PLEASE HELP Alice's freezer can be set to a range of temperatures, from

There are 30 students on the school's student council. A special homecoming dance committee is to be formed by randomly selectin

Oksana_A [137]

There can be a possible of 5 committees

7 0

3 years ago

The spring of a dart gun exerts a force on a 0.02 kg dart as it launched from the gun at 20 m/s. What is the dart ke

seraphim [82]

Answer: The dart comes out at 20.00 m/s.

7 0

2 years ago

Carmen paid $10.50 for a T-shirt at the mall. it was on sale for 30% off. what was the original price before the discount

Kruka [31]

The answer is 35 because if you do 30 over 100 it will be 0.3 so then you are going to take the 10.50 and divide that to 0.3 and that's how you get your answer your answer is going to be 35

8 0

3 years ago

Solve the system of equations. y = x + 2, y = x2 + 7x + 10

Monica [59]

Answer:

(- 2, 0 ) and (- 4, - 2 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = x² + 7x + 10 → (2)

Since both equations express y in terms of x we can equate them, that is

x² + 7x + 10 = x + 2 ( subtract x + 2 from both sides )

x² + 6x + 8 = 0 ← in standard form

(x + 2)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x + 4 = 0 ⇒ x = - 4

Substitute these values into (1) for corresponding values of y

x = - 2 : y = - 2 + 2 = 0 ⇒ (- 2, 0 )

x = - 4 : y = - 4 + 2 = - 2 ⇒ (- 4, - 2 )

Solutions are (- 2, 0 ) and (- 4, - 2 )

5 0

3 years ago

4 ( 2x-2 ) +2 = 4 ( x- 2 )

IRINA_888 [86]

Answer:

$x=-\frac{1}{2}$

Step-by-step explanation:

$4(2x-2)+2=4(x-2)$

First, let's go over the <em>distributive property </em>in math. When you have any expression within a parenthesis being multiplied by any expression outside a parenthesis, you are distributing the values outside onto the values inside, like so:
$a(b+c)$ ⇒ $ab+ac$
Hopefully this helps you break down how distribution works, but if you're still having trouble comprehending it, looking at examples will help. Now, back to the problem. Let's try this idea of distribution on the left side of the equation.

$4(2x-2)+2=4(x-2)\\((4)2x-(4)2)+2=4(x-2)\\(8x-8)+2=4(x-2)$

Hopefully you could follow this math, but if not, there are plenty of materials online and in books on this. Be sure to look at those if you still have trouble.
Now that we have done all the multiplication we can on the left side and only addition and subtraction remain, we can get rid of the parentheses.

$(8x-8)+2=4(x-2)\\8x-8+2=4(x-2)\\8x-6=4(x-2)$

Now let's do distribution for the other side as well. Doing this will help us easily isolate $x$ on one side after.

$8x-6=4(x-2)\\8x-6=((4)x-(4)2)\\8x-6=4x-8$

Now, using addition and subtraction, let's move all our $x$ values to one side of our equation and all other values to the other. It doesn't matter which side you choose.

$8x-6=4x-8\\4x=-2\\\frac{4x}{4}=\frac{-2}{4}$

In case you're confused by the last step there, what I did was divide both sides by the coefficient in front of our $x$ values. This will cancel the coefficient out and leave us with our solution.

$\frac{4x}{4}=\frac{-2}{4}\\x=\frac{-1}{2}=-\frac{1}{2}$

The fraction $\frac{-2}{4}$ is technically correct, but it isn't simplified. $\frac{-2}{4}$ can be simplified to $-\frac{1}{2}$ , so $-\frac{1}{2}$ is our final answer.

$x=-\frac{1}{2}$

5 0

3 years ago