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3 years ago

Solve the following equation by combining like terms: 4y - 2y = 18

Mathematics

2 answers:

Lelechka [254]3 years ago

8 0

Answer:

y = 9

Step-by-step explanation:

Collect the like terms:

2y = 18

Divide both sides by 2 to make y on its own

y = 9

olga nikolaevna [1]3 years ago

3 0

4y-2y=18
(Collect like terms)
2y=18
(Divide like terms)
y=9

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What is the solution to the system of equations graphed below?

padilas [110]

Step-by-step explanation:

The solution can be found by identifying the point of intersection of the 2 graphed lines.

As we can see, they intersect each other at the point (2, -3). This is our solution for the equations.

4 0

3 years ago

Show that a = −1 + √3i and b = 2 satisfy 1/a+b=1/a + 1/b

Zarrin [17]

Answer:

LHS = $\frac{1 - \sqrt3i}{4}$ = RHS = $\frac{1 - \sqrt3i}{4}$

Step-by-step explanation:

Data provided in the question:

a = −1 + √3i and b = 2

to prove:

$\frac{1}{a+b}=\frac{1}{a} + \frac{1}{b}$

Considering the LHS

⇒ $\frac{1}{a+b}$

substituting the value of a and b, we get

⇒ $\frac{1}{−1 + \sqrt3i+2}$

⇒ $\frac{1}{1 + \sqrt3i}$

on multiplying and dividing by conjugate ( 1 - √3i )

we get

$\frac{1}{1 + \sqrt3i}\times\frac{1 - \sqrt3i}{1 - \sqrt3i}$

$\frac{1 - \sqrt3i}{(1^2 - (\sqrt3i)^2}$

$\frac{1 - \sqrt3i}{1 + 3}$ (as (√i)² = -1 )

$\frac{1 - \sqrt3i}{4}$

Now,

considering the RHS

$\frac{1}{a} + \frac{1}{b}$

substituting the value of a and b, we get

⇒ $\frac{1}{-1 + \sqrt3i} + \frac{1}{2}$

⇒ $\frac{2\times1 + ( -1 + \sqrt3i)\times1}{(-1 + \sqrt3i)\times2}$

⇒ $\frac{2 + ( -1 + \sqrt3i)}{(-1 + \sqrt3i)\times2}$

⇒ $\frac{1 + \sqrt3i}{(-1 + \sqrt3i)\times2}$

now,

on multiplying and dividing by conjugate ( -1 - √3i )

we get

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1 - \sqrt3i}{-1 - \sqrt3i}$

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1( 1 + \sqrt3i)}{-1 - \sqrt3i}$

$\frac{(1 + \sqrt3i}^2\times(-1){((-1)^2 - (\sqrt3i)^2)\times2}$

$\frac{(1^2 + (\sqrt3i)^2+2(1)(\sqrt3i)\times(-1)}{(1 + 3)\times2}$

$\frac{(1 - 3 + 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{(-2 + 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{-2( 1 - 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{( 1 - 2\sqrt3i)}{(4)}$

Since, LHS = RHS

hence satisfied

3 0

3 years ago

A mechanic buys $14.56 worth of parts from a supplier. If he pays for the parts with a $20 bill, how much change will he receive

balu736 [363]

This is a basic subtraction problem :-).

You will subtract how much money the mechanic gives to the supplier; which in this case will be $20, by the total amount of the parts which is $14.56.

20-14.56 = 5.44

Therefore, he will receive $5.44 in change for the transaction.

7 0

4 years ago

Read 2 more answers

Please help me with this

weeeeeb [17]

The answer is B. -3 because that's x and you add them together and get greater than.

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3 years ago

Which expression is equivalent to 16(30x – 24y) –18 (32x – 16y)?

HACTEHA [7]

Answer:

\frac{1}{6}\left(30x-24y\right)-\frac{1}{8}\left(32x-16y\right)

Step-by-step explanation:

there ya go

3 0

3 years ago