Answer:
Step-by-step explanation:
Animal Person
y = 5.4x + 34 y = 12x + 8.5; where y - weight, x - years
looking for when weight (y) is the same, so we need
animal weight (y) = person weight (y)
5.4x + 34 = 12x + 8.5
<u> -5.4x -5.4x</u>
34 = 6.6x + 8.5
<u> -8.5 -8.5</u>
25.5 = 6.6x divide both sides by 6.6
x = 3.86 years
not sure if you need your answer in decimal or what, but you can adjust accordingly.
Answer:
1. sometimes true
A rhombus is a quadrilateral with all equal size and length. A square is a quadrilateral with all equal size and length, and all right angles around bus, however, can be a square if it has right angles.
2. always true
A square has to have all equal sides and all right angles, however, a rectangle has to have right angles and opposite sides are equal to each other. So if a square has equal sides, it can be considered a rectangle since both opposite sides are equal
3. sometimes true
A parallelogram is a quad roulette or with parallel and equal opposite sides, and a rectangle has right angles and equal opposite sides, therefore, if the parallelogram has right angles, then it is considered a rectangle
4. always true
A quadrilateral has to have 4 sides and the rectangle has 4 sides there, for it is considered a quadrilateral
5. never true
A parallelogram is a quadrilateral, therefore, it has to have 4 sides, but a hexagon has to have 6 sides, therefore, it is never a hexagon
Given:
The bases of triangular prism are right triangles with a base of 12 inches and height of 9 inches.
The height of the prism is 11 inches.
To find:
The surface area of the triangular prism.
Solution:
Using the Pythagoras theorem, the hypotenuse of the bases of the triangular prism is:
![Hypotenuse^2=Base^2+Height^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DBase%5E2%2BHeight%5E2)
![Hypotenuse^2=12^2+9^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D12%5E2%2B9%5E2)
![Hypotenuse^2=144+81](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D144%2B81)
![Hypotenuse^2=225](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D225)
Taking square root on both sides.
![Hypotenuse=15](https://tex.z-dn.net/?f=Hypotenuse%3D15)
The surface after of the triangular prism contains 3 rectangles of dimensions 12 inches by 11 inches, 9 inches by 11 inches, 15 inches by 11 inches and two triangles with base 12 inches and height 9 inches.
Area of the rectangle:
![Area=Length \times Width](https://tex.z-dn.net/?f=Area%3DLength%20%5Ctimes%20Width)
So, the area of three rectangles are:
![A_1=12 \times 11](https://tex.z-dn.net/?f=A_1%3D12%20%5Ctimes%2011)
![A_1=132](https://tex.z-dn.net/?f=A_1%3D132)
![A_2=9 \times 11](https://tex.z-dn.net/?f=A_2%3D9%20%5Ctimes%2011)
![A_2=99](https://tex.z-dn.net/?f=A_2%3D99)
![A_3=15 \times 11](https://tex.z-dn.net/?f=A_3%3D15%20%5Ctimes%2011)
![A_3=165](https://tex.z-dn.net/?f=A_3%3D165)
Area of a triangle is:
![Area=\dfrac{1}{2}\times base \times height](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20base%20%5Ctimes%20height)
So, the area of the triangles is:
![A_4=\dfrac{1}{2}\times 12 \times 9](https://tex.z-dn.net/?f=A_4%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2012%20%5Ctimes%209)
![A_4=6 \times 9](https://tex.z-dn.net/?f=A_4%3D6%20%5Ctimes%209)
![A_4=54](https://tex.z-dn.net/?f=A_4%3D54)
And, the triangles have same dimensions so their areas are equal.
![A_4=A_5=54](https://tex.z-dn.net/?f=A_4%3DA_5%3D54)
Now,
![Area=A_1+A_2+A_3+A_4+A_5](https://tex.z-dn.net/?f=Area%3DA_1%2BA_2%2BA_3%2BA_4%2BA_5)
![Area=132+99+165+54+54](https://tex.z-dn.net/?f=Area%3D132%2B99%2B165%2B54%2B54)
![Area=504](https://tex.z-dn.net/?f=Area%3D504)
Therefore, the surface area of the triangular prism is 504 sq. inches.
Answer:
GF = 25.2
Step-by-step explanation:
GF/BC = (AD-FE)/AD
GF = BC(AD-FE)/AD = 36(20-6)/20
GF = 25.2
__
The ratio of GF to BC is the ratio of DE to DC. The ratio of FE to AD is the ratio of CE to CD. That is ...
GF/BC = (CD-CE)/CD = 1 - FE/AD = (AD -FE)/AD . . . . . as above
answer: 105+3x
step by step: times 3 by 35 an then 3 times x