Q1. Look at the picture.
Q2. Look at the picture.
Q3.
Put the value of x = 2 to the equation 3x + y = 5:
<em>subtract 6 from both sides</em>
Q4.
Substitute (*) to (**):
<em>use distributive property</em>
<em>add 33 to both sides</em>
<em>divide both sides by 11</em>
Put the value of m to (*):
Q5.
w - width
3w - length
24 in - the sum of length and width
The equation:
<em>divide both sides by 4</em>
You've got five different problems in this photo ... four on top and the word problem on the bottom ... and they're all exactly the same thing: Taking two points and finding the slope of the line that goes through them.
In every case, the procedure is the same.
If the two points are (x₁ , y₁) and (x₂ , y₂) , then
the slope of the line that goes through them is
Slope = (y₂ - y₁) / (x₂ - x₁) .
This is important, and you should memorize it.
#1). (8, 10) and (-7, 14)
Slope = (14 - 10) / (-7 - 8) = 4 / -15
#2). (-3, 1) and (-17, 2)
Slope = (2 - 1) / (-17 - -3) = (2 - 1) / (-17 + 3) = 1 / -14
#3). (-20, -4) and (-12, -10)
Slope = [ -10 - (-4) ] / [ -12 - (-20) ]
=========================================
The word problem:
This question only gives you one point on the graph,
and then it wants to know what's the slope ?
What are you going to do for another point ?
A "proportional relationship" always passes through the origin,
so another point on the line is (0, 0) .
Now you have two points on THAT line too, and you can easily
find its slope.
The value of g would be 75 degrees.
No, these equations are not equivalent.
1/5, or one fifth, is part of a whole. Imagine you have a pie, cut into five pieces, and your friend comes over and eats four pieces, so now you have one of the five original pieces. That's what you have here.
5/5, or five fifths, is a whole. any number divided by itself is automatically one, so it is like making another pie and cutting it into five pieces, only this time no one eats any of it because it's burned or something. At the end, you have five pieces of pie
5/1 is actually just another way of writing plain old 5. To keep the pie example rolling, you have five pies, and no one eats any of these either, so they are all yours. You have 5 pies divided between one person, so at the end of the day you have 5 whole pies.
Hope that helped!
Answer:
1/7 (option d) of the sensors on the satellite have been upgraded
Step-by-step explanation:
Each unit contains the same number of non-upgraded sensors
number of non-upgraded sensors for each module (nus)
total number of upgraded sensors on the satellite (tus)
satellite is composed of 30 modular units
total number of non-upgraded sensors on the satellite (tnus):
tnus=30*nus
total number of sensors on the satellite (ts):
ts=tnus+tus = 30*nus + tus (I)
The number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite
nus=(1/5)*tus
tus = 5 * nus (II)
Fraction of the sensors on the satellite have been upgraded (FU):
FU = tus/ts
Using I and II
FU= (5* nus)/(30*nus + tus)
FU = (5* nus)/(30*nus + 5 * nus)
FU = (5* nus)/(35*nus)
FU = 1/7
1/7 (option d) of the sensors on the satellite have been upgraded
