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3 years ago

Triangle ABC is a right triangle with lengths shown.

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

4 0

<h3>Answer:</h3>

0.225

<h3>Step-by-step explanation:</h3>

The mnemonic SOH CAH TOA reminds you of the definition of the tangent of an angle.

... Tan = Opposite/Adjacent

The side opposite angle C is AB. The side adjacent to angle C is BC. Then ...

... tan(C) = AB/BC = 18/80 = 0.225

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A movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag.

scoundrel [369]

Answer:

<em>The price for a 60-ounce bag of popcorn would be $16</em>

Step-by-step explanation:

<u>Function Modeling</u>

The behavior of some parameters that depend on a set of variables can be modeled in several ways, like linear, quadratic, exponential, logarithmic, among many others.

The selection of the model is often a complex decision that involves statistics and data analysis.

The question provides us with four points where the volume of popcorn bags and the price in dollars. The easiest function that can be used is the line.

The equation of a line of the volume V and the price p can be found with the expression

$\displaystyle p-p_1=\frac{p_2-p_1}{V_2-V_1}(V-V_1)$

We'll use the first two values (6,10) (8,20)

$\displaystyle p-6=\frac{8-6}{20-10}(V-10)$

Simplifying and rearranging, we get the model

$\displaystyle p(V)=\frac{1}{5}V+4$

To test the accuracy of the model, we compute the values of p for V=35 and for V=48

$\displaystyle p(35)=\frac{1}{5}(35)+4=11$

$\displaystyle p(48)=\frac{1}{5}(48)+4=13.6$

Since the computed values are equal to those of the table, the model is accurate. We can now predict the price for V=60

$\displaystyle p(60)=\frac{1}{5}(60)+4=16$

The price for a 60-ounce bag of popcorn would be $16

6 0

3 years ago

Could anybody give me some help? I'm a little confused .-. <3

nika2105 [10]

What your teacher wants is for you to isolate y in the given equation. In other words, get y all by itself.

To do this, you'll do two basic steps:
Step 1) Subtract 2x from both sides
Step 2) Divide both sides by 3

Let's do that and we get...
2x+3y = 1470
2x+3y-2x = 1470-2x ... apply step 1
3y = 1470-2x
3y = -2x+1470
3y/3 = (-2x+1470)/3 ... apply step 2
y = (-2x)/3 + 1470/3
y = (-2/3)x + 490

After isolating y, we get y = (-2/3)x + 490
To get this into function notation, we simply replace y with f(x) to get the final answer f(x) = (-2/3)x+490 which is the same as writing $f(x) = -\frac{2}{3}x+490$

This graph represents all of the ordered pairs (x,y) that make the original equation true. For example, the point (x,y) = (0,490) is on the line where x = 0 and y = 490. This point is when 0 sandwiches are sold and 490 wraps are sold yielding a profit of $1470. Another point on this line is (x,y) = (3,488). Now 3 sandwiches have been sold along with 488 wraps leading to the same profit of $1470. Any ordered pair point you pick on the line should lead you to the same profit.

3 0

2 years ago

The length of a rectangle is 1 cm less than the width. The area of the rectangle is 12 cm². determine the dimensions of the rect

jarptica [38.1K]

Answer:

L= 3 cm

W= 4 cm

Step-by-step explanation:

Factors of 12:

1 and 12

2 and 6

3 and 4

Which of those is one number apart?

3 and 4

So the sides must be 3 by 4 cm.

6 0

2 years ago

A school requires 2 computers for every 5 students. If a school has 145 students, how many computers do they need?

defon

Step-by-step explanation:

145/5=23

23×2=46 computers

4 0

3 years ago

Expand and simplify (2c+1)(2c+3)

Mandarinka [93]

The answer would be 4c^2+8c+3

The arrow stands for squared off you didn’t already know but these are very easy to solve because you just multiply it out

6 0

2 years ago