All categories

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

You might be interested in

Huixian mother buys some shares of company A on day 0. on day 7, the share price of company a is $4.60. if she sells all her sha

Wewaii [24]

I think that u might want to do the share the company money i could be wrong but if i sm sorry

4 0

2 years ago

The word geometry has eight letters. three letters are chosen at random. what is the probability that two consonants and one vow

olga nikolaevna [1]

Answer:

0.536 is the required probability.

Step-by-step explanation:

We have been given the word the word "GEOMETRY"

we have to find the probability that two consonants and one vowel are chosen:

Number of consonants are: 5

Number of vowels are: 3

Hence, The required probability is: $\frac{^5C_2\cdot ^3C_1}{^8C_3}$

Using: $^nC_r=\frac{n!}{(r!)(n-r)!}$

$\frac{\frac{5!}{3!\cdot 2!}\cdot\frac{3!}{1!\cdot 2!}}{\frac{8!}{3!\cdot 5!}}$

Simplifying the above expression:

$\frac{\frac{5\cdot 4\cdot 3!}{3!\cdot 2}\cdot {\frac{3\cdot 2!}{2!}}}{\frac{8\cdot 7\cdot 6\cdot 5!}{5!\cdot 3\cdot 2}}$

Further simplification after cancelling out the common terms we get:

$\Rightarrow \frac{30}{56}=\frac{15}{28}=0.5357=0.536$

Hence, Option 1 is correct.

4 0

2 years ago

Read 2 more answers

Triangle X Y Z has centroid S. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form

Molodets [167]

Answer:Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Exclude leap years from the following calculations. (a) Compute the probability that a randomly selected person does not have a

Scrat [10]

Answer:

a) 99.73% probability that a randomly selected person does not have a birthday on March 14.

b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

d) 92.33% probability that a randomly selected person was not born in February.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

A non-leap year has 365 days.

(a) Compute the probability that a randomly selected person does not have a birthday on March 14.

There are 365-1 = 364 days that are not March 14. So

364/365 = 0.9973

99.73% probability that a randomly selected person does not have a birthday on March 14.

(b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

There are 12 months, so there are 12 2nds of a month.

(365-12)/365 = 0.9671

96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

(c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.

The following months have 31 days: January, March, May, July, August, October, December.

So there are 7 31st days of a month during a year.

Then

(365-7)/365 = 0.9808

98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

(d) Compute the probability that a randomly selected person was not born in February.

During a non-leap year, February has 28 days. So

(365-28)/365 = 0.9233

92.33% probability that a randomly selected person was not born in February.

6 0

2 years ago

Jeanne makes hair bows to sell at the craft fair. Each bow requires 1.5 yards of ribbon. If Jeanne wants to make 84 bows, how ma

mina [271]

Answer:

Jeanne must buy <u>378 feet</u> of ribbons to make 84 bows.

Step-by-step explanation:

Given:

Each bow required = 1.5 yards of ribbon

Number of bow to make = 84

We need to find the length of ribbon in feet to make 84 bows.

Solution:

First we will find length of ribbons in yards required to make 84 bows .

Now we know that;

1 bow =1.5 yards of ribbons

84 bows = length of ribbons in yards

By using Unitary method we get;

length of ribbons in yards = $1.5\times 84 = 126\ yards$

Now we know that;

1 yard = 3 feet

126 yard = length of ribbons in feet

Again by using Unitary method we get;

length of ribbons in feet to make 84 bows = $126 \times 3 = 378\ ft$

Hence, Jeanne must buy <u>378 feet</u> of ribbons to make 84 bows.

7 0

2 years ago