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klio [65]
2 years ago
11

If C = 1+ p2 + 3p and B = 2p + 6p, find an expression that equals 2C – – B in

Mathematics
1 answer:
drek231 [11]2 years ago
4 0

Answer:

2p² + 14p + 2

Step-by-step explanation:

Given that;

C= 1+p²+3p

B=2p+6p

The expression that equals to : 2C - -B will be;

2{1+p²+3p} - {-2p-6p}

2+2p²+6p + 2p + 6p

2p² + 6p +2p +6p +2

2p² + 14p + 2

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Which situation is best represented by the equation? 35p + 129.50 = 479.50
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2 years ago
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valentina_108 [34]

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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>
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3 years ago
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