Prove the identity.
sin(x+y) / cosxcosy = tanx+tany

Answer:

19 quarters and 13 nickles

Step-by-step explanation:

You have 32 coins in your pocket consisting of nickels and quarters with a total value of $5.40

How many nickels and quarters do you have?

Step 1: Setup Coin Value and Coin Total Equation:

Coin Value Equation → 0.05n + 0.25q = $5.40 where n = nickels and q = quarters

Coin Total Equation → n + q = 32

Step 2: Rearrange Coin Total Equation in terms of nickels (n)

n = 32 - q ← Revised Coin Total Equation

Step 3: Plug in our Revised Coin Total Equation for n into our Coin Value Equation:

0.05(32 - q) + 0.25q = $5.40

0.05(32) - 0.05(q) + 0.25q = $5.40

1.6 - 0.05q + 0.25q = $5.40

1.6 + (0.25 - 0.05)q = $5.40

1.6 + 0.2q = $5.40

Step 4: Subtract 1.6 from each side of the equation to isolate q

1.6 - 1.6 + 0.2q = $5.40 - 1.6

0.2q = 3.8

Step 5: Divide each side of the equation by 0.2 to isolate q

0.2q

0.2

=

3.8

0.2

q = 19

Step 6: Using our value for q, Solve for n using our Coin Total Equation:

n + 19 = 32

Subtracting 19 from both sides, we get n + 19 - 19 = 32 - 19

n = 13

Summarizing our word problem, we see that 19 quarters and 13 nickels adds up to $5.40

The conjugate of the expression a - square root of a - 1 is given as follows:

a + square root of a - 1

The conjugate of an expression is obtained for an expression that has two terms.

For the conjugate, we have that:

The expression is given as follows:

a - square root of a - 1

The parameters are given as follows:

Inverting the - sign to a + sign, the conjugate expression is given as follows:

a + square root of a - 1

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Answer:

40cm

Step-by-step explanation:

volume of a cylinder= πr²h

V=24litres, Area=πr²=600cm², height=?

converting litres to cm³

1litre=1000cm³

24litres= 24×1000

=24000cm³

24000=600× h

h= 24000/600

= 40cm

Answer:

[tex]?=4[/tex]

Step-by-step explanation:

[tex]\frac{?}{5}=\frac{8}{10}[/tex]

[tex]\frac{2?}{10}=\frac{8}{10}[/tex]

[tex]2?=8[/tex]

[tex]?=4[/tex]

Answer:

The answer is b

Step-by-step explanation:

Happy holidays ;)

Answer:

It is 1 unit to the right of 0.

Step-by-step explanation:

Answer:

1 , 2 , 4 , 8

Step-by-step explanation:

Factors of 16:

1, 2, 4, 8, 16

Factors of 24:

1, 2, 3, 4, 8, 6, 12, 24

Common factors are factors that are shared by both numbers, in this case, it i: 1 , 2 , 4, 8

Answer:

The answer is 3(+1)(+2)

Answer:

3(+1)(+2)

Step-by-step explanation:

Answer:

2.45

Step-by-step explanation:

Answer:

(- 3, - 1 )

Step-by-step explanation:

4x + 3y = - 15 → (1)

3y = 2x + 3 → (2)

Substitute 3y = 2x + 3 into (1)

4x + 2x + 3 = - 15

6x + 3 = - 15 ( subtract 3 from both sides )

6x = - 18 ( divide both sides by 6 )

x = - 3

Substitute x = - 3 into (2)

3y = 2(- 3) + 3 = - 6 + 3 = - 3 ( divide both sides by 3 )

y = - 1

solution is (- 3, - 1 )

Answer:

0.1536

Step-by-step explanation:

This is a binomial probability distribution with 2 successes in 4 trials.

The chance of a success is 1/5 =  0.2.

So there needs to be 2 successes and 2 failures in the 4 plays.

Reqd. Probability is 4C2*(0.2)^2(0.8)^2

= 0.1536.

The value of g(3) is 11

The function is given as:

g(x) = -4f(x) + 7

Start by calculating f(x) when x = 3

From the graph, we have:

f(3) = -1

So, we have:

g(3) = -4f(3) + 7

g(3) = -4* -1 + 7

Evaluate the product

g(3) = 4 + 7

Evaluate the sum

g(3) = 11

Hence, the value of g(3) is 11

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The missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

As we know,

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

From the graph of two parallel lines:

r ║ s

The slope is the ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Thus, the missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.

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Answer:

5

x

2

−

11

(

x

)

+

6

Step-by-step explanation:

[tex]5x^2-11x+6\\\\=5x^2-5x-6x+6\\\\=5x(x-1) - 6(x-1)\\\\=(x-1)(5x-6)[/tex]

Answer:

$20 is the sale price

Step-by-step explanation:

20% of $25 is (0.2*25)=$5

$25 -$5 = $20

Answer:

14.9

Step-by-step explanation:

50-5.03 = 44.97

44.97 ÷ 3 = 14.99

Answer:

x= 22 (number of parent teacher conferences) y=5 (number of school related assemblies)

Step-by-step explanation:

This word problem creates the following system of equations for x = number of parent-teacher conferences and y = number of school related assemblies.

x+y = 27 means that the number of parent teacher conferences plus the number of school related assemblies equals a total of 27 paid events.

35.50x + 42y = 991 means that $35.50 multiplied by a certain number of parent teacher conferences, plus $42 multiplied by a certain number of school related assemblies equals his total earnings of $991.

This sets up the following system

x+y=27

35.50x+42y=991

To solve this, we first need to take the first equation and solve for y.

y=27-x

plug in to the second equation and solve for x.

35.50x+42(27-x)=991

35.50x-42x+1134=991

Collect like terms

-6.5x=-143

divide both sides by -6.5 to solve for x.

x=22

Back substitute into other original equation to solve for y.

22+y=27

y=5

The interpreter attended 22 parent-teacher conference and 5 school related assembly

To solve this problem, we would write out two set of linear equations.

The data given on this problem are

Let x represent the number of parent-teacher conference

let y represent the number of school related conference

From equation (i)

[tex]x+y = 27\\x = 27-y...equation(iii)\\[/tex]

Put equation(iii) into equation (ii)

[tex]35.50x+42y=991\\35.50(27-y)+42y=991\\958.50-35.50y+42y=991\\6.50y=991-958.50\\y=5[/tex]

Put y = 5 into equation 1

[tex]x+y=27\\y = 5\\x+5=27\\x=27-5\\x=22[/tex]

From the above calculations, he attended 22 parent-teacher conference and 5 school related assembly.

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Answer:

20.

Step-by-step explanation:

That's the correct answer

Answer:

20

Step-by-step explanation:

To divide by a fraction, such as 1/4, we invert the fraction and then multiply instead of dividing.  Thus:

5÷1/4 = 5*(4/1) =20

Answer:3 or 6 over 2

Step-by-step explanation:

The formula is y2-y1

-------- =

x2-x1

y2=30 y1=24. X1=8. X2=10

So you do 30 minus 24 to get 6 and 10-8 to get 2 and yhen you will get the fraction of 6/2 so when you divde it your final answer will be 3

Answer:

See explanation

Step-by-step explanation:

Dilation of 1.5 about the origin. (Each new point is 1.5 times as far from the origin.)

G (-1, 3)  G' (-1.5, 4.5)

F (-2, -2)  F' (-3, -3)

G'x / Gx = -1.5/-1 = 1.5

G'y / Gy = 4.5 / 3 = 1.5

F'x / Fx = -3 / -2 = 1.5

F'y / Fy = -3 / -2 = 1.5

Answer:" m% = m/100. what = a variable ... "x". for example. "is" means "=". "of" means multiply. n = (m/100)•x.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find minutes per mile by dividing time by distance:

45 minutes / 6 miles = 7.5 minutes per mile

Now multiply his speed by each distance:

7.5 x 9 = 67.5 minutes

7.5 x 15 = 112.5 minutes

Now subtract the two:

112.5 - 67.5 = 45 minutes more

It will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.

Jesper's running speed is 6 miles in 45 minutes.

To find out how long it will take him to complete the races, you can use the formula:

Time = Distance / Speed

Let's calculate the times for both races:

For the 9-mile race:

Time = 9 miles / (6 miles/45 minutes)

= 9 × (45/6)

= 67.5 minutes

For the 15-mile race:

Time = 15 miles / (6 miles/45 minutes)

= 15 × (45/6)

= 112.5 minutes

The difference in time between the 15-mile race and the 9-mile race will be:

Difference = Time for 15-mile race - Time for 9-mile race

= 112.5 minutes - 67.5 minutes

= 45 minutes

So, it will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.

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Answer:

The answer is 0.75

Step-by-step explanation:

The line in a fraction that separates the numerator and denominator can be rewritten using the division symbol. So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.

Another method without a calculator is:

Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.

Step 2: Multiply both top and bottom by that number.

Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)

Example:

Convert 3/4 to a Decimal:

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25. It gives us 75/100.

Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);

Answer = 0.75

Answer:

no because there is a 10 which make it not proportional

Step-by-step explanation:

hope that helps.

Answer: No they are not proportional because the last row has -10 which obstructs the whole relationship.

Answer:

2.03% of 0.045=0.0009135

Step-by-step explanation:

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 0.045 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 0.045 is 100%, so we can write it down as 0.045=100%.

4. We know, that x is 2.03% of the output value, so we can write it down as x=2.03%.

5. Now we have two simple equations:

1) 0.045=100%

2) x=2.03%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

0.045/x=100%/2.03%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 2.03% of 0.045

0.045/x=100/2.03

(0.045/x)*x=(100/2.03)*x       - we multiply both sides of the equation by x

0.045=49.261083743842*x       - we divide both sides of the equation by (49.261083743842) to get x

0.045/49.261083743842=x

0.0009135=x

x=0.0009135

Answer:

0.09135

Step-by-step explanation:

when it says "of" a number, you simply multiply them

Answer: 42

6(9-2)

= 6 * 7

= 42

Answer:

6(9-2)

=6×7

=42 ans

Step-by-step explanation:

I think it help you I also you understand it

Answer:

Step-by-step explanation:

The product of 5 and 539 is 2695

Finding the product of numbers simply means multiplying 2 or more numbers.

Therefore, the product of 5 and 539 can be done as follows:

Multiplication or product sign is denoted as ×.

Therefore,

5 × 539 = 2695

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[tex]W(-2,-1) \to \\W \ ' \ (-4,4)\\\\X(0,2) \to \\X \ ' \ (0,4)\\\\Y(3,-1) \to \\Y \ ' \ (6,-2)\\\\V(-2,-1) \to \\V \ ' \ (-4,-2)\\\\[/tex]

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

Explanation:

The scale factor is 2, which means we double each coordinate of each point. The general rule is [tex](x,y) \to (kx,ky)[/tex] with k = 2. So we can say the more specific dilation rule is [tex](x,y) \to (2x,2y)[/tex]

Something like W(-2,2) moves to W ' (-4, 4) after multiplying each coordinate by 2. Do the same for the other points as well.

The given preimage points

will dilate to the corresponding image points

as shown below. This causes the image to be larger compared to the preimage (since the scale factor is larger than 1). Any given point is twice as far from the origin as compared to before, which in turn means the distance between any two points is twice as much.