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2 years ago

Identify a possible first step using the elimination method to solve the system and then find the solution to the system.

Mathematics

1 answer:

olchik [2.2K]2 years ago

8 0

Answer:x = 1

y = 1

Step-by-step explanation:

The given system of simultaneous equations is expressed as

3x - 5y = - 2 - - - - - - - - - - - - 1

2x + y = 3 - - - - - - - - - - - - - 2

The first step is to decide on which variable to eliminate. Let us eliminate x. Then we would multiply both rows by numbers which would make the coefficients of x to be equal in both rows.

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x - 10y = - 4

6x + 3y = 9

Subtracting, it becomes

- 13y = - 13

y = - 13/- 13 = 1

The next step is to substitute y = 1 into any of the equations to determine x.

Substituting y = 1 into equation 2, it becomes

2x + 1 = 3

2x = 3 - 1 = 2

x = 2/2 = 1

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Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 32feet above the ground,

Jlenok [28]

Answer:

There are two times for the ball to reach a height of 64 feet:

1 second after thrown ⇒ the ball moves upward

2 seconds after thrown ⇒ the ball moves downward

Step-by-step explanation:

* Lets explain the function to solve the problem

- h(t) models the height of the ball above the ground as a function

of the time t

- h(t) = -16t² + 48t + 32

- Where h(t) is the height of the ball from the ground after t seconds

- The ball is thrown upward with initial velocity 48 feet/second

- The ball is thrown from height 32 feet above the ground

- The acceleration of the gravity is -32 feet/sec²

- To find the time when the height of the ball is above the ground

by 64 feet substitute h by 64

∵ h(t) = -16t² + 48t + 32

∵ h = 64

∴ 64 = -16t² + 48t + 32 ⇒ subtract 64 from both sides

∴ 0 = -16t² + 48t - 32 ⇒ multiply the both sides by -1

∴ 16t² - 48t + 32 = 0 ⇒ divide both sides by 16 because all terms have

16 as a common factor

∴ t² - 3t + 2 = 0 ⇒ factorize it

∴ (t - 2)(t - 1) = 0

- Equate each bracket by zero to find t

∴ t - 2 = 0 ⇒ add 2 to both sides

∴ t = 2

- OR

∴ t - 1 = 0 ⇒ add 1 to both sides

∴ t = 1

- That means the ball will be at height 64 feet after 1 second when it

moves up and again at height 64 feet after 2 seconds when it

moves down

* There are two times for the ball to reach a height of 64 feet

1 second after thrown ⇒ the ball moves upward

2 seconds after thrown ⇒ the ball moves downward

3 0

2 years ago

In ΔKLM, k = 890 inches, ∠M=143° and ∠K=34°. Find the length of m, to the nearest 10th of an inch.

Vesna [10]

Answer: 957.8

Step-by-step explanation:

4 0

1 year ago

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-

stiks02 [169]

To get the points at which the two boats meet we need to find the equations that model their movement:
Boat A:
vertex form of the equation is given by:
f(x)=a(x-h)^2+k
where:
(h,k) is the vertex, thus plugging our values we shall have:
f(x)=a(x-0)^2+5
f(x)=ax^2+5
when x=-10, y=0 thus
0=100a+5
a=-1/20
thus the equation is:
f(x)=-1/20x^2+5

Boat B
slope=(4-0)/(10+10)=4/20=1/5

thus the equation is:
1/5(x-10)=y-4
y=1/5x+2

thus the points where they met will be at:
1/5x+2=-1/20x^2+5
solving for x we get:
x=-10 or x=6
when x=-10, y=0
when x=6, y=3.2
Answer is (6,3.2)

5 0

2 years ago

Read 2 more answers

Heidi is saving for a new bike. She has already saved $57. If Heidi earns

PtichkaEL [24]

Answer:

8 hours

Step-by-step explanation:

57 + 9h = 129

9h = 72

h = 8

7 0

2 years ago

Read 2 more answers

Abbey wants to use her savings of $1,325 to learn yoga. The total charges to learn yoga include a fixed registration fee of $35

Brums [2.3K]

So for this, this can be written into the equation $y=50x+35$ (x = number of months, y = total cost).

To solve this problem, we need to plug in 1325 into the y-variable and solve from there.

$1325=50x+35$

Subtract 35 on each side to get $1290=50x$

Then just divide by 50 on each side, and your answer should be $25.8=x$

And because we cannot go past budget, we will have to round down to 25. In context, the maximum amount of months Abbey can do is 25 months.

8 0

2 years ago

Read 2 more answers