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2 years ago

X − y = 12 x + 2y = 21

Mathematics

1 answer:

olga55 [171]2 years ago

5 0

Answer: x=15, y=3

Step-by-step explanation:

Subtracting the two equations, we get -3y=-9, meaning y=3.

Substituting this into the first equation, we get that x-3=12, and thus, x=15.

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One canned juice drink is 25% orange juice; another is 10% orange juice. How many liters of each should be mixed together in

Talja [164]

11 liters of 25% orange juice, 4 liters of 10% orange juice:

1' let x to be 25% orange juice and y be 10% orange juice

2' .25x+.10y=(15).21

3' x+y=15

4' 2.5x+y=31.5 divide all sides by 10

5' -x-y=-15 multiply all sides by -1

6' 1.5x=16.5

7' x=11

8' y=15-11=4

so 11 and 4 are the answers.

4 0

3 years ago

For the function f(x) = 7/2x-16, what is the difference quotient for all nonzero values of h?

sergey [27]

Answer:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}$

Step-by-step explanation:

Given

$f(x) = \frac{7}{2}x - 16$

Required

The difference quotient for h

The difference quotient is calculated as:

$\frac{f(x + h) - f(x)}{ h}$

Calculate f(x + h)

$f(x) = \frac{7}{2}x - 16$

$f(x+h) = \frac{7}{2}(x+h) - 16$

$f(x+h) = \frac{7}{2}x+ \frac{7}{2}h- 16$

The numerator of $\frac{f(x + h) - f(x)}{ h}$ is:

$f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -(\frac{7}{2}x - 16)$

$f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -\frac{7}{2}x + 16$

Collect like terms

$f(x + h) - f(x) = \frac{7}{2}x -\frac{7}{2}x + \frac{7}{2}h- 16 + 16$

$f(x + h) - f(x) = \frac{7}{2}h$

So, we have:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h \div h$

Rewrite as:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h * \frac{1}{h}$

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}$

5 0

3 years ago

A box contains 76 coins, only dimes and nickels. The amount in the box is $4.90. How many dimes and how many nickels are in the

dangina [55]

The number of dimes is 75 coins.

The number of nickels is 1 coin.

Step-by-step explanation:

It is given that,

A box contains 76 coins, only dimes and nickels.

The 10 cent coin is called a dime.
Let, the number of dimes be x.
The 5 cent coin is called a nickel.
Let, the number of nickels be y.

This is represented by the system of equations :

x + y = 76 -------(1)

10x + 5y = 4.90 ------(2)

Multiply eq (1) by 5 and subtract eq (2) from eq (1),

5x + 5y = 380

-(10x + 5y = 4.90)

-5x = 375.1

x = 375/5

x = 75 coins.

The number of dimes is 75 coins.

Substitute x=75 in eq (1),

y = 76 - 75

y = 1 coin.

The number of nickels is 1 coin.

6 0

3 years ago

Read 2 more answers

In a survey, a group of students were asked to name their favorite day of the week. There were 8 students who chose “other”.

lara [203]

5 % of the students choose other. 95% choose either Saturday or Sunday.
Let x be the number of students who participated.

(5/100) * x = 8 Multiply both sides by 100
5 * x = 8*100
5*x = 800 Divide by 5
x = 800/5
x = 160 students participated in the survey <<<<< Answer

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3 years ago

Amy and her friends have $12.50 to spend on lunch. They agree to share a

Anastaziya [24]

Good luck, I am not sure how to solve the next part of the question

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2 years ago