Answer:
a. LK = 4√3, JL= 4√6
b. PQ = 10√3, RP = 5√3
Step-by-step explanation:
a. LK =4√3,
LK=KJ= 4√3
sin(45°) = opposite/hypotenuse
hypotenuse (JL)= opposite/sin 45° = 4√3/√2/2 = 8√3/√2 = 8√3√2/2 = 4√6
b.
cos 30° = adjacent/hypotenuse = QR/PQ = 15/PQ
cos 30° = 15/PQ
PQ = 15/cos 30° = 15/√3/2)= 30/√3 = 30√3/3 = 10√3
tan 30° = opposite/adjacent = RP/QR
√3/3 = RP/QR
√3/3 = RP/15
RP = √3*15/3 = 5√3
Answer:
Yes
Step-by-step explanation:
Well let's solve it!
In order to solve this, plug in x into the equation.
Let's do the side on the LEFT of the equal sign first.
3(3+1) = 3(4) = 12
Now Let's do the side on the RIGHT of the equal sign.
3(3) + 3 = 9+3 = 12
So this means they are equal or congruent!
Hope this Helped!
What is the total number of students? you need to divide 260/total number
Let's take this problem step by step:
Step 1: First, the problem states that the caterer prepares four times as many pizzas as she usually prepares for a large party. It also states that she usually prepares six pizzas.
Step 2: 6 x 4 = 24
Step 3: The caterer estimates that each party guest will eat 1/4 of a pizza.
Step 4: 24 pizzas divided by 1/4 of a pizza is equivalent to 24/(1/4)
Step 5: You can take the reciprocal of 1/4 and multiply instead.
Step 6: 24 x 4 = 96
The answer is 96 party guests.
a. Notice that
1/(1*2) = 1/2 = 1 - 1/2
1/(2*3) = 1/6 = 1/2 - 1/3
1/(3*4) = 1/12 = 1/3 - 1/4
and so on, which suggests the n-th term of the sum can be written as
Then the sum itself is telescoping:
b. The proof is trivial:
so the formula found in (a) is correct.
