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3 years ago

Can someone help with question 51 please I need to break it down

Mathematics

1 answer:

dlinn [17]3 years ago

3 0

$\dfrac{2}{3}t-3\leq1|\cdot3\\
2t-9\leq3\\
2t\leq12\\
t\leq6\\\\
\dfrac{3}{4}t-2>7|\cdot4\\
3t-8>28\\
3t>36\\
t>12\\\\
t\leq6 \vee t>12\\
\boxed{t\in(-\infty,6]\cup(12,\infty)}
$

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We can use the ratios for special triangles (see the attachment below). We'll be using the 45-45-90 triangle. We notice that side BC is equal to $x \sqrt{2}$ , and side AC (x using the special right triangle) is equal to 16. We can therefore say that side BC is equal to $16 \sqrt{2}$ ft

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3 years ago

The height of a triangle is 8ft greater than the base. The area of the triangle is 136.5 square ft. Find the length of the base

mixer [17]

Answer:

the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.

Step-by-step explanation:

Note that the formula for the area of a triangle is A = (1/2)(base)(height). Let's abbreviate that to A = (1/2)(b)(h). We are told that h = b + 8.

Then A = 136.5 = (1/2)(b)(b + 8), or

(after multiplying both sides by 2)

A = 273 = b^2 + 8b

which, when put into standard quadratic form, becomes:

b^2 + 8b - 273 = 0

The coefficients of this quadratic are a = 1, b = 8 and c = -273.

Thus, the discriminant is b^2 - 4ac, or 64 - 4(1)(-273) = 1156 = 17^2.

The roots are then

-8 ± √1156 -8 ± 17

x = -------------------- = ------------ = 9/2 and -25/2

2 2

Only the root 9/2 makes sense here, because measurements of length are positive.

Thus, the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.

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