If
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
then m, the slope, is 5.5. We need to find b. When x = 11, y = 140, so:
![(140) = (5.5)(11) + b \\ 140 = 60.5 + b \\ b = 79.5](https://tex.z-dn.net/?f=%28140%29%20%3D%20%285.5%29%2811%29%20%2B%20b%20%5C%5C%20140%20%3D%2060.5%20%2B%20b%20%5C%5C%20b%20%3D%2079.5)
We plug in the values for x, y, and m. Then, we simplify and subtract 60.5 from both sides.
This makes the equation
![y = 5.5x + 79.5](https://tex.z-dn.net/?f=y%20%3D%205.5x%20%2B%2079.5)
Or, in the context of this equation,
First we define the variables:
x = weight of a large box
y = weight of a small box
We write the system of equations:
x + y = 95
50x + 65y = 5275
The solution to the system of equations by the graphic method is:
x = 60
y = 35
Note: see attached image.
Answer:
each type of box weigh:
weight of a large box = 60 pounds
weight of a small box = 35 pounds
Answer:
16
Step-by-step explanation:
The perpendicular diameter to the chord divides it into two congruent parts.
Since
we have that XT=TS.
Hence,
3b-1=b+5,
3b-b=5+1,
2b=6,
b=3.
So,
XT=3·3-1=9-1=8
TS=3+5=8
and
XS=XT+TS=8+8=16.
Answer:
Step-by-step explanation:
![\frac{10}{1 + 2i} \\ \\ = \frac{10}{1 + 2i} \times \frac{1 - 2i}{1 - 2i} \\ \\ = \frac{10(1 - 2i)}{ {1}^{2} - {(2i)}^{2} } \\ \\ = \frac{10 - 20i}{ {1} - {4i}^{2} } \\ \\ = \frac{10 - 20i}{ {1} - {4( - 1)} } \\ ( \because \: {i}^{2} = - 1) \\ \\ = \frac{10 - 20i}{1 + 4} \\ \\ = \frac{5(2 - 4i)}{5} \\ \\ = 2 - 4i](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B1%20%2B%202i%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%7D%7B1%20%2B%202i%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%20%20-%20%202i%7D%7B1%20%20-%20%202i%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%281%20-%202i%29%7D%7B%20%7B1%7D%5E%7B2%7D%20-%20%20%7B%282i%29%7D%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%20%3D%20%20%5Cfrac%7B10%20-%2020i%7D%7B%20%7B1%7D%20-%20%20%7B4i%7D%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%20-%2020i%7D%7B%20%7B1%7D%20-%20%20%7B4%28%20-%201%29%7D%20%7D%20%20%5C%5C%20%28%20%5Cbecause%20%5C%3A%20%20%7Bi%7D%5E%7B2%7D%20%3D%20%20-%201%29%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%20-%2020i%7D%7B1%20%2B%204%7D%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%282%20-%204i%29%7D%7B5%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%202%20-%204i)
The volume of the rectangular prism is the amount of space in the box
The volume of the rectangular prism is 22 cubic feet
<h3>How to determine the volume of the box</h3>
The dimension of the cube is given as:
Length = 1/2 ft
So, the volume of the cube is:
![V = (\frac 12)^3](https://tex.z-dn.net/?f=V%20%20%3D%20%28%5Cfrac%2012%29%5E3)
Evaluate the exponent
![V =\frac 18](https://tex.z-dn.net/?f=V%20%20%3D%5Cfrac%2018)
There are 176 cubes in the prism.
So, the volume of the prism is:
![V_2 = 176 * \frac 18](https://tex.z-dn.net/?f=V_2%20%3D%20176%20%2A%20%5Cfrac%2018)
![V_2 = 22](https://tex.z-dn.net/?f=V_2%20%3D%2022)
Hence, the volume of the rectangular prism is 22 cubic feet
Read more about volumes at:
brainly.com/question/1972490