First, convert 4 feet into inches - 48 inches. Then, divide 48 by 14 to get 3.43, so he can have 3 14-inch long pieces. To get the left over out of a foot, take 14 x 3 to get 42, then subtract 42 from your original 48 inches to get 6 inches left, which is half of a foot.
<h3>
Answer: Choice C. (1,0)</h3>
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Explanation:
Point H is at (-2,2) and J is at (4,-2)
Focusing on the x coordinates, the midpoint is (x1+x2)/2 = (-2+4)/2 = 1.
The y coordinates have a midpoint of (y1+y2)/2 = (2+(-2))/2 = 0.
The midpoint is at (1,0). That's why the answer is choice C.
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This next section is optional.
Points I and K are located at (4,3) and (-2,-3) respectively
Averaging the x coordinates gets us (x1+x2)/2 = (4+(-2))/2 = 1
Doing the same for the y coordinates gets us (y1+y2)/2 = (3+(-3))/2 = 0
We end up with the same midpoint (1,0)
The midpoint being the same for both diagonals proves that each diagonal is bisected, ie cut in half.
Solving a system of linear equations, we conclude that the measure of side Z is 2√13
<h3>How to find the measure of side Z?</h3>
Remember the Pythagorean theorem. It says that the square of the hypotenuse is equal to the sum of the squares of the legs.
In the image, we can identify 3 right triangles, and with the Pythagorean theorem, we can write a system of 3 equations.
x^2 = y^2 + 4^2
z^2 = y^2 + 9^2
(4 + 9)^2 = z^2 + x^2
We want to solve that for z.
Now, the second equation can be rewritten to:
y^2 = z^2 - 9^2
Now let's replace the first equation into the third one, so we get:
(4 + 9)^2 = z^2 + (y^2 + 4^2)
Now we can replace y^2 by z^2 - 9^2
(4 + 9)^2 = z^2 + ((z^2 - 9^2) + 4^2)
Now we can solve this:
(13)^2 = z^2 + z^2 - 9^2 + 4^2
(13)^2 + 9^2 - 4^2 = 2*z^2
104/2 = z^2
52 = z^2
√52 = z
√(4*13) = z
√4*√13 = z
2√13 = z
We conclude that the measure of side Z is 2√13
If you want to learn more about systems of equations:
brainly.com/question/13729904
#SPJ1
<h3>
Answer: H = {3, 5, 7}</h3>
Explanation:
We simply list any odd number that is between 2 and 8. The term "roster form" can be thought of as listing the roster of a sports team (eg: baseball). So instead of describing what the numbers look like, we list out the numbers themselves. Those numbers being 3, 5 and 7.
Something like {2,4,6,8} is ruled out because we're dealing with odd numbers only.
Diagram missing.
Question interpreted as:
ABC is a right triangle right angled at A.
BC=17 feet
angle C = 35 degrees.
AC=BCcos(35)=17*0.8192=13.93 feet to the nearest 1/100th of a foot.
