of 85 to find the area of the blue square.

85 units^2 = Area of Blue Square
To solve the other question we use the same formula again.

x = 5 units