Angle BCA = 180 - 100
angle BCA = 80

Isosceles triangle ABC has two congruent angles, A and B
2x + 80 = 180
2x = 100
Angles A and B = 50 or y and z = 50

I think lines AB and DE are supposed to be parallel, so angles y and x are consecutive interior angles (supplementary)

x = 180 - 50 = 130

5 0

2 years ago

Read 2 more answers

What is the equation of the parabola, in vertex form, with vertex at (-2,-4) and

Arlecino [84]

Answer:

Step-by-step explanation:

The distance between the vertex and the directrix is 4 units, that means that p = 4 in the equation

$(y-k)^2=4p(x-h)$ and h and k are the coordinates of the vertex. Filling in:

$(y+4)^2=4(4)(x+2)$ which simplifies to

$(y+4)^2=16(x+2)$ choice C

8 0

3 years ago

a 16 inch wire is to be cut. one piece is to be bent into the shape of a square, whereas the other piece is to be bent into the

Lyrx [107]

1. Let x be a length of square side, then the square perimeter is 4x (you need to cut 4x from 16 in. to make a square with side x in.). Then 16-4x is remained length of wire and you have to make form this piece a rectangle with sides one of which is twice bigger than another. If y is length of the smaller side, then 2y is length of the bigger side and rectangle perimeter is y+2y+y+2y=6y. You have 16-4x in. of wire left, so 6y=16-4x and $y= \frac{16-4x}{6}$ .

2.
$A_{square}=x^2 \\ A_{rectangle}=y\cdot 2y=\frac{16-4x}{6}\cdot2\cdot\frac{16-4x}{6}= \frac{(16-4x)^2}{18} \\ A(x)=A_{square}+A_{rectangle}=x^2+\frac{(16-4x)^2}{18}$ .

3. Find the derivative of the function A(x):
$A'(x)=2x+ \dfrac{2(16-4x)\cdot(-4)}{18} =2x- \dfrac{4(16-4x )}{9}$ .

4. Solve the equation A'(x)=0:
$2x- \dfrac{4(16-4x )}{9}=0 \\ 18x-64+16x=0 \\ 34x=64 \\ x= \frac{32}{17}$

5. Since $y= \frac{16-4x}{6}$ you have

$y= \dfrac{16-4 \frac{32}{17} }{6} = \dfrac{16\cdot17-4\cdot32}{6\cdot 17} = \dfrac{24}{17}$ .

Answer: <span>the width of the rectangle is $\frac{24}{17}$ </span>

6 0

3 years ago

Find m< AFE and include working out.

andreyandreev [35.5K]

Answer:

∠ AFE = 80°

Step-by-step explanation:

Since BD is a straight line , then

∠ AFB + ∠ AFE + ∠ EFD = 180°, that is

50° + ∠ AFE + 50° = 180°

100° + ∠ AFE = 180° ( subtract 100° from both sides )

∠ AFE = 80°

3 0

3 years ago