The length of ladder used is 12.25 ft.
<h3>What is Pythagoras theorem?</h3>
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .
The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
example:
The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.
Solution:
Given : Hypotenuse = 16 units
Let us consider the given side of a triangle as the perpendicular height = 8 units
On substituting the given dimensions to the Pythagoras theorem formula
Hypotenuse^2 = Base^2 + Height^2
16^2 = B^2 + 8^2
B^2 = 256 - 64
B = √192 = 13.856 units
Therefore, the measure of the third side of a triangle is 13.856 units.
given:
base= 2.5 ft,
perpendicular= 12 ft
Using Pythagoras theorem,
H² = B² + P²
H² = 2.5² + 12²
H² = 6.25+ 144
H= 12.25 ft
Learn more about Pythagoras theorem here: brainly.com/question/343682
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N = the value of the number in a sequence
a.) 5, 10, 15, 20, ........ 50
b.) -1, -3, -7, -15, ..... -1023
Answer:
Hi there!
The answer to this question is: A
y= [x] + 5
Answer:
The big container holds 30 gallons and the small container holds 20 gallons
Step-by-step explanation:
Let
The big container = x
Small container = y
The big container can hold 10 gallons less than twice the small
x = 2y - 10
Total gasoline in both containers = 50 gallons
x + y = 50
Substitute x = 2y - 10 into the equation
2y - 10 + y = 50
3y = 50 + 10
3y = 60
Divide both sides by 3
y = 60 / 3
= 20
y = 20 gallons
Recall,
x + y = 50
x + 20 = 50
x = 50 - 20
= 30
x = 30 gallons
The big container holds 30 gallons and the small container holds 20 gallons
<span>A) First function, y varies directly with x.
1) function: y = (3/4)x
2) graph: it is a straight line that passes through the origin and has slope 3/4. The slope means that the rate of change of the function is 3 units per every 4 units the x-value incresase or, what is the same 0.75 units per incresase unit of x - value.
3) real world example
A recipe of a cake instructs to use 3 cups of sugar for every 4 cups of flour. So, how much flour you need if you have 12 cups of sugar?
y = (3/4)x , so if x = 3, y = (3/4)*12 = 3*12/4 = 9.
So, given that the variation is direct you multiply the number of cups of sugar times the constant rate, 3/4, to get the number of cups of flour in relation with the given amount of sugar.
B) The second function: y varies inversely with x.
Inverse variation => y*x = constant or y = constant / x.
Tnat means that if x increase y will decrease in the same factor that x increases.
1) function: y = 12 / x
2) graph: the form of this graph is called hyperbola, it is a decreasing line from left to right. It has two asymptotes, the y-axis (x =0) and the x-axis (y = 0). That means that x and y can never be zero.
As the x-value approaches 0, the y value approaches positive or negative infinity; as the y-values approaches 0 the x-values approaches to positive or negative infinity.
If you take the positive values, the graph is a decreasing curve in the first quadrant (x and y are positive).
If you take the negative values, the graphs is a decreasing curve in the third quadrant (x and y are negative)
3) real world example.
The relatioship between velocity and time in a uniform motion.
If the distance run by an object is constant, as the velocity increases the time decreases in the same factor.
Suppse a distant of 100 km between cities A and B.
How long will it take to travel from A to B at 50 km/ h and 25 km/h ?:
100 km = velocity * time
at 50 km/h: 100 km = 50 km/h * t => t = [100 km ] / [50 km/h] = 2 hours
at 25 km/h: 100 kg = 25 km/h * t => t = [ 100 km ] / [25 km/h] = 4 hours.
C) Third case, the relationship between
x and y should is neither inverse variation nor direct variation.
Of course, there are infinite type of functions that are neither inverse variation nor direct variation: linear (that do not passe through the origin), quadratic, exponential, logarithmical, trigonometric sine, ...
1) example of function: y = 30 + 2x
2) graph: it is a straigh line with y-intercept 30 and slope 2.
3) real world example:
The cost of producing chairs consists of 30 dollars of rent for the facility plus 2 dollar to produce each chair, so the total cost y is 30 + 2x.
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