A rectangular garden is 14 ft. by 21 ft. and is bordered by a concrete walk 3 ft. wide as shown. How manu square feet are in the surface area of just the concrete walk

The equation of the parabola is x = -1/16(\(y^{2}\)+6y-7).

According to the question,

We have the following information:

A parabola can be drawn given a focus of (−3,−3) and a directrix of x=5.

Now, let's take (x,y) to be the points of parabola.

So, we have the following expression:

Distance between (-3,-3) and (x,y) = Distance between (x,y) and x = 5

Distance between (x,y) and x = 5 will be Ix-5I

Now, we will use distance formula to solve this expression further.

\(\sqrt{(y+3)^{2}+ (x+3)^{2} }= (x-5)} }\)

Squaring on both sides of the equation:

\({(y+3)^{2}+ (x+3)^{2} }= (x-5)^2} }\)

\(y^{2}\)+9+6y+\(x^{2}\)+9+6x = \(x^{2}\)+25-10x

\(y^{2}\)+6y+6x+18-25+10x = 0

\(y^{2}\)+6y+16x-7 = 0

16x = \(-(y^{2}\)+6y-7)

x = -1/16(\(y^{2}\)+6y-7)

Hence, the equation of the parabola is x = -1/16(\(y^{2}\)+6y-7).

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Answer:  x=25.9

Step-by-step explanation:

Tan = opp / adj

Tan 67 ° = x / 11

11 Tan (67 °)= x

x = 25.914

  = 25.9 ( 3 significant figures)

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

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Sample space=S=6

Dials not blue=R+Y=2+3=5

so probability

\(\\ \sf\longmapsto P(E)=\dfrac{|E|}{|S|}\)

\(\\ \sf\longmapsto P(E)=\dfrac{5}{6}\)

Step-by-step explanation:

x intercept, y = 0

y = x + 1

0 = x + 1

x = -1

x intercept = (-1 , 0)

y intercept, x = 0

y = x + 1

y = 0 + 1

y = 1

y intercept = (0 , 1)

Answer:

B i think

Step-by-step explanation:

Answer:

11y = -32  

Step-by-step explanation:

The given problem states that x and y vary inversely, and by using the given values, an equation is formed (x * y = 9) which can be used to find y when x = 3 (y = 3).

Since x and y vary inversely, we can write the equation as x * y = k, where k is a constant.

Using the given values x = 1 and y = 9, we can substitute them into the equation to find the value of k:

1 * 9 = k

k = 9

Therefore, the equation relating x and y is x * y = 9.

To find y when x = 3, we substitute x = 3 into the equation:

3 * y = 9

y = 9 / 3

y = 3

So, when x = 3, y = 3.

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Answer:

x=58 y=26

Step-by-step explanation:

32+90=122

180-122=58

x=58

64+90=154

180-154=26

y=26

Answer:

\(PQ=22\\\\QR=7\\\\PR=29\)

Step-by-step explanation:

To find the value of y, you can create an equation where two parts of the line are equal to the whole line:

\(PQ+QR=PR\)

Substitute given values:

\((8y+6)+(y+5)=(19y-9)\)

Solve for y. Simplify parentheses:

\(8y+6+y+5=19y-9\)

Combine like terms to simplify the equation:

\(8y+y+6+5=19y-9\\\\9y+11=19y-9\)

Get the variable on one side of the equation and the constants on the other. Add 9 to both sides:

\(9y+11+9=19y-9+9\\\\9y+20=19y\)

Subtract 9y from both sides:

\(9y-9y+20=19y-9y\\\\20=10y\)

Isolate the variable. Divide both sides by 10:

\(\frac{20}{10} =\frac{10y}{10} \\\\y=2\)

The value of y is 2. Insert this value into each line segment value and solve:

\(PQ=8(2)+6\\\\PQ=16+6\\\\PQ=22\)

\(QR=(2)+5\\\\QR=7\)

\(PR=19(2)-9\\\\PR=38-9\\\\PR=29\)

:Done

You can check by using:

\(PQ+QR=PR\\\\22+7=29\)

This statement is true, so the values are correct.

The correct answer is 500 yards. The largest area for the field will be when the cube is a forecourt. With 2000 yds. of fencing, each side would be 2000/4 =  500 yds.

Long, or 500 yds.  If there were no swash also, the largest area would be given by a square configuration since adding the length and dwindling the range of a square by the same value, t will drop the area by a square with sides of length.  Now add the swash on one side. The swash acts like a glass.

As we guard in a cube on one side of the swash, imagine an identical cube on the other side. The maximum area is given when the two blocks form a square, that's when we have a cube doubly as long as wide.

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The value of the largest area of the field will be 5000 sq. ft.

From the given data,

Total pasture area of fencing =2,000 feet

The shape of the field =rectangular

As the area of the rectangle = l*b

So, we can write it as;

2000=x+2y, (As the area of surrounded by a river from one side, so we need to only fence twice of width and only one length (Side) of the rectangle.

Now applying the formula of the area of the rectangle

we will get it as:

\($$\begin{aligned}& A(x)=x\left(\frac{2000-x}{2}\right)=\frac{1}{2}\left[2000 x-x^2\right] \\& A^{\prime}(x)=\frac{1}{2}[2000-2 x]=0 \\\end{aligned}$$\)

Solving the value,

We will get: x=100 ft y=50 ft

So, determining the value of the largest area,

We will get it as:

A_{max}=(100)(50)=5000 Sq. ft.

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Answer:

2) 2/3x - 5 = 14

Step-by-step explanation:

2x-15=42

2x=57

X=28.5

Answer:

B

Step-by-step explanation:

\(d \: = \frac{h}{24} \)

\(h \: = 24d\)

On solving the provided question, we can say that the linear equation formed will be y = -2x+18

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

In xx hours, Justin can iron 40x40x shirts since he can iron 40 shirts every hour. Daniel can iron 20 shirts each hour, or 20y20y shirts, in y hours. There were 360 shirts ironed in all (40x+20y):

\(40x+20y=360\\40x+20y=360\\x+y=14\\40x+20y= 360\\x+y=14\\40x+20y = 360 x+y = 14 20y = -40x+360 \\y = -2x+18\)

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The equation of the parabola is y = x² + 10x + 8

A parabola is a symmetrical plane curve that is shaped like a U or an arch. It is defined as the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix).

The standard equation of the parabola is given by

                              y = ax² + bx + c

Here we have

The graph shows a parabola

From the graph,

The parabola passes through the coordinate points  (-4, 0) (-2, 0), and

(0, 8)  

Let y = ax² + bx + c be the equation of the parabola

At (-4, 0)

=> a(-4)² + b(-4) + c = 0

=> 16a - 4b + c = 0 ---- (1)

At (-2, 0)

=> a(-2)² + b(-2) + c = 0

=> 4a - 2b + c = 0 --- (2)

At (0, 8)

=> a(0) + b(0) + c = 8  

=> c = 8

Since c = 8

From (1) =>  16a - 4b + 8 = 0

=> 4a - b + 2 = 0

=> b = 4a + 2 --- (3)

From (2)

=> 4a - 2b + 8 = 0

=> 2a - b + 4 = 0

=> b = 2a + 4 --- (4)

From (3) and (4)

=> 4a + 2 = 2a + 4

=> 4a - 2a = 4 - 2

=> 2a = 2

=> a = 1

From (4)

=> b = 2(1) + 8

=> b = 2 + 4

=> b = 6

Hence,

The equation of the parabola is y = x² + 10x + 8

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To find the total surface area of a cross-section solid, it is necessary to identify all the faces or surfaces of the solid, find the area of each individual face or surface, and then add them all together.

After finding the area of each individual face or surface, the final step is to add them all together to get the total surface area of the cross-section solid. This can be expressed mathematically as:

Total Surface Area = Area of Face 1 + Area of Face 2 + ... + Area of Face n

Where n represents the total number of faces or surfaces of the solid.

Pythagoras theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed mathematically as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

By using Pythagoras theorem to find the length of an unknown side, it is then possible to use the appropriate formula to find the area of the face or surface and then add it to the total surface area of the cross-section solid.

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Answer:

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Answer: 12.81 (look at the image for the explanation)

Step-by-step explanation:

The answer is that the director can fill the positions in 5040 ways.

A personnel director for a corporation has hired 10 new engineers. If four distinctly different positions are open at a particular plant, in how many ways can the director fill the positions?

The answer is that the director can fill the positions in 5040 ways.

First, let's find out how many ways there are to choose four distinct positions out of the ten engineers. This is a combination problem, so we can use the formula nCr (n choose r), where n is the total number of items and r is the number of items being chosen:

nCr = n! / r!(n-r)!

In this case, n = 10 and r = 4, so:

nCr = 10! / 4!(10-4)! = 10! / 4!6! = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1) = 210

Now, for each of these combinations of positions, there are 10 x 9 x 8 x 7 ways to choose one engineer for each of the four positions.

This is a permutation problem, so we can use the formula nPr (n permute r), where n is the total number of items and r is the number of items being chosen:

nPr = n! / (n-r)!

In this case, n = 10 and r = 4, so:

nPr = 10! / 6! = 10 x 9 x 8 x 7 = 5040

Therefore, the director can fill the positions in 5040 ways.

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Answer:

A=60

Step-by-step explanation:

A=l*w

A=12*5=60

Answer: The Area of the right triangle is 30(unit of measurement?)

Step-by-step explanation:

To find the area of a right triangle we need to use this formula

A=1/2·base·height

So A=1/2·5·12

Then we get A=1/2·60

So A=30

If we follow Kaizen's principle and improve by 1% each day, we can get approximately 37.78 times better in a year.

If we follow Kaizen's principle of improving by 1% each day, we can calculate how much better we will get in a year by using the formula:

Final Value = Initial Value x (1 + Daily Improvement Percentage)^Number of Days

Since we are trying to calculate how much better we can get in a year, we can plug in the following values:

Initial Value = 1 (assuming we are starting from our current level of performance)

Daily Improvement Percentage = 0.01 (since we are trying to improve by 1% each day)

Number of Days = 365 (since there are 365 days in a year)

Using these values, we get:

Final Value = 1 x (1 + 0.01)³⁶⁵

Final Value ≈ 1 x 37.78

Final Value ≈ 37.78

This shows the power of continuous improvement and the importance of consistent effort towards our goals.

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The given statement is true. Rank A = rank M

To prove this, we can use formula which states that rank of a matrix A is equal to the dimension of its row space or column space.

Let's consider the matrix M of TA with respect to bases B of Rm and B of Rn. Since M is the matrix of a linear transformation, its row space and column space are the same as the range of TA.

Now, according to the hint, we can use formula for both matrices A and M. We have rank A = dimension of row space of A and rank M = dimension of row space of M = dimension of column space of M (since row space and column space of M are the same).

Since M is the matrix of TA, its column space is a subspace of the range of TA. Therefore, dimension of column space of M ≤ dimension of range of TA. But we know that rank A = dimension of range of TA.

Hence, we have rank M ≤ rank A.

On the other hand, we can also consider the matrix A as the matrix of a linear transformation from Rn to Rm. Then, by the same argument, we can show that rank A ≤ rank M.

Therefore, we have rank A = rank M.

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Car insurance for an 18-year-old typically ranges from $200 to $400 per month.

The cost of car insurance for an 18-year-old can vary significantly depending on various factors. Young drivers, especially those with limited driving experience, are generally considered higher risk by insurance companies, which leads to higher premiums. Insurance providers take into account factors such as the driver's age, gender, location, type of vehicle, driving record, and credit history. Additionally, factors like the level of coverage and deductibles chosen, as well as discounts available, can also impact the cost. It's important for young drivers to shop around and compare quotes from different insurance companies to find the best coverage options at the most affordable rates. Additionally, taking driver's education courses and maintaining a clean driving record can help in reducing insurance costs over time.

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What is the average monthly cost of car insurance for an 18-year-old?

The average daily balance is calculated by taking the sum of all the daily balances during a billing period and dividing it by the number of days in that period. The interest to be paid on April 1 is $150 * 1.5% = $2.25.

a. The average daily balance for the billing period is calculated by taking the sum of all the daily balances during the billing period and dividing it by the number of days in that period. For example, if the daily balances for the billing period are $100, $150, and $200, then the average daily balance is ($100 + $150 + $200) / 3 = $150. This can be rounded to the nearest cent if necessary.

b. The interest to be paid on April 1 is calculated by multiplying the average daily balance by the monthly interest rate of 1.5%. For example, if the average daily balance is $150, then the interest to be paid on April 1 is $150 * 1.5% = $2.25. This can be rounded to the nearest cent if necessary.

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The smaller percent change of push-ups is on Monday with 50%

On Monday, the change in pushups is:

(30 - 20)/20 = 10/20 = 1/2

This represents (1/2) * 100 = 50 percent

On Friday, the change in pushups is:

(40 - 25)/25 = 15/25 = 3/5

This represents (3/5) * 100 = 60 percent

Monday is 50%

Friday is 60%

Therefore, the smaller percent change occured on Monday, with 50 percent

Expressed as fraction : \($\frac{116050}{59049}$\)

\(\begin{align*} S &= \frac{a(1-r^{n})}{1-r}= \frac{2}{3} \cdot \frac{1-\left(\frac{2}{3}\right)^{10}}{1-\frac{2}{3}}\\ & = \frac{2}{3}\cdot\frac{1-\frac{1024}{59049}}{\frac{1}{3}}=\frac{2}{3}\cdot\frac{3}{1}\cdot\frac{58025}{59049}=\frac{2\cdot58025}{59049}\\ & = \boxed{\frac{116050}{59049}}. \end{align*}\)\(S &= \frac{a(1-r^{n})}{1-r}= \frac{2}{3} \cdot \frac{1-\left(\frac{2}{3}\right)^{10}}{1-\frac{2}{3}}\\ & = \frac{2}{3}\cdot\frac{1-\frac{1024}{59049}}{\frac{1}{3}}=\frac{2}{3}\cdot\frac{3}{1}\cdot\frac{58025}{59049}=\frac{2\cdot58025}{59049}\\ & = {\frac{116050}{59049}}\)

The sum S is calculated using the formula for an infinite geometric series, which states that the sum of the series is equal to the first term divided by 1 minus the common ratio.

The first term in the series is \($\frac{2}{3}$\), and the common ratio is \($\frac{2}{3}$\), so the sum is equal to \($\frac{2}{3} \cdot \frac{1-(\frac{2}{3})^{10}}{1-\frac{2}{3}}$\)

This expression simplifies to \($\frac{2 \cdot 58025}{59049}$\), or \($\frac{116050}{59049}$\)

Complete question:

What is the value of sum \(\frac{2}{3}+\frac{2^2}{3^2}+\frac{2^3}{3^3}+ \ldots +\frac{2^{10}}{3^{10}}\)?

Express your answer as a common fraction

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Answer:

12 dollars

Step-by-step explanation:

9+3