Answer:
- The third side may be between 1 and 13 units
Step-by-step explanation:
Let the missing side is x.
According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than the third side.
<u>We have inequalities:</u>
- 6 + 7 > x ⇒ x < 13
- 6 + x > 7 ⇒ x > 1
- 7 + x > 6 ⇒ x > - 1
<u>The common solution is:</u>
Answer:
Width = 17.5 feet,
Length = 82.5 feet.
Step-by-step explanation:
We have been given that Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard. This means that perimeter of rectangular front yard is 200 feet.
We know that perimeter of rectangle is two times the sum of length and width of rectangle. We can represent this information in an equation as:

We are also told that the length is 5 feet less than 5 times the width. We can represent this information in an equation as:

Upon substituting equation (2) in equation (1), we will get:



Therefore, the width of rectangular front is 17.5 feet.
Upon substituting
in equation (2), we will get:



Therefore, the length of rectangular front is 82.5 feet.
Answer:
<u>The cube root parent function:</u>
- f(x) =
![\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D)
<u>Horizontally stretched by a factor of 4:</u>
- g(x) → f(1/4x) =
![\sqrt[3]{1/4x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1%2F4x%7D)
<u>Translated 5 units right:</u>
- h(x) → g(x - 5) =
![\sqrt[3]{1/4x - 5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1%2F4x%20-%205%7D)
<u>Translated 3 units up:</u>
- k(x) → h(x) + 3 =
![\sqrt[3]{1/4x - 5} + 3](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1%2F4x%20-%205%7D%20%2B%203)
Answer:
78%
Step-by-step explanation:
70 = 0.50 (62) + 0.50 (x)
70 = 31 + 0.5x
39 = 0.5x
x = 78
You must get at least a 78% on the test to have at least 70% in the class.
11. 9/20
12. 13/20
13. 12/20
that's if it doesn't have to be in percentage form