The sale price of an item is $160 after a 20% off discount. What was the original price of the item?

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Explanation:

Make sure your calculator is in radian mode. Use your calculator to find that tan(5pi/8) = -2.41421 which is approximate.

Since the value is negative, this means the answer is between choices C and D. You can use your calculator to compute those expressions given and you should find it matches with choice D.

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Further explanation:

We can apply the half angle identity for tangent like so

[tex]\tan\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\\\\\\\tan\left(\frac{5\pi/4}{2}\right) = -\sqrt{\frac{1-\cos(5\pi/4)}{1+\cos(5\pi/4)}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1-\left(-\frac{\sqrt{2}}{2}\right)}{1+\left(-\frac{\sqrt{2}}{2}\right)}}\\\\\\[/tex]

Simplifying further, we get

[tex]\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{1-\frac{\sqrt{2}}{2}}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}\\\\\\[/tex]

In the last step, I multiplied top and bottom of the outer fraction by 2 to clear out the denominators of the inner fractions.

Answer:

Answer D

Step-by-step explanation:

on edge 2023

I think you're missing part of the question?

013/16 = 0.266

Answer:

Step-by-step explanation:

The terms will be multiplied in order to get the simplified polynomials.

a. 6(x + 7)(x + 2)

[tex]6(x + 7)(x + 2)\\=6[x(x+2)+7(x+2)]\\=6(x^2+2x+7x+14)\\=6(x^2+9x+14)\\=6x^2+54x+84[/tex]

The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]

b. (2y – 5)^2

Using the formula: [tex](a-b)^2 = a^2+b^2-2ab[/tex]

[tex]=(2y)^2+(5)^2-2(2y)(5)\\=4y^2+25-20y[/tex]

The simplified form is: [tex]4y^2-20y+25[/tex]

c. (5x + 4y)(2x - y)

[tex]=5x(2x-y)+4y(2x-y)\\=10x^2-5xy+8xy-4y^2\\=10x^2+3xy-4y^2[/tex]

The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]

d. (3x + 7)(3x – 7)

Using the formula: [tex](a+b)(a-b) = a^2-b^2[/tex]

[tex]= (3x)^2-(7)^2\\= 9x^2-49[/tex]

The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]

e. (t + 2) – (4t +9) – t

[tex]=t+2-4t-9-t\\=t-4t-t+2-9\\= -4t-7[/tex]

The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]

Hence,

a. The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]

b. The simplified form is: [tex]4y^2-20y+25[/tex]

c. The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]

d. The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]

e. The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]

Answer:

4/15 gallons of juice

Step-by-step explanation:

Total gallon you have = 3/5gallons

Amount consumed = 1/3 gallons

Amount left = Total gallons + Amount consumed

Amount left = 3/5-1/3

Find the LCM

amount left = (3)(3)-5(1)/15

Amount left = (9-5)/15

Amount left = 4/15

Hence 4/15 gallons of juice is left

Answer:

The correct options are;

1) Which type needs the highest temperature to grow

2) Do all of the types make food the same way

3) How long does it take for a specific type to make seeds

Step-by-step explanation:

The number of types of species in the orchid family = Several thousand

The tasks the gardening clubs are devoted to = Collecting, Studying, and growing of the orchids

The manner of the growth of the orchids = Difficulty observed in growing outside the orchid's natural habitat

Scientific questions are objective questions that are measurable, well defined about parameters that can be controlled which can be answered by means of an experiment and meant to provide a deeper understanding of the nature of the world around us

Therefore, the scientific questions that can be asked about a collection of different orchid types are;

1) Which type needs the highest temperature to grow

The above is a question that has a defined parameter (temperature) which is measurable and the answer can be provided by experimenting

2) Do all of the types make food the same way

An experiment with different orchid types will provide an answer to the above question

3) How long does it take for a specific type to make seeds

The length of time for it takes the seed to grow is measurable within an experiment.

Answ do all types make food the same way? which type needs higher tempurturs to grow and do all types make food the same way

Step-by-step explanation:

i took the test

Answer:

8/17

General Formulas and Concepts:

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use trig to find the ratio.

Step 2: Identify

POV from angle S

Adjacent = 8

Hypotenuse = 17

Step 3: Write

Answer:

9.41

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

a.

-6a²/ b

b.

5y³

Step-by-step explanation:

a

-6a²b⁻¹

-6a²/ b

b.

5/ y⁻³

5 / 1/ y³

5 * y³/1

5y³

Answer:

y = 12

Step-by-step explanation:

proportions can be solved by cross-multiplying

to work with smaller numbers, you can simplify [tex]\frac{14}{10}[/tex] to be [tex]\frac{7}{5}[/tex]

[tex]\frac{7}{5}[/tex] = [tex]\frac{y+9}{15}[/tex]

7(15) = 5(y + 9)

105 = 5y + 45

60 = 5y

y = 12

9514 1404 393

Answer:

  (z, v)

Step-by-step explanation:

When the sides of the rectangle align with the axes, as here, the coordinates will be all (x, y) combinations from the sets x ∈ {w, z) and y ∈ {v, z}. Three of those combinations are shown. The fourth is (z, v).

Step-by-step explanation:

[tex]v \: cylinder = \pi \times r {}^{2} \times h \\ 3.14 \times 3.5 {}^{2} \times 20 \\ 3.14 \times 12.25 \times 20 \\ = 769.3[/tex]

you should round to nearest tenth place...I dont know...hope it helps

Answer:

Step-by-step explanation:

they both go thur the point (0,-4)  so they both have the same b in the slope intercept from  of  y =mx +b

but.. they have a different slope... m , the graph has a slope m of 4/3 while the table has a slope of 1  , both positive.. :)

The equation given by the graph is y = (4/3)x - 4 while the table is y = x - 4. Both equation have a y intercept of -4.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the graph, using the point (3, 0) and (0, -4):

y - 0 = [(-4 - 0)/ (0 - 3)](x - 3)

y = (4/3)x - 4

From the table using (0, -4) and (2, -2):

y - (-4) = [(-2-(-4))/(2-0)](x - 0)

y = x - 4

The equation given by the graph is y = (4/3)x - 4 while the table is y = x - 4. Both equation have a y intercept of -4.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ2

Answer:

$4.80/2sodas

4.80/2=2.40

C. 2.40 per soda

Answer:

with what

Step-by-step explanation:

Answer:

WHAT?!?!?!?!!?!

Step-by-step explanation:

Answer:

For every 1 cup of banana you have to add 6 cups of apples. So it means there's six times as much apples as there is bananas. If there's 3 cups of apples, which is half of 6, it means the banana would now also have to be halved from 1 to half a cup.

Whatever you do to the bananas or the apples, you have to maintain the same ratio. Which is that apples is 6 times as much as bananas.

So 1 cup of apple would need to be divided by 6, to get banana. That would be approximately 1÷6= 0.167 cups

Answer:

[tex]m=\frac{1}{6}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-4, -3)

Point (14, 0)

Step 2: Find slope m

Answer: I am only in 4th grade !

Step-by-step explanation: I dont know ?

Answer:

36, 45

Step-by-step explanation:

Using equations you get [tex]x + x+9=81[/tex] because one number is 9 more than the other and the sum is 81. Simplifying you get, [tex]2x = 72[/tex]. Divide both sides by 2 to get [tex]x=36[/tex]. Remember this is only x so to get the other number you have to add 9 to 36 to get 45 as the other number.

Answer:

No point

Step-by-step explanation:

This is a trick question because if you break down the graphing equations to y=mx+b, you see that it is a linear graph, so it will have a straight line. For the first equations, y=x+3, you look at the original equations, y=mx+b. m=slope, b=x-intercept. Slope is rise/run (y/x) so the slope would be up one, over one (1/1=1). The x-intercept is 3 so its a straight line but it intercepts at 3. The next equation is the exact same thing, but the x-intercept is at 1. A straight line that intercepts at 1. So it is two parallel lines that never ever touch. So this is a trick question.

Answer: U - (P - P∩Q)

Where U represents the universal set.

Step-by-step explanation:

In the image, we can see that the shaded part is all the region minus the part of P that does not share elements with Q.

This part of P can be written as:

P - P∩Q

there we write:

"The elements of P, minus the elements that P share in common with Q"

Then to write the shaded area, we need to write the universal set, U, minus the thing we wrote above, this is:

U - (P - P∩Q)

Answer:

x = 16[tex]\sqrt{3}[/tex]

y = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

For this type of equation, you are going to use the following trigonometric signs tangent and cosine.  Tangent is used for the y-variable and cosine is used for the x-variable.  For the y-variable, it is 24 tan 30 to get 8 root 3 as your answer.  For the x-variable, you would get ([tex]\sqrt{3}[/tex] / 2)x = 24.  Divide that root number to get 16[tex]\sqrt{3}[/tex] as your x variable.

Answer: 16 sqrt 3. 8 sqrt 3

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

im in algebra two so you can trust my answer. happy holidays and stay safe!

Answer:

-18

Step-by-step explanation:

A add and a minus makes a minus so you do -5  - 13 = -18

-18 + 10 = -8    -8 - 10 = -18   You do not have to write this out as positive 10 - 10 is equal to 0

Answer:

Please check the explanation and attached graph.

Step-by-step explanation:

Given the parent function

y = |x|

In order to translate the absolute function y = |x| vertically, we can use the function

g(x) = f(x) + h

when h > 0, the graph of g(x) translated h units up.

Given that the image function

y=|x|+4

It is clear that h = 4. Since 4 > 0, thus the graph y=|x|+4 translated '4' units up.

The graph of both parent and translated function is attache below.

In the graph,

The blue line represents the parent function y=|x|.

The red line represents the image function y=|x| + 4.

It is clear from the graph that the y=|x| + 4  translated '4' units up.

Please check the attached graph.

Answer:

136

Step-by-step explanation:

9*4=36+100=136

Answer:

t = 33 seconds

It is the amount of time when the temperature of the body will rise from 100 to fatal 104 in the absence of sweat.

Step-by-step explanation:

weight of the farmer = 176 lb

Sweating = 1 litre per hour

60% of above sweating is evaporated by the latent heat from farmers body.

Temperature outside = 104

Temperature of the Farmer = 100

Time to rise the temperature 4 degrees = ?

We need to use the specific heat formula to calculate the time to rise the temperature of the body of farmer.

Before, that let's convert weight of the farmer in Kg

W = 176 lb

1 lb = 0.453592 kg

176 lb = 79.8 kg

w = mg

g = 10

mass = m = 79.8/10

mass = 7.98 kg

Q = mc∆T

c = specific heat of water =  4,186

∆T  = Temperature Change = 104-100

∆T  = 4

Q = 7.98 x 4186 x 4

Q = 133617

t = Q/P

Power of Sun's Heat = 3.846×1026

t = 33 seconds

It is the amount of time when the temperature of the body will rise from 100 to fatal 104 in the absence of sweat.