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3 years ago

What is the justification for each step in the solution of the equation?

Mathematics

2 answers:

jeka57 [31]3 years ago

6 0

13x−4=−36−27x+12: Distributive property

13x−4=−24−27x: Combine like terms

40x=−20: Addition Property of equality

Crazy boy [7]3 years ago

6 0

<h2>Answer with Step-by-step explanation:</h2>

13x−4= −9(4+3x)+12 (Given)

13x−4= −36−27x+12 (Distributive property: -9(4+3x)= -36-27x)

13x−4= −24−27x (combining like terms on each side: -36+12= -24)

40x−4=−24 (Addition Property of Equality: adding 27x on both sides )

40x= −20 (Addition Property of Equality: adding 4 on both sides )

x= −1/2 (Division Property of Equality: dividing both sides by 40)

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Classify each number below as a rational number or an irrational number.<br> rational irrational

Vadim26 [7]

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6 0

3 years ago

Read 2 more answers

If tan θ =(√3)/3, 0◦< θ < 360◦,

svetlana [45]

Arctan (√3 /3) = 30°. = π/6 rad

That is the value searched, in degrees and radians.

You can verifiy that tan(30°) = sin(30°) / cos(30°) = [1/2] / [√3/2] = 1/√3 = √3 / 3

3 0

3 years ago

Consider an angle with a measure of θ=225∘.

wel

Answer:

cos 225° = $-\frac{\sqrt{2} }{2}$

sin 225° = $-\frac{\sqrt{2} }{2}$

tan 225° = 1

Step-by-step explanation:

I cannot sketch a diagram, but a 225° angle is a 3rd quadrant angle and the reference angle is 45° (225 - 180 = 45)

cos and sin are negative in the 3rd quadrant and the tan is positive

cos 225° = - cos 45° = $-\frac{\sqrt{2} }{2}$

sin 225° = -sin 45° = $-\frac{\sqrt{2} }{2}$

tan 225° = tan 45° = 1

8 0

2 years ago

a language arts test is worth 100 points there is a total of 26 questions . there are spelling word questions that ae worth 2 po

natka813 [3]

10 question of spelling words and 16 questions of vocabulary are present

<em><u>Solution:</u></em>

Let "x" be the number of spelling word questions

Let "y" be the number of vocabulary word question

<em><u>There is a total of 26 questions. Therefore, we get</u></em>

number of spelling word questions + number of vocabulary word question = 26

x + y = 26 --------- eqn 1

<em><u>There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each</u></em>

The language arts test is worth 100 points

Therefore, we frame a equation as:

number of spelling word questions x 2 + number of vocabulary word question x 5 = 100

$x \times 2 + y \times 5 = 100$

2x + 5y = 100 --------- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

From eqn 1,

x = 26 - y ------- eqn 3

<em><u>Substitute eqn 3 in eqn 2</u></em>

2(26 - y) + 5y = 100

52 - 2y + 5y = 100

3y = 100 - 52

3y = 48

<em><u>Substitute y = 16 in eqn 3</u></em>

x = 26 - 16

Thus 10 question of spelling words and 16 questions of vocabulary are present

4 0

3 years ago

Please show your work. Find XY

Sidana [21]

XY = 17.

Because YW is a perpendicular bisector, we can say that TW and WZ are both equal to 3. It tells us that XZ is 12, so that means that XW must be 12+3 which equals 15.

It also tells us that YW is 8. So we can use the Pythagorean Theorem to find the hypotenuse of Triangle XWY. Thus, $15^{2} + 8^{2} = XY^{2}$

To solve this equation, square and add both of the terms on the right like this:
$289 = XY^{2}$

And then take the square root of both sides. Your final answer should be:
XY = 17.

3 0

3 years ago