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sergejj [24]
3 years ago
15

Geometry math question no Guessing and Please show work

Mathematics
1 answer:
Andru [333]3 years ago
3 0
D. (7,0)
The original coordinates were (0,7)y and (1,5)x then I rotated it 90 degrees and the coordinates were (7,0)y and (5,1)x

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An equilateral triangle has a side length of 6. What is the height of the triangle?
vlabodo [156]
Since the height of an equilateral triangle in terms of its side s is s√3/2, the height of the triangle is 6√3/2 = 3√3 and so the area is (1/2)(6)(3√3) = 9√3. 

<span>If we draw a horizontal line a height of h from the base of the triangle, the region is split into two regions: the lower region consisting of a trapezoid of height h and the upper region consisting of a triangle of height 3√3 - h. </span>

<span>Since the upper triangle and the triangle itself are similar triangles, the base and height are proportional. If we let x denote the base of the length of the upper triangle, we have: </span>

<span>(S. of small triangle)/(S. of big triangle) = (Ht. of small triangle)/(Ht. of big triangle) </span>
<span>==> x/6 = (3√3 - h)/(3√3) </span>
<span>==> x = (6√3 - 2h)/√3 </span>

<span>Thus, the area of the upper triangle is: </span>

<span>A = (1/2)[(6√3 - 2h)/√3](3√3 - h) = [(6√3 - 2h)(3√3 - h)]/(2√3). </span>
<span>(Made a dumb mistake about the height here for some reason) </span>

<span>Since we require that the area of this triangle is to be half of the total area (9√3/2), we need to solve: </span>

<span>[(6√3 - 2h)(3√3 - h)]/(2√3) = 9√3/2 </span>
<span>==> (6√3 - 2h)(3√3 - h) = 27 </span>
<span>==> 54 - 6h√3 - 6h√3 + 2h^2 = 27 </span>
<span>==> 2h^2 - 12h√3 + 27 = 0. </span>

<span>Solving with the Quadratic Formula gives: </span>

<span>h = (6√3 + 3√6)/2 ≈ 8.87 units and h = (6√3 - 3√6)/2 ≈ 1.52 units. </span>

<span>Since h = (6√3 + 3√6)/2 would place the line outside of the triangle, we pick h = (6√3 - 3√6)/2. </span>

<span>Therefore, the line should be ==> (6√3 - 3√6)/2 units from the base. </span>

<span>I hope this helps! ^^ Brainliest Please?</span><span>
</span>
5 0
3 years ago
Read 2 more answers
Find the difference of 5 2/3 -4 5/9<br> A 3/4<br> B 1 1/9 <br> C 1 1/2<br> D 8/9
sergey [27]
Answer: B- 1 1/9
Work:
5 2/3 - 4 5/9
1 2/3 - 5/9
1 6/9 - 5/9
= 1 1/9
5 0
3 years ago
(-1,2),(3,6),(7,18),(11,54) linear or not linear
pentagon [3]

Answer:

           Linear

Dk if your asking for all or not

3 0
2 years ago
Suppose that the population of deer in a state is 1,500 and is growing 2% each year. Predict the population after 4 years.
frutty [35]
Required number
= 1500*(1+2%)^4
=1624(cor.to.the nearest integer)
7 0
3 years ago
What is the solution to this system?
katovenus [111]
The solution is where the two lines meet. From the the graph, it looks like
(1, -1)
6 0
3 years ago
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