9514 1404 393
Answer:
A. √13
Step-by-step explanation:
You can make an educated guess and come to the right conclusion.
The triangle is nearly an equilateral triangle. A triangle with two sides 3 and an angle of 60° would have a third side of 3. A triangle with two sides of 4 and an angle of 60° would have a third side of 4.
So, the third side must be between 3 and 4. Here is an evaluation of the answer choices:
__
A -- between 3 and 4, the correct choice
B -- 3, too short
C -- 1.73, too short
D -- more than 4, too long
__
The question can be answered using your triangle solver app on your calculator, or using the Law of Cosines.
c = √(a^2 +b^2 -2ab·cos(C))
c = √(3^2 +4^2 -2·3·4·(1/2)) = √(9 +16 -12)
c = √13 . . . . . length of the side opposite the 60° angle
Answer:
Option B. 2.75
Step-by-step explanation:
It has been given in the question that a wedge has a width of 2 cm and a slope of 5.5 cm.We have to calculate the mechanical advantage of the given wedge.
We know the formula to calculate the mechanical advantage of the wedge
Mechanical advantage = Length of slope/Thickness of the widest end
= 5.5÷2 = 2.75
Therefore the answer is option B. 2.75
Answer:
- The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.
Explanation:
By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.
You can check that analitically
Departing from the triangle: XYZ
- <u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)
- Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)
- Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)
- Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)
- <u>Translation 1 unit down</u>: (x,y) → (x, y-1)
- (-11,2) → (-11, 2 - 1) = (-11, 1)
- (-9,7) → (-9, 7 - 1) = (-9, 6)
- (-7, 2) → (-7, 2 - 1) = (-7, 1)
- <u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)
- (-11, 1) → (-11, -1), which are the coordinates of vertex X"
- (-9, 6) → (-9, -6), which are the coordinates of vertex Y""
- (-7, 1) → (-7, -1), which are the coordinates of vertex Z"
Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.
<h3>
Answer: (3, 0)</h3>
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Explanation:
Let's isolate x in the first equation.
x-2y = 3
x = 3+2y
Then we'll plug this into the second equation
Afterwards, solve for y.
2x + 4y = 6
2(3+2y)+4y = 6
6+4y+4y = 6
8y+6 = 6
8y = 6-6
8y = 0
y = 0/8
y = 0
Use this to find x.
x = 3+2y
x = 3+2(0)
x = 3
The solution is therefore (x,y) = (3, 0)
If you were to graph both lines, then they would intersect at the location (3,0).
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Checking the answer:
Plug x = 3 and y = 0 into the first equation.
x-2y = 3
3-2(0) = 3
3 - 0 = 3
3 = 3 that works
Repeat for the other equation
2x+4y = 6
2(3) + 4(0) = 6
6 + 0 = 6
6 = 6 that works as well
Both equations are true when (x,y) = (3,0).
The solution is confirmed.
Answer:
20 million
Step-by-step explanation:
5 million SUVs are 25% of the total number of vehicles.
0.25x = 5,000,000
x = 20,000,000
Answer: 20 million
