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Furkat [3]
3 years ago
13

How do you do 2 step eqations

Mathematics
1 answer:
Olin [163]3 years ago
3 0
It takes two steps to solve an equation or inequality that has more than one operation:
1- Simplify using the inverse of addition or subtraction.
2- Simplify further by using the inverse of multiplication or division. 
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Two trains are 210 miles apart, and their speeds differ by 17 mph. Find the speed of each train if they are traveling toward eac
Marizza181 [45]
V1 - velocity first train
v2 - velocity second train
v2 > v1

v2 - v1 = 17 mph

We know, that: 
s_1+s_2=210 \ [miles] \\ \\ t_1=t_2=2h

So:

v_1=\dfrac{s_1}{t_1}=\dfrac{s_1}{2} \\ \\ v_2=\dfrac{s_2}{t_2}=\dfrac{s_2}{2} \\ \\ \\ v_1+v_2= \dfrac{s_1}{2}+\dfrac{s_2}{2} \\ \\ v_1+v_2= \dfrac{s_1+s_2}{2} \\ \\  v_1+v_2= \dfrac{210}{2}=105

NOw we've got simple system of equations:

+\begin{cases} v_2-v_1=17 \\ v_2+v_1=105\end{cases} \\ \\ 2v_2=122 \qquad /:2 \\ \\ v_2=61 \qquad [mph] \\ \\ v_2-v_1=17 \\ \\ 61-v_1=17 \\ \\ v_1=44

Velocities of these trains are  61mph  and 44mph

3 0
3 years ago
Read 2 more answers
The water under a draw bridge was 15 feet deep at midnight. As the tide went out, the
Vsevolod [243]

Answer:

80 minutes or 1 h 20 minutes

Step-by-step explanation:

15-13=2

2/0.025=80

So we can conclude that it takes 80 minutes till it reaches 13 feet.

7 0
3 years ago
PLS PLS HELP, I DONT WANT TO FAIL!!
Flura [38]

Answer:

2.0 seconds

Step-by-step explanation:

<u>Given quadratic functions</u>:

\begin{cases}y=-7x^2+26x+3\\y=-6x^2 +23x+5\end{cases}

To find the time, in seconds, that the balloons collided at the highest point, <u>substitute</u> one equation into the other equation and rearrange to <u>equal zero</u>:

\begin{aligned}-6x^2+23x+5 & = -7x^2+26x+3\\-6x^2+23x+5+7x^2 & = -7x^2+26x+3+7x^2\\x^2+23x+5 & = 26x+3\\x^2+23x+5-26x & = 26x+3-26x\\x^2-3x+5& = 3\\x^2-3x+5-3& = 3-3\\x^2-3x+2& = 0\end{aligned}

<u>Factor</u> the quadratic:

\begin{aligned}x^2-3x+2 & = 0\\x^2-2x-x+2 & = 0\\x(x-2)-1(x-2) & = 0\\(x-1)(x-2) & = 0\\\end{aligned}

Apply the <u>zero-product property</u> to solve for x:

\implies (x-1)=0 \implies x=1

\implies (x-2)=0 \implies x=2

Therefore, the balloons collided at 1 second and 2 seconds.  

To find at which time the highest point of collision occured, substitute both values of x into one of the functions:

f(1)=-6(1)^2 +23(1)+5=22

f(2)=-6(2)^2 +23(2)+5=27

Therefore, the time, in seconds, that the balloons collided at the highest point is 2.0 seconds.

Learn more about quadratic systems of equations here:

brainly.com/question/27930827

8 0
1 year ago
Read 2 more answers
Will somebody please assist me what is 7x3x2+5-3=k
Svetllana [295]
In this case just do it left to right, as multiplication comes before addition/subtraction. So 7x3x2+5-3=21x2+5-3=42+5-3=47-3=44=k.
5 0
3 years ago
Read 2 more answers
Last fall, a middle school took a group of students on a trip to Space Camp, which is 360 miles away. The bus that they took to
mezya [45]

Answer:

The bus travelled 60 miles in 1 hour.

Step-by-step explanation:

To solve this problem we need to calculate the average speed at which the bus travelled. This is given by the distance travelled divided by the time that they took to get there. So we have:

average speed = distance/time

average speed = 360/6

average speed = 60 miles/h

Therefore in 1 hour they travelled 60 miles.

4 0
3 years ago
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