Answer:
see attached image
Step-by-step explanation:
F(x) = 2x + 5 is a linear graph because the exponent on x is 1. I tell my students that think of graphs having one less turn/corner that the value of the highest exponent. so since 2x has a exponent of 1, 1-1 =0 so it has no turns or its a straight line.
this has a slope of 2 or 2/1 or up 2 and right 1 from the y intercept which is 5
so mark 5 on the y axis and a from there go up 2 and right 1 and make another point. Join these points and you have your graph
and
g(x) = (x-5)/2 is its inverse and is found:
F(x) = 2x + 5 write it this way y = 2x + 5
now swap the x and y x = 2y - 5
solve for y
x = 2y + 5
- 5 -5
x - 5 = 2y
/2 /2
(x-5)/2 = y
it can be written as y = x/2 - 5/2
and graphed the same way as above with a 1/2 slope and -5/2 y intercept
<u>Answer</u>
c. buying it at a 10 percent discount without sales tax.
<u>Explanation</u>
We are going to compare the 3 choices and then determine the most cost effective.
<em>a. using a paid membership card to buy it at a 10 percent discount.</em>
10% of $100 = 10/100×100 = $10
cost = $100 - $10 = $90
On top of this $90 there is the charges of the membership card.
<em> b. buying it online at a 10 percent discount with a $5 shipping charge.</em>
100%-10% = 90%
90% of 100 = $90
Cost: $90 + $5 = $95
<em>c. buying it at a 10 percent discount without sales tax.</em>
100% - 10% = 90%
90/100 × 100 = $90. This is the must cost effective method since there is no other cost involved.
Answer:
B. 5 ≤ n≤ 8
f. 10 ≤ S ≤ 16
C. c=2n
d. S = c
Step-by-step explanation:
Jada is making lemonade for a get together with her friends. She expects a total of 5 to 8 people to be there (including herself).?
She plans to prepare 2 cups of lemonade for each person. The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups. Let n represent the number of people at the get together, c the number of cups of water, S the number of scoops of lemonade powder. Select all the mathematical statements that repsent the quantities and constraints in the situation.
A. 5<n<8
B. 5≤ n≤8
C. c=2n
d. S = c
e. 10<c<16
f. 10≤S≤16
Let
n = number of people at the get together,
c = number of cups of water,
S = number of scoops of lemonade powder.
She expects a total of 5 to 8 people to be there (including herself).
B. 5 ≤ n ≤ 8
She plans to prepare 2 cups of lemonade for each person.
With minimum of 5 people and maximum of 8 people
2 × 5 = 10
2 × 8 = 16
f. 10≤S≤16
The number of cups of water is twice the number of people at the party
C. c=2n
Number of scoops of lemonade powder is equivalent to number of cups of water
d. S = c
The residual is the difference between the plotted point and the line of best fit.
We first need to know the point at x=5 for the line of best fit.
y1 = -(5) - 3 = -8
Now we need to find the difference between the line of best fit and the plotted point.
residual = 9 -(-8) = 9 + 8 = 17 or C
Answer:
Parallel: y=-4x-1
Perpendicular: y=-4x+13/2
Step-by-step explanation:
For the equation y=-4x-41, the slope is -4. Writing a line related to this equation has two options:
- If the line will be parallel to it then this is the slope of the new line as well. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.
(y-7)=-4(x--2)
y-7=-4x-8
y=-4x-1
- If the line will be perpendicular to it then the slope is the negative reciprocal of the previous slope. It is 1/4.
(y-7)=1/4(x--2)
y-7=1/4x-1/2
y=-4x+13/2
