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3 years ago

Use the diagram of the right triangle above and round your answer to the nearest hundredth.

Mathematics

1 answer:

Yakvenalex [24]3 years ago

7 0

Answer: a = 23 ft.

Reasoning:

The question asks for the value of the leg a, given the tangent of the opposite angle and the length of the adjacent-leg, b.

The ratio that relates the three parameters is:

tan(A) = opposite-leg / adjacent-leg = a / b = a / 23 ft

Solve for a, wich is the unknown:

a = 23ft * tan(A) = 23ft * 1.0 = 23 ft

Answer: 23 ft.

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The model represents x2 â€" 9x 14. An algebra tile configuration showing only the Product spot. 24 tiles are in the Product spot

snow_lady [41]

The factors of the given model are (x+2) and (x+7)

Given the representation of the model expressed as;

$x^2+9x+14$

To get the factors, we will factorize the given quadratic function as shown:

$g(x) = x^2+2x+7x+14$

Group the functions to have;

$g(x) = (x^2+2x) + (7x+14)\\$

Factor out the GCF from both parenthesis:

$g(x) = x(x+2)+7(x+2)\\g(x)=(x+2)(x+7)$

Hence the factors of the given model are (x+2) and (x+7)

Learn more on factorization here: brainly.com/question/25829061

5 0

3 years ago

A farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. Find the maximum area he can close.

Margarita [4]

Answer:

Width of 37.5 feet and length of 50 feet will maximize the area.

Step-by-step explanation:

Let w represent width and l represent length of the pen.

We have been given that a farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. We are asked to find the dimensions that will maximize the area.

We can see from the attachment that the perimeter of the pens would be $4w+3l$ .

We can set our given information in an equation $4w+3l=300$ .

The area of the two pens would be $A=2l\cdot w$ .

From perimeter equation, we will get:

$w=\frac{300-3l}{4}$

Substituting this value in area equation, we will get:

$A=2l\cdot (\frac{300-3l}{4})$

Since we need to maximize area, so we need to find derivative of area function as:

$A=\frac{600l-6l^2}{4}$

Bring out the constant:

$A=\frac{1}{4}*\frac{d}{dl}(600l-6l^2)$

$A=\frac{1}{4}*(600-12l)$

$A=150-3l$

Now, we will set our derivative equal to 0 as:

$150-3l=0$

$150=3l$

$\frac{150}{3}=\frac{3l}{3}$

$50=l$

Now, we will substitute $l=50$ in equation $w=\frac{300-3l}{4}$ to solve for width as:

$w=\frac{300-3(50)}{4}$

$w=\frac{300-150}{4}$

$w=\frac{150}{4}$

$w=37.5$

Therefore, width of 37.5 feet and length of 50 feet will maximize the area.

8 0

3 years ago

What process do you use to find the percent change of a quantity?

Sever21 [200]

First, we need to get the amount of change:
The amount of change can either be an increase or a decrease.
It can be calculated as follows:
amount of change = $\frac{"new"value - "old"value}{"old" value}$

If the amount of change is positive, then it is an increase
If the amount of change is negative, then it is a decrease

Then, we need to convert this amount into a percentage:
Changing the amount into a percentage can simply be done by multiplying this amount by 100
This means that:
% of change = amount of change * 100

Combining the two steps:
% of change = $\frac{"new"value - "old"value}{"old" value}$ * 100

Examples:
The original price of a certain product was $10. It then became $12. Find the % of increase.
% of change = $\frac{12-10}{10} * 100$ = 20%
This means that the price increased by 20%

The temperature decreased from 25 degrees to 20 degrees. Find the percentage of decrease.
% of decrease = $\frac{20-25}{25} * 100$ = -20%
This means that the temperature decreased by 20%

Hope this helps :)

7 0

3 years ago

Read 2 more answers

Sean buys a packet of perfumed candles that contains 12 lavender, 8 vanilla, and 20 rose-perfumed candles. He randomly takes

11111nata11111 [884]

Answer:

05.

Step-by-step explanation:

trust me dude i just took this question :D

3 0

3 years ago

I have a few absolute value questions 20 POINTS AND BRAINLIEST TO THE RIGHT ANSWER