Speeds are s_c for car, s_m for motorcycle.
time is 2
distance of car is:
d_c = d_m + 20, d_m is distance of motorcycle.
speed is defined as:
s = d/t, distance over time.
hence:
d_c/2 = s_c = d_m/2 + 10
s_c = s_m + 10
from problem statement we know:
s_c = 2s_m - 30
so we have 2 simultaneous equations:
<span>s_c = s_m + 10
</span><span>s_c = 2s_m - 30
</span>
multiply second by -1 and sum them both:
<span> s_c = s_m + 10
</span>-s_c = -2s_m + 30
-------------------------
0 = -s_m + 40
s_m = 40
that is the speed of the motorcycle
s_c = <span>s_m + 10
</span> s_c = 40<span> + 10
</span>s_c = 50
that is the speed of car, both speeds in miles per hour
Answer:
You didnt ask a question or link any work?
Step-by-step explanation:???
Answer:
18
Step-by-step explanation:
125 = 7x - 1 ...... because if the two lines are parallel alternate interior angles are congruent
125 + 1 = 7x
126 = 7x
x = 18
hope it helps
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It looks like we have two unknowns here and two possible equations so to solve this we will need to utilize our systems of equations, I will be using the substitution method.
We know that all of the parts multiplied together is equal to the volume.
We know that the volume is 126 square inches
The height is seven inches
The width is unknown, let w be the width
The length is unknown, let l be the length
We know that the length is three inches more than the width (l=w+3)
We know that the height times the length times the width is equal to the volume (7lw=126)
Since we know that l=w+3, we can substitute w+3 in for l,
7(w+3)(w)=126
Now we can solve our equation
7(w+3)(w)=126
(7w+21)(w)
7w^2+21w=126
Now we will complete the square to solve for w
7w^2+21w=126
w^2+3w=18
w^2+3w+2.25=20.25
(w+1.5)^2=20.25
w+1.5=4.5
w=3
We have now found out using our knowledge of systems of equations that the width of this prism is 3 inches.