Answer:
6x + 1
Step-by-step explanation:
1. (10x + 3) + (-4x -2) --> sum means to add.
2. Combine like terms --> 10x - 4x = 6x; 3 - 2 = 1.
3. 6x + 1
If we have 2 more blue pens than black pens, our blue pens can be rewritten as blue = 2 + black. Now we can set up an equation. Originally this equation would involve both blue and black, but since we only have 1 equation to set up, we can only have 1 unknown. That's why we base the number of blue pens on the number of black pens and do a substitution. So instead of blue + black = 94, we have (black + 2) + black = 94. That simplifies to 2 black + 2 = 94, and 2 black = 92. Now if we divide by 2, we get that the number of black pens is 46. If we have 2 more blue than black, the number of blue pens we have is 48. 46 + 48 = 94, so there you go!
Answer:
Step-by-step explanation:
Answer:
(5,-1) or x=5 y=-1
Step-by-step explanation:
I used the substitution method to solve this!
<em>1. Pick one of your equations and solve for one of the variables. I chose the first equation and solved for x.</em>
x-2y=7
(Move the -2y to the other side of the equation in order to get the x by itself. You do the opposite, so it becomes +2y.)
x=2y+7
<em>2. Now take your second equation and plug in what you got for x into the x variable.</em>
2(2y+7)+5y=5
(Multiple 2 by everything inside of the parentheses.)
4y+14+5y=5
(We want to get the y by itself, so move the 14 to the other side.)
4y+5y=-14+5
(Combine all the like terms.)
9y=-9
(Divide the 9 from the y. What you do to one side you must do to the other.)
y=-1
<em>3. Since you have one variable solved for. Now take the first equation and plug in your y.</em>
x-2(-1)=7
(Multiple -2 by -1)
x+2=7
(Move the 2 to the other side in order to get the x by itself.)
x=5
<em>4. If needed, plug in your x and y values into the equations in order to check your answer.</em>
Hope this could help!
The magnitude of the final velocity of the cue ball is (B) 0.56m/s.
<h3>
What is Velocity</h3>
- The definition of velocity is a vector measurement of the rate and direction of motion.
- It is a moving body's speed and direction of motion.
How to calculate the magnitude of the final velocity?
The magnitude of the final velocity can be calculated by following the steps:
- The mass of the cue ball given is 0.4kg.
- The velocity of the cue ball given is +0.80m/s.
- The velocity of the striped ball before the collision is +0.38 m/s.
- The velocity of the striped ball after collision is +0.62m/s.
- We need to find the magnitude of the final velocity of the cue ball.
Assuming all pool balls have the same mass: 0.4kg
Let the final velocity of the cue ball be x.
Now, To find the final velocity:
- Mass of the cue ball × initial velocity of cue ball + Mass of striped ball + initial velocity of striped ball = mass of cue ball × final velocity + mass of striped ball × final velocity of the striped ball
- (0.40)×(0.80)+(0.4)(0.38) = (0.4)(x)+(0.4)(0.62)
- 0.32+0.152=0.4x+0.248
- 0.472=0.4x+0.248
- 0.472-0.248= 0.4x
- 0.224/0.4 =x
- x = 0.56m/s
Therefore, the magnitude of the final velocity of the cue ball is (B) 0.56m/s.
Know more about velocity here:
brainly.com/question/25749514
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The correct question is given below:
In a game of pool, a 0.4 kg cue ball is traveling at +0.80 m/s when it hits a slower striped ball moving at +0.38 m/s. After the collision, the striped ball moves off at +0.62 m/s. What is the magnitude of the final velocity of the cue ball? Assume all pool balls have the same mass.
A. 0.20 m/s
B. 0.56 m/s
C. 1.0 m/s
D. 1.8 m/s
