The graph shows the functions f(x), p(x), and g(x):Part A: What is the solution to the pair of equations represented by p(x) and f(x)?
Part B: Write any two solutions for f(x).
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer.
Answers
f(x)=x
This is because the line f(x) passes through the points (-1,-1), (0,0), (1,1) etc.
The function p(x) is:
p(x)=mx+C
Whereby (m) is the slope and (C) is a constant.
m=-4/3, as m=tan(ω)=O/A=-4/3 as slope is negative.
Now when y=-3, x=-3.
So:
-3=-4/3 *(-3) +C
-3= 4 + C
C=-7
This means that:
p(x)=-4/3x -7
Now, where p(x)=g(x), x=-6.
p(-6)=-4/3 * (-6) -7
p(-6)=24/3 -7
p(-6)=8-7
p(-6)=1
Therefore:
p(x) and g(x) meet at (-6, 1) and the solution to p(x)=g(x) is x=-6.
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What is the difference between points a (1,2) and b (9,17)
____________________
B. At the rate given, how many kilometers can Mikaela bike in 1 hour?
____________________
c. If Mikaela runs for 1 hour and bikes for 1 hour at the rates given, how far will she travel?
____________________
Answers
As she bikes 20km in 0.8 hours- she bikes 5km in 0.2 of an hour, therefore, she bikes 25km per hour.
If she continues at this rate, she will travel 35km in 2 hours.
A) 10km
B) 25Km
C) 35 KM
Hope this helps :)
Mikaela can run 10 kilometers in 1 hour.
Mikaela can bike 25 kilometers in 1 hour.
If Mikaela runs for 1 hour and bikes for 1 hour at the given rates, she will travel a totaldistance of 35 kilometers.
We have,
A.
To find the number of kilometers Mikaela can run in 1 hour, we can set up a proportion using the information given:
5 kilometers / 0.5 hour = x kilometers / 1 hour
Cross-multiplying, we get:
(5 kilometers) x (1 hour) = (0.5 hour) x (x kilometers)
Simplifying:
5 kilometers = 0.5x kilometers
To isolate x, we can divide both sides of the equation by 0.5:
5 kilometers / 0.5 = x kilometers
x = 10 kilometers
B.
Similarly, to find the number of kilometers Mikaela can bike in 1 hour, we can set up a proportion:
20 kilometers / 0.8 hour = x kilometers / 1 hour
Cross-multiplying:
(20 kilometers) x (1 hour) = (0.8 hour) x (x kilometers)
Simplifying:
20 kilometers = 0.8x kilometers
Dividing both sides by 0.8:
20 kilometers / 0.8 = x kilometers
x = 25 kilometers
C.
To find the totaldistance Mikaela will travel if she runs for 1 hour and bikes for 1 hour, we can simply add the distances:
Distance = distance run + distance biked
Distance = 10 kilometers + 25 kilometers
Distance = 35 kilometers
Therefore,
Mikaela can run 10 kilometers in 1 hour.
Mikaela can bike 25 kilometers in 1 hour.
If Mikaela runs for 1 hour and bikes for 1 hour at the given rates, she will travel a totaldistance of 35 kilometers.
Learn more about speed here:
#SPJ6
Answers
A = b * h
Where,
b: base
h: height
Clearing the base we have:
b = A / h
Substituting values we have:
b = (6x2 + x + 3) / 3x
Rewriting we have:
b = 2x + 1 / x + 1/3
Answer:
the length of the base is:
b = 2x + 1 / x + 1/3
Answer:
b =
Step-by-step explanation:
The area of the parallelogram is represented by
The height is
The base of the parallelogram, b, can be found by dividing the area by the height.
So, 'b' can be found as
In simplified form, we can write this as :
=>
=>
Hence, base or 'b' is
1. 2x + 6 = 8
2. 2x = 2
3. x = 1
In which step did Sarah use the distributive property?
1
2
3
Answers
Answer:
Step 1
Step-by-step explanation:
2(x + 3) = 8
1. 2x + 6 = 8
2. 2x = 2
3. x = 1
In step 1, she distributed the 2 to the x and 3 by multiplying them and getting 2x and 6.
Answers
First: Subtract 5x from each side.
Second: Subtract 3 from each side.
Third: Quickly step off to one side, as the answer
jumps off the page in your direction.
a. x = 8, y = 17
b. x = 6, y = 8
c. x = 8, y = 10
d. x = 8, y = 6
Answers
3x - 14 = x + 2
3x - x = 2 + 14
2x = 16
2x / 2 = 16/2
x = 8
To check: 3x - 14 = x + 2 ; 3(8) - 14 = 8 + 2 ; 24 - 14 = 10 ; 10 = 10
4y - 7 = y + 11
4y - y = 11 + 7
3y = 18
3y / 3 = 18 / 3
y = 6
To check: 4y - 7 = y + 11 ; 4(6) - 7 = 6 + 11 ; 24 - 7 = 17 ; 17 = 17
AC = c over 3
BD = 4 - c
Answers
|AC| = |BD|