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never [62]
3 years ago
8

Please help I’ll make you a branliest!!!!!!!

Mathematics
1 answer:
masya89 [10]3 years ago
7 0

Answer:

2 answer is right

Step-by-step explanation:

I think

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At a point on the ground 80 ft from the base of a tree, the distance to the top of the tree is 11 ft more than 2 times the heigh
Sergio039 [100]

Let h be the height of the tree and d the distance to the top of the tree from the point on the ground. Draw a diagram to visualize the situation:

Since the distance to the top of the tree is 11 ft more than two times the height, then:

d=2h+11

Use the Pythagorean Theorem to relate the length of the sides of the right triangle:

\begin{gathered} h^2+80^2=d^2 \\ \Rightarrow h^2+6400=(2h+11)^2 \\ \operatorname{\Rightarrow}h^2+6400=(2h)^2+2(11)(2h)+11^2 \\ \operatorname{\Rightarrow}h^2+6400=4h^2+44h+121 \end{gathered}

Notice that we have obtained a quadratic equation in terms of h. Write it in standard form and use the quadratic formula to solve for h:

\begin{gathered} \Rightarrow0=4h^2+44h+121-h^2-6400 \\ \Rightarrow0=4h^2-h^2+44h+121-6400 \\ \Rightarrow0=3h^2+44h-6279 \\ \Rightarrow3h^2+44h-6279=0 \\  \\ \Rightarrow h=\frac{-44\pm\sqrt{(44)^2-4(3)(-6279)}}{2(3)} \\  \\ \therefore h_1=39 \\ h_2=-53.666.. \end{gathered}

Since the height of the tree must be positive, the only solution is h=39ft. To the nearest foot, the height of the tree is 39.

Therefore, the height of the tree is 39 ft.

4 0
1 year ago
Rectangle ABCD and right triangle DCE have the same area. They are joined to form a trapezoid, as shown. What is DE?
vfiekz [6]
Since the areas are the same  (5 x 6 = 30 units), and the height of the triangle (DC) is 5 so the length of the triangle must be 12.  (1/2 of  5 x 12 is also 30)

So now we use the Pythagorean theorem

a² + b² = c²   we have 5² + 12² = c²  or 25 + 144 = c²  or 169 = c²

The square root of 169 is 13 so side DE is 13 units.
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4 years ago
What is the equation of a line passing through the points (-4,3) and (-1,6)?(slope intercept form)
rosijanka [135]
(6 - 3)/(-1 +4)= 3/3= 1 is the slope

y - 3 = x + 4

y = x + 7
4 0
4 years ago
At the beginning of year 1, Gracie invests $350 at an annual simple interest rate of 4%. She makes no deposits to or withdrawals
scZoUnD [109]

Answer:

Step-by-step explanation:

The answer is A

5 0
3 years ago
The coordinates of triangle BCD are B(8, 2), C(11, 13) and D(2, 6). Which equality proves that triangle BCD is isosceles? (d = (
solniwko [45]
<span>(d = (x2 - x1)
Hope it helped!</span>
8 0
4 years ago
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