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3 years ago

What are the steps to this equation

Mathematics

2 answers:

Harlamova29_29 [7]3 years ago

6 0

Answer:

$x=7$

Step-by-step explanation:

$\frac{2}{5}x+\frac{1}{3}=\frac{1}{3}x+\frac{4}{5}$

Subtract $\frac{1}{3}$ from both sides:

$\frac{2}{5}x+\frac{1}{3}-\frac{1}{3}=\frac{1}{3}x+\frac{4}{5}-\frac{1}{3}$

$\frac{2}{5} x=\frac{1}{3}x+\frac{12}{15}-\frac{5}{15}$

$\frac{2}{5}x=\frac{1}{3}x+\frac{7}{15}$

Subtract $\frac{1}{3} x$ from both sides:

$\frac{2}{5}x-\frac{1}{3}x=\frac{1}{3}x+\frac{7}{15}-\frac{1}{3}x$

$\frac{6}{15}x-\frac{5}{15}x=\frac{7}{15}$

$\frac{1}{15}x=\frac{7}{15}$

Multiply both sides by 15:

$15\times \frac{1}{15}x=\frac{7\times 15}{15}$

$x=\frac{105}{15}$

$x=7$

Elina [12.6K]3 years ago

4 0

Answer:

x=7 is the correct answer

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Healthy Gym

ehidna [41]

Answer:

$c=2d+5$

Step-by-step explanation:

Let

d ------> the number of days

c -----> the cost

we know that

The cost is equal to the number of days multiplied by $2 per day plus the initial fee of $5

The linear equation in slope-intercept form is

$c=md+b$

where

m is the slope

b is the c-intercept (value of c when the value of d is equal to zero)

in this problem we have

m=$2 per day

b=$5

substitute

$c=2d+5$

8 0

3 years ago

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Simplify<br>5/2y-1 - 6/3y-1

Kipish [7]

Answer:

Step-by-step explanation:

First Group like terms:

$5/2y-6/3y-1-1$

Add similar elements: $5/2y-6/3y=1/2y$

$1/2y-1-1$

$1/2y=y/2$

$=y/2-1-1$

$=y/2-2$

6 0

2 years ago

The area of a rectangle is 27 m^2 , and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the

vagabundo [1.1K]

Let $L$ be the length of the rectangle and $W$ be the width. In the problem it is given that $L=2W-3$ . It is also given that the area $LW=27$ . Substituting in the length in terms of width, we have $W(2W-3)=27 \\ 2W^2-3W-27=0 \\ (2W-9)(W+3)=0$ . Using the zero product property, $2W-9=0 \text{ or } W+3=0$ . Solving these we get the width $W=4.5 \text{ or } -3$ . However, it doesn't make sense for the width to be negative, so the width must be $\boxed{4.5 \text{ m}}$ . From that we can tell the length $L=2(4.5)-3=\boxed{6 \text{ m}}$ .

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3 years ago

A certain organization recommends the use of passwords with the following format: vowel commavowel, consonant comma consonant c

zimovet [89]

The password format is = inpray93

vowel , consonant, consonant, consonant, vowel, consonant, number, number.

There are 21 consonants, 5 vowels and 10 number choices (0-9)

Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices are available and for 7th and 8th position there are 10 choices (0 to 9).

Passwords are not case sensitive which means upper case and lower case letters are same.

So, the number of passwords can be =

$5\times21\times21\times21\times5\times21\times10\times10$

= 486202500

Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.

This means all the letters are different.

So, number of passwords will be =

$10\times42\times42\times42\times10\times42\times10\times10$

= 31116960000

4 0

3 years ago

Which expression has the same GCF as 15x2 - 21x?

Mice21 [21]

Answer:

$15x^2 +21 x$

Step-by-step explanation:

We have the following expression:

$15x^2 -21 x$

We can find the GCF with the following steps.

1. Find the GCF for the numerical part 15 and -21

The factors for 15 are : 1,3,5,15

The factors for -21 are -21,-7,-3,-1,1,3,7,21

And the common factors are 1,3

The GCF for the numerical part is 3*1 = 3

2. Find the GCF for the variable

The factors of x^2 are : x*x

The factors of x are: x

The common factors are x for this case, so then the GCF for the variable part is x

3. Multiply the two results from steps 1 and 2

GCf= 3*x = 3x

If we consider the new expression:

$15x^2 +21x$

We can find the GCF with the following steps.

1. Find the GCF for the numerical part 15 and -21

The factors for 15 are : 1,3,5,15

The factors for -21 are 1,3,7,21

And the common factors are 1,3

The GCF for the numerical part is 3*1 = 3

2. Find the GCF for the variable

The factors of x^2 are : x*x

The factors of x are: x

The common factors are x for this case, so then the GCF for the variable part is x

3. Multiply the two results from steps 1 and 2

GCf= 3*x = 3x

And as we can see both GCF are equal. So then we satisfy the condition required.

5 0

3 years ago

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