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2 years ago

For the equation 2(4x+10)=8x+k what value of k will create infineltly many solutions please help

Mathematics

1 answer:

PSYCHO15rus [73]2 years ago

3 0

Answer:

The value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.

Step-by-step explanation:

Given the expression

$2(4x+10)=8x+k$

solving

$2(4x+10)=8x+k$

$8x+20 = 8x+k$

We know that the equations with infinitely many solutions have the same expressions on both sides

It means the value of k can be determined by further simplifying such as

$8x+20 = 8x+k$

8x+20-8x = k

20 = k

Therefore, the value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.

VERIFICATION:

Given

$2(4x+10)=8x+k$

$8x+20 = 8x+k$

Put k = 20 in the equation

$8x+20 = 8x+20$

$8x+20 - 8x+20 = 0$

$0 = 0$

equations with infinitely many solutions have the same expressions on both sides.

This means the statement is always true.

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Answer: tea = 15 rupees per kg

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Step-by-step explanation:

Hi, to answer this question we have to write a system of equations with the information given:

"Two kg of tea and 3 kg of sugar cost rupees 39 in january 1997":

2 t + 3 s =39 (a)

Where:

t= price of 1 kg of tea
s = price of 1 kg of sugar

"in march 1997 the price of the tea increased by 25% (1.25)and the price of the sugar increased by 20%(1.20) and the same quantity of tea and sugar cost rupees 48.30. "

2(t1.25)+3(s1.2) = 48.30 (b)

Solving for t in (b)

2t =39-3s

t = (39 -3s)/2

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Replacing the value of t in (b)

2 x ((19.5-1.5s)1.25)+ 3 ( 1.2s) =48.30

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Replacing the value of s in (a)

2 t + 3 (3) =39

2 t + 9 =39

2 t =39 -9

2 t =30

t = 30/2

t= 15

Prices in january:

tea = 15 rupees per kg

sugar= 3 rupees per kg

Feel free to ask for more if needed or if you did not understand something.

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