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3 years ago

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a shipping box has the dimensions of 12inches, 16 inches, and 24 inches. what is the length of the longest item that could fit i

n the box?

1 answer:

Vladimir [108]3 years ago

8 0

Answer:

24 inches

Step-by-step explanation:

The dimensions of the box are 12 in, 16 in, 24 in

This means that the longest side of the box is 24 inches

It does not matter which side the box is long on

The longest item that you could fit in the box is 24 inches because you could turn the item vertical or horizontal to fit

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A rectangular prism has a length of 7 inches and a width of 5 inches. The lateral area is 192 square inches. What is the height

Dennis_Churaev [7]

Answer:

I think it would be 5.49 as the height of the prism.

Step-by-step explanation:

I just did 7 × 5 which is 35, and then I did 192 ÷ 35 and got 5.49. I'm not completely sure but that's my best answer I hope it helps!

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3 years ago

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Which linear function represent the table?

rodikova [14]

Answer:

Step-by-step explanation:So, if the graph is a straight line, it is the graph of a linear function. From a table, you can verify a linear function by examining the x and y values. The rate of change for y with respect to x remains constant for a linear function. This rate of change is called the slope.Mar 9, 2011

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2 years ago

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Find the limit, if it exists, or type dne if it does not exist.

Phantasy [73]

$\displaystyle\lim_{(x,y)\to(0,0)}\frac{\left(x+23y)^2}{x^2+529y^2}$

Suppose we choose a path along the $x$ -axis, so that $y=0$ :

$\displaystyle\lim_{x\to0}\frac{x^2}{x^2}=\lim_{x\to0}1=1$

On the other hand, let's consider an arbitrary line through the origin, $y=kx$ :

$\displaystyle\lim_{x\to0}\frac{(x+23kx)^2}{x^2+529(kx)^2}=\lim_{x\to0}\frac{(23k+1)^2x^2}{(529k^2+1)x^2}=\lim_{x\to0}\frac{(23k+1)^2}{529k^2+1}=\dfrac{(23k+1)^2}{529k^2+1}$

The value of the limit then depends on $k$ , which means the limit is not the same across all possible paths toward the origin, and so the limit does not exist.

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3 years ago

Solve the equation Square root of x minus 5+ 7 = 11 for the variable. Show each step of your solution process. (10 points)

Murrr4er [49]

$\sqrt{x - 5} + 7 = 11$

$(\sqrt{x-5}) ^{2} = (4)^{2}$

|x - 5| = 16

x - 5 = +/- 16

x - 5 = 16 or x - 5 = -16

<u> +5</u> <u>+5 </u> <u> +5 </u> <u>+5 </u>

x = 21 or x = -11

Answer: x = {21, -11}

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3 years ago

Prove the divisibility:<br><br>45^45·15^15 by 75^30

garri49 [273]

Answer:

$3^{75}$ .

Step-by-step explanation:

We have been an division problem: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(9*5)^{45}=9^{45}*5^{45}$

$15^{15}=(3*5)^{15}=3^{15}*5^{15}$

$75^{30}=(15*5)^{30}=15^{30}*5^{30}$

Substituting these values in our division problem we will get,

$\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}$

$\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}$

$\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}$

$\frac{3^{105}*5^{60}}{3^{30}*5^{60}}$

$\frac{3^{105}}{3^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{105}}{3^{30}}=3^{105-30}$

$3^{105-30}=3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

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3 years ago