Mr.jones filled his swimming pool with water

Answer: Choice C

4/(3*sqrt(3))

which is the same as writing [tex]\frac{4}{3\sqrt{3}}[/tex]

==============================================================

Explanation:

We have the line [tex]\left(\sqrt{2}\right)x+y +2 = 0[/tex] in which points B and C are on this line. In other words, all of segment BC is on that line.

Point A is somewhere off that line as the diagram below indicates. We need to find the line through A that is perpendicular to the given line.

Recall that for any line of the standard form [tex]Px+Qy+R = 0\\\\[/tex], any perpendicular line will look like this: [tex]Qx-Py+S = 0\\\\[/tex]. Note the swap and sign change for the P,Q coefficients.

So anything perpendicular to [tex]\left(\sqrt{2}\right)x+y +2 = 0[/tex] will be of the form [tex]x-\left(\sqrt{2}\right)y+S = 0[/tex]. The sub-goal here is to find what S is equal to.

If you plugged in the origin point (x,y) = (0,0), then you should find that S = 0.

Therefore, the equation [tex]x-\left(\sqrt{2}\right)y = 0[/tex] is perpendicular to the given line and it passes through point A(0,0).

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The reason why we computed that perpendicular line is to help determine the point D as shown in the diagram below. This point is at the intersection of the green perpendicular lines. This is at the base of the triangle such that BC is the base.

To find the location of point D, you need to solve this system of equations

[tex]\begin{cases}\left(\sqrt{2}\right)x+y +2 = 0\\\\x-\left(\sqrt{2}\right)y = 0\end{cases}[/tex]

Let's isolate x in the second equation

[tex]x-\left(\sqrt{2}\right)y = 0\\\\x=\left(\sqrt{2}\right)y\\\\[/tex]

Then substitute that into the other equation. Solve for y.

[tex]\left(\sqrt{2}\right)x+y +2 = 0\\\\\left(\sqrt{2}\right)*\left(\sqrt{2}\right)y+y +2 = 0\\\\2y+y +2 = 0\\\\3y +2 = 0\\\\3y = -2\\\\y = -2/3\\\\[/tex]

Now we can find x like so

[tex]x=\left(\sqrt{2}\right)y\\\\x=\left(\sqrt{2}\right)*(-2/3)\\\\x=\frac{-2\sqrt{2}}{3}\\\\[/tex]

The point D is located at the exact coordinates of

[tex]D=(x,y) = \left(\frac{-2\sqrt{2}}{3},\frac{-2}{3}\right)\\\\[/tex]

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Next, we use the distance formula to compute the distance between point A and point D.

I'll use lowercase d to represent distance.

[tex]A = (x_1,y_1) = (0,0)\\\\D = (x_2,y_2) = \left(\frac{-2\sqrt{2}}{3},\frac{-2}{3}\right)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{\left(0-\left(\frac{-2\sqrt{2}}{3}\right)\right)^2 + \left(0-\left(\frac{-2}{3}\right)\right)^2}\\\\d = \sqrt{\left(\frac{2\sqrt{2}}{3}\right)^2 + \left(\frac{2}{3}\right)^2}\\\\d = \sqrt{\frac{8}{9} + \frac{4}{9}}\\\\d = \sqrt{\frac{12}{9}}\\\\d = \sqrt{\frac{4}{3}}\\\\d = \frac{\sqrt{4}}{\sqrt{3}}\\\\d = \frac{2}{\sqrt{3}}\\\\[/tex]

This represents the exact length of segment AD.

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Since triangle ABC is equilateral, this means triangles ADB and ADC are identical mirrored copies of each other. Those two smaller triangles are equal in area and combine to form triangle ABC back again. Furthermore, they are right triangles. This last fact mentioned will allow us to use the pythagorean theorem like so

[tex]a^2+b^2 = c^2\\\\\left(\text{AD}\right)^2+\left(\text{DC}\right)^2=\left(\text{AC}\right)^2\\\\\left(\frac{2}{\sqrt{3}}\right)^2+\left(\frac{x}{2}\right)^2=\left(x\right)^2\\\\[/tex]

where x represents the lengths of AB, BC and AC.

After skipping a bit of steps, solving that said equation should lead to these two solutions

[tex]x = -\frac{4}{3}, \ x = \frac{4}{3}[/tex]

Because x is a side length, we ignore the negative solution.

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We can now compute the area of triangle ABC

[tex]\text{area of triangle} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{area of triangle ABC} = \frac{1}{2}*\text{BC}*\text{AD}\\\\\text{area of triangle ABC} = \frac{1}{2}*\frac{4}{3}*\frac{2}{\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{1*4*2}{2*3*\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{8}{6\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{4}{3\sqrt{3}}\\\\[/tex]

which points us to choice C as the final answer.

When writing this on a keyboard, we would write "4/(3*sqrt(3))" without quotes. The use of parenthesis is needed to ensure we divide by all of 3*sqrt(3). Otherwise, the computer might mistake it for [tex]\frac{4}{3}\sqrt{3}[/tex] which is entirely different.

Answer:

345

Step-by-step explanation:

9514 1404 393

Answer:

  3x +4

Step-by-step explanation:

Polynomial long division is done the same way numerical long division is done.

The next quotient term is found by dividing the highest-degree dividend term by the highest-degree divisor term. The result is the exact quotient term. There is no need to go back and make an adjustment as there sometimes is with numerical long division.

Once you have the quotient term, you multiply that by the divisor and subtract from the dividend. This is the same procedure as is used with numerical long division. The difference is the new dividend, and the process repeats.

When the dividend is lower-degree than the divisor, that dividend is the remainder. For this division, the remainder is zero, so the quotient has no fractional part.

__

Both the quotient and the divisor can have any degree and any number of terms. It is useful to write both so all powers of the variable are accounted for, using 0 as a coefficient where necessary. This helps keep things straight when you're multiplying and subtracting. As you know, only "like" terms (terms of the same degree) can be combined by addition or subtraction.

Answer: 200

Step-by-step explanation: 200 doubled would be 400 and it says that tonights attendence was 100 more than the doubled which would add up and equal 500 (400+100=500) so 200 is your answer.

Answer:

The vertex is the maximum or minimum point of the quadratic function. It can be used to solve real world problems optimization problems that can be modeled with quadratic functions

Step-by-step explanation:

hope this helps^^

brainliest maybe??<3

Answer:

[tex]y = - \frac{1}{5} x - 7[/tex]

Step-by-step explanation:

let's rewrite the equation

[tex]x + 5y = 25 \\ 5y = - x + 25 \\ y = - \frac{1}{5} x + 5[/tex]

Now let's use the given point and substitute it to find the y-intercept

[tex] - 6 = - \frac{1}{5} ( - 5) + b \\ - 6 = 1 + b \\ b = - 7[/tex]

The required solution of the given equation of the line that passes through the point (-5,-6) and is parallel to the line x+5y=25 is

[tex]y=\frac{-1x}{5} -7[/tex].

Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it.

Given:

The point is  (-5,-6) and is parallel to the line x+5y=25.

According to given question we have

By use of slope we get

x+5y=25

5y=25-x

Divide both sides 5 we get,

y=-1/5x+5

Where m= -1/5

Now you can find the equation of the parallel line using

[tex](y-y_{0} )=m(x-x_{0})[/tex]

Put the given point as (-5,-6) we have,

[tex](y+6)=\frac{-1}{5} (x+5)\\\\y=\frac{-1x}{5} -1-6\\\\y=\frac{-1x}{5} -7[/tex]

Therefore, the required solution of the given equation of the line that passes through the point (-5,-6) and is parallel to the line x+5y=25 is

[tex]y=\frac{-1x}{5} -7[/tex].

Learn more details about slope here:

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#SPJ2

Answer:

y = 18

Step-by-step explanation:

Without a picture or more information, this question is actually unsolveable. The answer could be multiple things, because there are multiple way to get from 8 to 14. But I will just assume that the equation for solving is:

x + 6 = y

So plug in 12 for x and you get y = 18.

Answer:

50-y

Step-by-step explanation:

Hope this helps :).

Answer:

A.

Step-by-step explanation:

The difference means subtraction. The number mean a variable which is N. Then it is 8 (is means equal sign). Then 22 is the answer. The answer is         N-8=22.

Have a great day!

Answer:

0.13000

there is 52 cards in a deck so you take 52 and divide it by 4 since there is only 4 face cards you then get 13 and turn it into 0.13 then round to the 6th digit or millionth after the decimal so you would get 0.130000

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The equation is given in "slope-intercept" form.

  y = mx + b

where m is the slope, and b is the y-intercept.

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For graphing, it is usually convenient to start with the y-intercept. The value of 'b' in your equation is +1, so the graph will go through the point y=1 on the y-axis. That point's coordinates are (0, 1).

The value of m represents the slope, or "rise"/"run" of the line. A slope of -2/3 means the line "rises" -2 units for each "run" of 3 units to the right. Then another point on the graph will be 3 units to the right of the y-axis, and 2 units down from y = 1. That point is (3, -1).

The line is drawn through these points you found on the graph.

Answer:

ok

Step-by-step explanation:

Answer:false true

Step-by-step explanation:

Answer:

5a/3+1/8-a/6-1/2

Step-by-step explanation:

Answer:

£18

Step-by-step explanation:

Ratio is 6:3:2

(john:robert:edward)

added together is 11, divide 99 by 11 to get 9, multiply the ratio numbers by 9

54:27:18

Check answers:

27 times 2 = 54     yes

18 times 3 = 54      yes

54 + 27 + 18 = 99   yes

Since it goes John : Robert : Edward (edward is last) and 54:27:18 (18 is last)

Edward got £18

Translation involves changing the position of a point in the coordinate plane.

The coordinate of  the translated point A' is (D) (0,0)

The coordinate of the point is given as:

[tex]A = (-9,-1)[/tex]

The rule of translation 9 units right, and 1 unit up is:

[tex](x,y) \to (x+9,y+1)[/tex]

So, we have:

[tex]A' = (-9+9,-1+1)[/tex]

Simplify the expression

[tex]A' = (0,0)[/tex]

Hence, the coordinate of  the translated point A' is (D) (0,0)

Read more about translation at:

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If the coordinate is translated 9 units right and 1 units up, the resulting coordinate will be at (-9 + 9, -1 + 1) which is A'(0, 0). Option D is correct

Given the coordinate point A (x, y),  if the coordinate is translated a unit right and b units up, the resulting coordinate will be at (x + a, y + b)

Note that both values are added to the coordinate points.

Given the coordinate point A (-9, -1), if the coordinate is translated 9 units right and 1 units up, the resulting coordinate will be at (-9 + 9, -1 + 1) which is A'(0, 0)

Learn more on translation here: https://brainly.com/question/12861087

(3p-p)/(2-(-8))= -3

2p/10= -3

2p= -30

p= -15

Answer:

-15

Step-by-step explanation:

Given that a line has a slope of -3 and passes through the points (-8,p) and (2,3p) . And we need to find out the value of p . As we know that the slope is ,

[tex]\longrightarrow\sf slope = y_2-y_1/x_2-x_1[/tex]

Substituting the respective values ,

[tex]\longrightarrow[/tex] -3 = (p - 3p)/(-8-2)

Simplify ,

[tex]\longrightarrow[/tex] -3 = -2p/-10

[tex]\longrightarrow[/tex] -3 = p/5

[tex]\longrightarrow[/tex] p = 5 * -3

[tex]\longrightarrow[/tex] p = -15

Answer:

yes your correct

Step-by-step explanation:

9514 1404 393

Answer:

  0.9114

Step-by-step explanation:

That multiplier would be ...

  (1 -2%)×(1 -7%)

  = (1 -0.02)(1 -0.07)

  = 0.98×0.93 = 0.9114

The confidence interval for the mean gives an estimated range in which the true population mean of the data resides. Since, the fan uses all the population data, then he could find the population mean directly.

Therefore, since the fan is already using all the population data, then he could just calculate the population mean directly.

Learn more :https://brainly.com/question/2396419

Answer:

if you have rational value then 4/5, this is equal to .8

Answer:

6 days

Step-by-step explanation:

This question becomes much easier when written out per day (shown below). The question tells us that she is reducing her run by half every day, so all we need to is divide the previous day by 2 to get the current day. She starts out with 26 miles so this is our day 1 value.

Day 1 = 26 miles

Day 2 = 13 miles (26÷2=13)

Day 3 = 6.5 miles (13÷2=6.5)

Day 4 = 3.25 miles (6.5÷2=3.25)

Day 5 = 1.625 miles (3.25÷2=1.625)

Day 6 = 0.8125 miles (1.625÷2=0.8125)

We can see that by day 6, her total running amount is less that 1 mile, so the final answer is 6 days.

Answer:

x = 32.5

Step-by-step explanation:

If ABC is congruent and equal to DEC then angle CDE = angle CBA since AB || DE

thus ABC = 2x = 65 where x = 65/2 = 32.5

Answer:

Not here.

Step-by-step explanation:

F. The converse of the conditional.

The converse would state the following:

"If it is January, then it is winter in the United States" (Original).

"If it is winter in the United States, then it is January" (Converse).

It is not true, as it can be December, January, or February during the winter season.

G. The inverse of the conditional.

The inverse would state the following:

"If it is January, then it is winter in the United States" (Original).

"If it is not January, then it is not winter in the United States" (Inverse).

Again, as the above states, the winter season encompasses more than just the month of January.

H. The contrapositive of the conditional.

The contrapositive would state the following:

"If it is January, then it is winter in the United States" (Original).

"If it is not January, then it is not winter in the United States" (Contrapositive).

Again, there is more than just January in the winter season.

~

Answer:

a. 19

Step-by-step explanation:

5/6x-1/5x=19

5/6(30)-1/5(30)=19

25-6=19

19=19

?/30(30)=19

19/30(30)=19

19=19

I'm not sure if this is exactly what you're looking for, but 19=19 if you plug in 19 for the box (and x=30 because of the first section, I'm guessing)

Answer:

153

Step-by-step explanation:

The formula is 3 mL of A to 5 mL of B.

Let's say the chemist uses just the numbers in the formula.

Add 3 mL of A to 5 mL of B.

3 mL + 5 mL = 8 mL

The chemist ends up with 8 mL of the drug.

He really want 408 mL.

408 mL is how many times greater than 8 mL?

408/8 = 51

He needs to use 51 times the numbers in the formula.

51 * 3 mL of A + 51 * 5 mL of B =

= 153 mL of A + 255 mL of B

= 408 mL of the drug

Answer: 153

9514 1404 393

Answer:

  C.  0.36 +0.27 = 0.63

Step-by-step explanation:

3 columns and 6 squares of a hundredths grid is a representation of ...

  0.30 +0.06 = 0.36

2 columns and 7 square is a representation of ...

  0.20 +0.07 = 0.27

The total shaded area is the sum of these:

  0.36 +0.27 = 0.63

Answer:

600 hives

Step-by-step explanation:

If 30 is 5% of the total number of hives Joshua has, then 5%x20=100%

So, 30x20=100%

      30x20=600

hope it helped :)