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3 years ago

Jill wants to solve the following system using the elimination method:

Mathematics

2 answers:

Mariulka [41]3 years ago

8 0

Answer:

-3

Step-by-step explanation:

To use the elimination method, we need the variable we want to eliminate to have the same coefficient number in both equations, but with the opposite sign. Thus, when adding the equations that variable will be eliminated.

The variable x in the first equation is the following:

and the x in the second equation is:

So we must multiply the first equation by -3, so it becomes:

-3y = -3x + 8

and we can see that now, the x's in both equation have the same coefficient number but a different sign (one positive and one negative) which is what we need to apply the elimination method.

asambeis [7]3 years ago

5 0

-3 as in the first equation x = 1x so multiply it by -3 you’ll get -3x.

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A ball is thrown from a height of 38 meters with an initial downward velocity of 3 m/s

ANTONII [103]

<h2>Hello!</h2>

The answer is:

The ball will hit the ground after $t=2.47s$

Since we are given a quadratic function, we can calculate the roots (zeroes) using the quadratic formula. We must take into consideration that we are talking about time, it means that we should only consider positive values.

So,

$\frac{-b+-\sqrt{b^{2} -4ac} }{2a}$

We are given the function:

$h=-5t^{2}-3t+38$

Where,

$a=-5\\b=-3\\c=38$

Then, substituting it into the quadratic equation, we have:

$\frac{-b+-\sqrt{b^{2} -4ac} }{2a}=\frac{-(-3)+-\sqrt{(-3)^{2} -4*-5*38} }{2*-5}\\\\\frac{-(-3)+-\sqrt{(-3)^{2} -4*-5*38} }{2*-5}=\frac{3+-\sqrt{9+760} }{-10}\\\\\frac{3+-\sqrt{9+760} }{-10}=\frac{3+-\sqrt{769} }{-10}=\frac{3+-27.731}{-10}\\\\t1=\frac{3+27.731}{-10}=-3.073s\\\\t2=\frac{3-27.731}{-10}=2.473s$

Since negative time does not exists, the ball will hit the ground after:

$t=2.473s=2.47s$

Have a nice day!

4 0

3 years ago

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The number of pepperoni slices that kim puts on a pizza varies directly as the square of the diameter of the pizza. If she puts

seropon [69]

You can make this into a fraction, and then simplify it.

15/10, right?

15/10 = 3/2

Then compare 3/2 to the rest of the equation

3/2 = x/16

2 * 8 = 16
so
3 * 8 = x
x = 24

Kim would put x number of pizza slices on her pizza.
So she would be putting on 24 slices on her pizza.

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2 years ago

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How can knowing how to represent proportional relationships in different ways be useful to solving problems

Anna35 [415]

Answer:

appropriately writing the proportion can reduce or eliminate steps required to solve it

Step-by-step explanation:

The proportion ...

$\dfrac{A}{B}=\dfrac{C}{D}$

is equivalent to the equation obtained by "cross-multiplying:"

AD = BC

This equation can be written as proportions in 3 other ways:

$\dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}$

Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.

I find this most useful to ...

a) put the unknown quantity in the numerator

b) give that unknown quantity a denominator of 1, if possible.

The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.

<u>Example</u>:

x/4 = 3/2

Usual method:

2x = 4·3

x = 12/2 = 6

Multiplying by the denominator:

x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step

<u>Example 2</u>:

x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...

x/1 = 4/2 . . . . . . written with 1 in the denominator

x = 2 . . . . simplify

Of course, this is the same answer you would get by multiplying by the denominator, 4.

The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.

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3 years ago

Tell whether the ratios form a proportion.

Alecsey [184]

No it does not form a proportion.
Proportion = equal
3 * 8 = 24
4 * 8 = 32 not 18

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3 years ago

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A Number is divided by 3. Then ,5 is added to the quotient snd the results is 8 what is the number

zheka24 [161]

Answer:

n=9

Explanation:

First, let's give a name to the number we are looking for and call it n.

So we can then write "A number is divided by 3" as n3

To add 5 to the quotient would then give us the expression n3+5

If this results in 8 we can finally write the equation we are trying to solve and solve the equation for n while keeping the equation balanced:

n3+5=8

n3+5−5=8−5

n3+0=3

n3=3

3⋅n3=3⋅3

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3 years ago

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