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faust18 [17]
2 years ago
8

Find the value of x such that the area of a triangle whose vertices have coordinates (6, 5), (8, 2) and (x, 11) is 15 square uni

ts.
Mathematics
1 answer:
Serjik [45]2 years ago
3 0

Answer:

x =12\ or\ -8

Step-by-step explanation:

Given

(x_1,y_1) = (6,5)

(x_2,y_2) = (8,2)

(x_3,y_3) = (x,11)

Area = 15

Required

Find x

The area is calculated as thus:

Area = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|

Substitute values

15 = \frac{1}{2}|6*(2 - 11) + 8*(11 - 5) + x(5 - 2)|

15 = \frac{1}{2}|6*(-9) + 8*(6) + x(3)|

15 = \frac{1}{2}|-54 + 48 + 3x|

15 = \frac{1}{2}|-6 + 3x|

Multiply through by 2

2 * 15 = \frac{1}{2}|-6 + 3x| * 2

30 = |-6 + 3x|

Remove absolute sign

30 = -6 + 3x\ or\ -30 = -6 + 3x

Add 6 to both sides

36 = 3x\ or\ -24 =  3x

Divide by 3

12 = x\ or\ -8 = x

x =12\ or\ -8

<em>So, the coordinates are (-8, 11) or (12,11)</em>

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Due to lace of funding,the number of students enrolled at the city college went from 7000 last year to 4000 this year . Fine the
AlladinOne [14]

There is 42.8% of decrease in enrollment comparing to previous year.

42.8% of 7000 is 3000 which is the difference. Just divide 3000/7000 to get the numbers

In other words, new enrollmeny is 57.1% of the previous one


7 0
3 years ago
What is the center and radius of -10x = -121 - y2 - x2 -22y
OlgaM077 [116]

We need to find the center and the radius of

-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y

The general circle equation is the following

(x-h)^2+(y-k)^2=r^2

where

(h,k) is the center and

r is the radius

1. rearrange the equation

(x^2-10x)+(y^2+22y+121)=0

2. Add 25 on both sides

(x^2-10x+25)+(y^2+22y+121)=25

3. Factor

(x-5)^2+(y+11)^2=5^2

Now we have an equation that is very similar to the circle equation, so let's compare them

Center -> (h,k) = (5,-11)

radius -> r = 5

8 0
1 year ago
A veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses
Licemer1 [7]

Answer:

Probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

Step-by-step explanation:

We are given that a veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses with colic is 12 years. The average age of all horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of all horses coming to the veterinary clinic is 8 years.

So, firstly according to Central limit theorem the z score probability distribution for sample means is given by;

                    Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \bar X = average age of the random sample of horses with colic = 12 yrs

            \mu = average age of all horses seen at the veterinary clinic = 10 yrs

   \sigma = standard deviation of all horses coming to the veterinary clinic = 8 yrs

         n = sample of horses = 60

So, probability that a sample mean is 12 or larger for a sample from the horse population is given by = P(\bar X \geq 12)

   P(\bar X \geq 12) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } \geq \frac{12-10}{\frac{8}{\sqrt{60} } } ) = P(Z \geq 1.94) = 1 - P(Z < 1.94)

                                                 = 1 - 0.97381 = 0.0262

Therefore, probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

4 0
3 years ago
If you multiplied 3x37, would the product be an even number or an odd number?
choli [55]
The answer would be an odd number, 111.
8 0
3 years ago
Whats 85 divided by 1500 rounded but like done already​
Yuri [45]

Answer is 17.647 or if rounded 18

5 0
3 years ago
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