Answer:
DE = 20 units
Step-by-step explanation:
<u><em>GIVEN</em></u><em> :-</em>
- D & E are the mid-points of AB & BC respectively.
- DE = 4x + 4
- AC = x + 36
<u><em>TO FIND</em></u><em> :-</em>
<u><em>FACTS TO KNOW BEFORE SOLVING</em></u><em> :-</em>
- The midsegment of a triangle is a line constructed by connecting the midpoints of any two sides of the triangle.
- The Triangle Midsegment Theorem tells us that a midsegment is one-half the length of the third side (the base), and it is also parallel to the base.
<u><em>PROCEDURE</em></u><em> :-</em>
According to Triangle Midsegment Theorem ,
![DE = \frac{AC}{2}](https://tex.z-dn.net/?f=DE%20%3D%20%5Cfrac%7BAC%7D%7B2%7D)
![=> 4x + 4 = \frac{x + 36}{2}](https://tex.z-dn.net/?f=%3D%3E%204x%20%2B%204%20%3D%20%5Cfrac%7Bx%20%2B%2036%7D%7B2%7D)
Multiplying 2 on both the sides ,
![=> 2(4x + 4) = x + 36](https://tex.z-dn.net/?f=%3D%3E%202%284x%20%2B%204%29%20%3D%20x%20%2B%2036)
![=> 8x + 8 = x + 36](https://tex.z-dn.net/?f=%3D%3E%208x%20%2B%208%20%3D%20x%20%2B%2036)
![=> 8x - x = 36 - 8](https://tex.z-dn.net/?f=%3D%3E%208x%20-%20x%20%3D%2036%20-%208)
![=> 7x = 28](https://tex.z-dn.net/?f=%3D%3E%207x%20%3D%2028)
![=> x = \frac{28}{7} = 4](https://tex.z-dn.net/?f=%3D%3E%20x%20%3D%20%5Cfrac%7B28%7D%7B7%7D%20%3D%204)
∴ DE = 4×4 + 4 = 20 units
Answer:
(1,1)
Step-by-step explanation:
we have
----> equation A
----> equation B
we know that
The solution of the system of equations is the intersection point both graphs
The intersection point both graphs is the point (1,1)
see the given graph
therefore
The solution is the point (1,1)
Remember that
if a ordered pair is a solution of a system of equations then the ordered pair must satisfy both equations of the system
<u><em>Verify</em></u>
Substitute the value of x=1 and y=1 in each equation and analyze the result
<em>Equation A</em>
![1=-2(1)+3](https://tex.z-dn.net/?f=1%3D-2%281%29%2B3)
---> is true
so
The ordered pair satisfy the equation A
<em>Equation B</em>
---> is true
so
The ordered pair satisfy the equation B
therefore
The ordered pair (1,1) is a solution of the system because satisfy both equations
Answer:
1,176 square centimeters
Step-by-step explanation:
The computation of the area of the mosaic is shown below:
As we know that
The Area of the triangle is
= 1 ÷ 2 × base × height
= 1 ÷ 2 × 7 × 4
= 14
Now 1 tile would be 14 square centimeters
And, there are 84 tiles in the mosaic
So, the total area is
= 84 × 14
= 1,176 square centimeters
Answer:
tanx·secx
Step-by-step explanation:
To simply this, you can begin by factoring sin x out of the numerator to become:
Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:
![\frac{sinx}{cos^{2}x }](https://tex.z-dn.net/?f=%5Cfrac%7Bsinx%7D%7Bcos%5E%7B2%7Dx%20%7D)
First of all, we can convert
to tanx. However, we have a remaining
which, using reciprocal identities, will become sec x.
Finally, we get our answer as tanx·secx.
Answer:
X= 10, 20, 30, 40, 50, 60
Step-by-step explanation:thats
thats all i know