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3 years ago

A) Rearrange the equation to make w the subject. 2(1 + W) = P

Mathematics

1 answer:

insens350 [35]3 years ago

4 0

Answer:

Step-by-step explanation:

$2(1 + W) = P\\Divide -both-sides-of-the-equation-by ; 2\\\frac{ 2(1 + W) }{2} = \frac{P}{2} \\1+ W = P/2\\W = \frac{P}{2} -1\\\\(b .) 2y = 10x + 6\\Re -write -in -slope-intercept-form : y= mx+b\\\frac{2y}{2} =\frac{10x}{2} +\frac{6}{2} \\y = 5x + 3\\Gradient = 5$

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3 years ago

A two-digit number becomes 5/6 of the reversed number obtained when the digits are interchanged. The difference between the digi

stealth61 [152]

<h3>Answer: 54</h3>

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

Work Shown:

T = tens digit

U = units digit (aka ones digit)

A number like 27 is really 20+7 = 2*10 + 7*1 = 10*2 + 1*7. We have 2 in the tens digit and 7 in the units digit. So 27 can be written in the form 10T + U where T = 2 and U = 7. Reversing the digits gives 72, so T = 7 and U = 2 now. Clearly the difference between the digits 7 and 2 is not 1, so 27 or 72 is not the answer (as it's just an example).

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

Let T be larger than U. This doesn't work if T = U.

Because T is larger, saying "The difference between the digits is 1" means T - U = 1. We can isolate T to get T = U+1. We'll use this later.

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

If T > U, then the original number 10T+U reverses to the new number 10U+T and it becomes smaller. We are told that it becomes 5/6 of what it used to be.

So,

new number = (5/6)*(old number)

10U + T = (5/6)(10T + U)

6(10U + T) = 5(10T + U)

60U + 6T = 50T + 5U

60U + 6(U+1) = 50(U+1) + 5U ... plug in T = U+1

60U + 6U + 6 = 50U + 50 + 5U

66U + 6 = 55U + 50

66U - 55U = 50-6

11U = 44

U = 44/11

U = 4 is the units digit of the original number

T = U+1

T = 4+1

T = 5 is the tens digit of the original number

The original number is therefore 10T + U = 10*5+4 = 54.

We see the difference in their digits is T-U = 5-4 = 1

The reverse of 54 is 45. The number 45 is 5/6 of 54

45 = (5/6)*54

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3 years ago

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3 years ago

Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

mars1129 [50]

Answer:

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If m∠E = m∠Y and m∠F = m∠X

then

Triangles EFG and YXZ are similar by AA Similarity Theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding sides are

FE and XY

EG and YZ

GF and ZX

so therefore

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!

A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.

From the figure in the attachment , we can conclude that:

m∠E = m∠Y

m∠F= m∠X

m∠G = m∠Z

∴ ΔEFG ~ ΔYXZ ( ΔEFG is similar to ΔYXZ )

Because of the similarity , then:

FE : XY = EG : YZ = GF : ZX

Conclusion:

ΔFG is similar to ΔYXZ.

Segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX , i.e:

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle

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KIM [24]

Answer:

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Step-by-step explanation:

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