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nydimaria [60]
3 years ago
10

HIJK is a rectangle. HJ=x and IK=2x-7 Find the length of each diagonal​

Mathematics
1 answer:
laila [671]3 years ago
3 0
The diagonals of a rectangle are congruent so set them equal to each other to get x = 2x - 7. isolate the variable (0 = x - 7 — x = 7) to get x = 7. the diagonals are seven.
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Sort each equation according to whether it has one solution, infinitely many solutions, or no solution.
Sedaia [141]

Answer:

Equations with one solution: -2(x-3) = 2x-6

Equations with no solution:

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Equations with infinite many solutions: -3(x-4) = -3x+12

Step-by-step explanation:

We will solve each equation to see if it has one solution, no solution or infinite many solutions.

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An equation with no solution has both sides different.

An equation with infinite solution will have both sides equal after solution(number)

So,

<u>Equation 1:</u>

5(x-2) = 5x-7

5(x-2) = 5x-7\\5x-10 = 5x-7\\5x-5x = -7+10\\0 = 3

As both sides are not equal, equation has no solution.

<u>Equation 2:</u>

-3(x-4) = -3x+12\\-3x+12 = -3x+12\\-3x+3x = -12+12\\0=0\\

As both sides are equal the equation has infinite many solutions.

<u>Equation 3:</u>

-2(x-3) = 2x-6\\-2x+6 = 2x-6\\-2x-2x = -6-6\\-4x = -12\\\frac{-4x}{-4} = \frac{-12}{-4}\\x = 3

As x=3, the equation has only one solution.

<u>Equation 4:</u>

6(x+5) = 6x+11\\6x+30 = 6x+11\\6x-6x+30 = 11\\30 =11

The equation has no solution.

Hence,

Equations with one solution: -2(x-3) = 2x-6

Equations with no solution:

6(x+5) = 6x+11\\5(x-2) = 5x-7

Equations with infinite many solutions: -3(x-4) = -3x+12

6 0
2 years ago
How do you change y=x^2-10x-6 into vertex form
In-s [12.5K]

Converting to vertex form is actually pretty simple so I think you might find something to help you out here. :)

https://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html

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