Vertical integration means that _________

Please help me with this problem:Which properties justify the steps taken to solve the system?{2x−4y=183x+3y=0Drag and drop the

Hatshy [7]

First step.

If we multiply by 3 the first equation and by 2 the second equation we get the first step:

$\begin{gathered} 6x-12y=54 \\ 6x+6y=0 \end{gathered}$

therefore, the answer for the first box is: Multiplication property of equality.

Second step.

If we subtract both equations, we have

$-18y=54$

then, the answer for the second box is: Subtraction property of equality

Third step.

By dividing both sides of our last result by -18, we get

$y=\frac{54}{-18}=-3$

then, the answer for the third step is: Division property of equality.

Fourth step.

Once we have obtained the result for variable y (which is -3), we need to find the result for variable x. So, by substituting our result for y into the first equation, we have

$2x-4(-3)=18$

Therefore, the answer for the fourth box is: Substitution property of equality.

Fifth step.

Then, by simplifying our last result, in which there is a product of -4 and -3, we get

$2x+12=18$

Thefore, the answer for the fifth box is: Simplify.

Sixth step.

Now, by subtracting 12 to both sides, we have

$2x=6$

then, the answer for the sixth box is: Subtraction property of equality.

Seventh step.

Finally, by dividing both sides by 2, we obtain

$x=3$

Then, the answer for the seventh box is: Division property of equality.

5 0

2 years ago

What is the perimeter of this title ?

Kryger [21]

Answer:

24 in

Step-by-step explanation:

Perimeter is adding the length of all the sides together. So, 10 + 6 + 8 = 24

7 0

3 years ago

Toby thinks of a number less than 15. He divides it by 2 and then he adds 4. He then divides it by 3. His awnser is 3. 5

satela [25.4K]

Answer:

The number he thought of was 13

Step-by-step explanation:

Revers the problem

3.5 * 3 = 10.5

10.5 - 4 = 6.5

6.5 * 2 = 13

7 0

3 years ago

there is a line includes the point (0,4) and has a slope of 7 what is its equation in slope-intercept form

Oliga [24]

Answer:

y=7x+4

Step-by-step explanation:

slope- intercept form is y=mx+c

m=7

so y=7x+c

substitute (0,4) into y=7x+c

so 4=(7x0)+c

c=4

so y=7x+4

3 0

3 years ago

Find the area enclosed between f(x)=0.3x2+7 and g(x)=x from x=−4 to x=8.

denis23 [38]

First, we sketch a picture to get a sense of the problem. g(x)=x is a diagonal line through (0,0) with slope = = 1. Since we are interested in the area between x = -4 and x = 8, we find the points on the line at these values. These are (-4, -4) and (8,8).

f(x) is a parabola. It's lowest point occurs when x = 0. It is the point (0,7). At x = -4 and x=8 it has the values 11.8 and 26.2 respectively. That is, it contains the points (-4, 11.8) and (8,26.2).

From these we make a rough sketch (see attachment). This is a sketch and mine is very incorrect when it comes to scale but what matters here is which of the curves is on top, which is below and whether they intersect anywhere in the interval, so my rough sketch is good enough. From the sketch we see that f(x) is always above (greater than) g(x).

To find the area between the curves over the given interval we integrate their difference and since f(x) is strictly greater than g(x) we subtract as follows: f(x) - g(x). The limits of integration are the values -4 and 8 (the x-values between which we are looking for the area.

Now let's integrate:
$\int\limits^{8}_ {-4}f(x)-g(x) \, dx = \int\limits^{8}_ {-4}.3 x^{2} +7-x \, dx$
The integral yields: $[tex](\frac{.3 (8)^{3} }{3} +7(8)- \frac{ (8)^{2} }{2}) -(\frac{.3 (-4)^{3} }{3} +7(-4)- \frac{ (-4)^{2} }{2}) = 117.6$ [/tex]
We evaluate this for 8 and for -4 subtracting the second FROM the first to get:

4 0

3 years ago

Vertical integration means that __________.