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3 years ago

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PLEASE HELP. WORTH 50 PINTS IF CORRECT. A gate casts a shadow that is 5 feet long. A nearby cactus is 9 feet tall and casts a sh

adow that is 15 feet long. What is the height of the gate?

2 answers:

brilliants [131]3 years ago

3 0

Answer:

The height of the cactus is three times the height of the gate

The gate is 3 feet tall

Leya [2.2K]3 years ago

3 0

The answer is 3 feet

9/15 = x/5
15/5 = 3
9/3 = 3
3/5 = 9/15

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Zoey made 6 1/2 cups of trail mix for a camping trip. She wants to divide the trail mix into 3/4 cup of servings. Twelve people

AlekseyPX

Answer:

No

Step-by-step explanation:

Given that:

Total number of cups of trail mix available for camping trip = $6\frac{1}{2}$

Amount of one serving contains = $\frac{3}{4}$ cups

Number of people at the trip = 12

To find:

Whether each person will be able to get the servings?

Solution:

Here, we can find the total number of servings by dividing the total number of cups of trail mix with the amount of one serving.

First of all, let us convert the mixed fraction into fractional number.

$6\dfrac{1}{2} = \dfrac{6\times 2+1}{2} = \dfrac{13}{2}$

Therefore, total number of servings available as per the given quantities:

$\dfrac{\frac{13}2}{\frac{3}4}\\\Rightarrow \dfrac{13\times 4}{2\times 3} \\\Rightarrow \dfrac{26}{3}\\\Rightarrow \approx 8$

So, With this type of servings Zoey will be able to serve only 8 people.

Therefore, there is not enough servings.

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2 years ago

What is the equation of the asymptote for this function?

77julia77 [94]

The equation of the horizontal asymptote for this function f(x) = (1/2)^x + 3 is option D y = 3.

<h3>When do we get horizontal asymptote for a function?</h3>

The line y = a is horizontal asymptote if the function f(x) tends to 'a' from the upside of that line y = a, or from downside of that line.

The function is given as;

f(x) = (1/2)^x + 3

The function is Exponential functions.

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is option D y = 3.

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2 years ago

a box with a square base and open top must have a volume of 70304 c m 3 cm3 . we wish to find the dimensions of the box that min

Dmitriy789 [7]

The box should have base 52 cm by 52 cm and height 26 cm.

What is volume?

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

The Volume of a box with a square base x by x cm and height h cm is

$V = x^2h$

Since the surface area directly affects the amount of material used, we can reduce the amount of material by reducing the surface area.

The surface area of the box described is $A = x^2 + 4xh$

We need A as a function of x alone, so we'll use the fact that

$V = x^2h= 70304 cm^3$

⇒ $h = \frac{70304}{x^2}$

So, the area becomes,

$A = x^2+4x(\frac{70304}{x^2})\\ A = x^2 + \frac{281216}{x}$

We want to minimize A, so

$A' = 2x - \frac{281216}{x^2} =0\\\frac{2x^3-281216}{x^2}=0\\ {2x^3-281216} = 0\\x^3 - 140608=0\\x^3 = 140608\\x = 52$

The second derivative test verifies that A has a minimum at this critical number:

$A'' = 2+\frac{562432}{x^3}$ which is positive at x = 52.

Now,

$h = \frac{70304}{x^2}= \frac{70304}{(52)^2}=26$

Hence, The box should have base 52 cm by 52 cm and height 26 cm.

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1 year ago

Describe how to find the vertex of a parabola if you are given the equation

emmainna [20.7K]

Answer:

The vertex of a parabola is (h,k)

Step-by-step explanation:

The vertex form of a parabola is y=a(x-h)^2+k where a is the stretch/compression factor and (h,k) is the vertex. So to find the vertex, you will need (h,k) which represents the horizontal and vertical shift of the parabola

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3 years ago

Select the correct answer.

Yuliya22 [10]

Answer: B is your correct answer.

Step-by-step explanation: If she has already made $95.00 from selling jam and made $24.00 from demonstrations you add those together to get $119. Then you subtract $119.00 from $450.00 and you'll have $331.00 left to make. Finally you divide $331.00 by $5.00 (cost of jam) and you'll find that you have to sell 66 more jars of jam.

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3 years ago

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