MATHEMATICS HIGH SCHOOL

Point m is the midpoint of line ab. if the coordinates of m are 2,8) and the coordinates of a are (10,12) what are the coordinates of b

Answers

Answer 1

Answer:

midpoint = (2, 8)

coordinate a = (10. 12)

let coordinate b = (x, y)

Find x:

0.5(10 + x) = 2

10 + x = 4

x = 4 - 10

x = -6

Find y:

0.5(12 + y) = 8

12 + y = 16

y = 16 - 12

y = 4

Answer: Coordinate b = (-6, 4)

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Molly is filling a pitcher that holds 2 gallons of water. She is filling the pitcher with a 1-cup measuring cup. How many times will she have to fill the cup 1-cup measuring cup to fill the pitcher

Answers

Answer:

32 times

Step-by-step explanation:

Molly is filling a pitcher that holds 2 gallons of water.

1 gallon = 16 cups

So, 2 gallons = $16* 2=32 cups$

So, it requires 32 cups to fill the pitcher.

Since we are given that She is filling the pitcher with a 1-cup measuring cup.

So, no. of times she will have to fill the cup 1-cup measuring cup to fill the pitcher = $(32)/(1)=32$

Hence she will need to fill cup 1-cup measuring cup 32 times to fill the pitcher.

2 cups in a pint
2 pints to a quart (therefore 4 cups to a quart)
4 quarts to a gallon (therefore 16 cups to a gallon)
And finally 2 gallons to 2 gallons (therefore 32 cups to 2 gallons)

32 times

How do you solve x to the second power +7x=O

Answers

well the answer is 0 because if anything = 0 then it has to be multiplied by 0 so x = 0

x^2+7x=0
use the square root something....
(7/2)^2=49/4(add it to both sides)
x^2+7x+49/4=49/4
(x+7/2)^2=49/4
x+7/2=posinega 7/2
x=0 or x=-7

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)

Answers

For this case we have the following functions:
$f (x) = 4 - x ^ 2 g (x) = 6x$
The first thing we must do is subtract both functions.
We have then:
$(g - f) (x) = g (x) - f (x)$
Substituting values we have:
$(g - f) (x) = (6x) - (4 - x ^ 2)$
Rewriting we have:
$(g - f) (x) = x ^ 2 + 6x - 4$
Then, we evaluate the function for x = 3.
We have then:
$(g - f) (3) = 3 ^ 2 + 6 (3) - 4$
Rewriting:
$(g - f) (3) = 9 + 18 - 4 (g - f) (3) = 23$
Answer:
An expression that is equivalent to (g - f) (3) is:
$(g - f) (3) = 23$

Answer:

$(g-f)(3)=23$

Step-by-step explanation:

Given : $f(x) = 4 -x^2$ and $g(x) = 6x$

To find : The value of $(g -f)(3)$

Solution :

First we find the value of (g-f)

$(g-f)(x)= g(x)-f(x)$

$(g-f)(x)=6x-(4-x^2)$

$(g-f)(x)=6x-4+x^2$

Now, put the value of x=3

$(g-f)(3)=6(3)-4+(3)^2$

$(g-f)(3)=18-4+9$

$(g-f)(3)=23$

Therefore, $(g-f)(3)=23$

Austin takes 1 minute and 45 seconds to run three-quarters of a circular track answer

Answers

Let's take full circular length is M
Time taken to reach M/3 is 1min and 45 seconds which is 105 seconds.

Time taken to reach full M
105 seconds / (1/3)
105*3
315 seconds
5 min 15 seconds

What is the solution to 2x+12=5x-9

Answers

so 2x+12=5x-9
you want all of the unknowns on one side and all of the known values on the other or
subtract 2x from both sides
12=3x-9
add 9 to both sides
21=3x
divide both sides by 3
7=x

$2x+12=5x-9\ \ \ \ |combine\ like\ terms\n\n2x-5x=-9-12\ \ \ \ \ |simplify\n\n-3x=-21\ \ \ \ \ |:-3\n\nx=7$

A computer simulation tossed a 10-faced die 5 times. How many possible outcomes exist?

Answers

The answer to the problem wherein a computer simulation tossed a 10-faced die 5 times and you have to compute for the possible outcomes is simple. The answer is 18,144, 000 possible outcomes (if it's a combination). I got this through simply getting the 10! (3,628,800) and multiplying it 5.

However, if order is important (permutation), the number of possible outcomes is is 30240.

Answer:

B 100,000

Step-by-step explanation:

10^5 = 100,000

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