Answer: choice C) -2/3
The line X is completely straight meaning that the slope of line X is the same no matter which two points you pick. Since we're given that line X has a slope of -2/3 through the points (-7,6) and (-4,4), this also applies to the portion from (-1,2) to (5,-2)
I think it would be easy to find it because its 30 feet away and even if he didn't know his feet he could always leave rocks/pebbles to the treasure so he won't lose it.
Answers:
- Problem 1) 40 degrees
- Problem 2) 84 degrees
- Problem 3) 110 degrees
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Explanation:
For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.
For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.
Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.
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For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.
This all means that angle DEF is a right angle and 90 degrees.
So,
(angle DEP) + (angle PEF) = angle DEF
(angle DEP) + (35) = 90
angle DEP = 90 - 35
angle DEP = 55
The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.
The ages are consecutive even numbers.
The youngest child is (x+3) years old.
Every even number is 2 more than the one before it.
So the three ages are
(x + 3), (x + 5), and (x + 7).
Their sum is x+3 + x+5 + x+7 = 3x + 15
But we're told that their sum is 42, so we can write
3x + 15 = 42 <== the equation
Subtract 15 from each side: 3x = 27
Divide each side by 3 : x = 9 <== the solution
So the three ages are 12, 14, and 16.
The oldest child is 16 years old.
Answer:
3/8
Step-by-step explanation:
3 1/3 = 10/3
1 1/4 = 5/4
Remember when dividing by a fraction you can also multiply by its reciprocal meaning flip the numerator and denominator.
so
(3 1/3) / (1 1/4) = (10/3) / (5/4) = (10/3) x (4/5) which is the same as (3/10) x (5/4)
= (3 x 5) / (10 x 4) = 15 / 40
the numerator and denominator have a common factor of 5 so divide the numerator and denominator by 5
15 / 40 = 3/8
