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professor190 [17]
3 years ago
10

Use the substitution method to solve the system of equations

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
3 0

You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).

In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.

The result is

14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8

So, the second equation turned to be an equality, i.e. an equation where both sides are the same.

This implies that the system has infinitely many solutions, because every couple (n,m) such that n=-7m-4 is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.

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3.1 Write the following in scientific notation<br>a) 217 000 000 b) 0,000 253​
AlekseyPX

Answer:

2.17 x 10^8

0.253 x 10^-4 if number is 0.000253 or 2.53 x 10^2 if number is 253

Step-by-step explanation:

6 0
3 years ago
Luis is a professional musician.He needs to
Deffense [45]

Step-by-step explanation:

The following prices for the same make  and model used guitar for his work are :

$699.20,$700.30,$680.50,$700.30, and  $800.25.

Mean of ungrouped data = sum of observations/total no of observations

\text{Mean}=\dfrac{699.20+700.30+680.50+700.30+800.25}{5}\\\\\text{Mean}=\$716.11

For median, arrange the given data in ascending order.

$680.50, $699.20, $700.30, $700.30, $800.25

Median = middle value

Median = $700.30

The value that comes most often is called mode.

$700.30 comes two times. So, mode is $700.30

Hence, Mean = $716.11, median = $700.30 and mode = $700.30

5 0
3 years ago
What is the value of this expression when f = 4?
ehidna [41]
Ok I got you First Distribute 9(3 f +2)-7f

27 f +18 -7f

Step 2 combine like terms

Step 3 common factor
Answer: 2(10 f + 9)
4 0
2 years ago
What is the equation of the line given the table
OLEGan [10]

Answer:

y=3x-1

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Please solve this question!!​
GaryK [48]

Answer:  (i) 1/221     (ii) 11/221      (iii) 95/663        (iv) 1/663

<u>Step-by-step explanation:</u>

(i) A deck of cards contains 4 Kings out of 52 total cards

1st draw: 4 Kings out of 52 total cards → 4/52 = 1/13

2nd draw: 3 remaining Kings out of 51 total remaining cards  →  3/51 = 1/17

  <u>1st Draw </u>                   <u>2nd Draw </u>                  <u>Outcome</u>         <u>Probability</u>

 King: P(K) = 1/13        King: P(K₂/K₁) = 1/17     King, King       (1/13) x (1/17) = 1/221

*************************************************************************************************

(ii) A deck of cards contains 4 Jacks, 4 Queens, & 4 Kings out of 52 total cards

1st draw: 12 Face cards out of 52 total cards → 12/52 = 3/13

2nd draw: 11 remaining Face cards out of 51 total remaining cards  →  11/51

<u>1st Draw </u>                 <u>2nd Draw </u>                  <u>Outcome</u>       <u>Probability</u>

 Face: P(F) = 3/13    Face: P(F₂/F₁) = 11/51   Face,Face     (3/13) x (11/51) = 11/221

*************************************************************************************************

(iiI) A deck of cards contains 26 black cards out of 52 total cards but there are 2 black Jacks, 2 black Queens, and 2 black Kings.

1st draw: 20 Black (not Face) cards out of 52 total cards → 20/52 = 5/13

2nd draw: 19 remaining Black (not Face) cards out of 51 total remaining cards  →  19/51

  <u>1st Draw </u>                 <u>2nd Draw </u>                       <u>Outcome</u>   <u>Probability</u>

Black: P(B~) = 5/13   Black: P(B~₂/B~₁) = 19/51    B~,B~    (5/13) x (19/51) = 95/663

*************************************************************************************************

(ii) A deck of cards contains 4 Aces out of 52 total cards

1st draw: 4 Aces out of 52 total cards → 4/52 = 1/13

2nd draw: 1 Queen of Hearts out of 51 total remaining cards  →  1/51

  <u>1st Draw </u>                 <u>2nd Draw </u>                   <u>Outcome</u>         <u>Probability</u>

 Ace: P(A) = 1/13      Qh: P(Qh₂/A₁) = 1/51   Ace,Queen(h)   (1/13) x (1/51) = 1/663

7 0
3 years ago
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