D has the commutative property because it just flip flopped the numbers.
Of 5 out of 12 (5/12) are sports games and 3 out of 12 (3/12) are educational, then you would add these together because you need a total for both because it would include one or the other, so both.
5/12 + 3/12= 8/12 or 2/3 are one or the other.
Answer:
40 km on the highway
30 km on the city roads
Step-by-step explanation:
Let x = highway
Let y = city road
The time formula: time = distance / speed.
1) Since we do not know the distance travelled on the highway and city roads but we do know the total time taken, we can say x + y = 70. Set the distances x and y and all equated to 2 hours, since we do not know them, nor do we know the time. This is called a system of equations.
x + y = 70
x/80 + y/20 = 2
2) Solve the system of equations using substitution.
x = 70 - y
---------------
70 - y/80 + y/20 = 2
70 + 3y/80 = 2
y = 30
---------------------------------
x + 30 = 70
x = 70 - 30
x = 40
Therefore, the delivery truck travelled 40 km on the highway and 30 km on the city roads.
The value of x is -2 and the value of y is -1.
Step-by-step explanation:
Step 1; The given equations are taken as
-3y -9x =21 or -9x -3y = 21, take this as equation 1
-18x +4y =32, take this as equation 2
Step 2; We multiply equation 1 with 2 and equation 2 with 1 so we can cancel out the variable x in both equations. By doing this we get
-18x -6y =42, take this as equation 3
-18x +4y =32, this is the same as equation 2
If we subtract 3 with 2, we cancel out the x variable and can calculate the value of y.
10y = -10 , y = -10/10 = -1
Step 3; Substituting this value of y in any of the previous equations we will get x's value. Here this value of y is substituted in equation 2.
-18x +4(-1) =32, -18x -4 = 32 , -18x = 36, x=-2.
So we have x = -2 and y = -1.
Answer:
m∠B ≈ 51.5°
Step-by-step explanation:
A triangle solver can find this answer simply by entering the data. If you do this "by hand," you need to first find length BC using the Law of Cosines. Then angle B can be found using the Law of Sines.
<h3>Length BC</h3>
The Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
a² = 21² +13² -2(21)(13)cos(91°) ≈ 619.529
a ≈ 24.8903
<h3>Angle B</h3>
The Law of Sines tells us ...
sin(B)/b = sin(A)/a
B = arcsin(sin(A)×b/a) = arcsin(sin(91°)×21/24.8903)
B ≈ 57.519°
The measure of angle B is about 57.5°.
