Gary wants to make a circular pond in his yard and put a low fence around the edge. If Gary has 124 feet of fencing, which is closest to the area of the largest circular pond he can make with the fencing?

The length of one of its sides is 7x - 3

The perimeter is given as:

P = 28x - 12

The length of one of its sides is calculated as:

L = P/4

So, we have:

L = (28x - 12)/4

Evaluate

L = 7x - 3

Hence, the length of one of its sides is 7x - 3

Read more about perimeter at:

https://brainly.com/question/24571594

#SPJ1

Answer:

x – 4y = 20

Step-by-step explanation:

Put the line above in Slope Intercept Form

You can do that by solving for y

y = (1/4)x - 5

The slope, m above is 1/4

The perpendicular will a negative inverse slope m = -4

In Slope Intercept Form your perpendicular line starts below

y = -4x + b

Use the coordinates of the given point on the line (2, -5) to insert and solve for b

-5 = -4(2) + b

-5 = - 8 + b

Add 8 to both sides of the equation

-5 + 8 = b

3 = b

Finally your perpendicular line

y = -4x + 3

I hope this helps

Check my arithmetic

Answer:

×4y=20

Step-by-step explanation:

mark me as brainlist please

The solution to the equation x3 + 2x - 16 = 16 x2 + 16 is approximately x = -2.4 and x = 4.4 when using the intersection of two graphs method.

To use the method of the intersection of two graphs to find the solution of the equation x^3 + 2x - 16 = 16 x^2 + 16, we first need to graph both equations on the same coordinate system. Then, we can look for the points where the two graphs intersect, which will correspond to the solutions of the equation.

First, let's rearrange the equation into the form f(x) = g(x), where f(x) = x^3 + 2x - 16 and g(x) = 16x^2 + 16. This gives:

x^3 + 2x - 16 = 16x^2 + 16

or

x^3 - 16x^2 + 2x - 32 = 0

We can see that the two graphs intersect at two points, which correspond to the solutions of the equation. Using the graph, we can estimate the solutions to be approximately x = -2.4 and x = 4.4.

To get a more precise estimate of the solutions, we can use numerical methods such as Newton's method or bisection method. Alternatively, we can use algebraic methods such as factoring or the rational root theorem to find the exact solutions.

To find more questions on Intersection of two graphs method

https://brainly.com/question/5146978

#SPJ4

$54,000

a portion at simple interest 4%

another portion simple interest 7%

earned in one year $3,270

How much on each rate ?

Simple interest formula: P * r * t where P is the principal, r is the rate, and t is the time

Earnings at 4% = P1 * 0.04 * 1 = 0.04 P1

Earnings at 7% = P2 * 0.07 * 1 = 0.07 P2

Both add 3270, so we can write:

Equation 1: 0.04 P1 + 0.07 P2 = 3270

also both quantities invested add 54000, so we can write:

Equation 2: P1 + P2 = 54000

Solving Equation 2 for P1:

P1 = 54000 - P2

Using this value into equation 1:

0.04(54000 - P2) + 0.07 P2 = 3270

Solving for P2:

2160 - 0.04 P2 + 0.07 P2 = 3270

0.03 P2 = 3270 -2160 = 1110

P2 = 1110/0.03 = 37000

P2 = 37000

Using this value into the expression we found for P1:

P1 = 54000 - P2 = 54000 - 37000 = 17000

P1 = 17000

Answer:

She invested $17,000 at 4% and $37,000 at 7%

Answer:

Below

Step-by-step explanation:

-40 -(-12/5) =  -200/5   +   12/5   = -188/5 =  - 37  3/5

The total tax that the employee is liable for paying will be $17,836 if the taxpayer declares $100,000 as income on the finished Form 1040.

An income range that is subject to a particular income tax rate is referred to as a tax bracket. A progressive tax system includes tax brackets, which indicates that when an individual's income increases, the amount of the tax rates increases gradually. Tax rates for low-income taxpayers are generally low, whereas those for high-income taxpayers are often higher.

For instance, a single filer in 2022 with $100,000 in taxable income will pay $17,836 in taxes, or an average tax rate of 18%. Your effective marginal tax rate, however, is 24%. As a result, the employee is accountable for paying a total of $17,836 in taxes.

Read more about tax bracket

brainly.com/question/29196852

#SPJ1

Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

yes!!! because the first 3 types of bus can hold 50 people and the other 3 types of bus can hold 56 people so the total will be 320 people

Explanation:

Anything parallel to Ax+By = C is of the form Ax+By = D, where C and D are different values.

The given equation is 3x+y = 3. Anything parallel to this is 3x+y = D

Plug (x,y) = (1,-7) into that second equation to compute D

3x+y = D

D = 3x+y

D = 3(1)+(-7)

D = 3-7

D = -4

Therefore, our answer is 3x+y = -4

If you wanted to solve for y, then you'd get y = -3x-4. Both parallel lines have a slope of -3 but different y intercepts.

50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.

10m = 90 - 50

10m = 40

m = 40/10

m = 4

The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

For more such questions on length, click on:

https://brainly.com/question/28322552

#SPJ8

Answer:

  h > 5

  h < 0

Step-by-step explanation:

We suppose that a "Special Solution" inequality is one that is technically incorrect, but is written using a compact "shorthand" form.

As written, the inequality claims that 17 < 2, which is false. There can be no value of the variable that will make this true. We presume the intended meaning is ...

  17 < 3h +2   or   3h +2 < 2

Subtracting 2 from the inequality gives ...

  15 < 3h < 0

Dividing by 3 gives ...

  5 < h < 0

There is no value of h that is both greater than 5 and less than 0, so we presume this means the OR (union) of the solution sets ...

  h > 5

  h < 0

Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

Answer:

x= -3

x= 2.

Step-by-step explanation:

x^2 + x - 6 = 0

(x+3)(x-2)=0

x= -3

x= 2

x={2, -3}.

Answer:

yes

Step-by-step explanation:

Using the converse of Pythagoras' identity.

If the square of the longest side is equal to the sum of the squares on the other 2 sides, then the triangle is right.

longest side = 17 and 17² = 289

8² + 15² = 64 + 225 = 289

Since 17² = 8² + 15² , then triangle is right

problem 1

The total for a pair of socks with a 15% sales tax.

Let

x ------> the original price of a pair of socks

y -----> the total cost

we know that

If the sales tax is 15%

then

the final price will be

100%+15%=115%

115%=115/100=1.15

so

y=1.15x

problem n 2

The original price of an item less a discount of 5%.​

Let

x ------> the original price of a pair of socks

y -----> the total cost

we know that

the original price represent 100%

if the price has a discount of 5%

then

100%-5%=95%

95%=95/100=0.95

the total cost is

y=0.95x

Given System of equation has multiple solution.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation:

-1 = 2x - y and  8x - 4y = -4​

From equation 1

-1 = 2x - y

y = 2x + 1

Substitute this value on equation 2

8x - 4y = -4​

8x - 4(2x + 1) = -4

-4 = -4

An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

Thus, Given System of equation has multiple solution.

Learn more about the System of equations here:

https://brainly.com/question/12628931

#SPJ1

Answer:

  ₹35,100

Step-by-step explanation:

You want to know the university cost if it is ₹45,000 reduced by 22%.

The discounted price of tuition and fees will be ...

   ₹45,000 - 0.22 × ₹45,000

  = 0.78 × ₹45,000 = ₹35,100

Mandla will pay ₹35,100 for the year.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

∠ 1 ≅ ∠ 2

∠ 3 ≅ ∠ 4

AB = BC = 5 cm

Step 02:

We must apply the rules of congruent triangles to find the solution.

∠ 1 ≅ ∠ 2

∠ 3 ≅ ∠ 4

∠ A ≅ ∠ C

Δ AEB:

∠ 3 ===> angle

AB = 5 cm ===> side

∠ A ===> angle

Δ CEB:

∠ 4 ===> angle

BC = 5 cm ===> side

∠ C ===> angle

A-S-A rule (angle-side-angle):

Δ AEB ≅ Δ CEB, are congruent because all values are equal.

The answer is:

Applying the ASA rule we can conclude that both triangles are congruent.

Answer:

  0

Step-by-step explanation:

Subtract 3x from both sides of the equation:

  3x -3x +4 = 3x -3x -5

  4 = -5

There are no values of x that will make this true.

The equation has NO SOLUTIONS.

The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

learn more about differential equations here :

https://brainly.com/question/14620493

#SPJ9

Explanation:

This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.

Answer: A

Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.

Answer:

1. No

2. No

3. Yes

4. No

5. Yes

Step-by-step explanation:

Given the systems of linear inequalities: y < -2x + 1 and y ≤ x - 1:

In order to determine whether the given ordered pairs are solutions to the system, you could simply substitute their values into both inequality statements to see whether the ordreed pairs will satisfy both linear inequalities in the given system.

y < -2x + 1  

1 < -2(0) + 1

1 < 0 + 1

1 < 1 (False statement).

y ≤ x - 1

1 ≤ 0 - 1

1 ≤ - 1 (False statement).  

Therefore, (0, 1) is not a solution.

y < -2x + 1  

2 < -2(1) + 1

2< -2 + 1

2 < - 1 (False statement).

y ≤ x - 1

2 ≤ 1 - 1

2 ≤ 0 (False statement).  

Therefore, (1, 2) is not a solution.

y < -2x + 1  

-1 < -2(0) + 1

-1 < 0 + 1

-1 < 1 (True statement).

y ≤ x - 1

- 1 ≤ 0 - 1

- 1 ≤ - 1 (True statement).  

Therefore, (0, 1) is a solution, as it satisfies both linear inequality statements.

y < -2x + 1  

-1 < -2(-1) + 1

- 1 < 2 + 1

- 1 <  3 (True statement).

y ≤ x - 1

-1 ≤ -1 - 1

- 1 ≤ -2 (False statement).  

Therefore, (-1, -1) is not a solution because the ordered pair only satisfies one of the linear inequalities, and not both.

y < -2x + 1  

-4 < -2(2) + 1

-4 < -4 + 1

-4 < -3 (True statement).

y ≤ x - 1

-4 ≤ 2 - 1

-4  ≤  1 (True statement).  

Therefore, (2, -4) is a solution.

Answer: No

To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.

If the equation is true, then the ordered pair is a solution to the equation.

If we put (-5,6) into y=-7, we get 6=-7, which is not true.

So, (-5,6) is not a solution to the equation y=-7.

Answer:

x=-2 y=7

Step-by-step explanation:

Multiple -5 for the second equation to get -5x-20y=-130. Adding -5x-20y=-130 to 5x+y=-3 should get you -19y=-133. Divide both sides by -19 to get y=7. Subsitute 7 in for y for the first equation. Subtract 7 on both sides to get 5x=-10. Divide both sides by 5 to get x=-2. So, x=-2 and y=7.

Answer:

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

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150