Find the value for each variable.

Step-by-step explanation:

We will use the LHS to find the RHS.

Step 1: Expand the LHS by multiplying through the brackets and simplify

(sinx + cosx)(1 − sinx cosx) ≡  sinx + cosx - (sinx + cosx (sinx cosx))

                                             ≡  sinx + cosx - sin²x cosx - sinx cos²x

Step 2: Use the identity sin²x + cos²x = 1, to rewrite the equation

                                           ≡ sinx + cosx - cosx (1 - cos²x) - sinx (1 - sin²x)

Step 3: Simplify the equation by adding like terms

                                           ≡ sinx + cosx - cosx + cos³x - sinx + sin³x

                                           ≡ sin³x + cos³x                 [QED]

Reminder:

Answer:

if the units is in m/s

Step-by-step explanation:

first work out using this triangle.

distance= speed x by time

so if we're trying to find out the speed we reaarange the triangle to :

   distance

---------------------

speed x   time

so speed = distance divided by time

distance = 45cm

divided by time = 90 seconds

But the units are cm and should be metres per second

change 45cm to m

that is 45cm = 45/ 100 = 0.45

0.45/ 90= 0.005cm

answer = 0.005 metres per second( m/s)

plz say thanks + rate !

        With this in mind,

                 x + y = -3

                 x * y = -18

        Then we will think about which ones could add up to 3

                 1 & 18, 2 & 9, 3 & 6 are factors of 18 (one being negative results in -18)

                 Well 1 and 18 cannot make 3, same for 2 and 9, that leaves us with 3 and 6.

        You can see our test shows this solution works!

                 -6 + 3 = -3

                 -6 * 3 = -18

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

The solution to -12x = -74 is X = 6.16.

As for a set? Elaborate on what you mean by set please

Answer:

m = 2/5

Step-by-step explanation:

2x - 5y = 52

-5y = -2x + 52

y = 2/5x - 52/5

The slope of the line with equation 2x−5y=52 is 2/5.

The given equation of line is 2x−5y=52.

The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis.

The given equation 2x−5y=52 can be rewritten as

2x-52=5y

⇒ y = 2x/5-52/5

Now, compare y = 2x/5-52/5 with the standard form of an equation y=mx+c

So, m=2/5

Therefore, the slope of the line with equation 2x−5y=52 is 2/5.

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Answer:

Step-by-step explanation:

pa BRAINLEST pls

Answer:

ok good morning

have a nice day

Step-by-step explanation:

#toxicsquad

Answer:

i think its 7, but you should probably check that...

Answer:

number 2 is c, number 3 is c

Answer:

-3

Step-by-step explanation:

Slope formula

Answer:

16 i believe

Step-by-step explanation:

Answer:

  33. $5.75

  34. 15 ft

  35. 8

  36. 32

Step-by-step explanation:

These questions pretty much cover the sorts of things you're supposed to learn in an Algebra course. If you don't get any of it, you may have a problem with follow-on courses.

__

You are expected to understand this question gives you two relations in two unknowns. The first step is to assign a variable to each of the unknowns. We can use ...

The given relations have to do with the prices of different quantities of these:

  2x +3y = 26.25 . . . . . . cost of 2 shakes and 3 sundaes

  4x +2y = 29.50 . . . . . . cost of 4 shakes and 2 sundaes

These two equations in two unknowns can be solved several ways. Here, it is convenient to use the method of "elimination", because the coefficients of x are related by a small integer. Subtracting the second equation from 2 times the first eliminates the x-variable (hence the name of the method).

  2(2x +3y) -(4x +2y) = 2(26.25) -(29.50)

  4y = 23.00 . . . . . . simplify

  y = 5.75 . . . . . . . . . divide both sides by 4

The cost of an ice cream sundae is $5.75.

We can substitute this value into either equation and solve for x. We would find the cost of a shake to be x=4.50. However, the question only asks for the price of a sundae.

__

There are formulas for the perimeter, area, and volume of various geometric figures of a generally circular or rectangular shape. You might find it convenient to memorize them. Here, you need the formulas for the volume of a cylinder and of a cone. You also need to know that the diameter of a circle is 2 times the radius of the circle, since most of the circle-related formulas are in terms of the radius.

Volume of a cone of radius r and height h: V = 1/3πr²h

Volume of a cylinder of radius r and height h: V = πr²h

It can be convenient to remember that a cone has 1/3 the volume of a cylinder the same height.

The relation of interest here is the volume of the silo is the sum of the volumes of the bottom cylinder and the top cone.

  V = π(20 ft)²(60 ft) + 1/3(20 ft)²(x ft) = 26000π ft³

  V = 24000π ft³ +(400/3)x·π ft³ = 26000π ft³ . . . . simplify a bit

  400/3·x = 2000 . . . . . . . divide by π ft³, and subtract 24000

  x = 2000(3/400) = 15 . . . . multiply by 3/400

The height of the top portion is 15 feet.

__

This has to do with understanding the meaning of a table and of an expression relating table values. The expression f(a) = g(b) means you're looking for table entries such that the number in the f(x) column is equal to the number in the g(x) column.

We find the only common function value to be -1, so f(-6) = -1 = g(1). Comparing this to f(a) = g(b), we see that a=-6.

The question asks for |g(a)|. The table tells us g(-6) = -8. Its absolute value will be the value without the negative sign:

  |g(-6)| = |-8| = 8 = |g(a)|

__

This is a polynomial division problem. It tells you the quotient of the quadratic, divided by (ax +2), is (3x -4) with a remainder of 66. We're concerned with the leading coefficient of the divisor, 'a'.

Polynomial long division is much simpler than numerical long division, because each quotient term is the leading dividend term divided by the leading divisor term. Here, that means ...

  96x²/(ax) = 3x

Multiplying by ax gives ...

  96x² = 3ax²

Dividing by 3x², we see that ...

  (96x²)/(3x²) = (3ax²)/(3x²)

  96/3 = a = 32

The value of 'a' is 32.

this is a relation because it has all of the same number more than once

Answer:

I believe so!

Step-by-step explanation: makes since to me!!

Answer:

1.

1.5 litre carton for $2.35 is the cheapest way since it's the cheapest out of all the other options.

2.

a. 1.25 / 0.5 = $2.50 per L

2.35 / 1.5 = $1.57 per L

3.25 / 2 = $1.63 per L

b. 2.50 x 8 = $20.00 per 8 L

1.57 x 8 = $12.56 per 8 L

1.63 x 8 = $13.04 per 8 L

Step-by-step explanation:

find unit rate (cost / quantity)

Answer: B

Step-by-step explanation: Hope this helps :)

The price of a used book in the bookstore after the percentage increase in its price is $7.50.

Percentage can be described as the fraction out of an amount that is usually expressed as a number out of hundred. Percentages are represented with this sign - %.

Price = 1.50 x ( 1 + 4)

1.5 x 5 = $7.50

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Answer:

j 6.00

Step-by-step explanation:

i took the test hope this helps good luck

Answer: f 500 Ft./sec

Step-by-step explanation:

By evaluating the derivate of the distance in t = 10s, we will see that at t =  10s the distance is changing at a rate of 464.2 ft/s

We can think of the situation as in a right triangle, one cathetus is equal to 2000ft, and the other cathetus increases at a rate of 500ft/sec.

The hypotenuse would be the distance between the radar and the rocket.

Then the distance function is:

[tex]D(t) = \sqrt{(2000ft)^2 + (500ft/s*t)^2}[/tex]

Now we need to get the rate of change, this is given by:

[tex]\frac{dD(t)}{dt} = (1/2)*\frac{2*(500ft)^2*t}{\sqrt{(2000ft)^2 + (500ft/s*t)^2} }[/tex]

Now we evaluate this in t = 10s to get:

[tex]\frac{dD(10s)}{dt} = (1/2)*\frac{2*(500ft/s)^2*10s}{\sqrt{(2000ft)^2 + (500ft/s*10s)^2} } = 464.2 ft/s[/tex]

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Answer:

I think 2 1/2 for flour and 2 eggs

1/4(16+9)-2

1/4(20)-2

5-2

3

Answer:

16 5c coins

34 10c coins

Step-by-step explanation:

(I prefer to use whole numbers)

5x + 10y = 420

x+y=50

multiply the bottom problem by -5

5x +10y =420

-5x -5y = -250

combine the problems

5y = 170

divide by 5

y = 34

that means x = 16

34 10c coins

16 5c coins

-- Gage Millar, Algebra 1/2 tutor

The number of 5 cent coins are 16 and the number of 10 cent coins are 34.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a trader has a mixture of 5 c and 10 c coins.

Let the the number of 5 c coins be x and the number of 10 c coins be y.

He has 50 coins in all, with a total value of $4.20.

So, x+y=50 ---------(I)

5x+10y=420 ---------(II)

Multiply equation (I) by 5, we get

5x+5y=250 ---------(III)

Subtract equation (III) from (II), that is

5x+10y-(5x+5y)=420-250

⇒ 5y=170

⇒ y=34

Substitute y=34 in equation (I), we get

x=16

Therefore, the number of 5 cent coins are 16 and the number of 10 cent coins are 34.

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Hi there! :)

A geometric sequence is a sequence where we use multiplication or division to get to the next term.

We use multiplication in the third sequence (we multiply by -5)

So the answer is Option C

Hope it helps

~Just a gloomy teen who misses her best friend

#CarryOnLearning

[tex]SilentNature[/tex]

Answer:

Step-by-step explanation:

We know x=2y=-1

So -5x-9y=2

<=> -5(1) +(-4)(1) - (y) =2

<=> -9- (y)=2

<=> y=-9-2

<=> y=-11

P/s: -9y= -8y-y = -4x-y = (-4)(1)-y

ok, i'm done. Thank to me :>

The equation that represents this situation is 8 + 3t = 25.50.

Let the sales tax for each book be represented as t.

Since Orion buys 3 books for a total of 25.50 and he pays $8 plus sales tax for each book. This will be illustrated as:

Cost of book + Tax = Total amount

8 + (3 × t) = 25.50

8 + 3t = 25.50

Collect like terms

3t = 25.50 - 8.

3t = 17.50

Divide

t = 17.50 / 3

t = 5.83

The sales tax is $5.83.

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Answer:

operations

Step-by-step explanation:

to solve two-step equations, it is useful to use reverse operations as a guide to isolate the variable efficiently.

Answer:

the answer is graph C

Step-by-step explanation:

babyface_wee

Answer: Graph A

Step-by-step explanation:

y-intercept = -3    So, Not Graph B

Slope = 3/4x = rise 3 run 4 or up 3 right 4. So not Graph C

Graph A meats all the criterias.

Answer:

infinity solution

solution:

-x-3y=-6

x+3y=6

Answer:

Set an equation x+47+48= 136

solve for x

x+95=136

x= 40

so they need to score a 40

Answer:

i think you need to add all that up

Step-by-step explanation:

Answer:

  £225

Step-by-step explanation:

The relationship between the cost price (cp) and the selling price (sp) is ...

  cp + 5% × cp = sp

  cp(1.05) = sp . . . . . . collect terms

  cp = sp/1.05 . . . . . . divide by 1.05

  cp = £236.25/1.05 = £225

The original wholesale price was £225.

We have

If,

Putting value:

➡ (-1×2 + 2×1)² - 2×-1²×2²×1

➡ (-2 + 2)² - 2×1×4×1

➡ (0)² - 8

➡ 0 - 8 = -8,answer