#19. find the perimeter and the area of the figure

Answer:

Make use of the fact that as long as [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex]:

[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex].

[tex]\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}[/tex].

[tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].

Step-by-step explanation:

Assume that [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex].

Make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] and [tex]\csc(\theta) = (1) / (\sin(\theta))[/tex] to rewrite the given expression as a combination of [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex].

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}[/tex].

Since [tex]\cos(\theta) \ne 0[/tex]:

[tex]\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}[/tex].

Substitute this equality into the expression:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].

By the Pythagorean identity, [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex]. Rearrange this identity to obtain:

[tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex].

Substitute this equality into the expression:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].

Again, make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] to obtain the desired result:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}[/tex].

Wrong answer sorry. Hope you find it!

Least Common Multiple = (x-3) (x+5) (x+4)

Step-by-step explanation:

First we solve for x² + x-12

=> x² + 4x - 3x - 12

=> x ( x+4 ) - 3 (x+4 )

=> (x-3) (x+4)

Now we will solve for x² + 2x - 15

=> x² + 5x - 3x - 15

=> (x-3) (x+5)

we see here (x-3) is common in both the equations so We write it only 1 time as we have to find least common multiple .

Ans. Lest common multiples are = (x-3) (x+5) and (x+4)

Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have:

The length Travis needs to cut = 114 inches

Percent of error = 10%

Let's assume he cuts x inches wide strip

So from the percent of error formula:

[tex]\rm \dfrac{x-114}{114} = \dfrac{10}{100}[/tex]

[tex]\rm x = \dfrac{114}{10}+114[/tex]

[tex]\rm x = \dfrac{1254}{10}\Rightarrow \dfrac {627}{5}[/tex]  or

[tex]\rm x = 125\dfrac{2}{5} \ inches[/tex]  

Thus, Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches

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Answer:

it’s 1 3/8 I don’t know what dude it’s talking about

Step-by-step explanation:

Answer:

x-3+2x+3+2x = 5x

x+8+4x-3x-4 = 2x+4

4x+x-11-5X+25+4x = 4x+14

3x+5-2x-5x+9+8x = 4x+14

5+9x-7-4X-3x+6 = 2x+4

6x-9-5x+4-x+5x+5 = 5x

Step-by-step explanation:

Simplified by adding like terms

Answer:

638.29

Step-by-step explanation:

This is the answer because 29 percent of 899 is somewhere around 260.71

Substract that and you get 638.29

Answer:

B

Step-by-step explanation:

The data shows a positive correlation so the gradient must be positive so B.

Step-by-step explanation:

i just answered this.

the average change rate is the change of the functional result in a given interval relative (= divided by) to the length of the interval of the input variable.

in short

( f (interval upper limit) - f (interval lower limit) ) /

(interval upper limit) - (interval lower limit)

upper limit = 0

lower limit = -2

the functional values (y) are 6 and 10 at these points.

so, we get

(6 - 10) / (0 - -2) = -4 / 2 = -2

=====================================================

Explanation:

The triangular face has area of base*height/2 = 4*10/2 = 40/2 = 20 square cm.

Multiply this prism base area by the depth of the prism to get 20*2 = 40 cubic cm.

It might help to place the triangular prism so the triangular face is along the ground, so you can think of that face as the floor of this triangular room. The volume of this room is equal to the floor area times the height of the room.

volume of the room = (floor area)*(height of the room)

volume of the prism = (base area)*(height of the prism)

For any prism, the base faces are always parallel and congruent to each other.

Answer:

D. 60 ft²

Step-by-step explanation:

Area formula :

Solving :

Answer:

D. 60 ft2

Step-by-step explanation:

Area of a parrelleogram:

bxh

base x hieght

The base is 10ft, the height is 6 ft

(it cannot be 8ft because that line is slanted)

10x6=60ft2

Answer:

Cos 0 = 15/17

Step-by-step explanation:

.................................................

Answer:

-5

Step-by-step explanation:

9+6-2*10

15-20

= -5

Answer:

you did not even show the answer

Step-by-step explanation:

you have to post it lol;)

The mistake that Kristy made in calculating the volume is that she treated it as a hemisphere instead of a Sphere.

We are given the volume of the sphere as 144π cubic units.

From the attached file, we see that the radius of the sphere is 6.

Formula for Volume of a Sphere is;

V = ⁴/₃πr³

Thus;

V = ⁴/₃π * 6³

V = 288π cubic units

Thus, the mistake that Kristy made in calculating the volume is that she treated it as a hemisphere instead of a Sphere.

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There are seven "0"s between the decimal point and the digit "6".

======================================================

Explanation:

The number [tex]6.51 \times 10^{-8}[/tex] is in scientific notation.

The exponent -8 tells us to move the decimal point exactly 8 spots to the left to get the answer 0.0000000651

In other words, we'll move the decimal point one spot to the left to go from 6.51 to 0.651

Then we move it another seven spots to the left to arrive at 0.0000000651

This is why there are seven "0"s between the decimal point and the digit "6".

At the end of the third year the population of beetles will be 11,576beetles

The standard form of an exponential function is given as:

y = ab^t

Given the following parameters

initial population 'a" = 10,000 beetles

Time = 3 years

rate b = 1.05

Substitute into the formula

y = 10,000(1.05)^3

y = 10,000(1.1576)
y = 11,576 beetles

Hence at the end of the third year the population of beetles will be 11,576beetles

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Answer:

12 inches.

Step-by-step explanation:

You have to use the pythagorean formula. The measurements you stated form a right angle. Therefore, a^2 + b^2 = c^2. In this equation, we know c=13, and b=5. So therefore c^2 - b^2 = 144. We have to solve for a, so square root 144 to get 12.

Answer:12 in

Step-by-step explanation:

The total amount of the fuel needed for the trip is 42.5 gallons if the distance from their old house to their new house is 1003 miles.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have total distance between from their old house to their new house:

d = 1003 miles

The car travel 23.6 miles per gallon

So the total amount of the fuel needed = 1003/23.6 = 42.5 gallons

42.5 gallons fuel will be required to travel 1003 miles

For the return trip (considering 23.6 miles per gallon) the same amount of fuel will be needed.

So the total fuel needed including roundtrip = 42.5×2 = 85 gallons

Thus, the total amount of the fuel needed for the trip is 42.5 gallons if the distance from their old house to their new house is 1003 miles.

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5x - 3 = 11 + 12x

---Subtract 5x from both sides

-3 = 11 + 7x

---Subtract 11 from both sides

-14 = 7x

---Divide both sides by 7 to leave x by itself

x = -2

Answer: x = -2

Answer Choice: A, -2

Hope this helps!

Answer:

A. The solution is x =-2.

Step-by-step explanation:

Given :

Subtract 11 from each side.

Subtract 5x from each side.

A. The solution is x =-2.

Answer:

I think the answer is b ill look into it a Lil more

Explanation:

Expression: d = 16t² where d is distance. t is time.

1)

Here t = 2

d = 16(2)²

d = 64 feet

2)

h = 906-t²

h = 906 - 16(2)²

h = 842 feet

3)

expression of height: y = 906 - 16t²

Answer:

Step-by-step explanation:

Q1

Q2

Q3

Answer:

Step-by-step explanation:

One

If the number was 1000, you just count the numbers starting at the right until you get a number that is between 1 and 10

So starting at the right, you get to go 3 places towards the left. You get the number one, so 1000 would be written as 1 * 10^3.

The the given number is a fraction the rule is Add a minus sign

Answer: 1/1000 = 1 * 10^-3

Two

10 is 10^1 in scientific notation

1/10 = 10^-1

Answer: 1/10

The rate of change of the linear function whose graph passes through points (-5, -2) and (-2, 6) is: 2.7.

The rate of change of a linear function is given as change in y over change in x.

Given the points:

(-5, -2) and (-2, 6)

Change in y = 6 -(-2) = 8 units

Change in x = -2 -(-5) = 3 units

Rate of change = 8/3 = 2.7.

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Answer:

$36.3 

Step-by-step explanation:

The total cost of the Green coffee beans is $7.25.

Total cost (TC) is the minimum cost of producing some quantity of output. This is the total economic cost of production and is made up of variable cost, which varies according to the quantity of a good produced and includes inputs such as labor and raw materials, plus fixed cost.

Here, Green coffee beans cost $0.58 for each ounce.

Amina and her mother buy 12.5 ounces of green coffee beans

Total cost = cost each ounce X Number of ounces

  TC = 12.5 X 0.58

  TC = $ 7.25

Thus, the total cost of the Green coffee beans is $7.25.

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Answer:

[tex]a^{4}-2a^{2} -24[/tex]

Step-by-step explanation:

We do FOIL to solve this

Answer:

5.51

Step-by-step explanation:

i used a calculator.

Answer:

Shade 10 of the pieces.

Step-by-step explanation: