Answer:
3. m∠1 = 106° ~ this is because ∠1 and ∠2 together make a straight line and are therefore supplementary, meaning added together, they equal 180° (so I did 180° - 74° = 106°)
4. m∠3 = 74° ~ again, it is supplementary to ∠1. It is also equal to ∠2
5. m∠8 = 114° ~ angles opposite of each other (like 1 and 4) are equal (as we know from question 4). From there, we can use the corresponding angle theorem, so we know 4 and 8 are congruent. (also you can just know 1 and 8 are congruent by using the opposite exterior angles theorem)
6. m∠6 = 124° ~ using same-side interior angle theorem, they are supplementary angles (or the corresponding angles theorem mentioned above, make 4 congruent to 8, and 8 is supplementary to 6)
7. m∠7 = 96° ~ using same side exterior angle theorem, these angles are supplementary
8. m∠2 = 64° ~ again, same side exterior angle theorem
The two unknown variable in the two given equations are "x" and "y".
3y + 3x = 24
Dividing both sides by 3 we get
y + x = 8
x = 8 - y
Putting the value of y in the second equation we get
6y + 3x = 39
Dividing both sides by 3 we get
2y + x = 13
2y + 8 - y = 13
y = 13 - 8
= 5
Putting the value of y in the first equation we get
y + x = 8
5 + x = 8
x = 8 - 5
x = 3
So the value of x is 3 and the value of y is 5. I hope the procedure is clear enough for you to understand.
19.00 3.50 11.00 4.47 makes it add up to hours so that will be answe C
In 2018, married filing separately taxpayers only receive a standard deduction of $12,000 compared to the $24,000 offered to those who filed jointly. If you file a separate return from your spouse, you are automatically disqualified from several of the tax deductions and credits mentioned earlier.
Answer:
1 quart blue + 1 1/2 quart red
Given:
Ratio of blue paint : red paint = 1/3 : 1/2
simplifying this ratio into whole numbers by multiplying both sides by 2 and 3, we get:
(1/3) x (3x2) : (1/2) x (3x2)
2 : 3
From this we can determine the fractions of red and blue paint used in any total purple mix
fraction of blue paint = 2/(2+3) = 2/5 of purple mix
fraction of red paint = 3/(2+3) = 3/5 of purple mix
we are given that we want to make 2 1/2 (= 5/2) quarts of purple paint
hence
amount of blue paint
= fraction of blue paint in purple mix x total amount of purple paint
= (2/5) x (5/2) = 1 quart
amount of red paint
= fraction of redpaint in purple mix x total amount of purple paint
= (3 /5) x (5/2) = 3/2 quart = 1 1/2 quart
Step-by-step explanation:
