Area 1st rectangle = 10 * 7 = 70 cm^2
length of 2nd rectangle is 2*7 = 14 cm
Area 2nd = 10 * 14 = 140 cm^2
140/70 = 2
The 2nd triangle was twice as big as the 1st. Answer A
well, since we know the endpoints for the diameter, its midpoint will be where the center of the circle is located, so

and if we get the distance between those endpoints, and take half of that, that'd be the radius of it.
![~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{11})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-4 - (-10)]^2 + [11 - 5]^2}\implies d=\sqrt{(-4+10)^2+6^2} \\\\\\ d=\sqrt{6^2+6^2}\implies d=\sqrt{72}~\hfill \stackrel{radius=half~that}{\cfrac{\sqrt{72}}{2}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%28%5Cstackrel%7Bx_1%7D%7B-10%7D~%2C~%5Cstackrel%7By_1%7D%7B5%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B-4%7D~%2C~%5Cstackrel%7By_2%7D%7B11%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bdiameter%7D%7Bd%7D%3D%5Csqrt%7B%5B-4%20-%20%28-10%29%5D%5E2%20%2B%20%5B11%20-%205%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%28-4%2B10%29%5E2%2B6%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%3D%5Csqrt%7B6%5E2%2B6%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B72%7D~%5Chfill%20%5Cstackrel%7Bradius%3Dhalf~that%7D%7B%5Ccfrac%7B%5Csqrt%7B72%7D%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-7}{ h},\stackrel{8}{ k})\qquad \qquad radius=\stackrel{\frac{\sqrt{72}}{2}}{ r} \\\\\\\ [x-(-7)]^2~~ + ~~[y-8]^2~~ = ~~\left( \frac{\sqrt{72}}{2} \right)^2\implies (x+7)^2~~ + ~~(y-8)^2~~ = ~~18](https://tex.z-dn.net/?f=%5Ctextit%7Bequation%20of%20a%20circle%7D%5C%5C%5C%5C%20%28x-%20h%29%5E2%2B%28y-%20k%29%5E2%3D%20r%5E2%20%5Cqquad%20center~~%28%5Cstackrel%7B-7%7D%7B%20h%7D%2C%5Cstackrel%7B8%7D%7B%20k%7D%29%5Cqquad%20%5Cqquad%20radius%3D%5Cstackrel%7B%5Cfrac%7B%5Csqrt%7B72%7D%7D%7B2%7D%7D%7B%20r%7D%20%5C%5C%5C%5C%5C%5C%5C%20%5Bx-%28-7%29%5D%5E2~~%20%2B%20~~%5By-8%5D%5E2~~%20%3D%20~~%5Cleft%28%20%5Cfrac%7B%5Csqrt%7B72%7D%7D%7B2%7D%20%5Cright%29%5E2%5Cimplies%20%28x%2B7%29%5E2~~%20%2B%20~~%28y-8%29%5E2~~%20%3D%20~~18)
Answer:
A
Step-by-step explanation:
A good trick for trigonometric functions is to remember SOHCAHTOA:
Sin=<u>O</u>pposite over <u>H</u>ypotenuse
Cos=<u>A</u>djacent over <u>H</u>ypotenuse
Tan=<u>O</u>pposite over <u>A</u>djacent
The red arrows on the attachment indicate where opposite, hypotenuse, and adjacent are for angle A.
So in this case, the sin of angle A (opposite over hypotenuse) would be
and cos A (adjacent over hypotenuse) would be
.
I hope this helps!
Answer:
Below.
Step-by-step explanation:
This factors to the product of 2 binomials like (x + a)(x + b), where a and b are 2 numbers.
40 = 4 * 10 and 14 = 4 + 10 so the answer is
(x + 4)(x + 10).
If we expand this we will get back to the quadratic expression:
(x + 4)(x + 10)
= x(x + 10) + 4(x + 10)
= x^2 + 10x + 4x + 40
= x^2 + 14x + 40.
Answer: B.
have the same length.
Step-by-step explanation:
We have given that
, where
are two line segments.
We know that if two line segments are congruent or equal then their lengths are equal.
Therefore, if
then it shows that
have the same length.
Hence, B is the right answer.