What is the solution to the equation 5x-7= 3x+5 ? x = 1 x = 6 x = 12 x = 24

Mathematics

2 answers:

zzz [600]3 years ago

6 0

Makovka662 [10]3 years ago

3 0

We can solve any equation by distributing and combining like terms if needed.
After that is done, we use the addition principle of equality and multiplication or division of equality.

The equation we have to solve for above does not need to be distributed and there is no like terms to combine on each side.

Using the addition principle of equality, we can add 7 to each side of the equation to simplify it further.

5x - 7 + 7 = 3x + 5 + 7
5x = 3x + 12

If we also use the addition principle of equality to add -3x to each side of the equation then the 3x on the right-hand side we disappear!

5x + (-3x) = 3x + (-3x) + 12
2x = 12

Now we can use the multiplication or division principle of equality on the equation.

Divide both sides by 2.

2x / 2 = 12 / 2
x = 6

So, x is equal to 6.

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Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2

lbvjy [14]

Step 1:
Start by putting $\frac{d}{dx}$ in front of each term

$\frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2]$
-----------------------------------------------------------------------------------------------------------------
Step 2:

Deal with the terms in 'x' and the constant terms
$\frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2]$
----------------------------------------------------------------------------------------------------------------
Step 3:

Use the chain rule for the terms in 'y'
$\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}$
--------------------------------------------------------------------------------------------------------------
Step 4:

Use the product rule on the term in 'x' and 'y'
$(y) \frac{d}{dx} cos x+(cos x) \frac{d}{dx}y =10x+6y \frac{dy}{dx}
$
$y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
--------------------------------------------------------------------------------------------------------------

Step 5:

Rearrange to make $\frac{dy}{dx}$ the subject
$-y sin(y)+cos(x) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
$cos(x) \frac{dy}{dx}-6y \frac{dy}{dx}=10x+y sin(y)$
$[cos(x) - 6y] \frac{dy}{dx}=10x + y sin(y)$
$\frac{dy}{dx}= \frac{10x+ysin(y)}{cos(x)-6y}$ ⇒ Final Answer

5 0

4 years ago

Marsha Green makes $9.19 per hour. Find her social security tax at the rate of 7.65% for a 40-hour work week.

ira [324]

Answer:

$28.12

Step-by-step explanation:

$9.19 x 40 = $367.60 x 7.65% = $28.12

5 0

4 years ago

Find the geometric mean of 8 and 253.

sveta [45]

The geometric mean of 8 and 253 is;

<h3>Geometric mean of numbers</h3>

According to the question;

The task requires that the geometric mean of 8 and 253 be determined.

The geometric mean of a two numbers is the square root the product of the he numbers.

Hence, in this scenario;

The geometric mean of 8 and 253 is;

G.M = √8×253

G.M = √2024

G.M = 45.

Ultimately, the geometric mean of 8 and 253 is approximately 45.