Answer:
1.5.80 miles
2.9.80ft
3.56 inches
4.5.20 units
5. 13 units
6.5.40 ft
Step-by-step explanation:
⇒These questions are on the Pythagorean relationship
⇒General expression is ;
a²+b²=c² where a and b are values for the legs and c is the hypotenuse
1. Isaiah waked 3 miles north and 5 miles east.
Finding the distance from starting point we apply the equation;
a²+b²=c² where a=5 miles and b=3miles
5²+3²=c²
25+9=c²
34=c²
c=√34 = 5.80 miles
2.The ladder is leaning against the wall to form the hypotenuse side of 10 ft.The distance from the base to the ladder forms side a= 2ft. The question requires you to calculate the height b.
a²+b²=c²
2²+b²=10²
4+b²=100
b²=100-4
b=√96
b=9.80 ft
3. The television has a diagonal of 70 inches to represent side c and a height of 42 inches to represent the side a. The question requires you to find the width of the television which represents the side b
a²+ b²=c²
42²+b²=70²
b²=70²-42²
b=√3136
c=56 inches
4. An equilateral triangle is one that has all its sides and angles equal. Here you have to introduce a perpendicular line from the apex point of the triangle to the base and get the distance a.The using the hypotenuse and the distance a, you can find the height/b.
c= 6 units and a=6/2= 3 units
a²+b²=c² 3²+ b²= 6²
9+b²=36
b²=36-9
b=√27 =5.20 units
5.In this question, you are given the height and the width of the right triangle thus apply the relationship as;
a²+b²=c²..........where a=5 and b=12
5²+12²=c²
25+144=c²⇒⇒⇒c=√169 =13 units
6. In this question, the height of the plant represents side b and the distance of the base from where the string is tied is side b.You are to find the length of the string which represents the hypotenuse side.
a²+b²=c²
5²+2²=c²
25+4=c²
29=c²
√29=c
c=5.40 ft
Hi, you've asked an incomplete question. However, I inferred you need a brief explanation about The Collatz conjecture.
<u>Explanation:</u>
Put simply, what the Collatz conjecture unsolved problem entails is that if any positive number is picked and it is:
- An even number (eg 2, 4, 6,...), then if they are divided by 2, the new number gotten should undergo the same process (that is to be divided by 2), it is believed your calculation would finally end up at 1. For example, let's pick the number 6, (6÷2=4; repeating the process 4÷2=<u>1</u>)
- An odd number, then if they are multiplied by 3 and 1 is added to the result, it is believed that your calculation would finally end up at 1.
Answer:
The correct option is (1,2), (0, 1), (1, 2), (2, 4).
Step-by-step explanation:
Consider the provided ordered pairs.
The exponential function is in the form of 
Where, a is the initial amount 
and b is the rate of change b>0, 
The graph of each exponential function passes through the point (0, a),
and
Therefore, Option 1 and 2 and 4 are false.
Hence, the correct option is (1,2), (0, 1), (1, 2), (2, 4).
Answer:
E'F'/EF = 4/2 = 2
F'G'/FG = 3/4 = 0.75
Step-by-step explanation:
From the graph shown, the distance between E' and F' is E'F'. Hence;
E'F' = 8 - 4 = 4
EF = 4 - 2 = 2
Hence E'F'/EF = 4/2 = 2
SIMILARLY,
F'G' = G' - F'
F'G = 9 - 6 = 3
FG = G - F
FG = 5 - 1 = 4
F'G'/FG = 3/4
F'G'/FG = 0.75
the length of SR is 
.
<u>Step-by-step explanation:</u>
Here we have , On square PQRS below, if Q is located at (7,0) and R is located at (5,-8) . We need to find Length of side SR . Let's find out:
We know that , In a square there are 4 sides , and length of every side is same . So side length of SR = side length of QR . Now , Let's find side length of QR .
We know that distance between two points 
given by :
⇒ 
Two points given are 
:
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
But QR=SR , Therefore , the length of SR is .
