Answer:
1) x = 8
2) ∠RPS = 36°
Step-by-step explanation:
<u>GIVEN :-</u>
- ∠QPS = 180°
- ∠QPR = 7x + 88
- ∠RPS = 3x + 12
<u>TO FIND :-</u>
- Value of x
- Measure of ∠RPS
<u>FACTS TO KNOW BEFORE SOLVING :-</u>
In a straight line , if there are two angles such that their sum is equal to straight angle (or 180° in other words) , then those angles are known as linear pair.
<u>PROCEDURE :-</u>
1)
Measure of ∠QPS = 180° and it comprises of ∠QPR & ∠RPS.
⇒ ∠QPR & ∠RPS are linear pair.
⇒ ∠QPR + ∠RPS = 180°
⇒ 7x + 88 + 3x + 12 = 180°
⇒ 10x + 100 = 180
⇒ 10x = 180 - 100 = 80
⇒ x = 80/10 = 8
2)
x = 8. So,
∠RPS = 3×8 + 12 = 24 + 12 = 36°
We can say that x is the largest number.
So the sum is x + (x - 1) + (x - 2) + (x - 3) + (x - 4) = -5
Now solve for x:
x + x + x + x + x - 1 - 2 - 3 - 4 = -5
5x - 10 = -5
5x = 5
x = 1
So the largest number is 1.
Check: 1 + 0 + -1 + -2 + -3 = -2 + -3 = -5 so 1 is correct.
Answer:
explain
Step-by-step explanation:
Answer:
2
Step-by-step explanation:

we start simplifying by removing the parenthesis
Multiply the exponents inside the the parenthesis
3^4 * 2^4

Now we apply exponential property
a^m * a^n = a^ (m+n)
3^4 * 3^-3 = 3^ (4-3) = 3^1
3 or 3^1 are same

3^1 at the top and bottom so we cancel it out
\frac{2^4}{2^3}
we apply log property . a^m / a^n = a^m-n
Now subtract the exponents
2^(4-3) = 2^1 = 2
Answer:
2879ft
Step-by-step explanation:
The level runway (x), height gained (h), and distance travelled (r) form a right-angled triangle with base angle
10
∘
.
We may hence use trig ratios to solve for any of the unknowns, in particular for the distance r as follows :