X=3

Explanation:

A straight line equals 180°, and they give you the one angle of 56°, so you know 56+ the other equation has to equal 180

56+4x+112=180
168+4x=180

Subtract 168 from both sides

4x=12

Divide 4 from both sides

X=3

You can check by filling it in.

56+4*3+112=

12+56+112=180

5 0

3 years ago

15℅ of 6th grade teachers give homework over the holiday break. If 12 teachers give homework, how many total 6th grade teachers

hoa [83]

Answer:

Step-by-step explanation:

Its a trick question, 15% of 6th grade teachers give HW, but there are 12 teachers. its not gonna be 15% of 12, because you would also get a fraction of a teacher.

4 0

3 years ago

Hillary pours 10 cups of orange juice into glasses that hold 1 2/3 cup each. How many glasses does Hillary fill?

Svetach [21]

$10 = \frac{30}{3 } \\ 1 + \frac{2}{3} = \frac{5}{3} \\ \frac{30}{3} \div \frac{5}{3} = \frac{30}{3} \times \frac{3}{5} = 8glasses$

3 0

3 years ago

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive an

sleet_krkn [62]

Answer:

-6re−r [sin(6θ) - cos(6θ)]

Step-by-step explanation:

the Jacobian is ∂(x, y) /∂(r, θ) = δx/δθ × δy/δr - δx/δr × δy/δθ

x = e−r sin(6θ), y = er cos(6θ)

δx/δθ = -6rcos(6θ)e−r sin(6θ), δx/δr = -sin(6θ)e−r sin(6θ)

δy/δθ = -6rsin(6θ)er cos(6θ), δy/δr = cos(6θ)er cos(6θ)

∂(x, y) /∂(r, θ) = δx/δθ × δy/δr - δx/δr × δy/δθ

= -6rcos(6θ)e−r sin(6θ) × cos(6θ)er cos(6θ) - [-sin(6θ)e−r sin(6θ) × -6rsin(6θ)er cos(6θ)]

= -6rcos²(6θ)e−r (sin(6θ) - cos(6θ)) - 6rsin²(6θ)e−r (sin(6θ) - cos(6θ))

= -6re−r (sin(6θ) - cos(6θ)) [cos²(6θ) + sin²(6θ)]

= -6re−r [sin(6θ) - cos(6θ)] since [cos²(6θ) + sin²(6θ)] = 1

6 0

4 years ago