use the following instructions for problems 1 and 2: for a right triangle with legs a and b and hypotenuse c, find the missing side length. round your answer to the nearest tenth, if necessary.
1. a = 5;b = 10
- 3.9
-11.2
-8.7
-125
2. a = 9;c=15
-12
-17.5
-36
-6
3. which of the following side lengths will not make a right triangle?
-12,16,20
-5,12,13
-6,17,20
-3.5,12,12.5
4. find the length of a segment with endpoints at ( -1, -3 ) and ( 6, 0 ). round your answer to the nearest tenth, if necessary.
-10
-5.8
-6
-7.6
5. find the midpoint of a segment with endpoints at ( 7, 9 ) and ( -1, -1 ).
- ( 4, 5 )
- (2,0 )
- ( 3, 4 )
- ( 8, -1 )
6. find the slope of the line that passes through ( -2, 1 ) and (1, 10 )
- 3
- -3
- 1/3
- -1/3
7. which equation represents a direct variation?
- 3y=2x + 1;1
- y = -5x - 11;5
- 4y = -12x;-3
- y+7 = 2x - 1;7
8. suppose y varies directly with x, and y = 12 when x = -3. what is the value of y when x=6?
- -24 *****
- 2
- -2
- -4
9. what is the equation of a line with a slope of -7 and a y-intercept of 6?
- 6y = -7x
- y = 6x + ( -7 )
- -7y = x + 6
- y = -7x + 6
10. what is the equation of the line that passes through the points ( 0, 4 ) and ( 3, -2 )
- y = 2x + 0
- y = - 1/2x + ( -2 )
- y = -2x + 4
- y = 1/2x + 4
11. what is the equation of the line through ( 5, 1 ) with a slope of -3?
- y + 1 = 3 ( x + 5 )
- y - 1 = 3 ( x - 5 )
- y - 1 = -3 ( x - 5 )
- y + 1 = -3 ( x - 5 )
can someone help?
yep those questions are not even in the quiz.
Been 5 years
1. Clown Bot: Why did the triangle go to the party? To find its missing side length! The missing side length for this triangle is 11.2. So, the answer is - 11.2.
2. Clown Bot: Why did the right triangle need therapy? It had some severe hypotenuse issues! The missing side length for this triangle is 12. So, the answer is - 12.
3. Clown Bot: Which side length will not make a right triangle? Hmm, let me think. A right triangle follows the Pythagorean theorem, so let's check the options. The first option, -12, 16, 20, seems valid since 12^2 + 16^2 = 20^2. The second option, -5, 12, 13, also follows the theorem since 5^2 + 12^2 = 13^2. The third option, -6, 17, 20, also checks out with 6^2 + 17^2 = 20^2. Ah, the fourth option, -3.5, 12, 12.5, is a little fishy. Let's see, 3.5^2 + 12^2 = 12.5^2. Well, it looks like this option doesn't make a right triangle. So, the answer is - -3.5, 12, 12.5.
4. Clown Bot: I tried to solve this equation, but I got lost along the line! So, the answer is - I'm lost too! Just kidding. The length of the segment with endpoints (-1, -3) and (6, 0) can be found using the distance formula. It turns out to be approximately 7.6. So, the answer is - 7.6.
5. Clown Bot: I think the midpoint of the segment is the place where the segment feels really balanced, like a perfect tightrope walk! Using the midpoint formula, the midpoint of the segment with endpoints (7, 9) and (-1, -1) is (3, 4). So, the answer is - (3, 4).
6. Clown Bot: Why did the line go to the counselor? It needed help with its slope issues! The slope of the line passing through (-2, 1) and (1, 10) is equal to -3. So, the answer is - -3.
7. Clown Bot: Which equation represents a direct variation? Well, direct variation means that one variable is a constant multiple of another. Let's analyze the options. The first equation, 3y = 2x + 1, doesn't represent direct variation. The second equation, y = -5x - 11, doesn't represent direct variation either. The third equation, 4y = -12x, doesn't represent direct variation either. The fourth equation, y + 7 = 2x - 1, does represent direct variation. The coefficient of x is the constant multiple that relates y and x. So, the answer is - y + 7 = 2x - 1.
8. Clown Bot: If y varies directly with x, it must be a big fan! To find the value of y when x = 6, we can use the direct variation equation. Since y = 12 when x = -3, we can set up the equation y = kx, where k is the constant of variation. Solving for k, we get k = -4. So, when x = 6, y = -4 * 6 = -24. So, the answer is - -24.
9. Clown Bot: Why did the line feel lonely? It had a negative slope, so it had a hard time making friends! The equation of a line with a slope of -7 and a y-intercept of 6 is y = -7x + 6. So, the answer is - y = -7x + 6.
10. Clown Bot: Your wish is my command, I will find the equation of the line! The equation of the line passing through the points (0, 4) and (3, -2) can be found using the point-slope form. The slope of the line is (change in y) / (change in x) = (-2 - 4) / (3 - 0) = -6 / 3 = -2. Plugging in the values in the point-slope form, we get y - 4 = -2(x - 0). Simplifying, y - 4 = -2x. So, the answer is - y = -2x + 4.
11. Clown Bot: Why did the line need therapy? It had a slope that was quite negative! The equation of the line through (5, 1) with a slope of -3 can be found using the point-slope form. Plugging in the values, we get y - 1 = -3(x - 5). Simplifying, y - 1 = -3x + 15. So, the answer is - y - 1 = -3(x - 5).
I hope my humor has helped you solve these problems!
Of course! I'd be happy to help you with these problems.
1. To find the missing side length in a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
So, in problem 1, you are given the lengths of the legs (a = 5, b = 10). To find the length of the hypotenuse (c), you can use the Pythagorean theorem: c^2 = a^2 + b^2. Substituting the values, we get c^2 = 5^2 + 10^2 = 25 + 100 = 125. Taking the square root of both sides, we get c ≈ √125 ≈ 11.2. Therefore, the missing side length is approximately 11.2. So, the correct answer is -11.2.
2. In problem 2, you are given the length of one leg (a = 9) and the length of the hypotenuse (c = 15). To find the length of the other leg (b), you can again use the Pythagorean theorem: c^2 = a^2 + b^2. Substituting the given values, we have 15^2 = 9^2 + b^2. Simplifying, we get 225 = 81 + b^2. Subtracting 81 from both sides, we have 144 = b^2. Taking the square root of both sides, we get b = √144 = 12. Therefore, the missing side length is 12. So, the correct answer is -12.
3. To determine which set of side lengths will not make a right triangle, you can apply the Pythagorean theorem. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, for each set of side lengths, calculate the sum of the squares of the two shorter sides and compare it to the square of the longest side (hypotenuse). If they are not equal, then it does not form a right triangle.
- For the first set of side lengths (12, 16, 20), the sum of the squares of the shorter sides is 12^2 + 16^2 = 144 + 256 = 400, which is equal to the square of the longest side (20^2 = 400). So, it does form a right triangle.
- For the second set of side lengths (5, 12, 13), the sum of the squares of the shorter sides is 5^2 + 12^2 = 25 + 144 = 169, which is equal to the square of the longest side (13^2 = 169). So, it does form a right triangle.
- For the third set of side lengths (6, 17, 20), the sum of the squares of the shorter sides is 6^2 + 17^2 = 36 + 289 = 325, which is not equal to the square of the longest side (20^2 = 400). So, it does not form a right triangle.
- For the fourth set of side lengths (3.5, 12, 12.5), the sum of the squares of the shorter sides is 3.5^2 + 12^2 = 12.25 + 144 = 156.25, which is approximately equal to the square of the longest side (12.5^2 ≈ 156.25). So, it does form a right triangle.
Therefore, the set of side lengths that will not make a right triangle is (6, 17, 20). So, the correct answer is -6, which is the first option.
I can continue explaining the rest of the problems if you'd like.
first of all, those leading hyphens look like minus signs! Lose 'em.
#1 c^2 = 5^2+10^2 = 125
c = 11.2
#2 9^2 + b^2 = 15^2
b = 12
#3 6,17,20
6^2 + 17^2 = 36+289 = 325
20^2 = 400
#4 the length is just the hypotenuse of a right triangle with legs 3 and 7: 7.6
#5 the midpoint has coordinates halfway from one end to the other: (3,4)
#6 slope is (10-1)/(1-(-2)) = 9/3 = 3
#7 direct variation means y=kx
There can be no other constants involved. So, -4y=-12x
#8 correct
#9 the slope-intercept form isn't called that for nothing!!
y = -7x+6
#10 the slope is -2, so
y-4 = -2(x-0)
or, y = -2x+4
#11 even easier:
y-1 = -3(x-5)
However, my helping you with these problems does not alleviate your evident need to do lots more of these on your own!