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3 years ago

Find the values of both x and y?

Mathematics

1 answer:

dlinn [17]3 years ago

8 0

$Answer: \\ 2x + 3y = 12 \: \vee \: 30x + 11y = 112 \\\Leftrightarrow 30x + 45y = 180 \: (1)\: \vee \:30x + 11y = 112 \: (2) \\ (1) - (2)\Rightarrow 34y = 68\Rightarrow y = 2 \\ 2x + 3 \times 2 = 12\Rightarrow x = 3$

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You saved $300 to spend over the summer. You decide to budget $50 to spend each week.

Oduvanchick [21]

Answer:

Part c)

The Slope of the line is: m=-50 and represents the amount of money spent per week.

Part d)

The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

Step-by-step explanation:

To solve this question we shall look at linear equations of the simplest form reading:

$y = mx+c$ Eqn(1).

where:

$y$ : is our dependent variable that changes as a function of x

$x$ : is our independent variable that 'controls' our equation of y

$m$ : is the slope of the line

$c$ : is our y-intercept assuming an $x$ ⇔ $y$ relationship graph.

This means that as $x$ changes so does $y$ as a result.

Given Information:

Here we know that $300 is our Total budget and thus our maximum value (of money) we can spend, so with respect to Eqn (1) here:

$c=300$

The budget of $50 here denotes the slope of the line, thus how much money is spend per week, so with respect to Eqn (1) here:

$m=50$

So finally we have the following linear equation of:

$y= - 50x + 300$ Eqn(2).

Notice here our negative sign on the slope of the line. This is simply because as the weeks pass by, we spend money therefore our original total of $300 will be decreasing by $50 per week.

So with respect to Eqn(2), and different weeks thus various $x$ values we have:

Week 1: $x=1$ we have $y= -50 *1 + 300 = -50 +300 = 250$ dollars.

Week 2: $x=2$ we have $y= -50 *2 + 300 = -100 +300 = 200$ dollars.

Thus having understood the above we can comment on the questions asked as follow:

Part c)

The Slope of the line is: $m=-50$ and represents the amount of money spent per week.

Part d)

The y-intercept is: $c=300$ and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

4 0

3 years ago

How do you go about doing this surface area problem?

hammer [34]

Break it down into 2-Dimensional shapes. Then add the areas together.

From the picture you can see;
front & back rectangles are 2*(4 x 8) = 64 m²
2 side rectangles are 2*(4 x 12) = 56 m²
2 triangular front & back pieces are (1/2)*8*3 = 12 m²
2 roof rectangles are 2*(5 x 12) = 120 m²

total Surface area = 64 m² + 56 m² + 12 m² + 120 m²
= 252 m²

For the volume; break it up into 3-dimenssional shapes and add the volumes together.

From the picture you can see;
Rectangular box volume is 4 x 8 x 12 = 384 m³
Triangular roof volume is area of front triangle multiplied through the length. (1/2)*8*3* 12 = 144 m³

Total volume = 384 m³ + 144 m³
= 528 m³

5 0

3 years ago

Alice wants to fence in a rectangular pay area for her rabbits. The length of the area should be at least 20ft, and the distance

dlinn [17]

This looks like common core which is never straight forward.It seems as though they are asking for the perimeter and not area,since they used feet for the distance around instead of sq.ft.

6 0

3 years ago

What is 68×53 pllllllzzz

Contact [7]

If my calculations are right 68 times 53 is 3,604

4 0

3 years ago

Read 2 more answers

Select the property that allows the statement 3=x to be written x=3

laiz [17]

My guess would be distributive. i maybe be wrong so don't get mad if I'm wrong.

3 0

3 years ago