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3 years ago

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In my closet I have 7 pairs of jeans and 4 pairs of slacks. I need to pack 6 of these items on vacation. In how many different w

ays could I pack at least 4 pairs of jeans?

1 answer:

jeka57 [31]3 years ago

3 0

You can have 3 ways.................... ;)

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Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

Read 2 more answers

How do you answer this

Elanso [62]

Okay so you take the 12 feet I'm pretty sure you multiply 12 and 30 and then that's one of your answers and then the 12 and a 75 you must put those to together and that's an answer and you subtract your 12 x 30 and you're 12 x 75 and that's how you get your answer I am pretty sure that's how you and that's how you get your answer I am pretty sure that's how you do it

5 0

3 years ago

Alice is playing checkers against a computer and has won 8 games out of the 12 she’s played so far

den301095 [7]

I do not know what kind of answer you may want but here is a few you might be asking for

(1). Every 12 games Alice wins 8 games and looses 4. ( 8/12 )

(2). Alice wins 2/3 games against a computer. ( 8/12 )

(3). Alice wins 66% of games she plays against a computer.

There you go.

3 0

3 years ago

Complete the given diagram by dragging expressions to each leg of the triangle. Then, correctly complete the equation to derive

Nimfa-mama [501]

The equation to derive the distance d is $\sqrt{(x2-x1)^2+(y2-y1)^2}$ . The lengths of the other legs of the given triangle are (y2 - y1) and (x2 - x1).

<h3>What is the formula for calculating the distance between two points?</h3>

Consider the two points (x1, y1) and (x2, y2)

The formula used for calculating the distance between the two points is

distance = $\sqrt{(x2-x1)^2+(y2-y1)^2}$

<h3>Calculation:</h3>

Given that,

The triangle in the graph has vertices (x1, y1), (x2, y2), and (x2, y1)

Since this triangle makes 90°, it is a right-angled triangle.

Hypotenuse = (x1, y1) to (x2, y2), Adjacent = (x1, y1) to (x2,y1), and Opposite = (x2, y1) to (x2, y2).

Consider the length of the hypotenuse = d

So, using the distance formula, the length of the hypotenuse(d) is,

$d = \sqrt{(x2-x1)^2+(y2-y1)^2}$

And the lengths of the other two legs of the given triangle are,

Length of the adjacent side: (x1, y1) to (x2,y1)

= $\sqrt{(x2-x1)^2+(y1-y1)^2}$

= $\sqrt{(x2-x1)^2+0}$

= $(x2-x1)$

Length of the opposite side: (x2, y1) to (x2, y2)

= $\sqrt{(x2-x2)^2+(y2-y1)^2}$

= $\sqrt{0+(y2-y1)^2}$

= $(y2-y1)$

Therefore, the derived distances for the given triangle are:

$d=\sqrt{(x2-x1)^2+(y2-y1)^2}$ , (x2 - x1), and (y2 - y1).

Learn more about the distance between two points here:

brainly.com/question/661229

#SPJ1

4 0

2 years ago

PLEASEEEEEEEE HELP

Rama09 [41]

Answer:

Using the point-slope form:

The equation of the line is given by:

$y-y_1 =m(x-x_1)$ .....[1] where

m is the slope of the line and $(x_1, y_1)$ is the point on the line.

As per the statement:

Given: Two points i,e (34, 76) and (42, 91)

First calculate slope(m):

Slope is given by:

$\text{Slope} = \frac{y_2-y_1}{x_2-x_1}$

Substitute the given values we have;

$\text{Slope (m)} = \frac{91-76}{42-34}=\frac{15}{8}=1.875$

Now, substitute the value of m and (34, 76) in [1] we have;

$y-76 =1.875(x-34)$

Using distributive property: $a \cdot (b+c) = a\cdot b+ a\cdot c$

$y-76 =1.875x-63.75$

Add 76 to both sides we get;

$y=1.875x+76$

Therefore, the equation of the trend line is: $y=1.875x+76$

8 0

3 years ago

Read 2 more answers