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kobusy [5.1K]
2 years ago
6

Does the ordered pair (2,1) satisfy the following system of equations?

Mathematics
1 answer:
love history [14]2 years ago
6 0

<u>To determine the whether the ordered pair satisfies the equation:</u>

     ⇒ we must plug in the values

          ⇒ since coordinates are (x,y) ⇒ (2,1)

             ⇒ there we must plug 2 into the 'x' position in the equation

                ⇒ and 1 into the 'y' position in the equation

<u>Let's try the first equation</u>:

   3x-y=5\\3(2)-1=5\\6-1=5\\5=5

  • <u>Ordered pair satisfies first equation</u>

<u />

Let's try the second equation

   5x-2y=8\\5(2)-2(1)=8\\10-2=8\\8=8<u />

  • <u>Ordered pair satisfies second equation</u>

<u />

Thus ordered pair satisfies the following system of equations

<u></u>

<u>Answer: Yes</u>

<u></u>

Hope that helps!

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Jordan is 12 years older than Anna. The
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Answer:

  • J = [12] +A
  • J + A = [50]

Step-by-step explanation:

If Anna's age is represented by A, then 12 more than Anna's age will be ...

  12 + A

Jason's age is said to be 12 more than Anna's age, so ...

  J = 12 + A

__

The sum of their ages will be J + A. That is said to be 50, so ...

  J + A = 50

_____

These equations can be solved by using the first to substitute for J in the second.

  (12 +A) +A = 50

  2A = 38 . . . . . . . . subtract 12

  A = 19 . . . . . . . . . . divide by 2

  J = 12 +19 = 31 . . . find Jason's age

Jason is 31; Anna is 19.

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3 years ago
Is n+4 equal to 8(n - 4)
weqwewe [10]
No, n+4=4n an 8(n-4)=32n
4 0
3 years ago
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the empire state building is 1250 feet tall. IF an object is thrown upward from the top of the building at an initial velocity o
ss7ja [257]

Answer:

Time for the object to get h(max)    s = 1.1875 sec

h (max)  = 1272.57 feet

Down time for the object to hit the ground   =  4.25 sec

Step-by-step explanation:

The relation

h(s)  =  -  16*s²  +  38* s  + 1250    (1)

Is equivalent to the equation for vertical shot

Δh = V(i)*t  -  1/2g*t²  (in this case we don´t have independent term since the shot is from ground level. We can see in (1), the independent term is 1250 feet ( the height of the empire state building), the starting point of the movement.

The description of the movement is:

V(s)  =  V(i)  - g*s     ⇒  V(s) = 38 - 32*s

At h(max)    V(s)  =  0      38/32  = s

So the maximum height is at  s = t = 1.1875 sec

The time for the object to pass for starting point is the same

t  =  1.1875 sec

h(max) is

h(max)  = - 16* (1.1875)² +  38 (1.1875) + 1250

h(max)  =  -  22,56  +  45.13  +  1250

h(max)  =  1272.57 feet

Time for the object to hit the ground is

h(s)  =  - 1250 feet

-1250  =  - 16 s² + 38*s  + 1250

-16s² +  38s  =  0

s ( -16s + 38 )  =  0

First solution for that second degree equation  is x = 0 which we dismiss

then  

( -16s + 38 )  =  0    ⇒ 16s   =  38     s  =  38/16

s =  2.375 sec    and  we have to add time between h (max) and to get to starting point  ( 1. 1875 sec)

total time is  = 2.375 + 1.875

Total time  =  4.25 sec

4 0
3 years ago
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3 0
3 years ago
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Barack walks 2 kilometers south and then x kilometers east. ​ ​He ends 5 kilometers away from his starting position. ​ ​ Find x
amid [387]

Answer:

4.6 km

Step-by-step explanation:

-This is a Pythagorean Theorem problem where the distances walked are effectively the base and height of the imaginary right triangle thereof.

#Apply Pythagorean theorem to solve:

b^2+h^2=H^2\\\\2^2+x^2=5^2\\\\x^2=5^2-2^2=21\\\\x=\sqrt{21}\\\\x=4.58\  km

\approx 4.6\ km

Hence, the distance x is 4.6 km

7 0
3 years ago
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