Just slot the value of x (which is 20), everywhere you see the letter x.
Similarly, slot the value of y (which is 17), everywhere you see the letter y.
So forth,
x + 8 - y
becomes
20 + 8 - 17
which evaluates to 11.
2 (t+5) > 4t-7 (t+3)
distribute
2t+10> 4t -7t-21
2t+10> -3t-21
add 3t to each side
5t+10>-21
subtract 10 from each side
5t>-31
divide by 5
t>-31/5
t> -6 1/5
Answer: t> -6 1/5
<u>Annotation</u>General formula for distance-time-velocity relationship is as following
d = v × t
The velocity of the first car will be v₁, the time is 2 hours, the distance will be d₁.
The velocity of the second car will be v₂, the time is 2 hours, the distance will be d₂.
One of them traveling 5 miles per hour faster than the others. That means the velocity of the first car is 5 miles per hour more than the velocity of the second car.
v₁ = v₂ + 5 (first equation)
The distance of the two cars after two hours will be 262 miles apart. Because they go to opposite direction, we could write it as below.
d₁ + d₂ = 262 (second equation)
Plug the d-v-t relationship to the second equationd₁ + d₂ = 262
v₁ × t + v₂ × t = 262
v₁ × 2 + v₂ × 2 = 262
2v₁ + 2v₂ = 262
Plug the v₁ as (v₂+5) from the first equation2v₁ + 2v₂ = 262
2(v₂ + 5) + 2v₂ = 262
2v₂ + 10 + 2v₂ = 262
4v₂ + 10 = 262
4v₂ = 252
v₂ = 252/4
v₂ = 63
The second car is 63 mph fast.Find the velocity of the first car, use the first equationv₁ = v₂ + 5
v₁ = 63 + 5
v₁ = 68
The first car is 68 mph fast.
Answer
In matrix multiplication, the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.
Multiply each element of the 1st row of the 1st matrix by the corresponding element of the 1st column of the 2nd matrix. Then add these products to obtain the element in the 1st row, 1st column of the product matrix.
The remaining elements of the product matrix are found in the same way.
Simplify each element by multiplying the individual terms.
Now, sum each element of the matrix.