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2 years ago

What is the value of $x$ if $-\frac23(x-5) = \frac32(x+1)$?

Mathematics

1 answer:

Ipatiy [6.2K]2 years ago

4 0

Answer:

x = (-29)/5

Step-by-step explanation:

Solve for x:

(2 (x - 5))/3 = (3 (x + 1))/2

Multiply both sides by 6:

(6×2 (x - 5))/3 = (6×3 (x + 1))/2

6/3 = (3×2)/3 = 2:

2×2 (x - 5) = (6×3 (x + 1))/2

6/2 = (2×3)/2 = 3:

2×2 (x - 5) = 3×3 (x + 1)

2×2 = 4:

4 (x - 5) = 3×3 (x + 1)

3×3 = 9:

4 (x - 5) = 9 (x + 1)

Expand out terms of the left hand side:

4 x - 20 = 9 (x + 1)

Expand out terms of the right hand side:

4 x - 20 = 9 x + 9

Subtract 9 x from both sides:

(4 x - 9 x) - 20 = (9 x - 9 x) + 9

4 x - 9 x = -5 x:

-5 x - 20 = (9 x - 9 x) + 9

9 x - 9 x = 0:

-5 x - 20 = 9

Add 20 to both sides:

(20 - 20) - 5 x = 20 + 9

20 - 20 = 0:

-5 x = 9 + 20

9 + 20 = 29:

-5 x = 29

Divide both sides of -5 x = 29 by -5:

(-5 x)/(-5) = 29/(-5)

(-5)/(-5) = 1:

x = 29/(-5)

Multiply numerator and denominator of 29/(-5) by -1:

Answer: x = (-29)/5

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2 years ago

You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how man

Ivenika [448]

Answer:

Total number of trials is 35.

Step-by-step explanation:

Given : Me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials $=\frac{3}{7}$

and probability of my friend's winning is $=1-\frac{3}{7}=\frac{4}{7}$

Let there be n numbers of trials.

Therefore, my score after n trials $=\frac{3n}{7}$

and my friend's score after n trials $=\frac{4n}{7}$

Now, the number of trials my friend won more than me is

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We know, that my friend won 5 more trials than me so comparing the actual and given we get,

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Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

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and my friend will win $\frac{4\times 35}{7}=20$ trials.

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2 years ago

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Alex17521 [72]

Answer:

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2) m∠3 + m∠6 = 180° by transitive property

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6) ∠8 and ∠9 are supplementary ${}$ Consecutive interior angles theorem

Step-by-step explanation:

1) Statement ${}$ Reason

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∴ m∠3 + m∠6 = 180° ${}$ Transitive property

3) Statement ${}$ Reason

p ║ q ${}$ Given

∠1 ≅ ∠5 ${}$ Given

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∠2 ≅ ∠1 ${}$ Alternate interior angles theorem

∠2 = ∠1 ${}$ Definition of congruency

∠2 = ∠5 ${}$ Transitive property

∠2 ≅ ∠5 ${}$ Definition of congruency.

4) Statement ${}$ Reason

∠1 ≅ ∠5 ${}$ Given

∠3 ≅ ∠4 ${}$ Given

∠1 = ∠5 ${}$ Definition of congruency

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∠5 ≅ ∠4 ${}$ Vertically opposite angles

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∠5 = ∠3 ${}$ Transitive property

∠1 = ∠3 ${}$ Transitive property

∠1 ≅ ∠3 ${}$ Definition of congruency.

t ║ v ${}$ Corresponding angle theorem

5) Statement ${}$ Reason

∠5 ≅ ∠16 ${}$ Given

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∠2 = ∠4 ${}$ Definition of congruency

EF ║ GH ${}$ Corresponding angle theorem

∠14 ≅ ∠16 ${}$ Corresponding angles

∠14 = ∠16 ${}$ Definition of congruency

∠5 = ∠14 ${}$ Transitive property

∠5 + ∠11 = 180° ${}$ Sum of angles on a straight line

∠14 + ∠11 = 180° ${}$ Transitive property

∠14 and ∠11 are supplementary ${}$ Definition of supplementary angles

6) Statement ${}$ Reason

l ║ m ${}$ Given

∠4 ≅ ∠7 ${}$ Given

∠4 = ∠7 ${}$ Definition of congruency

∠2 ≅ ∠7 ${}$ Alternate angles

∠2 = ∠7 ${}$ Definition of congruency

∠2 = ∠4 ${}$ Transitive property

∠2 ≅ ∠4 ${}$ Definition of congruency

∠2 and ∠4 are corresponding angles ${}$ Definition

DA ║ EB ${}$ Corresponding angle theorem

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