Answer:
Step-by-step explanation:
1.
Equation one:
x = -5, x = -1 (Both are real)
Equation two:
No real solutions
Equation three:
x = -3 (Real)
Equation four:
No real solutions
2.
The easiest way to figure out if an equation has real solutions is to factor it. If it is factorable, then it has real solutions. If it isn't, then it doesn't have real solutions.
Answer:
x = -0.6
y = 2.2
z = 2
Step-by-step explanation:
2x + y - 2z = -3
x + 3y - z = 4
3x + 4y - z = 5
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)
2 1 -2 -3
1 3 -1 4
3 4 -1 5
R1 / 2 → R1 (divide the 1 row by 2)
1 0.5 -1 -1.5
1 3 -1 4
3 4 -1 5
R2 - 1 R1 → R2 (multiply 1 row by 1 and subtract it from 2 row); R3 - 3 R1 → R3 (multiply 1 row by 3 and subtract it from 3 row)
1 0.5 -1 -1.5
0 2.5 0 5.5
0 2.5 2 9.5
R2 / 2.5 → R2 (divide the 2 row by 2.5)
1 0.5 -1 -1.5
0 1 0 2.2
0 2.5 2 9.5
R1 - 0.5 R2 → R1 (multiply 2 row by 0.5 and subtract it from 1 row); R3 - 2.5 R2 → R3 (multiply 2 row by 2.5 and subtract it from 3 row)
1 0 -1 -2.6
0 1 0 2.2
0 0 2 4
R3 / 2 → R3 (divide the 3 row by 2)
1 0 -1 -2.6
0 1 0 2.2
0 0 1 2
R1 + 1 R3 → R1 (multiply 3 row by 1 and add it to 1 row)
1 0 0 -0.6
0 1 0 2.2
0 0 1 2
x = -0.6
y = 2.2
z = 2
The thing that's true about the values p and q is that p = q.
The total <em>sum of the angles</em> in a triangle is 180°.
From the first triangle, the value of p will be:
80° + 20° + p = 180°
100° + p = 180°
p = 180° - 100°
p = 80°
From the second triangle, the value of q will be:
55° + 45° + q = 180°
100° + q = 180°
q = 180° - 100°
q = 80°
Therefore, p = q.
Read related link on:
brainly.com/question/16020981
Add the exponents and keep the same base. Then reciprocal it and change the sign of the exponent. Then the value of the exponent expression is 0.5.
<h3>What is an exponent?</h3>
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The exponent expression is 2³ × 2⁻⁴ can be simplified.
Add the exponents and keep the same base. Then we have
2³ × 2⁻⁴ = 2⁽³⁻⁴⁾
2³ × 2⁻⁴ = 2⁻¹
Then find the reciprocal and change the sign of the exponent.
The value is 0.5.
More about the exponent link is given below.
brainly.com/question/5497425
