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
Answer:
The least common denominator of the expression is 72g.
Step-by-step explanation:
First, let us write the expression out mathematically
The denominators in the expression are 9 and 24g. To find the least common denominator, we will determine the least common multiple of the numbers (9 and 24) first, and then find the least common multiple of the result and g (since it is the only letter).
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
Multiples of 24 = 24, 48, 72, 96, ...
The least common multiple of 9 and 24 is 72.
Then, the least common multiple of 72 and g is 72g
Hence, the least common denominator of the expression is 72g.
<span> Pythagorean right triangle
a^2 + b^2 = c^2
Let the length of the ladder be x.
One side is x - 16.
The other side is x - 8.
</span><span>(x-16)^2 + (x-8)^2 = x^2
</span>
x^2 - 32x + 256 + <span>x^2- 16 x+64 = x^2
x^2 - 48 x + 320 = 0
( x- 40 ) (x-8) = 0
x = 40 or x= 8
we discard the second so x = 40
</span>
It is in the attachment.
Let me know if this helps.
also let me know if it shows up for you and if it don't ill post your answer in the comments.
Answer:
The number of ways of attaching the 10 resistors = 5¹⁰ = 9,765,625 ways
Step-by-step explanation:
Given;
total number of resistors, n = 10
number of slots available, = 5
The first resistor can be attached in 5 ways,
The second resistor can also be attached in 5 ways,
The third resistor can also be attached in 5 ways, etc
Each of the resistors can be attached in 5 different ways;
The number of ways of attaching the 10 resistors = 5¹⁰ = 9,765,625 ways