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maw [93]
3 years ago
7

4 plates and 3 cups cost 20.70 dollars. 5 plates and 4 cups cost 26.40 dollars . each plates cost the same amount as the other p

lates , and each cup cost the same amount as the other cups. what is the cost of 1 plates ? what is the cost of 1 cup?
Mathematics
1 answer:
Basile [38]3 years ago
7 0
Here, we need to construct 2 linear equation.
Let x be the plate and y be the cup.
1) 4x + 3y = 20.70
2) 5x + 4y = 26.40

From equation 1, we solve for y.
3y = 20.70 - 4x
y = (20.70 - 4x) / 3

Substitute into equation 2.
5x + 4((20.70 - 4x) / 3) = 26.40
5x + 27.60 - 5.33x = 26.40
-0.33x = 26.40 - 27.60
-0.33x = -1.2
x = 3.64

We already get value of x. Now, calculate for value of y.
y = (20.70 - 4x) / 3
y = (20.70 - 4(3.64)) / 3
y = 2.05

The cost for 1 plate is 3.64 dollars and 1 cup is 2.05 dollars.
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Answer:

(23, 4)

Step-by-step explanation:

If we use substitution, we need to rewrite the 2nd equation so we can substitute it into the first.

Step 1: Rewrite 2nd equation

x = 5y + 3

Step 2: Substitution

2(5y + 3) - 5y = 26

Step 3: Distribute

10y + 6 - 5y = 26

Step 4: Combine like terms

5y + 6 = 26

Step 5: Isolate <em>y</em>

5y = 20

y = 4

Step 6: Find <em>x</em>

x - 5(4) = 3

x - 20 = 3

x = 23

And we have our final answer!

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3 years ago
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4(x + 3) + 2x in the simplest form
leonid [27]

Answer:

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Step-by-step explanation:

Distribute the 4 first. Now you have 4x + 12 + 2x. 4x + 2x are like terms and therefore they can be added. Your final simplified answer is therefore 6x + 12.

3 0
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What is the truth value for the following conditional statement?
Studentka2010 [4]

Answer:

TT→T

Step-by-step explanation:

If p is false, then ~p is true.

If q is false, then ~q is true.

Now note that

  • If a and b are both true, then a→b is true.
  • If a is true, b is false, then a→b is false.
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In your case, both~p and ~q are true, then ~p→~q is true too (or TT→T)

3 0
3 years ago
What are 2 possible values for x where x ≥ 6?
seropon [69]

Answer:

6-7-8-9-10-11-12-13-14-15 etc...

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5 0
2 years ago
(10-P) Help please, thanks.
Anuta_ua [19.1K]
The formula of linear equation is:
y1  -  y2 = m(x1  -  x2)
Where
x1 and x2: x coordinates(-1 and 3)
y1 and y2: y coordinates(-2 and 10)
m is the slope

We can then choose a point from the line to find the eqaution.

We need to first find the slope:
\frac{y1 - y2}{x1 - x2}
In this case:
\frac{ - 2 - 10}{ - 1 - 3}   \\ =  \frac{ - 12}{ - 4}  \\  = 3

In this case, as the y2 is given as 1,put (-1,-2) , and the slope(3 )into the eqaution :

y-(-2) = 3(x-(-1))
y+2 = 3(x+1)

Therefore
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is the answer.

Hope it helps!
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3 years ago
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