The order of the start of the proof seems fine; we're to choose the next steps I guess.
segment UV is parallel to segment WZ Given
Points S, Q, R, and T all lie on the same line. Given
m∠SQT = 180° Definition of a Straight Angle
m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠SQV + m∠VQT = 180° Substitution Property of Equality
That's all valid up to here. It seems to me sort of the hard way to get to linear supplements but here we are.
ZRS is mentioned in the rest of the lines; let's find the one that comes first.
III m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
Now we have two things equal to 180 degrees, so they're equal to each other.
II m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
Now comes
I m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
And we conclude,
∠SQV ≅ ∠ZRS Definition of Congruency
Answer:
See diagram below. This is a relation and not a function.
Step-by-step explanation:
An arrow diagram has two ovals - one for x -values and one for y-values. Inside the ovals, all values ONLY appear ONCE and generally from least to greatest. Then draw an arrow from each value to its matching value from input to output according to the table.
Be sure to draw two ovals around the lists below:
Inputs Outputs
1 ----------------> 2
11 -----------------> (POINTS DIAGONAL TO 2)
15 -----------------> 12
16 ------------------> 32
This is not a function because each output must only match to one input. The output 2 matches to both 1 and 11. This is a relation.
Answer:
8
Step-by-step explanation:
so when you’re dividing fractions alwayes apply keep change flip keep the 4/1 change the division sign to a multiplication sign and flip 1/2 To 2/1 and 4/1 times 2/1 is 8
Answer:
Step-by-step explanation:
Given is a system of equations as
We have 5 variables and 3 equations
a) coefficient matrix of this system is
1 -4 0 -1 0\\
0 1 0 -2 0\\
0 0 0 1 2\\
We find that x3 has no coefficient in any of the equations so we can omit x3 and write as equations for 4 variables as
1 -4 -1 0\\
0 1 -2 0\\
0 0 1 2\\
b) Augmented matrix is
1 -4 -1 0\\ 7
0 1 -2 0\\
3
0 0 1 2\\3
c) For row operations to ehelon form
we can do R1+4R2 = R1
We get
1 0 -9 0 \\ 19
0 1 -2 0 \\ 3
0 0 1 2 \\ 3
Now let us do R1 = R1+9R3 and R2 = R2+2R3
1 0 0 0 \\ 46
0 1 0 0 \\ 9
0 0 1 2 \\ 3
d) We find that there are infinite solutions to the system in parametric form, since x4 and x5 are linked with only one equation
e) x1 = 46, x2 = 9, x4+2x5 =3
Or x1 =46, x2 =9, x4 = 3-2x5, x5 = x5 is the parametric solution