Answer:
The value of x is 7 ⇒ 1st answer
Step-by-step explanation:
* Lets revise a fact in the circle
- The two tangents drawn from a point out side the circle are equal
∵ RSTUV is circumscribed about a circle
∴ Each side of the pentagon is a tangent to the circle
- Look to the attached figure to know how we will solve the problem
- Each tangent divided into two parts
# RS = x + y
∵ RS = 8
∴ x + y = 8 ⇒ (1)
# RV = x + n
∵ RV = 12
∴ x + n = 12 ⇒ (2)
- Subtract (2) from (1)
∴ y - n = -4 ⇒ (3)
# ST = y + z
∵ ST = 12
∴ y + z = 12 ⇒ (4)
# TU = z + m
∵ TU = 15
∴ z + m = 15 ⇒ (5)
- Subtract (5) from (4)
∴ y - m = -3 ⇒ (6)
# UV = m + n
∵ UV = 9
∴ m + n = 9 ⇒ (7)
- Add (6) and (7)
∴ y + n = 6 ⇒ (8)
- Lets solve equation (3) and equation (8) to find y
∵ y - n = -4 ⇒ (3)
∵ y + n = 6 ⇒ (8)
- Add (3) and (8)
∴ 2y = 2 ⇒ divide two sises by 2
∴ y = 1
- Lets substitute the value of y in equation (1)
∵ x + y = 8 ⇒ (1)
∵ y = 1
∴ x + 1 = 8 ⇒ subtract (1) from both sides
∴ x = 7
* The value of x is 7
If Jim missed 6 out of 16 free throws, then he made 10/16 free throws. At the same time Gracia made 4/15 free rows. The common denominator of those fractions (if we simplify 10/16 to 5/8) is 120, so:
Garcia made 4/15 = 32/120 free throws
Jim made 5/8 = 75/120 free throws
We can clearly see that Jim was more than two times better than Garcia.
Answer:
Step-by-step explanation:
This is the sum of perfect cubes. There is a pattern that can be followed in order to get it factored properly. First let's figure out why this is in fact a sum of perfect cubes and how we can recognize it as such.
343 is a perfect cube. I can figure that out by going to my calculator and starting to raise each number, in order, to the third power. 1-cubed is 1, 2-cubed is 8, 3-cubed is 27, 4-cubed is 64, 5-cubed is 125, 6-cubed is 216, 7-cubed is 343. In doing that, not only did I determine that 343 is a perfect cube, but I also found that 216 is a perfect cube as well. Obviously, x-cubed and y-cubed are also both perfect cubes. The pattern is
(ax + by)(a^2x^2 - abxy + b^2y^2) where a is the cubed root of 343 and b is the cubed root of 216. a = 7, b = 6. Now we fill in the formula:
(7x + 6y)(7^2x^2 - (7)(6)xy +6^2y^2) which simplifies to
(7x + 6y)(49x^2 - 42xy + 36y^2)
Answer:
The advantage to the lender would be that he’s getting money & if the person doesn’t pay the rest of the price they at least got some money , and the advantage for the borrower is that they can pay the rest later.
Step-by-step explanation:
Answer:
$50.16
Step-by-step explanation:
There is a sale tax on the item to be purchased, and the tax is 4.5% of the amount of the flag i.e 4.5% × $48.00 = $2.16
After the rate of the sale tax has been changed to dollars, we then add the amount of the sales to the amount of the flag to give the total amount to be paid i.e $2.16 + $48.00 = $50.16
Thank You
