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3 years ago

How do I solve for the variable? 3(x-14) + 1= -4x + 5

Mathematics

2 answers:

bearhunter [10]3 years ago

6 0

Answer:

3·(x - 14) + 1 = - 4·x + 5

3·x - 42 + 1 = - 4·x + 5

3·x - 41 = - 4·x + 5

7·x - 41 = 5

7·x = 46

x = 46/7

Evgesh-ka [11]3 years ago

6 0

The answer is 46/7.

First you distribute. So it would be 3x-42. Now add the 1 to the 42. your equation should look like 3x-43=-4x+5. Now add 4x to both sides. 7x-43=5. Now add -43 to both sides. Which is -37. Once you divide (don't ask about the division lol) you should get 46/7.

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Sort the words into a category based on whether they indicate a positive number or a negative number

ankoles [38]

Answer:

POSITIVE: gain, adding, above

NEGATIVE: loss, below, taking away

5 0

2 years ago

The inchworm moves 1/5 inch per hour. How far will the inchworm have moved after 6 hours?

melisa1 [442]

Answer: 1 1/5 inches.

Step-by-step explanation:

1/5 * 6

1/5 * 6/1

6/5 = 1 1/5

5 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

3 years ago

How do you solve 2(y + 1) – 2 = 4 + 2y - y

Elina [12.6K]

Answer:

y=4

Step-by-step explanation:

2(y+1)-2=4+y

2y+2-2=4+y

2y=4+y

2y-y=4

y=4

7 0

3 years ago

Read 2 more answers

a zoo charges an admission price of $85 for the first 12 members of a group and $6 for each additional member of the group. What

elena-14-01-66 [18.8K]

The largest group that can go to the zoo is 23 members

Step-by-step explanation:

The given is:

A zoo charges an admission price of $85 for the first 12 members of a group and $6 for each additional member of the group
We need to find the largest group that can go to the zoo and spend less than $155 on admission

Assume that the number of members in the group is x

∵ There are x members in the group

∵ The zoo charges an admission price of $85 for the first 12

members of a group and $6 for each additional member

of the group

- Take 12 members from x and multiply the rest members by

6 and then add 85 to the product

∴ The group will spend = 6(x - 12) + 85

∵ The group wants to spend less than 155 to go to the zoo

- use the symbol < between the expression above and 155

∴ 6(x - 12) + 85 < 155

- Simplify the left hand side

∴ 6x - 72 + 85 < 155

- Add like terms in the left hand side

∴ 6x + 13 < 155

- Subtract 13 from both sides

∴ 6x < 142

- Divide both sides by 6

∴ x < 23.67

- Take the largest integer less than 23.67

∵ 23 is the largest integer less than 23.67

∴ The group has 23 members

The largest group that can go to the zoo is 23 members

Learn more:

You can learn more about the inequalities in brainly.com/question/1465430

#LearnwithBrainly

6 0

3 years ago