Answer:
both
Step-by-step explanation:
<u><em>Answer:</em></u>
∠BOY = 38°
<u><em>Explanation:</em></u>
<u>From the diagram, we can note that:</u>
m∠TOY = m∠TOB + m∠BOY ...................> equation I
We are given that ray OB bisects the angle
<u>Therefore:</u>
m∠TOB = m∠BOY
<u>Substitute in equation I:</u>
m∠TOY = m∠TOB + m∠TOB = 2m∠TOB ............> equation II
<u>We are given that:</u>
m∠TOY = 8x-36
m∠TOB = x+24
<u>Substitute with the givens in equation II and solve for x:</u>
m∠TOY = 2m∠TOB
8x - 36 = 2(x + 24)
2(4x-18) = 2(x+24)
4x - 18 = x + 24
3x = 42
x = 14
<u>This means that:</u>
m∠TOB = x + 24 = 14 + 24 = 38°
<u>Since </u>
m∠TOB = m∠BOY
<u>Therefore:</u>
m∠BOY = 38°
<u>Check:</u>
m∠TOY = 8x - 36 = 8(14) - 36 = 76° which is twice m∠TOB
Hope this helps :)
Answer:
C
Step-by-step explanation:
A and c are parallel
B and d are parallel
A and c are intersecting
Answer:
See explanations below
Step-by-step explanation:
Given the simultaneous equations;
2x - 3y = 9... 1
2x + y = 13 ... 2
From 2;
y = 13-2x
Substitute into 1;
2x - 3(13-2x) = 9
2x -39 + 6x = 9
8x - 39 = 9
8x = 9+39
8x = 48
x = 6
Since y = 13-2x
y = 13-2(6)
y = 13-12
y = 1
The soluton to the system of equation is (6, 1)
Given the equations;
99x + 101y = 499; .... 1 * 101
101x + 99 y = 501 ... 2 * 99
______________
9999x + 10,201y = 50,399
9999x + 9801y = 49,599
Subtract
10201y - 9801y = 50399-49599
400y = 800
y = 2
Substitute y = 2 into 1;
From 1;
99x + 101y = 499
99x + 101(2) =499
99x +202 = 499
99x = 499 - 202
99x = 198
x = 198/99
x =2
Hence the solution is (2,2)
For the equations;
49x - 57y = 172 .... * 57
57x - 49y = 252 __ * 49
____________________
2793x -3249y = 9804
2793x - 2401y = 12348
Subtract
-3249y+2401y = 9804-12348
-848y = -2544
y = 3
Substitute into 1;
49x - 57y = 172
49x - 57(3) = 172
49x - 171 = 172
49x = 171+172
49x = 343
x = 7
Hence the solution is (7, 3)
Answer:
m = -1/2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define</u>
9m - m + 3 = -2(m + 1)
<u>Step 2: Solve for </u><em><u>m</u></em>
- Combine like terms: 8m + 3 = -2(m + 1)
- Distribute -2: 8m + 3 = -2m - 2
- Add 2m on both sides: 10m + 3 = -2
- Isolate <em>m</em> term: 10m = -5
- Isolate <em>m</em>: m = -1/2
