Answer:
option 4
Step-by-step explanation:
|a| represents Absolute value, it is the distance from zero that a number is on the number line. And we know distance cannot be negative.
So,
![|a| = a](https://tex.z-dn.net/?f=%7Ca%7C%20%3D%20a)
![|-a| = a\\\\| \frac{-a}{b}| = \frac{a}{b}\\\\|\frac{a}{-b}| = \frac{a}{b}](https://tex.z-dn.net/?f=%7C-a%7C%20%3D%20a%5C%5C%5C%5C%7C%20%5Cfrac%7B-a%7D%7Bb%7D%7C%20%3D%20%5Cfrac%7Ba%7D%7Bb%7D%5C%5C%5C%5C%7C%5Cfrac%7Ba%7D%7B-b%7D%7C%20%3D%20%5Cfrac%7Ba%7D%7Bb%7D)
Answer:
d. ![8\sqrt{2}](https://tex.z-dn.net/?f=8%5Csqrt%7B2%7D)
Step-by-step explanation:
This is a 45-45-90 right triangle with a Pythagorean triple of (x, x, x√2). Because this is a 45-45-90, both legs have the same measure, namely 8. Therefore, according to the Pythagorean triple, x = 8 (NOT the x in your diagram...the x in the Pythagorean triple). That means that the hypotenuse has a measure of
, which is d.
So essentially an adjacent angle is when two angles have a common side and a common vertex.
So knowing that we can determine from the picture all the adjacent angles:
D) <2 and <3 are adjacent angles
E) <1 and <3 are adjacent angles
F) <1 and <5 are adjacent angles
I hope this helps.
Let's assume
length of rectangle =L
width of rectangle =W
You enclose 3 sides of the garden with 40 feet of fencing
so, we get
![L+2W=40](https://tex.z-dn.net/?f=L%2B2W%3D40)
now, we can solve for L
![L=40-2W](https://tex.z-dn.net/?f=L%3D40-2W)
we know that
area of rectangle is
![A=L*W](https://tex.z-dn.net/?f=A%3DL%2AW)
![100=L*W](https://tex.z-dn.net/?f=100%3DL%2AW)
now, we can plug
![100=(40-2W)*W](https://tex.z-dn.net/?f=100%3D%2840-2W%29%2AW)
now, we can solve for W
![-2W^2+40W-100=0](https://tex.z-dn.net/?f=-2W%5E2%2B40W-100%3D0)
we can use quadratic formula
![W=\frac{-40+\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B-40%2B%5Csqrt%7B40%5E2-4%5Cleft%28-2%5Cright%29%5Cleft%28-100%5Cright%29%7D%7D%7B2%5Cleft%28-2%5Cright%29%7D)
![W=\frac{-40-\sqrt{40^2-4\left(-2\right)\left(-100\right)}}{2\left(-2\right)}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B-40-%5Csqrt%7B40%5E2-4%5Cleft%28-2%5Cright%29%5Cleft%28-100%5Cright%29%7D%7D%7B2%5Cleft%28-2%5Cright%29%7D)
we can take anyone value ..because both are giving positive value
first dimensions:
![W=2.929](https://tex.z-dn.net/?f=W%3D2.929)
now, we can find L
![L=40-2*2.929](https://tex.z-dn.net/?f=L%3D40-2%2A2.929)
![L=34.142](https://tex.z-dn.net/?f=L%3D34.142)
so, length is 34.142feet
width is 2.929 feet
Second dimensions:
![W=17.071](https://tex.z-dn.net/?f=W%3D17.071)
now, we can find L
![L=40-2*17.071](https://tex.z-dn.net/?f=L%3D40-2%2A17.071)
![L=5.858](https://tex.z-dn.net/?f=L%3D5.858)
so, length is 5.858feet
width is 17.071 feet
Answer:
A. 2(16+12)
Step-by-step explanation:
1. 2x16=32
2. 2x12=24
3. 32+24=56