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2 years ago

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A lighthouse has a shadow that is 36 feet long. Zara is 4 feet tall, and she is standing next to the lighthouse. Zara has a shad

ow that is 3 feet long. Use this information to complete the statement about the lighthouse

1 answer:

pychu [463]2 years ago

7 0

Answer:

48 feet

Step-by-step explanation:

At a particular time, objects and their shadows are proportionate.

Therefore, in figure,

AB/FD = BC/DE --- (1)

where AB is the height of the lighthouse, BC, its shadow and FD is the height of Zara and DE is her shadow.

From the given information,

BC = 36 feet

FD = 4 feet and DE = 3 feet

(1) becomes

AB/4 = 36/3

AB = 12

AB = 48

Hence, the height of the lighthouse is 48 feet.

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Which are the solutions of x2 = 19x + 1?

Finger [1]

Answer:

$(\frac{19-\sqrt{365}} {2},\frac{19+\sqrt{365}} {2})$

Step-by-step explanation:

we have

$x^2=19x+1$

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-x^{2}-19x-1=0$

so

$a=1\\b=-19\\c=-1$

substitute in the formula

$x=\frac{-(-19)\pm\sqrt{-19^{2}-4(1)(-1)}} {2(1)}$

$x=\frac{19\pm\sqrt{365}} {2}$

$x=\frac{19+\sqrt{365}} {2}$

$x=\frac{19-\sqrt{365}} {2}$

$(\frac{19-\sqrt{365}} {2},\frac{19+\sqrt{365}} {2})$

therefore

StartFraction 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 365 EndRoot Over 2 EndFraction

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2 years ago

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Zucchini weights are approximately normally distributed with mean 08 pound and standard deviation 0.25 pound. Which of the follo

marissa [1.9K]

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 0.8 \ pounds$

The standard deviation is $\sigma = 0.25 \ pounds$

Generally the the probability that a randomly selected zucchini will weigh between 0 55 pound and 13 pounds is mathematically represented as

$P(0.55 < X < 1.3) = P(\frac{0.55 - 0.8}{ 0.25} < \frac{X - \mu}{\sigma } < \frac{1.3 - 0.8}{0.25})$

=> $P(0.55 < X < 1.3) = P( -1 < Z < 2 )$

So looking the option of normal curves given in the question we see that it is option A that matches our interval

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2 years ago

A sand dune stands 5 feet above sea level. The hill is eroding at a rate of 1 foot per 20 years. Let y represent the height of t

sergejj [24]

Answer:

y = 1/20 x + 5

Step-by-step explanation:

Let the height of the sand dune after x years be represented by the equation

y = mx+c where;

m is the rate at which the hills is eroding

c is the height of the dunes above the sea

If The hill is eroding at a rate of 1 foot per 20 years,then the rate of eroding per year will be;

1foot = 20years

m = 1year

Cross multiply

20m = 1

m = 1/20 foot/yr...

c = 5foot

Substitute into the formula:

y = 1/20 x + 5

Hence the equation that represent the situation is y = 1/20 x + 5

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In a basketball tournament, Team A scored 5 fewer than twice as many points as Team B. Team C scored 80 more points than Team B.

nekit [7.7K]

Answer:

(2b - 5) + b + (b + 80) = 983

Step-by-step explanation:

Given that,

Total score of three teams = 983

Since the teams' scores are given in reference to team B's score, let 'b' be the score of team B.

So,

The scores of Team A = (2 * b) - 5

The scores of Team B = b

The scores of Team C = (b + 80)

Thus,

The equation for determining the total points of Team B would be:

(2b - 5) + b + (b + 80) = 983

On solving,

(2b - 5) + b + (b + 80) = 983

⇒ 2b + b + b = 983 + 5 - 80

⇒ 4b = 908

⇒ b = 908 ÷ 4

⇒ b = 227

Team B's score = 227

Team A's score = (2 * 227 - 5)

= 449

Team C's score = 227 + 80

= 307

Total ⇒ 449 + 227 + 307 = 983

Hence proved.

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2 years ago

Lyles height is twice the difference of the height of his brother, harry, and the height of his dad, vince. Lyle is 2 1/2 feet t

Greeley [361]

Answer:

$5 = 19 - 4v$

Step-by-step explanation:

We are given the following in the question:

$\text{Lyle's height} = 2( \text{Harry's height - Vince's height})$

Let l be Lyle's height, h be Harry's height and v be Vince's height.

Thus, we can write:

$l = 2(h-v)$

Lyle's Height =

$2\dfrac{1}{2}\text{ feet}$

Harry's height =

$4\dfrac{3}{4}\text{ feet}$

Putting the value in the equation:

$2\dfrac{1}{2} = 2(4\dfrac{3}{4}- v)\\\\\dfrac{5}{2} = \dfrac{19}{2} - 2v\\\\5 = 19 - 4v\\4v = 19-5\\\\v = \dfrac{14}{4}\\\\v = 3\dfrac{2}{4} = 3\dfrac{1}{2}$

Thus, Vince's height is 3.5 feet.

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2 years ago