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3 years ago

15

Midpoint of (16,5) and (-6,-9)?

1 answer:

Zigmanuir [339]3 years ago

8 0

To solve this problem, we need to use the midpoint formula, where M = (x1+x2/2, y1+y2/2). To solve, we must plug in the given (x,y) values from our ordered pairs and then simplify, shown below:

(x1+x2/2, y1+y2/2)

( (16 + -6)/2, (5 + -9)/2 )

Now, we can begin to simplify by computing the addition in the numerators of both fractions.

(10/2, -4/2)

Next, we can finish the simplification process by dividing these fractions.

(5, -2)

Therefore, the midpoint of (16,5) and (-6,-9) is (5,-2).

Hope this helps!

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Which equation has infinitely many solutions? A) 4x + 3 3 = 4x + 5 B) 10x + 8 2 = 5x + 4 C) 8x − 5 3 = 2x − 2 D) 8x − 5 2 = 4x −

abruzzese [7]

Answer: If the left side and the right side of the equation are equal, the equations has infinitely many solutions.

Step-by-step explanation:

The options are not clear, so I will give you a general explanation of the procedure you can use to solve this exercise.

The Slope-Intercept form of the equation of a line is the following:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

For this exercise you need to remember that, given a System of Linear equations, if they are exactly the same line, then the System of equations has Infinitely many solutions.

If you have the following system:

$\left \{ {{y=2x+1} \atop {y=\frac{12}{6}x+1}} \right.$

You can simplify the second one:

$y=2x+1$

Then, both equations are the same line.

By definition you can also write the systemf making both equations equal to each other:

$2x+1=2x+1$

So, if the left side and the right side are equal, the equations has infinitely many solutions.

3 0

3 years ago

A culture started with 3000 bacteria. After 2 hours it grew to 3300 bacteria. Predict how many bacteria will be present after 16

bixtya [17]

Answer:

$6,430\ bacteria$

Step-by-step explanation:

we have a exponential function of the form

$y=a(1+r)^{x}$

where

y is the population of bacteria

a is the initial value

r is the rate of growth

x is the number of hours

we have

a=3,000 bacteria

$y=3,000(1+r)^{x}$

For x=2, y=3,300

substitute

$3,300=3,000(1+r)^{2}$

$(3,300/3,000)=(1+r)^{2}$

Apply square root both sides

$1+r=\sqrt{3.3/3}$

$r=\sqrt{3.3/3}-1$

$r=0.0488$

$r=4.88\%$

substitute in the equation

$y=3,000(1+0.0488)^{x}$

$y=3,000(1.0488)^{x}$

<u><em>Predict how many bacteria will be present after 16 hours</em></u>

For x=16 hours

substitute

$y=3,000(1.0488)^{16}$

$y=6,430\ bacteria$

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3 years ago

What is 0.5 repeating as a fraction in simplest form

Solnce55 [7]

Answer:

5/9

Step-by-step explanation:

Start be letting x = 0.555...

Our original equation is:

x = 0.555...

There is only one digit repeating, the 5, so we multiply both sides of that equation by 10 and write it above the original equation.

10x = 5.555...

x = 0.555...

Now we subtract the second equation from the first equation as written above.

9x = 5

Divide both sides by 9.

x = 5/9

0.555... = 5/9

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3 years ago

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2 years ago

Find the measure of each angle (in degrees) of

d1i1m1o1n [39]

Answer:

∠A = 88°

∠B = 92°

∠C = 88°

∠D = 92°

Step-by-step explanation:

∠A + ∠B = 180°

(2x + 4) + (3x - 34) = 180

reduce:

5x - 30 = 180

5x = 210

x = 42

∠A = 2(42) + 4 = 88°

∠B = 3(42) -34 = 92°

∠C = ∠A = 88°

∠D = ∠B = 92°

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3 years ago