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3 years ago

Find the distance BF for the points B(1,-1) and F(-3,5)

1 answer:

Nadusha1986 [10]3 years ago

6 0

Use the distance formula:
 $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Plug in the given coordinates:
 $\sqrt{(-3-1)^2 + (5-(-1))^2}$

Simplify:
 $\sqrt{(-3-1)^2 + (5+1))^2}$

$\sqrt{-4^2+ 6^2}$

$\sqrt{16+36}$

$\sqrt{52}$
You can leave it as: $\sqrt{52}$ or in decimal form as: 7.2

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Solve the equation, and check the solutions 2(√x+3)=6.

zhannawk [14.2K]

Answer:

x = 0

Step-by-step explanation:

$2(\sqrt{x}+3)=6$

Expanding the left hand side we get

$\Rightarrow 2\sqrt{x}+6=6$

Taking 6 from left hand side to right hand side

$\Rightarrow 2\sqrt{x}=6-6\\\Rightarrow 2\sqrt{x}=0$

Dividing both sides by 2

$\Rightarrow \sqrt{x}=\frac{0}{2}\\\Rightarrow \sqrt{x}=0\\\Rightarrow x=0$

So, x = 0

4 0

3 years ago

How to solve this question

VMariaS [17]

The variance method is as follows.

-Sum the squares of the values in data set, and then divide by the number of values in data set
- From that, subtract the square of the mean (add all values and divide by number of values in the data set)

Our variance is

 $\displaystyle\sigma^2 = \frac{2^2 + 5^2 + m^2}{3} - \left(\frac{2 + 5 + m}{3}\right)^2$

Since variance has to be 14, we set $\sigma^2 = 14$ and solve for m

$14= \frac{4 + 25 + m^2}{3} - \left(\frac{7 + m}{3}\right)^2\ \Rightarrow \\ \\
14 = \frac{29}{3} + \frac{1}{3}m^2 - \frac{1}{9}(7+m)^2 \\ \\
14 = \frac{29}{3}+ \frac{1}{3}m^2 - \frac{1}{9}(49 + 14m + m^2) \\ \\
14 = \frac{29}{3}+ \frac{1}{3}m^2 - \frac{49}{9}- \frac{14}{9}m- \frac{1}{9}m^2 \\ \\
0 = \frac{-88}{9} -\frac{14}{9}m + \frac{2}{9}m^2
$

quadratic formula

$m = \displaystyle\frac{-b \pm \sqrt{b^2 -4ac}}{2a} \\
m = \frac{-(-\frac{14}{9}) \pm \sqrt{\left(-\frac{14}{9}\right)^2 - 4(2/9)(-88/9)} }{2(2/9)} \\
m = \frac{\frac{14}{9} \pm \sqrt{ \frac{196}{81} + \frac{704}{81} } }{\frac{4}{9} } \\
m = \frac{\frac{14}{9} \pm \sqrt{ \frac{900}{81} } }{\frac{4}{9} } \\
m = \frac{\frac{14}{9} \pm \sqrt{ \frac{100}{9} } }{\frac{4}{9} } \\
m = \frac{\frac{14}{9} \pm \frac{10}{3} }{\frac{4}{9} } \\
m = 11, -4$

-4 doesnt' work as it is not a positive integer

m = 11

5 0

3 years ago

On a particular Saturday, 60% of the visitors to an art museum were students. If 144 students visited the museum, how many total

pentagon [3]

Hello! To solve this question, we can write and solve a proportion. Because we are looking for the whole, which is the total amount of visitors on a Saturday, set the proportion up like this: 144/x = 60/100. This is because we are looking for the total amount of visitors, and we know that 144 is 60% of x number of visitors. Cross multiply the values in order to get 14,400 = 60x. Now, divide each side by 60 to isolate the "x". 14,400/60 is 240. x = 240. The art museum had 240 visitors that Saturday.

5 0

3 years ago

Read 2 more answers

Erin caught 8 more fish than Juan caught

Gennadij [26K]

Answer:

Second option: Equation, because 8 plus the fish that Juan caught equals the fish that Erin caught

Step-by-step explanation:

You can for sure make an equation, all you need is to have variables and that's allowed in this case.

E=J+8

E=Erin J=Juan

7 0

3 years ago

What is the solution to the system of equations?

Trava [24]

Call the two equations above A and B, in order to not confuse them.

A: -2x + 6y = -38

B: 3x - 4y = 32

For this system we have opposites in x and y, so Elimination (or Linear Combination) works best. Either variable works, so let's work with x first and multiply A by 3 and B by 2. This is done so we get opposites in A and B then when added together give zero.

-2x + 6y = -38 ------> multiply by 3 ----> -6x + 18y = -114

3x - 4y = 32 ------> multiply by 2 -----> 6x - 8y = 64

Now we add the new equations. The -6x and 6x are opposites and go away. We are left with

10y = -50. We divide both sides by 10 and get that y = -5.

Now we take y = -5 and put it into an original equation. Let's use A.

-2x + 6y = -38 the original equation A

-2x + 6(-5) = -38 we found y = -5

-2x + (-30) = -38 evaluating and multiplying

-2x - 30 = -38 apply the parentheses

-2x = -8 add 30 to both sides

x = 4 divide on both sides by -2

Thus x = 4 and y = -5, or (4, -5) is the solution.

6 0

3 years ago

Read 2 more answers