Answer:
Step-by-step explanation:
First, identify the slope.
We are given the line y=7x-5.
This is in slope intercept form or y=mx+b where m is the slope and b is the y-intercept. So, the coefficient to x, or 7 in this case, is the slope.
Now, find the parallel and perpendicular slopes.
1. Parallel Slope
Parallel lines never intersect, so they have the same slope. A parallel line has a slope of 7.
2. Perpendicular Slope
Perpendicular slopes intersect to form right angles. They have negative reciprocal slopes.
- Negate the slope: 7⇒ -7
- Find the Reciprocal (flip the numerator and denominator: -7/1 ⇒ -1/7
A parallel line has a slope of 7 and a perpendicular line has a slope of -1/7.
<h3>
Answer: b) 18 cm </h3>
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Work Shown:
Since the parallelogram has perpendicular diagonals, this means that we're dealing with a rhombus. A rhombus has all four sides equal to one another.
One diagonal is bisected, or cut in half, to form the smaller pieces of length (150/x) + 10 and x-10. Set these two expressions equal to each other and solve for x
(150/x) + 10 = x-10
1500/x = x-10-10
1500/x = x-20
1500 = x(x-20)
1500 = x^2-20x
0 = x^2-20x-1500
x^2-20x-1500 = 0
(x-50)(x+30) = 0
x-50 = 0 or x+30 = 0
x = 50 or x = -30
We'll ignore the negative x value as it leads to a negative length which doesn't make sense.
If x = 50, then
- x-10 = 50-10 = 40
- (150/x)+10 = (150/50)+10 = 30+10 = 40
Each piece of this diagonal is 40 cm long.
The two smaller pieces combine to 40+40 = 80, which is the length of one of the diagonals. If this was the shorter diagonal, then 80 would be listed as part of the answer choices. However, 80 is not one of the answers.
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Note how the two diagonals of the rhombus cut the figure into four right triangles.
Each right triangle has one known leg to be 40 and an unknown leg of y. The hypotenuse is 164/4 = 41 since we divide the perimeter by the four equal sides of the rhombus.
We'll use the pythagorean theorem to find the value of y
a^2 + b^2 = c^2
40^2 + y^2 = 41^2
1600 + y^2 = 1681
y^2 = 1681-1600
y^2 = 81
y = sqrt(81)
y = 9
This represents half of the other diagonal, so the full length of this other diagonal is 2*9 = 18 cm.
Answer:
2
Step-by-step explanation:
With regards to the above, we can sum up the foods ate together by the 5 cats, then we have;
= 1/5 + 1/5
= 2/5
Then we can multiply the value above by the 5 cats
= 2/5 × 5
= 10/5
= 2
The cats eat 2 foods together.
Answer:
thx
Step-by-step explanation:
