The solution to given system of equations is x = 2 and y = -5
<em><u>Solution:</u></em>
<em><u>Given the system of equations are:</u></em>
4x + y = 3 ---------- eqn 1
-2x + 3y = -19 ---------- eqn 2
We have to find the solution to above system of equations
<em><u>We can solve the system by substitution method</u></em>
From eqn 1,
4x + y = 3
Isolate y to one side
y = 3 - 4x ----------- eqn 3
<em><u>Substitute eqn 3 in eqn 2</u></em>
-2x + 3(3 - 4x) = -19
-2x + 9 - 12x = -19
Combine the like terms
-14x = -19 - 9
-14x = -28
Divide both sides of equation by -14
<h3>x = 2</h3>
<em><u>Substitute x = 2 in eqn 3</u></em>
y = 3 - 4(2)
y = 3 - 8
<h3>y = -5</h3>
Thus the solution is x = 2 and y = -5
Answer:
Evaluated, you get 4x^4
Step-by-step explanation:
Differentiated, you get 16x^3
It all depends on what you're looking for, really
Answer:
1/8÷7
Step-by-step explanation:
I think
Answer:
We can see that this is dependent probability. We can find dependent probability of happening event A then event B by multiplying probability of event A by probability of event B given that event A already happened.
Step-by-step explanation:
In our case event A is pirate hitting captain's ship and event B is captain missing pirate's ship. We have been given that pirate shoots first so pirate's ship can't be hit before pirate shoots his cannons. So probability of hitting captain's ship is 1/3. We have been given that if Captain Ben's ship is already hit then Captain Ben will always miss. So the probability of Captain missing the dread pirate's ship given the pirate Luis hitting the Captain ship is 1. Now to find probability that pirate hits Captain, but Captain misses we will multiply our both probabilities.
The answer is 5.13 in²
Step 1. Calculate the diameter of the circle (d).
Step 2. Calculate the radius of the circle (r).
Step 3. Calculate the area of the circle (A1).
Step 4. Calculate the area of the square (A2).
Step 5. Calculate the difference between two areas (A1 - A2) and divide it by 4 (because there are total 4 segments) to get <span>the area of one segment formed by a square with sides of 6" inscribed in a circle.
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Step 1:
The diameter (d) of the circle is actually the diagonal (D) of the square inscribed in the circle. The diagonal (D) of the square with side a is:
D = a√2 (ratio of 1:1:√2 means side a : side a : diagonal D = 1 : 1 : √2)
If a = 6 in, then D = 6√2 in.
d = D = 6√2 in
Step 2.
The radius (r) of the circle is half of its diameter (d):
r = d/2 = 6√2 / 2 = 3√2 in
Step 3.
The area of the circle (A1) is:
A = π * r²
A = 3.14 * (3√2)² = 3.14 * 3² * (√2)² = 3.14 * 9 * 2 = 56.52 in²
Step 4.
The area of the square (A2) is:
A2 = a²
A2 = 6² = 36 in²
Step 5:
(A1 - A2)/4 = (56.52 - 36)/4 = 20.52/4 = 5.13 in²
