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3 years ago

A 6-ft-tall person casts a shadow 5 ft long. A nearby tree casts a shadow 40 feet long. What is the height of the tree?

Mathematics

1 answer:

taurus [48]3 years ago

8 0

Answer:

The tree is 48 feet tall.

Step-by-step explanation:

Cross multiply. ⇒ $\frac{5}{6} x\frac{40}{x}$

5 times 8 equals 40, so 6 times 8 equals ___?

Solve. ⇒ $\frac{5}{6} x\frac{40}{x} =48$

The tree is 48 feet tall.

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Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what coul

aev [14]

The length of the rug is 4 ft.

The width of the rug is 2.5 ft.

Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

Let us convert the inches to feet.

Thus, $18 inches = 1.5 ft$

Thus, the length of the rug is $l=1.5+w$

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

$A=length\times width$

$10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0$

Solving the expression using the quadratic formula,

$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Substituting the values, we have,

$$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\$

$w=\frac{-15 \pm \sqrt{4225}}{20}$

$w=\frac{-15 \pm 65}{2 0}$

Thus,

$w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5$ and $w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4$

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

Substituting $w=2.5$ in $l=1.5+w$ , we get,

$l=1.5+2.5\\l=4$

Thus, the length of the rug is 4 ft.

4 0

3 years ago

896, -448, 224, -112 next in the sequence

faltersainse [42]

56, you are dividing by -2 each time

4 0

3 years ago

What inequality symbol belongs in the circle: -4 _ 5<br> 30 POINTS!

navik [9.2K]

Answer:

Step-by-step explanation:

Inequality symbols:

< less than

> greater than

= equal to

≤ less than or equal to

≥ greater than or equal to

In this case, it is known that -4 is less than 5, or:

-4 < 5.

7 0

3 years ago

Read 2 more answers

Find the area of a regular octagon with an apothem of 7 inches and a side length of 5.8 inches. (nearest tenth)

Kisachek [45]

Answer:

162.4 in²

Step-by-step explanation:

LETS GET INTOOOOEEETTT

Let's start with what we know:

Area of regular octagon = 1/2 x perimeter x apothem

We know the apothem, so all that we need to find to fill in the above equation is the perimeter:

perimeter = 8 x 5.8 = 46.4in

Now we can fill in our original equation and solve:

Area of regular octagon = 1/2 x perimeter x apothem

Formula = n (s/2)² divided by tan( π /n)

= 8 (5.8/2)² divided by tan ( π /8)

= 162.4283 in²

ORRR when rounded to the nearest tenth,

=162.4 in²

6 0

3 years ago

Expand the fraction 72/125 .so that it has a denominator of 1000.

Dmitrij [34]

X/1000=72/125 multiply both sides by 1000

x=72000/125

x=576

So the fraction is 576/1000

5 0

3 years ago