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9966 [12]
3 years ago
12

PLEASE HELP- John and Ariana bought school supplies. John spent $10.60 on 5 notebooks and 5 pens. Ariana spent $7.30 on 3 notebo

oks and 4 pens. What is the cost of 1 notebook & what is the cost of one pen? PLEASE HELP
Mathematics
1 answer:
stepan [7]3 years ago
7 0

Answer:

Cost of one notebook is 1.40 and one pen is1.40andonepenis0.90

Step-by-step explanation:

Let,

Notebook = x

Pen = y

According to given statements;

\begin{gathered}Multiplying\ Eqn\ 1\ by\ 4\ and Eqn\ 2\ by\ 5\\4(5x+4y=10.60)\\20x+16y=42.40 \ \ \ Eqn\ 3\\ 5(4x+3y=8.30)\\20x+15y=41.50 \ \ \ Eqn\ 4\\Subtracting\ Eqn\ 4\ from\ Eqn\ 3\\(20x+16y)-(20x+15y)=42.40-41.50\\20x+16y-20x-15y=0.90\\y=0.90\\Putting\ value\ of\ y\ in\ Eqn\ 1\\5x+4(0.90)=10.60\\5x+3.60=10.60\\5x=10.60-3.60\\5x=7\\Dividing\ both\ sides\ by\ 5\\\frac{5x}{5}=\frac{7}{5}\\x=1.40\end{gathered}Multiplying Eqn 1 by 4 andEqn 2 by 54(5x+4y=10.60)20x+16y=42.40   Eqn 35(4x+3y=8.30)20x+15y=41.50   Eqn 4Subtracting Eqn 4 from Eqn 3(20x+16y)−(20x+15y)=42.40−41.5020x+16y−20x−15y=0.90y=0.90Putting value of y in Eqn 15x+4(0.90)=10.605x+3.60=10.605x=10.60−3.605x=7Dividing both sides by 555x=57x=1.40

Cost of one notebook is 1.40 and one pen is1.40andonepenis0.90

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4 is greater than x, and x is greater than -7. Write the following as an inequality.
Artemon [7]

Answer:

4 > x > -7

Step-by-step explanation:

4 > x > -7

Because we usually put lower numbers to the left on a number line

the convention is to present this as

-7 < x < 4

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(1/8)(x+7). Just take the 1/8 out of the whole thing. You have 1/8 * x = 1/8x and 1/8 * 7 = 7/8.
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3 years ago
I need help plssss..
maw [93]

6x+42°=180°(ANGLES ON A STRAIGHT LINE)

6x = 180 - 42 \\ 6x = 138 \\  \frac{6x}{6}  =  \frac{138}{6}  \\ x = 23

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IF DF IS PERPENDICULAR TO AC IT MEANS m<DBC =90°m<DBE+m<EBC= m<DBC

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Hope THIS helps

5 0
1 year ago
For what values of x and y is the equation (x2 + y2)2 = (x2 – y2)2 + (2xy)2 true?
denis-greek [22]

Answer:

A) all values of x, and all values of y

B) (3a + 4b) (9a² − 12ab + 16b²)

Step-by-step explanation:

(x² + y²)² = (x² − y²)² + (2xy)²

x⁴ + 2x²y² + y⁴ = x⁴ − 2x²y² + y⁴ + 4x²y²

x⁴ + 2x²y² + y⁴ = x⁴ + 2x²y² + y⁴

27a³ + 64b³

(3a)³ + (4b)³

(3a + 4b) (9a² − 12ab + 16b²)

6 0
2 years ago
SOMEONE HELP ASAP!!
Anuta_ua [19.1K]

9514 1404 393

Answer:

  (c)  dZ/dt = 11/√544, so moving away at about 0.47 m/s

Step-by-step explanation:

The (x, y) coordinates of the car are related by the fact that they are on a circle centered at (12, 7) with a radius of 5. Then their rates of change are related by the derivative of the circle equation with respect to time.

  (x -12)^2 + (y -7)^2 = 25

  2(x -12)x' +2(y -7)y' = 0

  y' = -(x -12)/(y -7)x'

At the time and point of interest, we have ...

  y' = -(15 -12)/(11 -7)(1) = -3/4

__

The distance (z) to the observer is given by the Pythagorean theorem:

  z^2 = (x -0)^2 +(y -2)^2

and its rate of change with time is ...

  2z·z' = 2(x-0)x' +2(y -2)y'

The distance d at the point of interest is ...

  z = √((15 -0)^2 +(11 -2)^2) = √(225 +81) = √306 = 3√34

So, the rate of change of distance to the observer at the time and point of interest is ...

  z' = (x(x') +(y -2)y')/z

  z' = ((15)(1) +(11-2)(-3/4))/(3√34) = (33/4)/(3√34)

  z' = 11/√544 ≈ 0.47 . . . m/s

3 0
3 years ago
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