Answer:
From the graph attached, we know that 
by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like 
and 
.
We also know that, by definition of linear pair postulate, 
and are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.
They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that and together are 180°, because they are on a straight angle. That is, 
If we substitute for , we have 
, which means that and are also supplementary by definition.
Answers:
- C) x = plus/minus 11
- B) No real solutions
- C) Two solutions
- A) One solution
- The value <u> 18 </u> goes in the first blank. The value <u> 17 </u> goes in the second blank.
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Explanations:
- Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.
- There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.
- The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.
- We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.
- Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.
Answer:
1323 cubic inches
Step-by-step explanation:
Volume of rectangular prism is (8)(14)(9)=1008
Volume of rectangular prism is (1/2)(5)(14)(9)=315
So total volume is 1008 + 315 = 1323
Equation 1) 4x + 2y = 8
Equation 2) 16x - y = 14
Multiply all of equation 2 by 2.
2) 2(16x - y = 14)
2) 32x - 2y = 28
1) 4x + 2y = 8
Add equations together.
36x = 36
Divide both sides by 36.
x = 1
Plug in 1 for x in the first equation.
4x + 2y = 8
4(1) + 2y = 8
4 + 2y = 8
Subtract 4 from both sides.
2y = 8 - 4
2y = 4
Divide both sides by 2.
y = 4/2
y = 2
So, x = 1, y = 2
~Hope I helped!~
Answer:
It should be 1,628 
.
Step-by-step explanation:
We see two shapes in the figure and those shapes are a rectangle and a circle. Let's find the area of the circle first. 25m won't help us find the area of the circle so let's pretend that 25m isn't there for now. 40m seems to be the diameter of the circle and to find the area of the circle we need to multiply the radius squared by Pi or 3.14. Half of 40 is 20 so we can multiply 20 squared by Pi to give us 1,256.63706. Do not round this number yet. As you can see this circle isn't a full circle. It's a semicircle. We can divide 1,256.63706 by 2 to find the area of a semicircle. You should get 628.31853 and round that to the nearest tenth and we get 628.32. Now let's keep that number in mind and find the area of the rectangle. Using a calculator we can easily multiply 40 and 25 to find the area of the rectangle, which is 1,000. Add 1,000 and 628.32 and our final results should be 1,628.32. I don't see this number in your options but option B is closely related to this answer. I hope this helps and if this answer is wrong then please give me some feedback on what I did wrong! Thank you!
