Answer:
1st Option;
j = 4.5
k = 2
Step-by-step explanation:
Let's solve for "j" first:
=> We know that by the definition of midpoint segment theorem we can say;
3j = 5j - 9
0 = 5j - 3j - 9
0 = 2j - 9
0 + 9 = 2j
9 = 2j
9/2 = j
4.5 = j
=> Now that we have j-value we use the same method to solve for k-value;
6k = k + 10
6k - k = 10
5k = 10
k = 10/5
k = 2
Therefore;
j = 4.5
k = 2
<u>So the first option would be correct!</u>
Hope this helps!
Answer:
12
Step-by-step explanation:
The first cave has 7 times more bats than the last cave. So if the 45th cave has b bats, then the first cave has 7b bats.
There are 77 bats in every row of 7 caves. So if there are 7b bats in the first cave, then there are 77−7b bats in caves 2 through 7.
Since there are also 77 bats in caves 2 through 8, that means cave #8 must have 7b bats. Repeating this logic:
#1 = 7b
#2-#7 = 77−7b
#8 = 7b
#9-#14 = 77−7b
#15 = 7b
#16-21 = 77−7b
#22 = 7b
#23-28 = 77−7b
#29 = 7b
So the first 29 caves have 5(7b) + 4(77−7b) = 308 + 7b bats.
Now we do the same thing from the other end. If cave #45 has b bats, then caves #39-#44 have 77−b bats. And since caves #38-44 have 77 bats, then cave #38 has b bats. Therefore:
#45 = b
#39-44 = 77−b
#38 = b
#32-37 = 77−b
#31 = b
So caves 31 through 45 have 3b + 2(77−b) = 154 + b bats.
Adding that to the first 29 caves, plus x number of bats in cave #30:
308 + 7b + x + 154 + b = 462 + 8b + x
We know this equals 490.
490 = 462 + 8b + x
28 = 8b + x
x is a maximum when b is a minimum, which is b = 2.
28 = 8(2) + x
x = 12
There are at most 12 bats in the 30th cave.
The equivalent expression is 30x + 15y
<em><u>Solution:</u></em>
Given that we have to find the equivalent expression for given expression
<em><u>Given expression is:</u></em>
5(6x + 3y)
We can find the equivalent expression by using distributive property
The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.
<em><u>By distributive property,</u></em>
a(b + c) = ab + ac
Therefore, in given expression 5(6x + 3y), 5 can be multiplied with both 6x and 3y
Multiply the numbers and simplify
Thus the equivalent expression is 30x + 15y
Answer: 35.2101
( Hope your day goes well :) )
The distance between the anchor points of the two guy wires holding radio antenna is 181 feet (to the nearest foot)
<h3>How to determine the distance between the two anchor points of the guy wire</h3>
The problem will be solved using SOH CAH TOA
let the distance between the 150 ft long guy wire and the radio antenna be x
let the distance between the 180 ft long guy wire and the radio antenna be y
cos 65° = x / 150
x = cos 65° * 150
x = 63.39 ft
The height of the antenna
sin 65° = height of antenna / 150
height of antenna = sin 65 * 150
height of antenna = 135.95
using Pythagoras theorem
(length of guy wire)² = (height of the antenna)² + (anchor distance)²
(anchor distance)² = 180² - 135.95²
anchor distance = √(180² - 135.95²)
anchor distance = 117.97
The anchor points distance apart
= 63.39 + 117.97
= 181 (to the nearest foot)
Learn more on Pythagoras theorem here:
brainly.com/question/29241066
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