1. You have that:
- The<span> lengths of the bases are (6x-1) units and 3 units.
- The midsegment has a length of (5x-3) units.
2. To solve this exercise, you must apply the formula for calculate the length of the midsegment of a trapezoid, which is shown below:
Midsegment=Base1+Base2/2
As you can see, the midsegment is half the sum of the bases of the trapezoid.
3. When you substitute the values, you obtain:
(5x-3)=[(6x-1)+3]/2
4. Now, you can solve the problem by clearing the "x":
</span>
(5x-3)=[(6x-1)+3]/2
2(5x-3)=6x-1+3
10x-6=6x+2
10x-6x=2+6
4x=8
x=8/4
x=2
Given:
The figure of a triangle LMN.
P is the centroid of triangle LMN.
To find:
14. Find the value of PN if QN=30.
15. Find the value of PN if QN=9.
Solution:
We know that the centroid in the intersection of medians of a triangle and centroid divides each median in 2:1.
Since P is the centroid it means NQ is the median from vertex N. It means P divides the median NQ in 2:1. So, PN:PQ=2:1.
14. We have QN=30.
Therefore, the value of PN is 20 when QN=30.
15. We have QN=9.
Therefore, the value of PN is 6 when QN=9.
Answer:
<em>D </em><em>$0.60</em>
Step-by-step explanation:
Since <em>a dozen is equal to 12</em>, we will first <em>multiply $2.75 by 12</em>, and we get <em>$33</em>. Now <em>subtract $33 by $25.80</em> dollars, which is <em>$7.2.</em> Now we know that we saved <em>$7.2 </em>out of a dozen cupcake's, but we have to find <em>how much we saved on </em><u><em>each</em></u><em> cupcake</em>. So lets <em>divide $7.2 by 12</em> and we get <em>$0.60. </em> Therefore, you saved <em>$0.60</em> on each cupcake.
Functions 6 and 7 are linear, 8 is not. This means 6 and 7 have a degree of 1. Since 8 is a quadratic, it has a degree of 2.
The slope is 1 for function 6 and 5 for function 7. Remember, in slope-intercept format, linear equations are written as y=mx+b. X and Y stand for coordinates you can plug in, m represents the slope of the line, and b represents the y-coordinate of the function’s y-intercept. I assume you are familiar with these terms so I won’t explain them.
Number 9 is linear, and you can tell because f(x), which is the output, increases with a constant difference as x increases by 1. In other words, the delta y and delta x is the same between all points.
Number 10 is clearly not linear, because two different x values have the same y value. This is a parabola.
I recommend you graph some of these functions for practice, so you can visualize it better. Imagine the functions as machines. You input a number (x) and you get a number out (y).
For example, in the function f(x)=3x+5, I can input any x, let’s take x as 6, and when I plug it in, I’ll get an output, f(x). 3(6)+5=18+5=23. So my f(x)=23 when x is 6.
Answer:
500π ≈ 1570.796
Step-by-step explanation:
diameter = 10
radius = diameter / 2 = 10 / 2 = 5
height = 4 * radius = 4 * 5 = 20
volume = π * height * (radius)² = π * 20 * (5)² = 500π ≈ 1570.796
