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3 years ago

BC = x + 14, AB = x + 10, AC = 22

1 answer:

4 0

$ab = x + 10 \\ bc = x + 14 \\ ac = 22 \\ (x + 10) + (x + 14) = 22 \\ x + x + 10 + 14 = 22 \\ 2x + 24 = 22 \\ 2x = 22 - 24 \\ 2x = - 2 \\ x = \frac{ -2}{2} \\ x = - 1$

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Find an equation of the circle that satisfies the given conditions.

hodyreva [135]

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

$P(-1,1) \\
x_1=-1 \\ y_1=1 \\ \\ Q(5,9) \\ x_2=5 \\ y_2=9 \\ \\
\frac{x_1+x_2}{2}=\frac{-1+5}{2}=\frac{4}{2}=2 \\ \frac{y_1+y_2}{2}=\frac{1+9}{2}=\frac{10}{2}=5$

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(-1,1) \\ x_1=-1 \\ y_1=1 \\ \\ (2,5) \\ x_2=2 \\ y_2=5 \\ \\ d=\sqrt{(2-(-1))^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

The radius is 5.

$(x-2)^2+(y-5)^2=5^2 \\
\boxed{(x-2)^2+(y-5)^2=25}$

4 0

3 years ago

Find the Slope for <br> (3,-4) and (5,4)

REY [17]

The picture below shows the formula for calculating slope

In this example:
y2 = 4
y1 = -4
x2 = 5
x1 = 3
(These are the numbers you substitute into the formula)

Calculations:
4 - (-4) = 8
5 - 3 = 2
8/2 = 4

As you can see, after the values are substituted into the equation & simplified, the slope is equal to 4

8 0

2 years ago

Read 2 more answers

Please!! 10 points but adding 5 more!! so 15 points!!

ololo11 [35]

1. 6+ -35 = -29

2. -29+ 6 = -35

1. 37 + -33 = 4

2. -33 + 4 = 37

5 0

3 years ago

Read 2 more answers

3. The odds of winning a bike is 7:15. The probability of winning a remote control car is 50%. For

Elenna [48]

50% - .5
7/15 - .46

the remote control car

5 0

2 years ago

c. Using a standard deck of 52 cards, the probability of selecting a 4 of diamonds or a 4 of hearts is an example of a mutually

dybincka [34]

Answer:

True

Step-by-step explanation:

If two events X and Y are mutually exclusive,

Then,

P(X∪Y) = P(X) + P(Y)

Let A represents the event of a diamond card and B represent the event of a heart card,

We know that,

In a deck of 52 cards there are 4 suit ( 13 Club cards, 13 heart cards, 13 diamond cards and 13 Spade cards )

That is, those cards which are heart can not be diamond card,

⇒ A ∩ B = ∅

⇒ P(A∩B) = 0

Since, P(A∪B) = P(A) + P(B) - P(A∩B)

⇒ P(A∪B) = P(A) + P(B)

By the above statement,

Events A and B are mutually exclusive,

Hence, the probability of selecting a 4 of diamonds or a 4 of hearts is an example of a mutually exclusive event is a true statement.

4 0

3 years ago