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2 years ago

Point A is at (3, -8) and point B is at (7, 3). Point M is the midpoint of point A and point B.

Mathematics

1 answer:

IgorC [24]2 years ago

7 0

The midpoint of point A and point B is (5, -2.5)

<h3>How to determine the midpoint?</h3>

The coordinates are given as:

A = (3, -8)

B = (7, -3)

The midpoint is calculated as:

(x, y) = 0.5 * (x1 + x2, y1 + y2)

So, we have:

(x, y) = 0.5 * (3 + 7, -8 + 3)

This gives

(x, y) = 0.5 * (10, -5)

Evaluate

(x, y) = (5, -2.5)

Hence, the midpoint of point A and point B is (5, -2.5)

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Carrie has 40 more nickels than Joan has dimes. They both have the same amount of money. How many coins does each girl have? Wha

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Answer:

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Step-by-step explanation:

Let be $x$ and $y$ the amounts of nickels and dimes that Carrie and Joan have, as $c$ the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.

The following equations are constructed after a careful reading on statement:

Carrie's amount of money:

$0.05\cdot x = c$ (Eq. 1)

Joan's amount of money:

$0.10\cdot y = c$ (Eq. 2)

Relation between amounts of coins:

$x = y+40$ (Eq. 3)

First we eliminate $c$ by equalizing (Eq. 1) and (Eq. 2):

$0.05\cdot x = 0.10\cdot y$

Then, we reduce the resulting formula by (Eq. 3):

$0.05\cdot (y+40) = 0.10\cdot y$

$y+40 = 2\cdot y$

$y = 40$

And rest of variable are now determined:

$x = 40+40$

$x = 80$

$c = 0.05\cdot (80)$

$c = 4$

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

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3 years ago

What are the equations of lines m and q? Please

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Answer:

Step-by-step explanation:

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3 years ago

A single card is drawn from a standard 52-card deck. Let B be the event that the card drawn is a black, and let F be the event

Galina-37 [17]

Answer:

0.6154 or 61.54%

Step-by-step explanation:

The joint probability P(B′∪F) is given by the sum of each individual probability minus the intersection between both probabilities (red face cards).

$P(B'\cup F) = P(B')+P(F)-P(B'\cap F)$

The inverse probability of a card being black is also the probability of a card being red, which is 26 in 52. There are 12 face cards in a 52-card deck, 6 of which are not black, therefore:

$P(B'\cup F) = \frac{26}{52} +\frac{12}{52}-\frac{6}{52}\\P(B'\cup F) = \frac{32}{52} = \frac{8}{13} =0.6154$