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3 years ago

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CAN ANYONE HELP ME PLEASE? Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and fo

ur children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.

1 answer:

arsen [322]3 years ago

4 0

Answer:

The adult ticket costs $18 and the children ticket costs $13.

Step-by-step explanation:

Let the price of the adult ticket be a.

Let the price of the children ticket be c.

Three adults and four children must pay $106. This implies that:

3a + 4c = 106 _______(1)

Two adults and three children must pay $75. This implies that:

2a + 3c = 75 ________(2)

We have two simultaneous equations:

3a + 4c = 106 _____(1)

2a + 3c = 75 ______(2)

Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):

6a + 9c = 225

- <u>(6a + 8c = 212)</u>

c = $13

Put this value of c in (2):

2a + 3*13 = 75

2a + 39 = 75

=> 2a = 75 - 39

2a = 36

a = 36/2 = $18

Therefore, the adult ticket costs $18 and the children ticket costs $13.

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Duffy was analyzing the trajectory made after throwing a football. his coach was able to measure that his throw reached a maximu

gregori [183]

Answer:

4.35 seconds.

Step-by-step explanation:

Let x represent the time the independent variable and y be dependent variable (height of the ball).

We are told that Duffy figured that the ball left his hand at a height of 5 feet. This means at x equals 0, y was 5 or initial height of ball is 5 feet.

We have been given that Duffy's coach measured that his throw reached a maximum height of 18 feet after 2 seconds. This means that at x equals 2 y was 18.

As point (2,18) represents maximum height of ball, so it will be vertex of parabola.

Since initial height of ball is less than maximum height, so our parabola will be downward opening and leading coefficient will be negative.

We know that vertex form of a downward opening parabola is in form: $y=-a(x-h)^2+k$

$y=-a(x-2)^2+18$

Let us find value of a using point (0,5).

$5=-a(0-2)^2+18$

$5=-a*4+18$

$5-18=-a*4+18-18$

$-13=-4a$

$\frac{-13}{-4}=\frac{-4a}{-4}$

$\frac{13}{4}=a$

Therefore, the equation $y=-(\frac{13}{4})(x-2)^2+18$ can be used to find the height of ball after x seconds.

To find the time it will take the ball to hit the ground, we will substitute y equals 0 in our equation.

$0=-(\frac{13}{4})(x-2)^2+18$

$0-18=-(\frac{13}{4})(x-2)^2+18-18$

$0-18=-(\frac{13}{4})(x-2)^2$

$-18*(\frac{4}{13})=-(x-2)^2$

$\frac{72}{13}=(x-2)^2$

Taking square root of both sides of our equation we will get,

$\sqrt{\frac{72}{13}}=x-2$

$x-2\pm 2.35339$

$x-2=2.35339\text{ (or) } x-2=2.35339$

$x-2+2=2.35339+2\text{ (or) } x-2+2=-2.35339+2$

$x=4.35339\text{ (or) } x=-0.35339$

$x\approx 4.35\text{ (or) } x\approx -0.35$

Since time can not be negative, therefore, the ball will hit the ground approximately after 4.35 seconds.

7 0

2 years ago

You are driving along the coast at 45 mph. How many minutes should it take you to get to Ventura?

valkas [14]

45 miles per hour is 3/4 mile per minute. Divide 4.8 by 0.75.

3 0

3 years ago

Graph y=-6(3)^x<br><br> please do the table and the graph <br><br> 20 POINTS!

Margarita [4]

Answer:

<em>Explanation to the answer below... (Answers in the Explanation</em><em>)</em>

Step-by-step explanation:

We Know that our rule is y = $y = -6(3)^{x}$ , which means we can use this rule to find y from x. Since we don't know what X, is, we have to assume numbers like 1, to 7. And there is no space to write on the graph, I'll put a virtual copy of a graph.

1st Point,

$y = -6(3)^{x}\\y = -6(3)^{1}\\y = -6(3)\\y = -18\\x = 1, y = -18$

2nd, point

$y = -6(3)^x\\ y = -6(3)^2\\y = -6(9)\\y = -54\\x = 2, y = -54$

3rd Point

$y = -6(3)^x\\y = -6(3)^3\\y = -6(27)\\y = -162\\x = 3, y = -162$

4th Point

$y = -6(3)^4\\y = -6(81)\\y = -486\\x = 4, y = -486\\$

5th Point

$y = -6(3)^5\\y = -6(243)\\y = -1458\\\x = 5, y = -1458$

6th Point

$y = -6(3)^x\\y = -6(3)^6\\y = -6(729)\\y = -4,374\\x = 6, y = -4,374\\$

7th Point (Last Point)

$y = -6(3)^x\\y = -6(3)^7\\y = -6(2,187)\\y. = -13,122\\x = 7, y = -13,122$

Let's now plot them on the Graph, the values are so big, the graph might look a little odd.

Always remember that we can continue the points infinitely, and there is no stop, The Graph is attached below...

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2 years ago

Because of the commutative property of multiplication 3/4X4=4X3/4 However these expressions can be calculated in different ways

elena55 [62]

Answer:

We obtain same product by both the methods.

Step-by-step explanation:

We are given the following in the question:

Commutative property of multiplication:

$\dfrac{3}{4}\times 4 =4\times \dfrac{3}{4}$

Different ways to find the product:

1. First way

$\dfrac{3}{4}\times 4\\\\=3\times \dfrac{4}{4}\\\\=3$

2. Second way

$\dfrac{3}{4}\times 4\\\\=\dfrac{12}{4}\\\\=3$

We get the same product for both the calculations.

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3 years ago

Ap:3, 2, 1....<br>what is its coomon difference

Nastasia [14]

Answer:

-1

Step-by-step explanation:

3-1=2

2-1=1

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1 year ago