Answer:
The measure of angle T is 135 degrees.
Step-by-step explanation:
Let's just say the measure of angles T and S are variables t and s.
So the equation would be...
t + s = 180
Since they are supplementary angles, they add up to 180.
Also, we know that t is 3 times s.
t = 3s
Now we can solve this system of equations.
Substitute 3s into t of the first equation.
3s + s = 180
4s = 180
s = 45
Then, since we know that the measure of angle t is 3 times the measure of angle s, we can just multiply 45 by 3 and find the measure of angle t.
45 * 3 = 135
t = 135
So the measure of angle t is 135.
*<em>Just copied from my previous answer, don't know why you needed it again but here you go.</em>
From the information given,
x represents number of small boxes while y represents number of large boxes.
If each small box can hold 6 books and each large box can hold 10 books, it means that the expression for the number of books that x small boxes and y large boxes can hold is
6x + 10y
If James can pack up to 110 books, it means that the number of books that he can pack is less than or equal to 110. The inequality representing this scenario is
6x + 10y ≤ 110
10y ≤ - 6x + 110
Dividing both sides of the equation by 10, we have
y ≤ - 6x/10 + 110/10
y ≤ - 3x/5 + 11
The graph is shown below
The inequality that represents this sitaution is 6x + 10y ≤ 110
The graph of the inequality wil have solid boundary at y = - 3x/5 + 11
and will be shaded below the line.
Multiples of 3
: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 4
: 4, 8, 12, 16, 20, 24, ...
Multiples of 8
: 8, 16, 24, ..
2
Find the smallest number that is shared by all rows above. This is the LCM.
LCM = 2424
Method 2: By Prime Factors
1
List the prime factors of each number.
Prime Factors of 3
: 3
Prime Factors of 4
: 2, 2
Prime Factors of 8
: 2, 2, 2
2
Find the union of these primes.
2,2,2,32,2,2,3
3
Multiply these numbers: 2\times 2\times 2\times 3=242×2×2×3=24. This is the LCM.
LCM = 2424
Answer:
y= -3
Step-by-step explanation:
(-7/2)y =21/2
Divide both sides by (-7/2) = Multiply by (-2/7)
On the left side ,after cancellation you have only y
On the right side you multiply 21/2 by (-2/7)
y= (21*-2) / 2*7
y=(-42)/14
y=(-21)/7
y=- 3
check:
-(7/2) of- 3 is 10.5 21/2=10.5