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3 years ago

Challenge A box is 15 in high, 18 in. long, and 6 in, wide. What is the longest poster you could fit in

Mathematics

1 answer:

taurus [48]3 years ago

3 0

Answer:

a. 24.2 in

b. Paths of the internal diameter, where the longest poster is placed cross each other

Step-by-step explanation:

a. The longest poster that can be fitted into the box is the size of the internal diagonal of the box, that is

√((8² + 6²) +15²) = 3·√65 = 24.2 in

b. Since the above give the diagonal of the box, there can only be one poster of the dimension 24.2 in as due to path interference of the longest poster that is placed at the internal diagonal of the volume of the box

However, for the surface diagonal we have the dimension given by;

√(8² + 15²) = 23.4 in. Therefore since the side diagonal is parallel to the side of the box, one can fit several 23 in. posters which are lesser than the length of the diagonal of the side of the box side by side in the box.

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A restaurant served 27,500 customers in 2012. In 2014, the restaurant served 29,000 customers. Write a linear model that represe

rjkz [21]

Answer:

In 2012, a restaurant served 27,500 customers and in 2014, the restaurant served 29,000 customers.

First determine the increase in the number of customer served each year.

the number of customer increase in each year is, $\frac{29000-27500}{2} =\frac{1500}{2} =750$

therefore, the linear model is;

y = 750x+ 27500 , where y represents the number of customers that the restaurant serves x years after 2012.

Now, to predict the number of customers that the restaurant will serve in 2020 is;

since, x = 2020-2012 = 8 years

$y = 750 \times 8 +27500$ or

$y= 6000+27500=33,500$

therefore, the number of customers that the restaurant will serve in 2020 = 33,500

3 0

3 years ago

-14.9=x/8 -2.1 Please help me answer

Romashka [77]

-14.9 = $\frac{x}{8}$ - 2.1 (Add 2.1 to both sides)
-12.8 = $\frac{x}{8}$ (Multiply both sides by 8)
-102.4 = x

~~~Hope this helps!~~~

4 0

3 years ago

Express 0.0057 in scientific notation

andrew-mc [135]

Answer:

$5.7 \times {10}^{ - 3}$

Step-by-step explanation:

0.0057

first number

then the rest

equal

5.7

There's three zeros behind the number 5 which mean it will be -3

$\times {10}^{ - 3}$

final answer

$5.7 \times {10}^{ - 3}$

another example and it will be clear

0.0000403

first number

then the rest

equal

4.03

There's five zeros behind the number 4 which mean it will be -5

$\times {10}^{ - 5}$

final answer

$4.03 \times {10}^{ - 5}$

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3 years ago

Solve the following system by any method -8x-8y=0 -8x+2y=-20

iVinArrow [24]

$\fbox{Solution by using Matrix}$

$\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20$

$\text{Rewrite the linear equations above as a matrix}$

$\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right]$

$\text{Apply to Row2 : Row2 + Row1}$

$\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right]$

$\text{Note: The matrix is now in echelon form.}$ $\text{The steps below are for back substitution.}$

$\text{Apply to Row1 : Row1 + 8 Row2}$

$\left[\begin{array}{ccc}8&0&80/30\\0&1&10/3\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right]$

$\text{Therefore, the solution is}$

$x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}$

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3 years ago

Shana is at the grocery store comparing two brands of juice. Brand A costs $3.84 for a 16-ounce bottle. Brand B costs $4.50 for

DaniilM [7]

I hope this helps, it is correct.

5 0

3 years ago