Answer:
<u>Option b. (x = 3, y = 20, z = -14)</u>
Step-by-step explanation:
Given:
2x + 2y + 3z = 4
5x + 3y + 5z = 5
3x + 4y + 6z = 5
Solve using Cramer’s rule
∴ ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] =\left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
∴A = ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] = -1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-1)
Ax = ![\left[\begin{array}{ccc}4&2&3\\5&3&5\\5&4&6\end{array}\right] = -3](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%263%5C%5C5%263%265%5C%5C5%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-3)
Ay = ![\left[\begin{array}{ccc}2&4&3\\5&5&5\\3&5&6\end{array}\right] =-20\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%263%5C%5C5%265%265%5C%5C3%265%266%5Cend%7Barray%7D%5Cright%5D%20%3D-20%5C%5C)
Az = ![\left[\begin{array}{ccc}2&2&4\\5&3&5\\3&4&5\end{array}\right] = 14](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%264%5C%5C5%263%265%5C%5C3%264%265%5Cend%7Barray%7D%5Cright%5D%20%3D%2014)
∴ x = Ax/A = -3/-1 = 3
y = Ay/A = -20/-1 = 20
z = Az/A = 14/-1 = -14
<u>So, the answer is option b. (x = 3, y = 20, z = -14)</u>
<span>x – 12 ≥ 18
Let's break down the sentence and create an inequality from it. We'll use X to represent the number.
"Twelve fewer than a number is at least 18."
The "Twelve fewer than a number" indicates subtraction, so let's do that.
X - 12
"is at least 18." would be a greater than or equal relationship. So we have
X - 12 ≥ 18
And we're done. The desired equation is:
x – 12 ≥ 18</span>
Answer:
D. The triangle is a right triangle, the lengths of its sides are 1 and 1 with a hypotenuse of √2.
Step-by-step explanation:
The Pythagorean Theorem is modeled by a² + b² = c².
c represents the hypotenuse and a and b represent the other two sides.
The Pythagorean Theorem can only be applied to right triangles.
Problem 1
<h3>Answer: B. M<3 would need to double.</h3>
Explanation: This is because angles 3 and 6 are congruent corresponding angles. Corresponding angles are congruent whenever we have parallel lines like this. If they weren't congruent, then the lines wouldn't be parallel. We would need to double angle 3 to keep up with angle 6.
=====================================================
Problem 2
<h3>Answer: D. none of these sides are parallel</h3>
Explanation: We have angles A and C that are same side interior angles, but they add to A+C = 72+72 = 144, which is not 180. The same side interior angles must add to 180 degrees for parallel lines to form. This shows AB is not parallel to CD.
A similar situation happens with angles B and D, since B+D = 108+108 = 216. This also shows AB is not parallel to CD. We can rule out choices A and C.
Choice B is false because AD is a diagonal along with BC. The diagonals of any quadrilateral are never parallel as they intersect inside the quadrilateral. Parallel lines never intersect.
The only thing left is choice D. We would say that AC || BD, since A+B = 72+108 = 180 and C+D = 72+108 = 180, but this isn't listed as an answer choice.
