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Step-by-step explanation:
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<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:
3.7feet
Step-by-step explanations
Using the sin rule
A/sin a = B/sin b
Let A = PQ = 8.5feet
B = QR = x feet
a = R = 90°
b = P = 26°
Substitute the values into the Sin rule
8.5/sin90 = x/sin26
8.5×sin 26 = x × sin 90
8.5×0.4383 = x× 1
3.7255 = x
Hence the length of QR to the nearest tenth 3.7feet
Answer:
-2x² + 90x + 500
Step-by-step explanation:
Use FOIL method
Area of rectangle = length * width
= (50 - x)(2x + 10)
= 50*(2x) + 50*10 + (-x)*2x + (-x)*10
= 100x + 500 - 2x² - 10x
= -2x² + 10<u>0x - 10x </u>+ 500 {Combine like terms}
= -2x² + 90x + 500
Volume of the Triangular prism = 1/2 (base*height*length)
<span>V = 1/2 (2 * 2 * 5) </span>
<span>V = 10 cubic inches. </span>
<span>For the surface area, you can divide the prism into parts: </span>
<span>It's made of three rectangles and two equal triangles. </span>
<span>For the two triangles: </span>
<span>The area of each of the triangles is 1/2(base x height) </span>
<span>Area of each triangles = 1/2 (2 * 5) </span>
<span>Area of each triangles = 5 inches^2. </span>
<span>For the three rectangles: </span>
<span>* one is equal to base x length, </span>
<span>Rectangle1 = 2 x 5 </span>
<span>Rectangle1 = 10 inches^2. </span>
<span>* another is equal to side 1 x length </span>
<span>Rectangle2 = 3 x 5 </span>
<span>Rectangle2 = 15 inches^2 </span>
<span>* and the last is equal to side 2 x length. </span>
<span>Rectangle3 = 3 x 5 </span>
<span>Rectangle3 = 15 inches^2 </span>
<span>Adding all the components up, </span>
<span>10 + 15 + 15 + 5 + 5 = 50 inches^2 </span>
<span>Therefore, the surface area of the prism is greater than volume 50 > 10
hpe this helps:)</span>
