So J is jelly beans and T is trail mix :)
so J= $3.50
T= $1.50
Answer:
![9](https://tex.z-dn.net/?f=9)
Step-by-step explanation:
As per the problem, the given triangle is a right triangle. This is signified by the box around one of its angles, this box states that the angle it is surrounding is a right angle.
Since it is a right triangle, one can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that; (
), where (
) and (
) are the legs of the right triangle, or the sides adjacent to the right angle. (
) is the hypotenuse or the side opposite the right angle.
Substitute in the given values and solve, note that (
) represents the unknown leg (side).
![a^2 + b^2 = c^2\\\\a^2 + (\sqrt{19})^2 = (100)^2\\\\a^2 + 19 = 100](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%5C%5C%5C%5Ca%5E2%20%2B%20%28%5Csqrt%7B19%7D%29%5E2%20%3D%20%28100%29%5E2%5C%5C%5C%5Ca%5E2%20%2B%2019%20%3D%20100)
Inverse operations,
![a^2 + 19 = 100\\-19\\\\a^2 = 81\\\\a = \sqrt{81}\\\\a = 9](https://tex.z-dn.net/?f=a%5E2%20%2B%2019%20%3D%20100%5C%5C-19%5C%5C%5C%5Ca%5E2%20%3D%2081%5C%5C%5C%5Ca%20%3D%20%5Csqrt%7B81%7D%5C%5C%5C%5Ca%20%3D%209)
Answer: option c
Step-by-step explanation:
Find the x-intercept and y-intercept of each line.
To find the x-intercept, substitute
into the equation and solve for "x".
To find the y-intercept, substitute
into the equation and solve for "y".
- For the first equation:
x-intercept
![4x + 3y = 29\\\\4x + 3(0)= 29\\\\4x=29\\\\x=\frac{29}{4}\\\\x=7.25](https://tex.z-dn.net/?f=4x%20%2B%203y%20%3D%2029%5C%5C%5C%5C4x%20%2B%203%280%29%3D%2029%5C%5C%5C%5C4x%3D29%5C%5C%5C%5Cx%3D%5Cfrac%7B29%7D%7B4%7D%5C%5C%5C%5Cx%3D7.25)
y-intercept
![4x + 3y = 29\\\\4(0) + 3y = 29\\\\3y=29\\\\y=\frac{29}{3}\\\\y=9.66](https://tex.z-dn.net/?f=4x%20%2B%203y%20%3D%2029%5C%5C%5C%5C4%280%29%20%2B%203y%20%3D%2029%5C%5C%5C%5C3y%3D29%5C%5C%5C%5Cy%3D%5Cfrac%7B29%7D%7B3%7D%5C%5C%5C%5Cy%3D9.66)
Graph a line that passes through the points (7.25, 0) and (0, 9.66)
- For the second equation:
x-intercept
![2x - 3y = 1 \\\\2x - 3(0) = 1 \\\\2x=1\\\\x=0.5](https://tex.z-dn.net/?f=2x%20-%203y%20%3D%201%20%5C%5C%5C%5C2x%20-%203%280%29%20%3D%201%20%5C%5C%5C%5C2x%3D1%5C%5C%5C%5Cx%3D0.5)
y-intercept
![2x - 3y = 1\\\\2(0) - 3y = 1\\\\-3y=1\\\\y=-0.33](https://tex.z-dn.net/?f=2x%20-%203y%20%3D%201%5C%5C%5C%5C2%280%29%20-%203y%20%3D%201%5C%5C%5C%5C-3y%3D1%5C%5C%5C%5Cy%3D-0.33)
Graph a line that passes through the points (0.5, 0) and (0, -0.33)
Observe the graph attached. You can see that point of intersection of the lines is (5,3); then this is the solution of the system. Therefore:
![x=5\\y=3](https://tex.z-dn.net/?f=x%3D5%5C%5Cy%3D3)
Of means multiplication. So the question is 1/3 X 1 1/2. First make 1 1/2 improper: 3/2. Then multiply the numerators (top numbers) and denominaters (bottom numbers): 1x3=3, 3x2=6, =3/6. Now simplify 3/6=1/2. Then multiply that by 2, since he used 2 pieces: 1/2x2=1. John used 1 meter :)
Slope intercept form: y=x-6
Y intercept: -6
Hope I helped!(: