NotGuest

Because Taylor is 900 feet above ground, and the car is 1550 feet away from her, we can assume that the building is a straight vertical building so that we can use the Pythagorean Theorem to solve this.

\({a}^{2} + {b}^{2} = {c}^{2}\)

So:

Because 1550 is the hypotenuse, and 900 is the length of the vertical leg, we can make this equation:

\({a}^{2} + {900}^{2} = {1550}^{2}\)

\({1550}^{2} - {900}^{2} = {a}^{2}\)

\(2,402,500 - 810,000 = {a}^{2}\)

\(1592500 = {a}^{2}\)

\(\sqrt{1592500} = a\)

\(1261.9429464123962526 = a\)

So, a is aproximately 1261.94.

Hope this helps :)

I don't know if there is some kind of algebraic way to find this (I'm pretty sure there isn't) so let's just list the multiples of 21.

Green = Possible answer

Red = Not possible answer

21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029

In total, we have 7 positive multiples of 21 that have no digits smaller than 5. Now, we need to figure out the smallest one, which is easy:

The first green number is 567, which will therefore be our answer.

Ans = 567

Hope this helps :)

Because Miguel rode 16 miles, by ways of simple addition and subtraction we can figure out how many miles they all rode.

Miguel = 16 miles

Will = 16 + 5 miles

Belle = 16 + 5 - 18 miles

So:

Miguel = 16 miles

Will = 21 miles

Belle = 3 miles

Now, if we add them all up, we get:

16 + 21 + 3 miles

= 40 miles

To figure this out, I'll list the amount of money each type of change/bill adds up to.

Two dollar bill = 2.00

One dollar bill = 1.00

8 quarters = 2.00

11 dimes = 1.10

10 nickels = 0.50

3 pennies = 0.03

Now, I will add it all up.

2.00 + 1.00 + 2.00 + 1.10 + 0.50 + 0.03 = 6.63 dollars

To find the radius of a cone, you need not one, but two criteria to derive it. Because all that is given is the volume, it is not possible to find the radius of this cone unless given the height, too. This is because to determine a variable such as the radius, we must have all other criteria for the formula to find the volume to figure it out. Because the formula for the volume of a cone is 1/3 * pi * r^2 * h, we need the height to find out the radius.

So it is not possible.

But, if you were to have said a sphere, we would be able to figure it out because the volume of a sphere is 4/3 * pi * r^3 so there are no other criteria except for the radius needed to figure out the volume.

Now, I noticed that the question title actually says "volume of a pyramid", so maybe there was a typo. Still, this would be impossible due to the fact that the volume of a pyramid formula states, \({\displaystyle V={\frac {1}{3}}lwh},\) where l is the slant height, w is the width, and h is the height.

That is another way to do it, but for me it was definitely easier to solve through the whole problem instead of going through each and every way to get a coefficient of three. It's just my opinion, though.

I am going to mathematically show you how to solve these problems:

1. \(\sqrt{\frac{25}{144}}=\frac{\sqrt{25}}{\sqrt{144}}=\frac{5}{12}\) = 5/12

2. \(\sqrt{\frac{1}{9}}=\frac{\sqrt{1}}{\sqrt{9}}=\frac{1}{3}\) = 1/3

3. \(\sqrt{\frac{25}{49}}=\frac{\sqrt{25}}{\sqrt{49}}=\frac{5}{7}\) = 5/7

Hope this helps :)

The multiplication of a monomial with a monomial will always result in a monomial. Here is my reasoning:

The definition of a binomial (in my own words) is an algebraic expression consisting of more than one terms. Now, a term is a product of multiplication of numbers and variables. Because of this, no matter what monomials you take, a binomial will always have a plus or minus sign between two terms. So, if you multiply two monomials, no matter what, it will be impossible to get a plus or minus sign. Let me show you some examples:

(4a) * (2a) = 8a

(3z) * (3w) = 3z3w

(2x^3) * (4z^2) = 2x^3 * 4z^2

And these are all monomials. A monomial cannot have a plus/minus sign, or else it would be a binomial, and so if you multiply two monomials, it will result in:

a) a monomial

In this question, it is probably possible to represent it as an algebraic equation, but I think it would be easier to look at it from a different perspective. Because the Goofy Gardener (weird name, by the way) found that the pigeon plant was 1 foot high and the monster fern was 7 feet high, we can represent the height with a table.

We can stop at day 5, because on this day, the monster fern is three times as big as the pigeon plant. So, you have your answer:

The monster fern will be three times as big as the pigeon plant in 5 days.

This is a pretty long question, but I think I'm up for answering it.

First, we need to multiply the two expressions given, and then combine like terms.

(24x^4 + 6x^3 + 4x^2 + 7x - 5) * (6x^3 + 3x^2 - 3x + 4)

I'm going to switch them around to make it easier:

(6x^3 + 3x^2 - 3x + 4) * (24x^4 + 6x^3 + 4x^2 + 7x - 5)

= 6x^3 (24x^4 + 6x^3 + 4x^2 + 7x - 5) + 3x^2 (24x^4 + 6x^3 + 4x^2 + 7x - 5) - 3x (24x^4 + 6x^3 + 4x^2 + 7x - 5) + 4 (24x^4 + 6x^3 + 4x^2 + 7x - 5)

= (144x^7 + 36x^6 + 24x^5 + 42x^4 - 30x^3) + (72x^6 + 18x^5 + 12x^4 + 21x^3 − 15x^2) + (−72x^5 − 18x^4 − 12x^3 − 21x^2 + 15x) + (96x^4 + 24x^3 + 16x^2 + 28x − 20)

= 144x^7 + 36x^6 + 24x^5 + 42x^4 - 30x^3 + 72x^6 + 18x^5 + 12x^4 + 21x^3 − 15x^2 −72x^5 − 18x^4 − 12x^3 − 21x^2 + 15x + 96x^4 + 24x^3 + 16x^2 + 28x − 20

= 144x^7 + 36x^6 + 72x^6 + 24x^5 + 18x^5 − 72x^5 + 42x^4 + 12x^4 − 18x^4 + 96x^4 - 30x^3 + 21x^3 − 12x^3 + 24x^3 − 15x^2 − 21x^2 + 16x^2 + 15x + 28x − 20

= 144x^7 + 108x^6 - 30x^5 + 132x^4 + 3x^3 - 20x^2 + 43x - 20

So, now let us figure out the coefficient of x^3. We can see in our final answer that we have 3x^3, so the coefficient would be 3.

Therefore, our answer is 3.

P.S. I certainly hope this helps, but as it was an extremely time-taking and quite difficult problem, my answer may be incorrect. I do believe I worked through it correctly, though, so I hope this helps :)