Answer: The perimeter is 95 + 15 sqrt 3, and the area is 600 + 35 sqrt 3 / 2
Step-by-step explanation:
We can draw an imaginary line to form a 30 60 90 triangle. The ratio of side lengths in this special triangle is 1 sqrt 3 2. We are given that the side length opposite to 60 degrees is 15. 15 divided by sqrt 3 is equal to 5 sqrt 3. Now, to find the diagonal we can do 5 sqrt 3 * 2 = 10 sqrt 3. So now, we can find the perimeter. The perimeter is equal to 15 + 40 + 40 + 5 sqrt 3 + 10 sqrt 3 = 95 + 15 sqrt 3. Now, we can find the area. The area can be split into the rectangle's area and the triangle's area. The rectangle's area is 15 * 40 = 600. The triangle's area is 15 * 5 sqrt 3 / 2 = 35 sqrt 3 / 2. The total area is 600 + 35 sqrt 3 / 2.
2/3 of 6 parts would be:
2/3=x/6
X=4
So shade 4 of the 6 parts.
Answer:
x = 7
Step-by-step explanation:
2x + 1 = -3x + 36
2x + 3x + 1 = -3x + 3x +36
5x + 1 = 36
5x + 1 - 1 = 36 - 1
5x = 35
5x/5 = 35/5
x = 7
The correct answer is: [D]: "<span>supplementary angles, 180° " .
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<u>Note:</u>
</span><span>
Choices:
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[B]: "complementary angles, 180° " ; and:
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[C]: "supplementary angles, 90° " ;
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can automatically be ruled out ; since by definition:
</span>→ Complementary angles always add up to 90° — NOT 180° ;
and: supplementary angles always add up to 180° — NOT 90° .
<span>_____________________________________________________
Note: "Adjacent angles" refer to "supplementary angles" ; which, by definition add up to 180</span>° . Futhermore, looking at the image provided,
we see that ∠1 and ∠2 are, in fact "adjacent" and that ∠1 and ∠2 comprise the entire portion of a "straight line" (being intersected by a transversal)" ;
and as such; ∠1 and ∠2 are supplementary angles—
and as such—add up to 180° .
(which rules out: Choice [A]: "complementary <span>angles, 90°) ;
</span>→ <span>and demonstrates the correct answer:
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Answer choice: [D]: "</span><span>supplementary angles, 180°</span><span> " .
</span> <span>______________________________________________________
</span>
Answer:
False
Step-by-step explanation:
This is false. We can disprove this by plugging in the number into the function f(x) = lnx
f(0) = ln0
Since 
, 
This is not 0 so f(0) cannot be equal to 0, thus disproving the statement.
