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3 years ago

Re-write in slope-intercept form of an equation: x- 2y = 4

Mathematics

1 answer:

creativ13 [48]3 years ago

8 0

Answer:

The final equation is $\bold{y=-\frac{1}{2}x -2}$ .

Step-by-step explanation:

To rewrite an equation in slope-intercept form, our equation must be in $\text{y = mx + b}$ form. This means the <em>y</em>-variable must be on the left side of the equation and the slope and y-intercept must be on the right side of the equation. We can do this by moving the equation around.

$\text{y = mx + b \ \ This is the equation we want to reach.}\\\\\text{x - 2y = 4 \ \ This is what we are given.}\\\\\text{-2y = -x + 4 \ \ Move the x to the right by subtracting it from both sides.}\\\\{y = -\frac{1}{2}x - 2} \ \ \text{When we divide by two, we get this.}$

And then, we're done! Our final answer is $y=-\frac{1}{2}x -2$ .

You might be interested in

Which expression is equivalent to 18 − 20?

Sveta_85 [38]

The answer is 18+(-20) because if if you were going to solve that equation you would use the absolute value of -20 and then the opposite of the sign giving you 18-20. Hope this helps:)

6 0

3 years ago

There are 36 total people in the movie theater and the ratio of adults to children is 4 to 2. How many kids are in the movie the

Pepsi [2]

Answer:

12 kids are in the theater.

Step-by-step explanation:

4+2=6

36÷6=6

6×2=12

So, 12 kids are in the theater.

6 0

2 years ago

I am Lyosha [343]

You have the right idea that things need to get multiplied.

What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.

Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.

The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.

So we multiply the entire complex fraction by (5)(x + 6)(x -3).

Numerator: $(\frac{1}{5} -\frac{5}{x + 6})(5)(x +6)(x-3) =\frac{1}{5}(5)(x +6)(x-3) - \frac{5}{x + 6}(5)(x +6)(x-3)$

= (x+6)(x-3) - (5)(5)(x-3)

= (x+6)(x-3) - 25(x-3)

= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3

= (x -3)(x - 19)

Denominator:

$\frac{25}{x - 3} * (5)(x + 6)(x - 3) = (25)(5)(x + 6) = 125(x + 6)$

Now we put the pieces together.

Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)

5 0

3 years ago

Half an hour after leaving her house Beverly was 20 miles from home. At this point she merged onto the highway and was traveling

N76 [4]

Answer:

1. 45.71 miles

2. 10 miles

3. 89.43 miles

4. 0.79 hr

5. 0.025 hr

Step-by-step explanation:

speed = distance/time

After 4 hrs Beverly was 200 miles from home , however she had spent 0.5hr travelling for 20 miles prior to getting to the highway.

Therefore;

Constant speed before Highway = 20/0.5 = 40 miles/hr

Constant speed at Highway = $\frac{(200-20)}{(4-0.5)}$ = 51.43 miles/hr

1. in 1 hr beverly will have travelled;

⇒ (20 miles in 0.5 hr ) + (0.5 hr at speed 51.43 miles/hr)

⇒ 20 + (0.5 x 51.43) = 45.71 miles

2. In 0.25 hr beverly had not reached the highway

⇒ distance = speed x time

⇒ distance = 40 x 0.25 = 10 miles

3. in 1.85 hrs beverly will have travvelld;

⇒ (20 miles in 0.5 hr ) + (1.35 hr at speed 51.43 miles/hr)

⇒ 20 + 69.43 = 89.43 miles

4. Time taken to get to 35 miles

⇒ (20 miles in 0.5 hr ) + (15 miles at speed 51.43 miles/hr)

⇒ 0.5hr + (15/51.43) hr = 0.79 hr

5. Time taken to travel 1 mile

⇒ time = distance / speed = 1 mile / 40 miles/hr

⇒ time = 0.025 hr

8 0

3 years ago

You are a traffic accident investigator. You have arrived at the scene of an accident. Two trucks of equal mass (3,000 kg each)

Kazeer [188]

Answer:

1) Kinetic energy of the truck 1 is 600,000 joules.

Kinetic energy of the truck 2 is 1,837,500 joules.

2 a)Potential energy of truck 1 is 646,800 Joules.

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

Step-by-step explanation:

Mass of the truck 1 and truck 2,m = 3000 kg

Velocity of the truck 1, $v_1$ = = 20 m./s

Velocity of the truck 2, $v_2$ = 35 m./s

1. Kinetic energy of the truck 1: $\frac{1}{2}mv_{1}^2=\frac{1}{2}\times 3000 kg\times (20 m/s)^=600,000 joules$

Kinetic energy of the truck 2: $\frac{1}{2}mv_{2}^2=\frac{1}{2}\times 3000 kg\times (35 m/s)^=1,837,500 joules$

2.a) Energy loose by the truck 1:

Initial height of the truck on the hill = 22 m

At that height potential energy will be maximum:

Potential energy of truck 1 at that height = $mgh=3000\times 9.8 m/s^2\times 22 m=646,800 Joules$

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

3 0

3 years ago