Will do first question of each concept only because the rest of the questions are the same concept (the same few repeat but whatever).
1. <em>Total angle = (n - 2) * 180 --> 4 * 180 = 360°</em>
<em>70 + 130 + 120 + θ = 360</em> --> 320 + θ = 360 --> θ = 40
4. Total angle =<em> (10 - 2) * 180</em> --> 8 * 180 = <em>1440</em>
<em>1440/10</em> = 144°
6. Interior: (n - 2) * 180 --> 10 * 180 = 1800
Exterior: 12 * 180 = 2160 --> 2160 - 1800 = 360
9. (n - 2) * 180 --> 3 * 180 = 540
90 + 90 + 150 + 160 + θ = 540 --> 490 + θ = 540 --> θ = 50
13. Interior: (n - 2) * 180 --> 2 * 180 = 360
Exterior: n * 180 - (n - 2) * 180 --> 180n - 180n + 360 --> 360 (always the same)
16. 7r + 4r + 8r + 5r = 360 --> 24r = 360 --> r = 15
1(6x-9)=(4x-6)
One solution was found :
x = 3/2 = 1.500
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
1*(6*x-9)-((4*x-6))=0
Step by step solution :
Step 1 :
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
6x - 9 = 3 • (2x - 3)
Equation at the end of step 2 :
3 • (2x - 3) - (4x - 6) = 0
Step 3 :
Equation at the end of step 3 :
2x - 3 = 0
Step 4 :
Solving a Single Variable Equation :
4.1 Solve : 2x-3 = 0
Add 3 to both sides of the equation :
2x = 3
Divide both sides of the equation by 2:
x = 3/2 = 1.500
One solution was found :
x = 3/2 = 1.500
Answer:
see below
Step-by-step explanation:
14. We can represent 1 as √1 and 2 as √4 and because 1 < 3 < 4, we know that √3 is in between 1 and 2. However, 3 is closer to 4 than it is to 1 so √3 is about 2.
15. Again, 3 is √9 and 4 is √16. 9 < 10 < 16 so √10 is in between 3 and 4, however, since 10 is closer to 9 as it is to 16, we know that √10 is about 3.
16. -4 = -√16 and -5 = -√25, since 16 < 22 < 25, we know that -√22 is in between -4 and -5 but 22 is closer to 25 so the answer is -5.
17. -10 = -√100 and -11 = -√121 so -√120 is in between -10 and -11. Since 120 is closer to 121, the answer is -11.
Gradient is synonymous to slope.
y = 6x + 5 is an example of a slope-intercept form of a straight-line equationl.
The slope-intercept equation is like this:
y = mx + b
where : m = slope ; b = "y-intercept"
y = 6x + 5
6 is the slope
5 is the y-intercept.
Since slope and gradient are synonymous, 6 is the gradient of the above equation.
Answer:
If you cube the numbers in the left column, you get the numbers in the right column! We can figure this out by understanding that 1^3 = 1, 3^3 = 27, and 6^3 = 216. Then it all falls into place!
1 -> 1
2 -> 8
3 -> 27
5 -> 125
6 -> 216
11 -> 1331
8 -> 512
10 -> 1000
7 -> 343
14 -> 2744
p -> 
-> q
