A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.

Answer:

no

Step-by-step explanation:

substitute the (x,y) values into the inequality.

4(-4)+5(2) less than or equal to -7

-16+10≤-7

-6≤-7 not a valid answer so ((-4,2) is not a solution

Answer:

Trey = 9 text messages

Rachel = 19 text messages

Juan = 57 text messages

Step-by-step explanation:

Let

Number of messages Trey sent = x

Number of messages Rachel sent = x + 10

Number of messages Juan sent = 3(x + 10)

Total messages = 85

Total = Trey + Rachel + Juan

85 = x + (x + 10) + 3(x + 10)

85 = x + x + 10 + 3x + 30

85 = 5x + 40

85 - 40 = 5x

45 = 5x

x = 45/5

x = 9

Number of messages Trey sent = x = 9 text messages

Number of messages Rachel sent = x + 10

= 9 + 10

= 19 text messages

Number of messages Juan sent = 3(x + 10)

= 3(9 + 10)

= 3(19)

= 57 text messages

Answer: [tex]4[/tex] pairs

Step-by-step explanation:

Given

Profit on selling 'x' pairs of shoes is [tex]P(x)=-4x^2+32x-39[/tex]

Find the derivative of the function to find out the critical points

[tex]\Rightarrow -8x+32=0\\\Rightarrow x=4[/tex]

Thus, for 4 pair of shoes profit is maximize.

Answer:

4 pairs of shoes.

Step-by-step explanation:

Answer:

f=x−32

Step-by-step explanation:

Subtract 3232 from both sides.

Answer:

f=32.2m

Step-by-step explanation:

got it right on edge

Answer:

255 is the answer

Step-by-step explanation:

Divide 765 by 3 and the answer will come .

Hope it will help u

Answer:

Enlargement

k =[tex]\frac{18}{4}[/tex] =  [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

k = [tex]\frac{new}{old}[/tex]

If k > 1 then its an enlargement.

If k < 1 then its a reduction

Given:

The given equation is:

[tex]\dfrac{\sqrt{2x}}{\sqrt{x-1}}=2[/tex]

To find:

The solution for the given equation.

Solution:

We have,

[tex]\dfrac{\sqrt{2x}}{\sqrt{x-1}}=2[/tex]

On simplification, we get

[tex]\sqrt{2x}=2\sqrt{x-1}[/tex]

Squaring both sides, we get

[tex]2x=4(x-1)[/tex]

[tex]2x=4x-4[/tex]

[tex]2x-4x=-4[/tex]

[tex]-2x=-4[/tex]

Divide both sides by -2.

[tex]x=\dfrac{-4}{-2}[/tex]

[tex]x=2[/tex]

Therefore, the correct option is B.

Answer: 7(n + 4)

Step-by-step explanation:

I'm not sure how to explain this one, but I'll try:

Seven times the sum of a number, n, and four

7 times n + 4   (sum means addition)

Answer:

2000

Step-by-step explanation:

Since the number must be odd, it can have either 1, 3, 5, 7 or 9 in its one's place.

With a 4-digit number starting with 6, any of these digits can be in the one's place and it will still be greater than 6,000.

For the one's place, since we can choose from 5 digits, we have ⁵P₁. In the thousands place, we have one digit which is 6. For the tens and hundreds, place, we can choose from ten digits. So, we have ¹⁰P₁ and ¹⁰P₁ respectively.

So, the total number of 4 digit odd numbers greater than 6000 starting with 6 are 1 × ¹⁰P₁ × ¹⁰P₁ × ⁵P₁ = 1 × 10 × 10 × 5 = 500 numbers.

For the thousands place, we are left with the digits 7, 8 and 9. So, to arrange these 3 digits in the thousands place, we have ³P₁. For the tens and hundreds, place, we can choose from ten digits. So, we have ¹⁰P₁ and ¹⁰P₁ respectively. For the one's place, since we can choose from 5 digits, we have ⁵P₁.

So, the total number of 4 digit odd numbers greater than 6000 starting with 7, 8 or 9 are  ³P₁ × ¹⁰P₁ × ¹⁰P₁ × ⁵P₁ = 3 × 10 × 10 × 5 = 1500 numbers.

So, the total number of 4-digit numbers greater than 6000 that can be constructed is 500 + 1500 = 2000 numbers.

Answer:

3

Step-by-step explanation:

Area = 1/4 * √(5(5+2√5)) * a^2

Area ≈387.11

because each bag only covers 150 we need 3 bags

Answer:

area = 387 ft^2

3 bags

Step-by-step explanation:

See the picture below.

The pentagon is made up of 5 congruent triangles. One triangle is shown on the bottom right figure.

The left figure shows half of the triangle. We need to find h, the height of the triangle.

For a regular pentagon, the measure of each interior angle is

(n - 2)180/5 = 108

Half of the angle is 54 deg.

tan A = opp/adj

tan 54 = h/7.5

h = 7.5 * tan 54

h = 10.32 ft

Area of half triangle = bh/2 = 7.5 ft * 10.32 ft/2 = 38.7 ft^2

The pentagon is made up of 5 larger triangles or 10 half triangles.

Area of pentagon = 10 * 38.7 ft^2

Area of pentagon = 387 ft^2

1 bag is good for 150 ft^2.

387 ft^2/150 ft^2 = 2.6

She needs 2.6 bags, so she must buy 3 bags.

Answer: 3 bags

Answer:

$20

Step-by-step explanation:

5 copies cost $1.

25 copies cost $5.

So you have to do 100/5=$20 for 100 copies.

Answer:The answer is 20

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

8^3 = 512

.................

Answer:

512

Step-by-step explanation:

Given

[tex]m^{n}[/tex] ( substitute m = 8, n = 3 into the expression

= 8³

= 8 × 8 × 8

= 64 × 8 = 512

Answer:

C

Step-by-step explanation:

its asking for y, on the graph, the line is placed on point 4

Step-by-step explanation:

here is the answer to your question

Answer:

Step-by-step explanation:

I would start from the beginning and find the slope myself, just so I know what's going on (as opposed to being dropped in the middle of the problem). The slope formula is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and for us:

[tex]m=\frac{5-3}{4-3}=2[/tex] so the slope is indeed 2. Now we need to write the equation in slope-intercept form. I find it easier to first write the equation in point-slope form and then solve it for y. Point-slope form is

[tex]y-y_1=m(x-x_1)[/tex] where m is the slope (2) and x1 and y 1 are from one of the coordinates (whichever one you want; as long as you do the math correctly, you will NOT get an incorrect answer. In other words, you can't pick the "wrong" point to use to write the equation.) I'm going to use (3, 3):

y - 3 = 2(x - 3) and

y - 3 = 2x - 6 and

y = 2x - 6 + 3 so

y = 2x - 3 and that's your equation. Of course, you will enter a (-3) in that box with the ? in it.

Answer:

x ≈ 2.0794

Step-by-step explanation:

Given

[tex]e^{x}[/tex] = 8 ( take ln of both sides )

ln [tex]e^{x}[/tex] = ln 8

x lne = ln 8 [ lne = 1 ]

x = ln 8 ≈ 2.0794 ( to 4 dec. places )

Answer:

x ≈ 2.0794

Step-by-step explanation:

[tex] \small \sf \: e {}^{x} = 8[/tex]

Take the natural logarithm of both side of equation

[tex] \small \sf \: Use \: In(e {}^{x} ) = x \: to \: simplify \: the \: expression.[/tex]

Write the number in exponential form.

Use In(aⁿ) = n × In ( a ) to transform the expression.

Round to four decimal places = 2.0794

Answer: $268.75

Step-by-step explanation:

First, find the amount he earned from his sales:

1500(0.0125) = $18.75

Next, add that to his monthly salary:

$250 + $18.75 = $268.75

Answer:

Step-by-step explanation:

Second hand on a clock rotates at rate 360 degrees per 60 seconds.

360 degrees - 60 sec

x degrees - 15 sec

90 clockwise rotation (none hand of a clock rotates counter-clockwise :))

Answer:

90 degrees clockwise rotation

Step-by-step explanation:

Answer:

27/10 is the value of (3/10)^3.

Step-by-step explanation:

It is also written as 0.027

Answer:

Step-by-step explanation:

To solve this, we can use polynomial long division.

Seeing the picture, we first divide x (the variable to the largest degree in x+1) from 2x³. We divide from 2x³ because that is the variable with the largest degree in the polynomial. That is equal to 2x², so we put that on top and subtract (x+1) * (2x²) from the polynomial. Then, we repeat the process, but with x² instead of 2x³, and again with -6x as the variable with the largest degree.

Answer:

y=2/3x-11/3

Step-by-step explanation:

line is parallel so the gradient will be the same ( m=2/3)

using the point (4,-1)

y=2/3x+c

-1=2/3*4+c

-1=8/3+c

c= -11/3

equation ---> y=2/3x-11/3

Répondre:

Benoit a 10 ans

Explication étape par étape :

Laisser :

Âge de Thomas = x

Benoit age = y

il y a 5 ans :

x - 5 = 5 (y - 5)

x - 5 = 5y - 25 - - (1)

Aujourd'hui :

x = 3y - - (2)

Mettez x = 3y dans (1)

3 ans - 5 = 5 ans - 25

Recueillir des termes similaires

3 ans - 5 ans = - 25 + 5

-2a = - 20

Diviser les deux côtés par - 2

y = 10

Answer:

1 minute and 12 seconds is 2 % of an hour.

Step-by-step explanation:

Answer:

12%

Step-by-step explanation:

Answer:

B = 7x - 6 is the correct answer.

Answer:

[tex]180ft^{3}[/tex]

Step-by-step explanation:

Volume of a cone:

[tex]V=\pi r^{2} \frac{h}{3}[/tex]

Take [tex]\pi[/tex] as 3, as mentioned in the question

'r' is 'radius' ⇒ {diameter is given so divide by 2: 12/2 = 6}

'h' is 'height'

[tex]V=(3)(6)^{2} (\frac{5}{3} )[/tex]

[tex]V=(3)(36)(\frac{5}{3} )[/tex]

[tex]V=108(\frac{5}{3} )[/tex]

{multiply 108 with 5 and then divide the answer by 3}

[tex]V=108[/tex] × [tex]5[/tex]

[tex]V=540[/tex]

[tex]V=540/3[/tex]

[tex]V=180ft^{3}[/tex]

Answer:

Using the net below, find the surface area

of the pyramid.

sto

5 in

5 in.

Surface Area

=

[?] in?Step-by-step explanation: