Can someone please professionally explain the math equations below. (Not just answer the question)

Mathematics

1 answer:

Rus_ich [418]3 years ago

4 0

Step-by-step explanation:

We will solve this system of equations using two methods: elimination and substitution.

Method 1: Elimination

2x - y = -8. #1

-5x + y = 26. #2

Note that by adding these two equations, the y-variable is eliminated (thus the name) and you're only left with an equation with one variable. So upon adding, we get

-3x = 18 or x = -6

Using this value for x, put this back in either one of the equations. Let's use the 2nd one.

-5(-6) + y = 26

--> 30 + y = 26

Moving 30 to the right side, we get y = -4.

Method 2: Substitution

This is done by isolating one variable to the left side in one equation and then using it on the other equation. Let's take equation #2 and put the y-variable on the left side and you should get

y = 5x + 26

Now use this equation and plug it into the y in equation #1:

2x - (5x + 26) = -8

--> 2x - 5x - 26 = -8

--> -3x = 26 - 8 = 18 or x = -6.

Use this value for x into either one of the equations. Let's use equation #1 this time.

2(-6) - y = -8

--> -12 + 8 = y or y = -4.

Notice that using either method will give you the same result, as one might expect.

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What place value would i put 805 tens in

AveGali [126]

In 805 tens this would result to 8,050 wherein 805 is multiplied by 10.

In using the place value chart, you put the 5 in the tens place still resulting to 8,050.

Therefor, eight thousands and 0 hundreds and 5 tens and 0 ones.

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3 years ago

A square is inscribed in a right triangle so that they have a common right angle. The legs of the triangle are 6 in and 8 in lon

IceJOKER [234]

Answer: Approximately 3.42857142857142 inches

Round this value however you need to. For instance, if you need to round to 2 decimal places, then the answer would be 3.43 inches.

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How I got this answer:

A square has side lengths that are the same value and it has four right angles. For example, a square could have all four sides equal to 7 inches. We want this square to fit snugly inside a right triangle. Put another way, we want this square as big as possible without it overflowing outside the triangle.

If one vertex of the square is at (0,0) then the opposite vertex will be on the line y = x meaning this opposite vertex's location is (x,x). The x refers to the side length of the square. Replace x with any number. Going back to the previous example, if x = 7 then the square has two opposite vertices at (0,0) and (x,x) = (7,7), so this square has side length of 7. We will use the equation y = x later on (see figure 2 in the attached images below). I marked (0,0) as point A and (x,x) as point D in figure 3.

We will also use the equation of the line that goes through the two points B(0,6) and C(8,0) as shown in figure 3. The line that goes through points B and C is the line that forms the hypotenuse of the right triangle. If we can find the equation of this line, then we can use algebra to find the intersection point D (see figure 3)

It turns out that the equation of the line through B and C is y = (-3/4)x + 6. Check out figure 1 in the attached images below to see how I got that.

Then head over to figure 2 to see how I'm using the two equations to solve for x. The exact solution is the fraction x = 24/7 which approximates to x = 3.42857142857142 and you can round this however you want for the final answer.