The solutions to the system of equations are given as follows: (1, -3) and (-4,2).
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The equations are given as follows:
- (x + 3)² + (y + 2)² = 17.
From the second equation:
y = -2 - x.
Replacing in the first:
(x + 3)² + (y + 2)² = 17.
(x + 3)² + (-2 - x + 2)² = 17
x² + 6x + 9 + x² = 17
2x² + 6x - 8 = 0
2(x² + 3x - 4) = 0
2(x + 4)(x - 1) = 0.
Then the solutions for x are:
The solutions for y are:
- When x = 1, y = -2 - 1 = -3.
- When x = -4, y = -2 -(-4) = 2.
Hence the solutions are:
(1, -3) and (-4,2).
More can be learned about a system of equations at brainly.com/question/24342899
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Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Midpoint Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
Endpoint A (-2, 1)
Endpoint B (-1, 1)
<u>Step 2: Find Midpoint</u>
Simply plug in your coordinates into the midpoint formula to find midpoint
- Substitute [MF]:
- Subtract/Add:
- Divide:
Answer:
7 )
x =
8 )
Step-by-step explanation:
7 ) 8)
In Δ ABC In Δ XYZ
∠ C = 45° ∠ X = 60°
∠ A = 90° ∠ Y = 90°
To Find :
x = ?
y = ?
Solution:
We Know
In Δ ABC
∠ C = 45°
∠ A = 90°
∴ ∠ B = 45° ......Angle sum property of a triangle i.e 180°
∴ Δ ABC is an Isosceles Triangle
∴ AC = AB = x =
Now appplying Trignometry identity we get
Now In Δ XYZ
∠ X = 60°
∠ Y = 90°
∴∠ Z = 30° . .....Angle sum property of a triangle i.e 180°
Now appplying Trignometry identity we get
Now,
This is how you solve this problem:
.10d + .05n = 5.25
(plug in the number of dimes we have)
(21 x .1) + .05n = 5.25
(multiply number of dimes x value of the dime)
2.10 + .05n = 5.25
(subtract 2.10 from both sides)
.05n = 3.15
(divide both sides by .05 to get the number of nickels)
n = 63 nickels
Hope this helps!