A flagpole broke in a storm. 7 meters are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground at a point 24 meters away horizontally.How tall was the flagpole before it broke?
Answers
It would form a right triangle, in which the shorter leg is 7m and the longer leg is 24m. You're looking for the last side, the hypotenuse. So use the Pythagorean theorem. a^2 + b^2 = c^2 , in which a and b are the legs and c is the hypotenuse.
Therefore, you get 7^2 + 24^2 = c^2.
Which is, 49 + 576 = c^2
Add, 625 = c^2.
Take the square root of 625, which is 25. So, the length of the hypotenuse (last side) is 25m. Add the 7m that is sticking out of the ground, to get 32m.
So we have a right angled triangle, the vertical part is 7m, and the horizontal is 24m.
From Pythagoras' Theorem:
x² = 24² + 7²
x² = 576 + 49
x² = 625
x = √625
x = 25
So the broken part is 25m long.
The length of the flagpole before it was broken = 25 + 7
= 32m.
Really beautiful question.
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Final answer: Sarah has traveled 6 miles after an hour.
Hope this helped! :)
Helping tip: The reason it is not 4 is because they are not traveling west and east away from each other. They are traveling north and east, so they are moving in two directions to form a right triangle, and the hypotenuse would be 10 (miles). The side, or distance, that Beth has traveled is 8. So as this is a typical variation of a 3x4x5 triangle, Sarah will have traveled 6 miles.
wouldn't it actually be 2 miles but since its not listed I would say 4 because if there 10 miles apart and Sarah is 8miles from the school were they both started then 10-8=2. or you can take the two and divide it by 8 and get 4
Answers
Answer:
The equation which can be used to determine the minimum and maximum optimal angles of launch is:
|x – 45| = 3
and the minimum angle that is still optimal is:
42 degrees.
Step-by-step explanation:
Let x be the optimal angle by which the balloon is launched.
Also, it is given that the they launch the balloon at an angle within 3 degrees of 45 degrees.
i.e. the range at which the angle is launched lie between 3 degree less than 45 degree and 3 degree more than 45 degree.
Hence, the equation that will represent this relationship is:
|x-45|=3
Hence, on solving for the maximum value we have:
and the smallest optimal angle is given by:
Answers
nine 5 pound bags
distributed into 10-ounce bags
1 pound = 16 ounces
9 x 5 pounds = 45 pounds
45 pounds * 16 ounces/lbs = 45 * 16 oz = 720 ounces
720 ounces / 10 ounce bags = 720/10 = 72 bags.
The workers at the food pantry will be able to make 72 bags.
Answers
Reorder the terms: 8 + -2x + -15x2 = 0 Solving 8 + -2x + -15x2 = 0 Solving for variable 'x'.
Factor a trinomial. (2 + -3x)(4 + 5x) = 0 Subproblem 1Set the factor '(2 + -3x)' equal to zero and attempt to solve:
Simplifying 2 + -3x = 0 Solving 2 + -3x = 0
Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2
Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2
Combine like terms: 0 + -2 = -2 -3x = -2
Divide each side by '-3'. x = 0.6666666667
Simplifying x = 0.6666666667
Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:
Simplifying 4 + 5x = 0
Solving 4 + 5x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4
Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4
Combine like terms: 0 + -4 = -4 5x = -4
Divide each side by '5'. x = -0.8 Simplifying x = -0.8
Solutionx = {0.6666666667, -0.8}
Answers
2.1 Factoring 16x2+40x+25
The first term is, 16x2 its coefficient is 16 .
The middle term is, +40x its coefficient is 40 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 16 • 25 = 400
Step-2 : Find two factors of 400 whose sum equals the coefficient of the middle term, which is 40 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 20 and 20
16x2 + 20x + 20x + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (4x+5)
Add up the last 2 terms, pulling out common factors :
5 • (4x+5)
Step-5 : Add up the four terms of step 4 :
(4x+5) • (4x+5)
Which is the desired factorization
2.2 Multiply (4x+5) by (4x+5)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (4x+5) and the exponents are :
1 , as (4x+5) is the same number as (4x+5)1
and 1 , as (4x+5) is the same number as (4x+5)1
The product is therefore, (4x+5)(1+1) = (4x+5)2
hope this helps hope i am brainliest i need it
Answers
5W = 3L .........(a)
Perimeter = 2*(L+W) = 80
2*(L+W) = 80
(L+W) = 80/2. Divide both sides by 2.
L+W= 40......(b)
5W = 3L
L + W = 40 Multiply both sides by 5.
5*(L+W) = 5*40
5L+5W = 200. Recall from (a) 5W = 3L
5L + 3L = 200
8L = 200
L = 200/8
L = 25.
5W = 3L
5W = 3*25
W = 3*25/5
W = 15.
Therefore, the length, L = 25 and width , W = 15.