Answer:
<h2>a) Average velocity = 1.25 m/s to the right</h2><h2>b) Average speed = 3.75 m/s</h2>
Step-by-step explanation:
A woodchuck runs 20 m to the right in 5 s, then turns and runs 10 m to the left in 3 s.
Total displacement = 20 - 10 = 10 m to the right
Total time = 5+3 = 8 s
Total distance = 20 + 10 = 30 m
a) We have
Total displacement = Average velocity x Time
10 = Average velocity x 8
Average velocity = 1.25 m/s to the right
b)We have
Total distance = Average speed x Time
30 = Average speed x 8
Average speed = 3.75 m/s
An equation for the parabola would be y²=-19x.
Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis. This means we will use the standard form
(y-k)²=4p(x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.
Beginning with the directrix:
x=h-p=4.75
h-p=4.75
Since the vertex is at (0, 0), this means h=0 and k=0:
0-p=4.75
-p=4.75
p=-4.75
Substituting this into the standard form as well as our values for h and k we have:
(y-0)²=4(-4.75)(x-0)
y²=-19x
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Problem 3: Let x = price of bag of pretzels Let y = price of box of granola bars
We have Lesley's purchase: 4x+2y=13.50
And Landon's: 1x+5y=17.55
We can use the elimination method. Let's negate Landon's purchase by multiplying by -1. -1x-5y=-17.55
We add this four times to Lesley's purchase to eliminate the x variable.
2y-20y=13.50-70.2
-18y=-56.7
y = $3.15 = Price of box of granola bars
Plug back into Landon's purchase to solve for pretzels.
x+5*3.15=17.55
x+15.75=17.55
x = $1.80 = price of bag of pretzels
Problem 4.
Let w = number of wood bats sold
Let m = number of metal bats sold
From sales information we have: w + m = 23
24w+30m=606
Substitution works well here. Solve for w in the first equation, w = 23 - m, and plug this into the second.
24*(23-m)+30m=606
552-24m+30m=606
6m=54
m=9 = number of metal bats sold
Therefore since w = 23-m, w = 23-9 = 14. 14 wooden bats were sold.
Answer:
x = 2/5
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-step explanation:
<u>Step 1: Write equation</u>
5x = 2
<u>Step 2: Solve for </u><em><u>x</u></em>
- Divide both sides by 5: x = 2/5
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution</em>.
- Substitute: 5(2/5) = 2
- Multiply: 10/5 = 2
- Divide: 2 = 2
