A farmer wants to build a rectangular fence to enclose a 144\ \textup{ft}^2 yard. If the yard is square, how many feet of fence will he need?

Answer:

Step-by-step explanation:

Given functions are,

f(x) = x + 6

g(x) = 2x + 6

(f - g)(x) = (x + 6) - (2x + 6)

                   = -x

(f . g)(x) = f(x) × g(x)

            = (x + 6)(2x + 6)

            = 2x² + 6x + 12x + 36

            = 2x² + 18x + 36

(f + g)(x) = (x + 6) + (2x + 6)

             = 3x + 12

(f + g)(1) = 3(1) + 12

            = 15  

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Answer:

  3x +y -13 = 0

Step-by-step explanation:

The perpendicular line will have the variable coefficients swapped and one of them negated. The new constant will be appropriate to the given point.

  3(x -4) +1(y -1) = -0

  3x +y -13 = 0

_____

Additional comment

The given equation is in "general form", so that is the form of the equation we have given as the answer. This form is convenient in that the general form equation for a line through the origin, ax+by=0, is easily translated to make it pass through a point (h, k): a(x -h) +b(y -k) = 0. Eliminating parentheses puts the equation back into general form.

Answer: -4/6 or -2/3

Step-by-step explanation:

First, you find a common denominator among the fractions, which would be 6.

Convert -1/2 to have 6 as its denominator.

-1/2* 3/3 = -3/6

And then subtract them.

-3/6 - 1/6 = -4/6

-4/6 simplified is -2/3

When you subtract a positive number from a negative number, you are adding their absolute values.

Answer:

D) 3

Step-by-step explanation:

Rise/run, rise is 3, run is 1

Answer:

3

Step-by-step explanation:

Pick two points on the line

(0,0) and ( 1,3)

The slope is found by

m = ( y2-y1)/(x2-x1)

    = ( 3-0)/(1-0)

    = 3/1

   = 3

Answer:

x = 60

Step-by-step explanation:

The sum of the angles of a triangle add to 180

x+x+x = 180

3x = 180

Divide by 3

3x/3 =180/3

x = 60

Answer:

it's going to be 4n so its going to be 4...

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Assuming you meant when n=14

10(n-6)

plug in 14 for n

10(14-6)

work out parenthesis first

10(8)=

80

Write each equation in standard form:

3x + y + 3z = 11

x + 2y + z = 7

-x + y + z = 0

In matrix form, this is

[tex]\begin{bmatrix}3&1&3\\1&2&1\\-1&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}11\\7\\0\end{bmatrix}[/tex]

and in augmented matrix form,

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\1&2&1&7\\-1&1&1&0\end{bmatrix}\right][/tex]

Now for the row operations:

• Add row 1 to -3 (row 2), and add row 1 to 3 (row 3):

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&-5&0&-10\\0&4&6&11\end{bmatrix}\right][/tex]

• Multiply row 2 by -1/5:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&4&6&11\end{bmatrix}\right][/tex]

• Add -4 (row 2) to row 3:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&6&3\end{bmatrix}\right][/tex]

• Multiply row 3 by 1/6:

[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

• Add -1 (row 2) and -3 (row 3) to row 1:

[tex]\left[\begin{array}{ccc|c}3&0&0&\frac{15}2\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

• Mutiply row 1 by 1/3:

[tex]\left[\begin{array}{ccc|c}1&0&0&\frac52\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]

Then the solution to the system is (x, y, z) = (5/2, 2, 1/2).

Answer:

obtuse angle that's the answer

Answer:

-40

Step-by-step explanation:

-55 + 15 = x

-40 =x

Answer:

v<1 23/25

Step-by-step explanation:

The inequality simplifies to 48/25, which is equivalent to 1 23/25.

point slope form:

y + 3= -1/5 x (x+0)

Step-by-step explanation:

-use the point slope form equation: y - y1 = m (x - x1).

-using the given information we know that m = -1/5 and that the y intercept is (0,-3).

- y and x will be kept as a variable.

-plug in the y1 and x1 from the y intercept:

y + 3 = m(x + 0)

-once you've plugged in the y intercept then plug in the slope which gives you the answer:

y + 3= -1/5 x (x+0)

Step-by-step explanation:

Amount of acid = 14.9% of 331 mL solution

= 0.149×(331 mL)

= 49.3 mL acid

Answer:

Step-by-step explanation:

Arranging the data in the ascending order:

108.6 98.3 103.7 112 117.4 120 121.5 123.2 128.4

The median is the middle value of the data set:

a)

Hence,

median = 117.4

b)

When the value of blood pressure is 117.7 instead of 117.4 then the median will be:

Median = 117.7

c)

This indicates that the median of a well sorted set of data is depends upon the middle value of the data set.

Answer:

edge of cube = root 13.5/6 = 1.5

volume of cube = (Edge of cube)^3= (1.5)^3 = 3.37500 m^3

Answer:

3y(2x-1)(x-4y)

Step-by-step explanation:

Apply exponent rule:

6x^2y-3xy-24xyy+12yy

Rewrite 12 as 4*3

Rewrite -24 as 8*3

Rewrite 6 as 2*3

2*3x^2y-3xy+8*3xyy+4*3yy

Factor out common term 3y:

3y(2x^2-x-8xy+4y)

Factor 2x^2-x-8xy+4y:

3y(2x-1)(x-4y)

Your Answer Is 3y(2x-1)(x-4y)

Answer:

There are 2,598,960 ways to receive 5 cards from a deck of 52.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

a. How many ways are there to receive 5 cards from a deck of 52?

[tex]C_{52,5} = \frac{52!}{5!(47)!} = 2598960[/tex]

There are 2,598,960 ways to receive 5 cards from a deck of 52.

so

82-(-2)

=84

then ur answer is 84

Answer:

[tex]y=\sqrt{x} -2[/tex]

Step-by-step explanation:

If you were to replace x with 0 in each of the equations, you would get

from top to bottom choices:

[tex]\sqrt{2}[/tex]

[tex]\sqrt{-2}[/tex]

2

-2

Since we can see that the line touches the y-axis on the number -2, we know that it is the last choice that is the answer

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Answer:

  78.5 km

Step-by-step explanation:

Measured at the airport, the angle between the two planes is ...

  180° -60° -50° = 70°

The law of cosines tells us the distance between the planes is ...

  d = √(50² +80² -2·50·80·cos(70°)) ≈ √6163.84 ≈ 78.5 . . . km

The planes are about 78.5 km apart.

Answer: Yes, but only if he houses 37, 38, 39, or 40 fish

Anything larger than 40 and he'll need more room.

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

Explanation:

The tank is 30 cm by 30 cm by 100 cm. The volume is 30*30*100 = 90,000 cm^3 which is shorthand for "cubic centimeters".

We're told that 1000 cm^3 = 1 liter, which means the 90,000 cm^3 converts to (90,000)/(1000) = 90 liters.

The fish tank is 90 liters.

Since 1 gallon = 4.5 liters, this means the 90 liter tank converts to 90/(4.5) = 20 gallons

----------------------------

Your teacher mentions "He can keep 2 small fish for every 1 gallon".

Since the tank is 20 gallons, that means he can keep 20*2 = 40 fish. This value is larger than 36, so Matt is correct to a point. If Matt is thinking 37, 38, 39, or 40 fish then he would be correct. If Matt is wanting more than 40 fish, then he'll need a bigger tank.

In short, he can't have any number over 36 and can only have 4 specific values (the four values mentioned earlier).

So technically, Matt is correct, but strong clarification is needed.

Part A

To find the mean, we add up the values and divide by n = 8 since there are 8 values in this set.

Adding the values gets us

28+45+12+34+36+45+19+20 = 239

Dividing this over 8 then leads to 239/8 = 29.875

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

Part B

We'll subtract each data value from the mean. We apply absolute value to ensure the result is never negative.

The list of results we get so far is:

1.875, 15.125, 17.875, 4.125, 6.125, 15.125, 10.875, 9.875

This represents the distance each value is from the mean.

Add these values up and divide by n = 8

1.875+15.125+17.875+4.125+6.125+15.125+10.875+9.875 = 81

81/8 = 10.125

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

Part C

The result of part A is one way to measure the center of the distribution of values. It's the average value, which can more or less represent the entire group. Think of it being like how people vote in a senator to represent them in congress. Ideally, this senator is a supposed "average" person to represent everyone.

The result of part B builds on what part A found. The result of part B is the average distance each value is from the center. This is because each time we subtracted and applied absolute value, we found the distance that item was from the mean.

Example: The calculation |28 - 29.875| = 1.875 shows that 28 is exactly 1.875 units from the mean 29.875

By adding up those results and dividing by 8, we are finding the average distance from the mean. Effectively, it tells us how spread out the data set is. The mean absolute deviation (MAD) is a measure of spread in a similar fashion that the standard deviation is, or in a more looser sense, the range is as well.

---------------

In short, the result of part A is a measure of center while the result of part B is a measure of spread. I use "a" instead of "the" because there are other measures of center and other measures of spread.

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Answer:

  (a)  2

Step-by-step explanation:

Each inch is 2.54 cm, so 5.08 cm is ...

  x / (5.08 cm) = (1 in) / (2.54 cm)

  x = (1 in)(5.08/2.54) = (1 in)(2)

  x = 2 in

5.08 cm equals 2 inches.

The answer is D. Because if we put 16 in place of x, MP, NO will be 24, 16 respectedly

Step-by-step explanation:

So all horizontal line will be decrease from line MP to No.

As result MP will be = 24, QR = 20, NO = 16. We can see there's different of 4.

The value of x in the trapezoid is 16.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

In a trapezoid, the median is the average of the parallel sides,

So we have:

QR

= (NO + MP)/2

= (x + x + 8)/2

= (2x + 8)/2

= x + 4

Since we also know that QR = 20, we can set the two expressions equal to each other and solve for x:

x + 4 = 20

x = 16

Therefore,

The value of x is 16.

Learn more about trapezium here:

https://brainly.com/question/22607187

#SPJ7

Answer:

Step-by-step explanation:

Concept:

Here, we need to know the idea of a special triangle 30-60-90.

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.

The ratio between the corresponding side of each angle is 1 : √3 : 2

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

30-60-90 ⇔ 1 : √3 : 2

Given the side corresponding to 90° is 20

30° : 90° = 1 : 2

30° : 20 = 1 : 2

30° = 10

30° : 60° = 1 : √3

10 : 60° = 1 : √3

60° = 10√3

Hope this helps!! :)

Please let me know if you have any questions

Answer:

6 and 2/3

Step-by-step explanation:

you do 1 2/3 x 4 because that is the amount of flour you need to make one batch. That is the correct answer.

Answer:

465/1178 = .395 = 39.5%

Step-by-step explanation:

        224 + 245

224+ 387 + 245 + 322

465/1178 = .395 = 39.5%