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2 years ago

8

The area of Mammoth Cave NationalPark in Kentucky is about fifty-two thousand, eight hundred thirty and nineteen hundredths acre

s. Which shows this number of acres as a base ten numeral?

1 answer:

frutty [35]2 years ago

4 0

Answer:it’s the first one

Step-by-step explanation:

You might be interested in

Consider the function f(x)= (x+4)(x-2) what is the equation of the axis of symmetry

almond37 [142]

if we zero out f(x), namely make y = 0, we can get the roots or x-intercepts for this quadratic equation

$\bf 0 = (x+4)(x-2)\implies \begin{cases} 0=x+4\implies &-4=x\\ 0=x-2\implies &2=x \end{cases}$

now, the equation is in x-terms, meaning is a vertically opening parabola, so the axis of symmetry will be x = something, a vertical line.

well, we have two x-intercepts, one at -4 and another at 2, and the vertex is right half-way between those guys

-4------------(-1)------------2

so the vertex is at x=-1, namely the axis of symmetry is x = -1.

8 0

3 years ago

Jennifer hit a golf ball from the ground and it followed the projectile ℎ(t)= −15t^2+100t, where t is the time in seconds, and ℎ

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

In order to find the max height the ball reached, we have to complete the square on that quadratic. That will also, conveniently so, give us the number of seconds it will take the ball to reach that max height, that answer to part b. Let's begin to complete the square. Normally, you would move the constant over to the other side of the equals sign, but there is no constant here. The next step is to get the leading coefficient to be a 1, and ours right now is a -15. So we have to factor it out. Here's where we start the process of completing the square.

$-15(t^2-\frac{20}{3}t)=0$ Next step is to take half the linear term, square it, and add it to both sides. Our linear term is 20/3. Half of 20/3 is 20/6, and 20/6 squared is 400/36.

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0+???$ Because this is an equation, what we add to the left side also has to be added to the right. BUT we didn't just add in 400/36, because we have that -15 out front as a multiplier that refuses to be ignored. What we actually added in was -15(400/36):

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0-\frac{500}{3}$

The reason we do this is to create a perfect square binomial on the left which will serve as the number of seconds, h, in the vertex (h, k), where h is the number of seconds it takes the ball to reach its max height, k. Simplifying both sides then gives us:

$-15(t-\frac{20}{6})^2=-\frac{500}{3}$ Finally, we will move the right side over by the left and set the quadratic back equal to h(t):

$h(t)=-15(t^2-\frac{20}{3})^2+\frac{500}{3}$ and from that you can determine that the vertex is $(\frac{20}{3},\frac{500}{3})$ .

The answer to a. is vound in the second number of our vertex: k, the max height. The max of the golf ball was 500/3 feet or 166 2/3 feet.

Part b is found in the first number of the vertex: h, the number of seconds it took the golf ball to reach that max height. The time it took was 3 1/3 seconds.

Part c. is to state the domain (the time) and the range (the height) of the ball.

Domain is

D: {x | 0 ≤ x ≤ 3 1/3} and

Range is

R: {y | 0 ≤ y ≤ 166 2/3}

8 0

3 years ago

(PLEASE HELP)An elevator car in a skyscraper can hold at most 15 people. For safety reasons, each car can carry a

natali 33 [55]

Answer:

$70x + 25y + 4x + 4y \leqslant 1500$

where x = number of adults

y = number of children

and the extra weights of 4kg of each person.

8 0

2 years ago

The length of each side of a regular pentagon is increased by 8 inches, so the perimeter is now 65 inches. What is the original

evablogger [386]

<em>Here</em> as the <em>Pentagon</em> is <em>regular</em> so it's <em>all sides</em> will be of <em>equal length</em> . And if we assume It's each side be<em> </em><em><u>s</u></em> , then it's perimeter is going to be <em>(s+s+s+s+s) = </em><em><u>5s</u></em>.And as here , each <em>side</em> is increased by <em>8 inches</em> and then it's perimeter is <em>65 inches</em> , so we got that it's side after increament is<em> (s+8) inches</em> and original length is <em>s inches </em>. And if it's each side is <em>(s+8) inches</em> , so it's perimeter will be <em>5(s+8)</em> and as it's equal to <em>65 inches</em> . So , <em><u>5(s+8) = 65</u></em>

${:\implies \quad \sf 5(s+8)=65}$

${:\implies \quad \sf 5s+5\times 8=65}$

${:\implies \quad \sf 5s+40=65}$

${:\implies \quad \sf 5s=65-40}$

${:\implies \quad \sf 5s=25}$

${:\implies \quad \sf s=\dfrac{25}{5}=5}$

${:\implies \quad \bf \therefore \quad \underline{\underline{s=5\:\: Inches}}}$

As we assumed the original side to be <em><u>s</u></em> .

<em>Hence, the original side's length 5 inches </em>

8 0

2 years ago

On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the

Daniel [21]

Answer:

hello your question is incomplete attached below is the complete question

answer :

H0 : <em> u </em>= 21.62 ( Null hypothesis )

H1 : <em> u</em> = 21.62 ( alternative hypothesis )

Step-by-step explanation:

Formulating hypothesis that can be used to determine whether the population mean rate at 5 CCF of residential water discharged by U.S public utilities differs from $21.62

H0 : <em> u </em>= 21.62 ( Null hypothesis )

H1 : <em> u</em> = 21.62 ( alternative hypothesis )

3 0

3 years ago