A=20
5a-4=3a+36 (subtract 3a from both sides and add 4 to both sides)
2a=40. Divide 40by 2
A=20
<span>1)The table below represents a linear function f(x) and the equation represents a function g(x):
x y
-1 -11
0 -1
1 9
g(x) = 5x + 1
Part A: Write a sentence to compare the slope of the two functions and
show the steps you used to determine the slope of f(x) and g(x). (6
points)
slope of the data of the table:
slope = rise / run = Δy / Δx = [ 9 - ( - 1) ] / [1 - 0] = 10/1 = 10
Also Δy / Δx = [-1 - (-11) ] / [ 0 - (-1) ] = 10 / 1 = 10
the slope of the function given in the form f(x) = mx + b is m, so the slope of g(x) = 5x - 1 is 5.
Comparisson: the slope of the function g(x) = 5x - 1 is half the slope of the function f(x) represented by the table.
Part B: Which function has a greater y-intercept? Justify your answer.
The y-intercept is the value of y when x = 0, so it is - 1 for the function represented by the table.
The y-intercept of a function given in the form f(x) = mx + b is b, so the y-intercept of g(x) = 5x - 1 is - 1.
So, both functions have equal y-intercept.
2)The table below shows the values of y for each value of x:
x y
1 0
1 -1
2 1
2 -2
Part A: Does the table represent a relation that is a
function? Justify your answer by using the values shown in the table. (4
points)
No, it is not a function, because the relation is ambiguous: the x-coordinate 1 may have two differente values, and the x-coordinate 2 may have two different. So you cannot determine the images of x = 1 and x = 2.
Part B: The function f(x) shown below represents the number of baskets
Jess made at different distances, x, in meters, from the hoop:
f(x) = -x + 6
Calculate and interpret the meaning of f(4). (4 points)
f(4) = - 4 + 6 = 2
It means that Jess made 2 baskets at the distant of 4 meters.
Part C: Write an ordered pair to represent the input and output of the
function in Part B when Jess is at a distance of p meters from the hoop.
(2 points)
input, p output, f(p)
6 -6 + 6 = 0
So the ordered pair is (6,0)
</span>
Answer:
1. 1 in 5
2. There are 5 colors it could land on, and orange is one of them.
3. 40 different combinations
4. There are 5 colors with 8 corresponding numbers. 5x8=40
Step-by-step explanation:
Answer:
The answer to your question is given below
Step-by-step explanation:
Let 'a' and 'b' be the length of the first two sides of the triangle and let 'c' be the longest length of the triangle.
The following data were obtained from the question:
Length of a = 17 m
Length of b = 144 m
Length of c = 145
For the triangle to be a right-angled triangle, then it must certify the pythagoras theory which states that the square of the two sides in a right-angled triangle is equal to the square of the longest side.
Thus, we can prove that the triangle is a right-angled triangle as illustrated below:
a² + b² = c²
Length of a = 17 m
Length of b = 144 m
Length of c = 145
17² + 144² = 145²
289 + 20736 = 21025
21025 = 21025
From the above illustration, we can see clearly that the square of two sides of the triangle is equal to the square of the longest side. Therefore, the triangle is a right-angled triangle.
