A farmer plans to build a rectangular garden behind his house such that he only needs fencing on 3 sides of the garden. If he wants the second side of the garden to be 30 feet longer than the back of his house, and the area of the garden is going to be equal to 400 square feet, how much fencing dose he need to buy?

The formula for y in terms of x is a cubic equation:

y = 0.25*x³

We know that y is directly proportional to x³, then we can write the equation:

y = k*x³

Where k is the constant of proportionality.

In this case, we know that when x = 10, the value of y is 250, then we can replace these values in the above equation to find the value of x:

250 = k*10³

250 = k*1,000

Dividing both sides by 1,000 we get:

250/1,000 = k

0.25 = k

Then the equation is:

y = 0.25*10³

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Answer:

y=3x+1

y=-17

Step-by-step explanation:

y=3x+1

7=3(2)+1

7=6+1

7=7

y=3(-6)+1

y=-18+1

y=-17

Hopes this helps please mark brainliest

According to the product rule of logarithms, the given equation is written as,  log₄(x² + 13x + 40) = 1

Product rule of logarithm

Basically, the product rule states that the sum of two logarithms is equal to the product of the logarithms.  

And it is the first law and it can be represented as;

logₐ(x) + logₐ(y) = logₐ(xy)

Given,

Here we have the logarithmic equation log 4(x+8) + log 4(x+5) = 1

And we have to rewrite the equation.

Here we have the logarithmic equation,

=> log₄(x+8) + log₄(x+5) = 1

By using the product property of logarithms, 

We have to rewrite the equation as,

=> log₄(x+8)(x+5) = 1

Now, we have to expand (x+8)(x+3) using the FOIL Method.

Then we get,

=> log₄(x² + 5x + 8x + 40) = 1

=> log₄(x² + 13x + 40) = 1

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Answer:

540 cm₂

Step-by-step explanation:

       [tex]\sf \boxed{Area = (b_1+b_2+b_3)*l + bh}\\\\[/tex]

[tex]\sf \text{where $b_1$, $b_2$ and $b_3$ are the sides of the triangle l is the length of the rectangle}\\\\ \text{and b is the base of the triangle and h is the altitude of the triangle}[/tex]

    b₁ = 12 cm ; b₂ = 5 cm ; b₃ = 13 cm

   l = 16 cm  ;  b = 12 cm and h = 5 cm

Area  = (12 + 5 + 13)*16 + (12*5)

          = 30*16 + 60

          = 480 + 60

          = 540 cm²

The time taken by Ashley and Laura to meet each other is 3 hrs

The speed of an object tells us how slow or fast an object moves. The formula for speed is given below

The speed of an object is directly proportional to Distance and Inversely proportional to Time. Hence,

Here we have,

Ashley and Laura are 60 miles apart, traveling toward each other

This means the distance between Ashley and Laura is 60 miles

Speed of Laura = 12 mph

Speed of Ashley = 8 mph

Let us assume that Both Ashley and Laura meet after t hours

Then

The distance traveled by Laura in t hours = 12 mph × t hrs = 12t m

The distance traveled by Ashley in t hours = 8 mph × t hrs = 8t m

As we know the distance between Laura and Ashley is 60 miles

=>  12t m + 8t m = 60 miles

=>  20t miles = 60 miles

=> t = 60/20

=> t = 3hrs

Therefore,

The time taken by Ashley and Laura to meet each other is 3 hrs

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The area of the hula hoop is equal to 450π square inches.

A hula hoop is a toy with the form of a circle, whose area (A), in square inches, has to be found. The area of a circle is described by the following formula:

A = 2π · R²

Where R is the radius of the hula hoop, in inches.

If we know that R = 15 inches, then the area covered by the hula hoop is:

A = 2π · (15 in)²

A = 450π in²

The area is equal to 450π square inches.

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Answers:

1 yard by 72 yards

4 yards by 18 yards

6 yards by 12 yards

8 yards by 9 yards

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

Explanation:

Let's list out all the ways to multiply to 72 using two values

1*72

2*36

3*24

4*18

6*12

8*9

Then cross off something like 2*36 since 2 is prime. We also cross off 3*24 since 3 is prime.

We're left with this list

1*72

4*18

6*12

8*9

which represent the possible dimensions of this rectangle.

Keep in mind that 1 is not prime.

Suban need to leave $10000 investment in the bank at 5% per year simple interest for 10 years so that it grows to $15000

According to question,

Principal (P) = 10,000

Rate of interest (I) = 5%

Interest = Amount - Principal

= 15000 - 10000

= 5000

We need to find the number of years

T = ?

Interest = P * R * T / 100

5000 = 10000 * 5 * T / 100

T = 10 years

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The lines which are skewed in the rectangular prisms shown are Line QT (↔QT) and Line WX(↔WX).

What is skew in geometry?

This refers to two lines that do not cut across (intersect)  each other and are not parallel to each other. the pair of lines must also be opposite edges of the shape. The lines are not also lying or acting in the same plane. i.e non-coplanar.

How to identify skew lines?

a) Locate lines that do not intersect each other.

b)Find out if these pairs of lines are also not parallel to each other.

c) Examine if these non-intersecting and non-parallel lines are non-coplanar.

If yes then the chosen pair of lines are skew lines.

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Part a

The equation for the way Michelle is paid is

Total weekly payment y = 495.50 + 0.105x

Part b

The total payment in a  month = $4021.625

She makes a 10.5% commission on every kayak she sells

Consider the total value of kayaks she sold = x

The rate of commission = 10.5%

The amount of commission = x × (10.5/100)

= 0.105x

The weekly fixed payment = $495.50

Total weekly payment y = 495.50 + 0.105x

Part b

The total value of the kayaks she sold = $19425

Total number of weeks in a month = 4

Then the total payment in a month = (4 × 495.50) + (0.105×19425)

= 1982 + 2039.625

= $4021.625

Hence,

part a

The equation for the way Michelle is paid is

Total weekly payment y = 495.50 + 0.105x

Part b

The total payment in a  month = $4021.625

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Answer:

38.88in²

Step-by-step explanation:

Area of shaded region = Area of square - Area of semi circle

First lets find the area of the square and semi circle

Area of square = s²

Where s = side length

Here we have a given side length of 8in

So s = 8

This means area = 8² = 64in²

Area of semicircle = (πr²)/2

Where r = radius

Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in

To convert from diameter to radius we simply divide by 2

So radius = 8 / 2 = 4

Now we have Area = (πr²)/2

==> plug in r = 4 and π = 3.14

Area = (3.14(4)²))/2

==> simplify exponent

Area = (3.14(16))/2

==> multiply 3.14 and 16

Area = 50.24/2

==> simplify division

Area = 25.12in²

Area of shaded region

We now subtract the two areas

Area of shaded region = Area of square - Area of semi circle

Area of square = 64in² and Area of semicircle = 25.12in²

Area of shaded region = 64in² - 25.12in² = 38.88in²

Juan have earned of interest after 36 months at the rate of 7.5% interest per year.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. The formula of simple interest is as follows:

S.I = p×r×t

Where p is principle value, r is rate and t is time in years.

Here, the principle amount is $7,850 and rate is 7.5% i.e  [tex]\frac{7.5}{100}=0.075[/tex] and time is 36 months i.e 3 years.

Now, putting the values,

SI = 7850×0.075×3

= $ 1766

Therefore, the interest Juan have earned in 36 months is $1,766.

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Answer:

13

Step-by-step explanation:

if b = 5, then 3(5) - 2 = 15 - 2 = 13

Step-by-step explanation:

let angles of a triangle a=86

b= 180-3z , c= 180-4z

a+b+c = 180 {angle sum property}

86 +180+180-3z-4z=180

446 -7z = 180

-7z = -266

[tex]z = \frac{ - 266}{ - 7} = 38[/tex]

so other angle are

3z = 3 x 38 = 114

4z = 4 x 38 = 152

Answer:

Step-by-step explanation:

Instead you do 45 divided by 8

And you will get 5.625

Answer:

x would be 3 by 2

I am 90% sure but I hope this helps!

Answer:

The answer to this problem is 0.0013.

Answer:

I think its 108 each Box is going to cost 108

By the principle of mathematical induction, it has been proved that

[tex]p^3 + 11p[/tex] is divisible by 6

What is Principle of mathematical induction?

Let the statement be given by P(n). At first P(n) is proved to be true for 1. Then it is assumed that P(n) is true for all n. If P(n) is true for (n+1) then by Principle of Mathematical induction, P(n) is true for all natural numbers

The given expression is [tex]p^3 + 11p[/tex]

For p = 1

[tex](1)^3 + 11 \times 1\\12[/tex]

which is a multiple of 6

Let it be true for p = m

[tex]m^3 + 11m[/tex] is a multiple of 6

[tex]m^3 + 11m = 6k[/tex], where k is any integer

For p = m + 1

[tex](m+1)^3 + 11(m+1) \\m^3+3m^2+ 3m +1+11m+11\\m^3+11m +3m^2+3m+12\\m^3+11m + 3m(m+1) + 12[/tex]

Now,

[tex]m^3 + 11m[/tex] is divisible by 6

We know that the product of two consecutive integers are divisible by 6

[tex]3m(m+1)[/tex] is divisible by 6

12 is divisible by 6

[tex](m+1)^3 + 11(m+1)[/tex] is divisible by 6

So it is true for p = m + 1

By the principle of Mathematical induction, it is true for all natural numbers and eventually for all integers

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Answer:

3

Step-by-step explanation:

When you substitute 0 in for x in the equation. You are left with f(0) = 3.

The set of side measurements that could be used to form a triangle are 8, 14, 20.

The concept that will be used is the concept of triangle inequality theorem.

To know if the given 3 side lengths are a triangle, then the use of the  triangle inequality theorem comes into play.

This rule tells us that when we sum 2 sides of a triangle  the value must be greater than the third side.

Then this rule can be applied as

The first option; 8, 14, 20

a+b>c  = 8+14>20

a+c>b  =  8+20>14

b+c>a   = 20+14>8

Therefore, first option is correct.

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The equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.

The standard equation of a circle is given by:

(x – h)² + (y – k)² = r²

Where (h, k) is the center of the circle and r is the radius.

We are given:

The circle has a center at (–4, 0) and passes through the point (–2, 1).

Substitute (h, k) with (–4, 0) in the above equation, we will get;

(x – (-4))² + (y – 0)² = r²

(x + 4)² + y² =  r²

Substitute (x, y) with (–2, 1) in the above equation to get the value of r:

(-2 + 4)² + 1² =  r²

(2)² + 1² =  r²

r² = 5

Put the value r² = 5 in (x + 4)² + y² =  r², we will get;

(x + 4)² + y² =  5

So, the equation of the circle is (x + 4)² + y² =  5.

Thus, the equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.

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Answer:

Step-by-step explanation:

Ok:

1. Anything times zero always equals zero.

So: 55555555555555555555555555555555555555555555555555555555555555555555555555x0=

Answer:0

                  The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]

Cone:

        A cone is a three-dimensional geometric shape that tapers smoothly from a flat base.

Given,

        The height of a cone is two times its base diameter.

         we have to find the volume of cone in terms of base radius.

let us assume the base radius of cone is equal to r units

                    so diameter(d) of cone will be, d= 2r units

so,

     height(h) of cone will be equal to, h = 2d units

                                                           h = 2x2r units

                                                           h = 4r  units

We know,

              Volume of the cone(V) = [tex]\pi r^{2} h/3[/tex]

                Where,

                             r = radius of base

                            h = height of cone

                            π = 22/7

Thus by using formula,

                                   Volume of cone(V) = [tex]\pi r^{2} h/3[/tex]

                                                                 = 22/7 * [tex]r^{2}[/tex] * 4r/3

                                                                 = 88[tex]r^{3}[/tex]/21

                                                                 = [tex]\frac{88r^{3} }{21}[/tex]

  Hence,

              The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]

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Answer:

dd

Step-by-step explanation:d

Answer:

Step-by-step explanation:

a0 - x-y=3

Cost for each pound of chocolate chips is equal to $3.5.

Cost for each pound of walnuts is equal to $1.75

In order to solve this word problem, we would assign variables to the cost for each pound of chocolate chips and each pound of walnuts respectively, and then translate the word problem into algebraic equation as follows:

For 3 pounds of chocolate chips and 2 pounds of walnuts, we have:

3c + 2w = 14              .....equation 1.

For 5 pounds of chocolate chips and 6 pounds of walnuts, we have:

5c + 6w = 28      .....equation 2.

Solving the system of equations by using the elimination method, we have:

3 × (3c + 2w = 14) = 9c + 6w = 42

                                5c + 6w = 28_

4c = 14

c = 14/4

c = $3.5

For the cost for each pound of walnuts, we have:

3c + 2w = 14

3(3.5) + 2w = 14

10.5 + 2w = 14

2w = 14 - 10.5

2w = 3.5

w = 3.5/2

w = $1.75.

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The absolute value function is represented by f(x) = |x+3| and the

x-intercept of the function is -3.

The function is represented as absolute value of 3 more than x.

hence the function 3 more than x is given by

f(x)=x+3

Now for absolute function:

f(x)=|x+3|

The graph of the function will have no negative value for f(x).

The graph will pass through the point (0,3) which is the y-intercept.

The x-intercept is at (-3,0) .

The domain of the function is all real vales of x.

The range of the function is (0,∞)

The parent function is given by y=|x| .

An procedure that establishes the absolute value of a number or variable is known as a modulus function. It produces the variable count's size.

It is also known as an absolute value function. No matter what input was given to this function, a positive result is always the result.

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After the firm work year reduced to 48 weeks at the same rate, the architect annual pay decrease to 43,392 dollars.

An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects

The company cuts the work year to 48 weeks but keeps the same rate of pay.  The amount the architect should expect his annual pay to decrease can be calculated as follows:

Let's find the rate.

Therefore,

52 weeks = 47008

1 week = ?

cross multiply

rate = 47008 / 52

rate = 904 dollars per weeks

He collects the same rate after the company cuts the work year to 48 weeks.

Therefore,

annual pay of the architect after the cut = 48 × 904

annual pay of the architect after the cut = 43,392 dollars

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Step-by-step explanation:

1. if to rewrite the given equation, then

y= -3(x+5)²+1;

2. the vertex of the parabola is (-5;1) and it is the highest point. Then

3. domain: x is any value, x∈(-∞;+∞);

range: y not greater than 1, y∈(-∞;1].

For the parabola f(x) = -3x² - 30x - 74, the domain is all real numbers (-∞, ∞), and the range is also all real numbers (-∞, ∞).

To determine the domain and range of the given parabola f(x) = -3x² - 30x - 74, we need to understand the behavior of parabolas.

The domain of a function represents all the possible x-values for which the function is defined. In this case, there are no restrictions on the x-values for the given quadratic function. Therefore, the domain is all real numbers, expressed as (-∞, ∞).

The range of a function represents all the possible y-values that the function can produce. For a parabola, if the coefficient of the squared term (in this case, -3) is negative, the parabola opens downward. Since the coefficient is negative, the parabola will have a maximum value. In this example, there is no minimum or maximum specified; thus, the range will also be all real numbers.

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