Because you're multiplying
![2x](https://tex.z-dn.net/?f=2x)
by
![4x](https://tex.z-dn.net/?f=4x)
.
![2*4](https://tex.z-dn.net/?f=2%2A4)
is
![8](https://tex.z-dn.net/?f=8)
,
![x*x](https://tex.z-dn.net/?f=x%2Ax)
is
![x^2[tex], and [tex]8*x^2](https://tex.z-dn.net/?f=x%5E2%5Btex%5D%2C%20and%20%5Btex%5D8%2Ax%5E2)
is
![8^2](https://tex.z-dn.net/?f=8%5E2)
. Since you're multiplying them all together, it doesn't matter what order you multiply them in. For example,
![2*x=2x](https://tex.z-dn.net/?f=2%2Ax%3D2x)
,
![x*4=4x](https://tex.z-dn.net/?f=x%2A4%3D4x)
, and [2x*4x=8x^2[/tex] (but that's just the same.)
<em>
</em><em>Hope that helps! :)</em>
Answer: b:23/21
Step-by-step explanation:
To get the value of w that makes the expression equal a number greater than 15.3, we multiply 15.3 by the values given in the options. This will be:
a: 13/14
= 15.3 × (13/14)
= 14.2
b:23/21
= 15.3 × (23/21)
= 16.8
c:42/42
= 15.3 × (42/42)
= 15.3
d:100/101
= 15.3 × (100/101)
= 15.2
From the illustrations given from a-d, we can see that only option b with w given as 23/21 makes the expression greater than 15.3
Answer:
Step-by-step explanation:
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-1,\:3\right),\:\\\left(x_2,\:y_2\right)=\left(5,\:11\right)\\\\m=\frac{11-3}{5-\left(-1\right)}\\\\m =\frac{11-3}{5+1}\\\\m=\frac{8}{6}\\\\Simplify\\\\m=\frac{11-3}{5-\left(-1\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5C%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-1%2C%5C%3A3%5Cright%29%2C%5C%3A%5C%5C%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%285%2C%5C%3A11%5Cright%29%5C%5C%5C%5Cm%3D%5Cfrac%7B11-3%7D%7B5-%5Cleft%28-1%5Cright%29%7D%5C%5C%5C%5Cm%20%3D%5Cfrac%7B11-3%7D%7B5%2B1%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B8%7D%7B6%7D%5C%5C%5C%5CSimplify%5C%5C%5C%5Cm%3D%5Cfrac%7B11-3%7D%7B5-%5Cleft%28-1%5Cright%29%7D)
Yes (-4, -1) is on the same line with the other wo points.
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\\\mathrm{Slope\:}\left(-4,\:-1\right),\:\left(5,\:11\right)\\\left(x_1,\:y_1\right)=\left(-4,\:-1\right),\:\\\left(x_2,\:y_2\right)=\left(5,\:11\right)\\\\m=\frac{11-\left(-1\right)}{5-\left(-4\right)}\\\\Simplify\\m=\frac{4}{3}\\\\\mathrm{Slope\:}\left(-1,\:3\right),\:\left(-4,\:-1\right)\\\\\left(x_1,\:y_1\right)=\left(-1,\:3\right),\:\\\left(x_2,\:y_2\right)=\left(-4,\:-1\right)\\\\m=\frac{-1-3}{-4-\left(-1\right)}\\\\Simplify\\\\m=\frac{4}{3}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5C%5C%5C%5Cmathrm%7BSlope%5C%3A%7D%5Cleft%28-4%2C%5C%3A-1%5Cright%29%2C%5C%3A%5Cleft%285%2C%5C%3A11%5Cright%29%5C%5C%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-4%2C%5C%3A-1%5Cright%29%2C%5C%3A%5C%5C%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%285%2C%5C%3A11%5Cright%29%5C%5C%5C%5Cm%3D%5Cfrac%7B11-%5Cleft%28-1%5Cright%29%7D%7B5-%5Cleft%28-4%5Cright%29%7D%5C%5C%5C%5CSimplify%5C%5Cm%3D%5Cfrac%7B4%7D%7B3%7D%5C%5C%5C%5C%5Cmathrm%7BSlope%5C%3A%7D%5Cleft%28-1%2C%5C%3A3%5Cright%29%2C%5C%3A%5Cleft%28-4%2C%5C%3A-1%5Cright%29%5C%5C%5C%5C%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-1%2C%5C%3A3%5Cright%29%2C%5C%3A%5C%5C%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%28-4%2C%5C%3A-1%5Cright%29%5C%5C%5C%5Cm%3D%5Cfrac%7B-1-3%7D%7B-4-%5Cleft%28-1%5Cright%29%7D%5C%5C%5C%5CSimplify%5C%5C%5C%5Cm%3D%5Cfrac%7B4%7D%7B3%7D)
So the longer lines are 2x longer than the shorter lines
Look at line segment BD
40 is 2x as long as 9x+2
In order to make the equation true, multiple 9x+2 by 2
So, you should get:
40=18x+4
36=18x
x=2
Plug the 2 into 19X+14, and divide that answer by 2, because GF is 2x smaller than AG
19x+14
19(2)+14
52
52/2=26
Hope this helps!!