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3 years ago

Solve the equation. Check for extraneous solutions. 2|7−7x|=2x+4

Mathematics

1 answer:

Vesna [10]3 years ago

5 0

2|7 − 7x| = 2x + 4

|7 - 7x| = x + 2

7 - 7x = x + 2 or 7 - 7x = -(x + 2)

-8x = -5 or 7 - 7x = -x - 2

x = 5/8 or -6x = -9

x = 5/8 or x = 9/6

x = 5/8 or x = 3/2

To check for extraneous solutions, we check both solutions in the original equation.

Check solution 5/8:

2|7 - 7x| = 2x + 4

|7 - 7x| = x + 2

|7 - 7 * 5/8| = 5/8 + 2

|56/8 - 35/8| = 5/8 + 16/8

21/8 = 21/8

Solution x = 5/8 works.

Check solution 3/2:

2|7 - 7x| = 2x + 4

|7 - 7x| = x + 2

|7 - 7 * 3/2| = 3/2 + 2

|14/2 - 21/2| = 3/2 + 4/2

|-7/2| = 7/2

7/2 = 7/2

Solution 3/2 also works.

Answer: x = 5/8 or x = 3/2

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Mrrafil [7]

Answer:

The generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

Step-by-step explanation:

We are given the following from what she knows

m∠3=2⋅m∠1... 1

m∠2=2⋅m∠4 ... 2

m∠2+m∠3=360 ... 3

From what is given, we can substitute equation 1 and 2 into equation 3 as shown:

From 3:

m∠2+m∠3=360

Substituting 1 and 2 we will have:

2⋅m∠4 + 2⋅m∠1 = 360

Factor out 2 from the left hand side of the equation

2(m∠4+m∠1) = 360

Divide both sides by 2

2(m∠4+m∠1)/2 = 360/2

m∠4+m∠1 = 180°

Since the sum of two supplementary angles is 180°, hence the generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

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3 years ago

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lys-0071 [83]

Answer:

136

Step-by-step explanation:

multiply 4 times 6, divide by two to get the area of the front side, then multiply that by two to get eh area of the two triangles.

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3 years ago

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3 years ago

The temperature in Toronto was 14 F. The temperature that same night fell to -5 F. What was the difference in temperatures?

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Answer:

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Step-by-step explanation:

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3 years ago

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azamat

By definition of conditional probability,

$P(X_1=4\text{ or }X_2=4\mid X_1+X_2=7)=\dfrac{P((X_1=4\text{ or }X_2=4)\text{ and }X_1+X_2=7)}{P(X_1+X_2=7)}$

$=\dfrac{P((X_1=4\text{ and }X_1+X_2=7)\text{ or }(X_2=4\text{ and }X_1+X_2=7))}{P(X_1+X_2=7)}$

Assuming a standard 6-sided fair die,

if $X_1=4$ , then $X_1+X_2=7$ means $X_2=3$ ; otherwise,
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Both outcomes are mutually exclusive with probability $\frac1{36}$ each, hence total probability $\frac2{36}=\frac1{18}$ .

Of the 36 possible outcomes, there are 6 ways to sum the integers 1-6 to get 7:

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and so a sum of 7 occurs $\frac6{36}=\frac16$ of the time.

Then the probability we want is

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3 years ago