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3 years ago

Question 2 (1 point)

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

4 0

Answer:

See answers below

Step-by-step explanation:

For the expression

The sum of two numbers is 25. The first number is 37 more than 2 times the second number

Let the two numbers be x and y

If the sum is 25, then;

x + y = 25 .... 1

37 more than 2 times the second the number is expressed as;

37+2y

If the first number is 37 more than 2 times the second number, then;

x = 37 + 2y

x - 2y = 37 ...2

This shows that the simultaneous equation that fits the expressions are;

x - 2y = 37

x + y = 25

For the expression

A child has a piggy bank full of $1 and $2 coins totaling $37. There are 25 more $1 coins than there are $2 coins.

Let x be the $1 coins

Let y be the $2 coins

If a child has a piggy bank full of $1 and $2 coins totaling $37, then;

x + 2y = 37 ... 1

Also, if there are 25 more $1 coins than there are $2 coins, then;

x = 25 + y

x - y = 25 ...2

The equivalent expressions for the statement will be;

x + 2y = 37

x - y = 25

This hence leaves us with the last;

An exam that is worth 37 marks contain 25 questions. The questions are either worth 1 mark or 2 marks. The resulting simultaneous equation will be;

x + 2y = 37

x + y = 25

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PLEASE HELP ME If 0 < z ≤ 90 and sin(9z − 1) = cos(6z + 1), what is the value of z? z = 3 z = 4 z = 5 z = 6

Burka [1]

Answer:

z = 6

Step-by-step explanation:

We know that ...

sin(x) = cos(90 -x)

Substituting (9z-1) for x, this is ...

sin(9z -1) = cos(90 -(9z -1))

But we also are given ...

sin(9z -1) = cos(6z +1)

Equating the arguments of the cosine function, we have ...

90 -(9z -1) = 6z +1

90 = 15z . . . . . . . . . add (9z-1) to both sides

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Comment on the graph

The attached graph shows 5 solutions in the domain of interest. These come from the fact that the relation we used is actually ...

sin(x) = cos(90 +360k -x) . . . . . for any integer k

Then the above equation becomes ...

90 +360k = 15z

6 +24k = z . . . . . . . . . for any integer k

The sine and cosine functions also enjoy the relation ...

sin(x) = cos(x -90)

sin(9z -1) = cos(9z -1 -90) = cos(6z +1)

3z = 92 . . . . . equating arguments of cos( ) and adding 91-6z

z = 30 2/3

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3 years ago

Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task li

tankabanditka [31]

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The easiest one to use if it is available to you, is factoring. The quadratic may not be factorable. But if it is and you can see it, then this gives you 2 points immediately (the roots) and a third without much trouble (the y intercept). Factoring will also give you the x value of the vertex. (Find the average between the 2 roots)

This needs an example
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Completing the square always gives you the minimum or maximum right away. For example if you have y = (x - 2)^2 - 5 it means you have the vertex at (2,-5) You can get the roots easily enough. So this form is useful, but not as sure as the quadratic equation or as simple as factoring.

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Vinvika [58]

Step-by-step explanation:

Left hand side:

tan 203° + tan 22° + tan 203° · tan 22°

From angle sum identities, we know:

tan (α + β) = (tan α + tan β) / (1 − tan α · tan β)

Therefore:

tan (203° + 22°) = (tan 203° + tan 22°) / (1 − tan 203° · tan 22°)

tan (225°) = (tan 203° + tan 22°) / (1 − tan 203° · tan 22°)

1 = (tan 203° + tan 22°) / (1 − tan 203° · tan 22°)

tan 203° + tan 22° = 1 − tan 203° · tan 22°

Substituting:

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