Answer:
1) Yes 2)No
Step-by-step explanation:
1) Yes because the two shorter lines combined are longer than the base and so those two lines are able to make a triangle.
2) No because the two lines on top will be equal to base line and so the two shorter lines will not be able to make a third angle because it will be level with the base.
Answer:
Step-by-step explanation:
If two polygons are similar, then corresponding sides are in proportion.
The corresponding sides:
4 → x
y → 15
3 → w
2 → 6
z → 9
therefore:
<em>cross multiply</em>
<em>divide both sides by 6</em>
Hey there!
Okay, so when you get a problem like this, all you need to do in insert the given value into the function and solve.
For example:
As you can see, they state that <em>(a) = 27, </em>so you insert 27 in for a in the function and it will look like this:
h(27) = 3(27) + 5
Now you solve on the right side of the equal sign:
3(27) = 81 (you multiply them)
81 + 5 = 86
When you plug the value of 27 in for a in this function, your output is equal to 86.
Answer: Yes
Step-by-step explanation:
When using the distributive property, 6(2x + 4) becomes 12x + 24
6 * 2x = 12x and 6 * 4 = 24
12x + 24 = 12x + 24
Therefore, the expressions are equivalent.
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>
