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3 years ago

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If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen

t to x from the second equation is substituted into the first equation. 3x + 2y = −21 x − 3y = 4

1 answer:

Svetllana [295]3 years ago

3 0

Hello,

$\left \{ {{3x+2y=-21} \atop {x-3y=4}} \right. \\\\
 \left \{ {{3x+2y=-21} \atop {x=4+3y}} \right. \\\\
 \left \{ {{3(4+3y)+2y=-21} \atop {x=4+3y}} \right. \\\\

 \left \{ {{12+9y+2y=-21} \atop {x=4+3y}} \right. \\\\
 \left \{ {{12+11y=-21} \atop {x=4+3y}} \right. \\\\
 \left \{ {{11y=-21-12} \atop {x=4+3y}} \right. \\\\
 \left \{ {{11y=-33} \atop {x=4+3y}} \right. \\\\
 \left \{ {{y=-3} \atop {x=4+3(-3)}} \right. \\\\
 \left \{ {{y=-3} \atop {x=5}} \right. \\\\
Sol=\{(5,-3)\}\\\\



$

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The sum of liz's and melinda's ages is 28. if liz was 1/3 melinda's age 6 years ago, how old will liz be next year?

Mrrafil [7]

The first thing we must do for this case is to define variables:
We have then:
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y: melinda's age
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Answer:
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Note: see attached image for the graphic solution.

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3 years ago

Consider the line =+3x6y−8 . what is the slope of a line parallel to this line? what is the slope of a line perpendicular to thi

Reil [10]

<span>Two lines are parallel if their slope is the same.
You want to write 8x + 4y = 5 in the form y = mx + b, where m represents the slope and b is the y-intercept.
We need to isolate y in the given equation. The number next to x is the slope.
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y = -2x + 5/4
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3 years ago

Find the missing side of the triangle. Round your answers to the nearest tenth if necessary.

Alik [6]

Given:

In a right angle triangle, the measures of two legs are 5 ft and 5.6 ft. The measure of the hypotenuse is x.

To find:

The value of x.

Solution:

Pythagoras theorem: In a right angle triangle,

$(Hypotenuse)^2=(Base)^2+(Perpendicular)^2$

Using Pythagoras theorem, we get

$(x)^2=(5)^2+(5.6)^2$

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$x^2=56.36$

Taking square root on both sides, we get

$x=\sqrt{56.36}$

$x=7.50733$

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The measure of missing side is 7.5 ft. Therefore, the correct option is D.

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3 years ago

Ana drinks chocolate milk out of glasses that each hold 1/8 of a leader. she has 7/10 of a liter of chocolate milk in her refrig

PIT_PIT [208]

Amount of chocolate milk Ana drinks = $\frac{1}{8}$ liter

Total amount of chocolate milk in refrigerator = $\frac{7}{10}$ liter

We have to determine the total number of glasses she will pour $\frac{1}{8}$ liter of milk from $\frac{7}{10}$ liter of milk.

Total number of glasses will be determined by dividing the total amount of milk by the amount of milk required for one glass

Total number of glasses = $\frac{7}{10} \div \frac{1}{8}$

= $\frac{7}{10} \times 8$

= $\frac{56}{10}$

= 5.6 glasses

So, 5.6 glasses will be poured from the given amount of chocolate milk.

3 0

3 years ago

The curve y = |x|/ 5 − x2 is called a bullet-nose curve. find an equation of the tangent line to this curve at the point (2, 2).

diamong [38]

We have the following curve:

$y=\frac{\left | x \right |}{5-x^2}$

So we need to find <span>an equation of the tangent line to this curve at the point $(2,2)$ . So let's find out if this point, in fact, belongs to the curve:

</span> $If \ x=2 \\ \\ y=\frac{\left | 2 \right |}{5-2^2}=\frac{\left | 2 \right |}{5-4}=2$ .
<span>
We also know that:

</span> $\left | x \right |= \left \{ {{x \ if \ x \ \geq 0} \atop {-x \ if \ x\ \textless \ 0}} \right.$ <span>

Given that the point is:

</span> $(2,2)\ that \ is: \\ x=2\ \textgreater \ 0$

Then we will say that:

$\left | x \right |=x$

Therefore:

$y=\frac{x}{5-x^2}$

Computing the derivative:

$y=\frac{x}{5-x^2} \\ \frac{dy}{dx}= \frac{(1)(5-x^2)-(-2x)x}{(5-x^2)^2}=\frac{5+x^2}{(5-x^2)^2}$

So the derivative solved for $x=2$ is in fact the slope of the line at the point $(2,2)$ , then:

$\frac{dy}{dx} |_{x=2}=\frac{5+x^2}{(5-x^2)^2}|_{x=2}=\frac{5+2^2}{(5-2^2)^2}=9 \\ \\ \therefore m=\frac{dy}{dx} |_{x=2}=9$

Finally, the tangent line is:

$y-y_1=m(x-x_1) \\ \therefore y-2=9(x-2) \\ \therefore \boxed{y=9x-16}$

<em>This is shown in the figure below.</em><span>
</span>

8 0

3 years ago