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2 years ago

Find the midpoint M of the line segment joining the points C = (-1, -1) and D = (5, -5).

Mathematics

1 answer:

Nadusha1986 [10]2 years ago

7 0

Answer:

The midpoint between the joining points C and D is (2, -3)

Step-by-step explanation:

How to find a midpoint

1: Label the coordinates(x₁,y₁) and (x₂,y₂).

2: Input the values into the formula.

3: Add the values in the parentheses and divide each result by 2.

4: The new values form the new coordinates of the midpoint.

Suppose we have a line segment and want to cut that section into two equal parts. To do so, we need to know the center. We can achieve this by finding the midpoint. You could measure with a ruler or just use a formula involving the coordinates of each endpoint of the segment. The midpoint is simply the average of each coordinate of the section, forming a new coordinate point. We shall illustrate this below.

Midpoint formula

If we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. This forms a new coordinate you can call (x₃,y₃). It is possible to divide a line segment into any given ratio, not just 1:1.

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Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.5

Fynjy0 [20]

Answer:

Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

Step-by-step explanation:

Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.

Since a total of 14 cups of coffee was served:

$a+b+c=14$

A total of 204 ounces of coffee was served. Therefore:

$10a+14b+20c=204$

A total of $16.70 was collected. Hence:

$0.95a+1.15b+1.5c=16.7$

This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.

From the first equation, let's subtract a and b from both sides:

$c=14-a-b$

Substitute this into both the second and third equations:

$10a+14b+20(14-a-b)=204$

And:

$0.95a+1.15b+1.5(14-a-b)=16.7$

In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:

For the Second Equation:

$\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}$

And for the Third:

$\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}$

We can solve this using substitution. From the second equation, isolate a:

$\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b$

Substitute into the third:

$-0.55(7.6-0.6b)-0.35b=-4.3$

Distribute and simplify:

$-4.18+0.33b-0.35b=-4.3$

Therefore:

$-0.02b=-0.12\Rightarrow b=6$

Using the equation for a:

$a=7.6-0.6(6)=4$

And using the equation for c:

$c=14-(4)-(6)=14-10=4$

Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

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3 years ago

Solve for x 7(x - 3) = 4(x + 5)

Advocard [28]

Answer:

13 2/3

Step-by-step explanation:

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2 years ago

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3 years ago

I NEED HELP...finding the slope-intercept form equation

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Answer: y=-13/12x-7

Step-by-step explanation:

To find the slope-intercept form, we first need to find the slope. To find the slope, you use the formula $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ . We use the two given points to find the slope.

$m=\frac{32-6}{-36-(-12)} =\frac{26}{-24} =-\frac{13}{12}$

Now that we have our slope, we can start filling out the slope-intercept form equation.

y=mx+b

y=-13/12x+b

Since we don't know the y-intercept, we can use one of the given points and solve for b.

6=(-13/12)(-12)+b [multiply (-13/12) and -12]

6=13+b [subtract both sides by 13]

b=-7

With the y-intercept, we can complete our equation.

y=-13/12x-7

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3 years ago

Find the midpoint M of the line segment joining the points C = (-1, -1) and D = (5, -5). ​

Find the midpoint M of the line segment joining the points C = (-1, -1) and D = (5, -5).