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2 years ago

Find the coordinates of the midpoint of ST with endpoints S(−2, −1) and T(1, −4)

Mathematics

1 answer:

seraphim [82]2 years ago

7 0

Answer:

( -1/2, -2 1/2)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates and divide by 2

( -2+1)/2 = -1/2

To find the y coordinate of the midpoint, add the y coordinates and divide by 2

( -1+-4)/2 = -5/2 = -2 1/2

( -1/2, -2 1/2)

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3 years ago

Jose wants to build a rectangular kennel for his dog. His dad will let him use a spot in the corner of the yard that is 12 feet

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Hello!

We don't need to find the exact perimeter of the fencing, just an estimate.

We will round 12 ft 3 in to 12 ft, because it is closer to 12 ft than 13 ft.

We will also round 8 ft 11 in to 9 ft because there are 12 inches in a foot, which makes 9 ft closer.

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3 years ago

A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Selec

Paraphin [41]

Answer:

A. The solutions are $x=3i,\:x=-3i$ .

B. The factored form of the quadratic expression $x^2+9=(x-3i)(x+3i)$

Step-by-step explanation:

A. To find the solutions to the quadratic equation $x^2+9=0$ you must:

$\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}$

$x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i$

The solutions are:

$x=3i,\:x=-3i$

B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.

To factor $x^2+9$ :

First, multiply the constant in the polynomial by $i^2$ where $i^2$ is equal to -1.

$x^2+9i^2$

Since both terms are perfect squares, factor using the difference of squares formula

$a^2-i^2=(a+i)(a-i)$

$x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)$

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3 years ago