Answer:
The measure of ∠EFG is 52°
Step-by-step explanation:
Given line m is parallel to line p. m∠HEF = 39º and m∠IGF = 13º.we have to find m∠EFG.
In ΔJFG,
By angle sum property of triangle, which states that sum of all angles of triangle is 180°
m∠FJG+m∠JGF+m∠JFG=180°
⇒ 39°+13°+m∠JFG=180°
⇒ m∠JFG=180°-39°-13°=128°
As JFE is a straight line ∴ ∠JFG and ∠EFG forms linear pair
⇒ m∠JFG+m∠EFG=180°
⇒ 128°+m∠EFG=180°
⇒ m∠EFG=52°
The measure of ∠EFG is 52°
Part A:
Given a square with sides 6 and x + 4. Also, given a rectangle with sides 2 and 3x + 4
The perimeter of the square is given by 4(x + 4) = 4x + 16
The area of the rectangle is given by 2(2) + 2(3x + 4) = 4 + 6x + 8 = 6x + 12
For the perimeters to be the same
4x + 16 = 6x + 12
4x - 6x = 12 - 16
-2x = -4
x = -4 / -2 = 2
The value of x that makes the <span>perimeters of the quadrilaterals the same is 2.
Part B:
The area of the square is given by
![Area=(x+4)^2=x^2+8x+16](https://tex.z-dn.net/?f=Area%3D%28x%2B4%29%5E2%3Dx%5E2%2B8x%2B16)
The area of the rectangle is given by 2(3x + 4) = 6x + 8
For the areas to be the same
![x^2+8x+16=6x+8 \\ \\ \Rightarrow x^2+8x-6x+16-8=0 \\ \\ \Rightarrow x^2+2x+8=0 \\ \\ \Rightarrow x= \frac{-2\pm\sqrt{2^2-4(8)}}{2} \\ \\ = \frac{-2\pm\sqrt{4-32}}{2} = \frac{-2\pm\sqrt{-28}}{2} \\ \\ = \frac{-2\pm2i\sqrt{7}}{2} =-1\pm i\sqrt{7}](https://tex.z-dn.net/?f=x%5E2%2B8x%2B16%3D6x%2B8%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%5E2%2B8x-6x%2B16-8%3D0%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%5E2%2B2x%2B8%3D0%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%3D%20%5Cfrac%7B-2%5Cpm%5Csqrt%7B2%5E2-4%288%29%7D%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-32%7D%7D%7B2%7D%20%3D%20%5Cfrac%7B-2%5Cpm%5Csqrt%7B-28%7D%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B-2%5Cpm2i%5Csqrt%7B7%7D%7D%7B2%7D%20%3D-1%5Cpm%20i%5Csqrt%7B7%7D)
Thus, there is no real value of x for which the area of the quadrilaterals will be the same.
</span>
Answer:
8 hours 48 mins
Step-by-step explanation:
h m
5:15
+3:33
--------------
8:48
or
5 hours + 3 hours =8 hours,
15 mins + 33 mins = 48 mins
Therefore, it's 8 hours 48 mins.
Answer:
337285
Step-by-step explanation:
The answer to number 17 is c