The total amount paid by Jennifer for 14.75 gallons of gasoline at the cost of $2.95per gallons is equal to $43.51.
Total gallons of gasoline bought by Jennifer for her car = 14.75 gallons
Cost of gasoline per gallons = $2.95
The total amount Jennifer paid for the gasoline is equal to,
Amount paid by Jennifer
= Number of gallons of gasoline x Cost per gallon
Substitute the value in the formula we get,
⇒ Amount paid by Jennifer = 14.75 gallons x $2.95/gallon
⇒ Amount paid by Jennifer = $43.5125
⇒ Amount paid by Jennifer = $43.51
Therefore, the closest amount Jennifer paid for the gallons of gasoline is equal to $43.51.
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if 2400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:
The value of the investment at the end of 10 years would be $3,905.76 if the interest rate is 5% per year and compounds annually.
The value of an investment after a certain number of years depends on several factors, including the initial amount invested, the interest rate, and the compounding frequency.
Assuming a fixed interest rate and compounding frequency, we can use the formula for compound interest to calculate the value of the investment after 10 years.
For example, if the interest rate is 5% per year and the investment compounds annually, the formula would be:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Plugging in the given values, we get:
A = 2400(1 + 0.05/1)^(1*10)
A = 2400(1.05)^10
A = 2400(1.6289)
A = $3,905.76
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10. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
Flying to Kampala with a tail wind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and I child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
Let's assume that each van and each bus can carry "x" number of students.
What is the equations based information?Let's assume there are "x" students in each van and each bus. Therefore, the total number of students in High School A's senior class is 8x + 8x = 16x. We know that the total number of students in High School A's senior class is 240, so we can set up an equation:
16x = 240
Solving for x, we get:
x = 15
So, each van and each bus had 15 students in it for High School A's senior class.
Similarly, for High School B, the total number of students is 4x + 1x = 5x. We know that the total number of students in High School B's senior class is 54, so we can set up an equation:
5x = 54
Solving for x, we get:
x = 10.8
Since the number of students must be a whole number, we can round up to 11. Therefore, each van and each bus had 11 students in it for High School B's senior class.
Therefore, the total number of students in High School A's senior class is 1x + 6x = 7x. We know that the total number of students in High School A's senior class is 372, so we can set up an equation:
7x = 372
Solving for x, we get:
x = 53
Therefore, each van and each bus can carry 53 students for High School A's senior class.
Similarly, for High School B, the total number of students is 4x + 12x = 16x. We know that the total number of students in High School B's senior class is 780, so we can set up an equation:
16x = 780
Solving for x, we get:
x = 48.75
Since the number of students must be a whole number, we can round up to 49. Therefore, each van and each bus can carry 49 students for High School B's senior class.
Let's assume that the price of one senior citizen ticket is "s" and the price of one child ticket is "c". Therefore, we can set up two equations based on the given information:
[tex]3s + 9c = 75[/tex]
[tex]8s + 5c = 67[/tex]
We can solve these equations simultaneously to find the values of "s" and "c". One way to do this is to multiply the first equation by 8 and the second equation by 3, so that we can eliminate "c" and solve for "s":
[tex]24s + 72c = 600[/tex]
[tex]24s + 15c = 201[/tex]
Subtracting the second equation from the first, we get:
57c = 399
Solving for "c", we get:
c = 7
Substituting this value into one of the original equations, we can solve for "s":
[tex]3s + 9(7) = 75[/tex]
[tex]3s + 63 = 75[/tex]
[tex]3s = 12[/tex]
[tex]s = 4[/tex]
Therefore, one senior citizen ticket costs $4 and one child ticket costs $7.
Let's assume that the speed of the boat in still water is "b" and the speed of the current is "c".
Therefore, we can set up two equations based on the given information:
[tex]336 = (b + c) * 12[/tex]
[tex]336 = (b - c) * 14[/tex]
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I’m stuck please help …
….
Step-by-step explanation:
If you take the sides you already have, 2, 7, 4, and 3, and add them together, you get 16. Lets take the portion of the perimeter you already have, and lets say this figure is a rectangle.
Divide 16 by 2 to give two sides of the rectangle a portion of the perimeter.
Since the area of a rectangle is width times height, lets create a formula:
8x = 44, 44 being the area, and 8x being the width times the variable of the height.
You get 5.5. for the height of the rectangle.
Add 8+8 to 5.5+5.5
you get 27
a restaurant offers a special pizza with any 6 toppings. if the restaurant has 16 topping from which to choose, how many different special pizzas are possible?
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we can use the combination formula:C(16,6) = 16! / (6! * (16-6)!) = (161514131211) / (654321) = 8008
there are 8,008 different special pizzas possible with any 6 toppings out of 16.
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we need to use the combination formula, which is given by:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of items to choose from, and k is the number of items we want to choose.
In this case, n = 16 (the total number of toppings available), and k = 6 (the number of toppings we want to choose).
Plugging these values into the formula, we get:
C(16, 6) = 16! / (6! * (16 - 6)!)
= (16 * 15 * 14 * 13 * 12 * 11) / (6 * 5 * 4 * 3 * 2 * 1)
= 8008
Therefore, there are 8,008 different special pizzas possible with any 6 toppings out of 16.
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latrell's pool table is 3 feet wide and 7 feet long. latrell wants to replace the felt on the pool table. the felt costs $5.00 per square foot. how much would it cost in total to replace the felt on the pool table?
Latrell would need to pay 105 to replace the felt on his pool table.
Latrell has a pool table that is 3 feet wide and 7 feet long.
The pool table's felt needs to be replaced, and the cost of the felt per square foot is $5.00.
Let's find out how much it would cost Latrell to replace the pool table's felt.
What is the surface area of the pool table.
To determine the surface area of the pool table,
we need to multiply the length by the width, as shown below:
Surface area = length × width
Surface area = 7 ft × 3 ft
Surface area = 21 square feet
Now that we know the surface area of the pool table, we can determine the cost of the felt.
Latrell will need 21 square feet of felt, and it costs $5.00 per square foot.
We can use the following formula to determine the total cost of the felt:
Total cost of felt = cost per square foot × surface area.
Total cost of felt = $5.00 × 21 square feet.
Total cost of felt = $105
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Grace plans on going to the amusement park this Friday. It costs $10.00 to enter the park, and then $2.50 for every ride that Grace goes on. What will be the total cost if Grace goes on 7 rides?
Answer: 27.50
Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50
There are 10 horses in a race. In how many ways can thre first three positions of the order of the finsih occur assuming noties
There are 720 ways the first three positions of the order of finish can occur assuming no ties in a race with 10 horses.
To calculate the number of ways the first three positions can occur, we use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects we are choosing.
In this case, we have 10 horses and we want to choose the first three positions, so we get:
10P3 = 10! / (10 - 3)! = 10! / 7! = (10 x 9 x 8) / (3 x 2 x 1) = 720
Therefore, there are 720 ways the first three positions of the order of finish can occur assuming no ties.
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What are the integer solutions to the inequality below?
−
1
≤
x
≤
3
Answer:
i don't know i haven't done integers in a long time
Step-by-step explanation:
Determine the area and perimeter of the figure below. Note that each square is 1 unit in length.
Answer:
area = 127[tex]units^{2}[/tex]
perimeter = 46 units
Step-by-step explanation:
count them
If you flipped a coin 550 times, how many times would you expect it to land on heads?
Answer:
275
Step-by-step explanation:
You have a 1 in 2 chance
550/2
275 times
Quadratic function in standard form having zeros of 3 and 1/2
The standard form of a quadratic function is:
`f(x) = ax^2 + bx + c`
If the zeros of the function are 3 and 1/2, then the factors of the function are:
`(x - 3)` and `(x - 1/2)`
To find the quadratic function using these factors, you can first multiply them together:
`(x - 3)(x - 1/2) = x^2 - 7/2x + 3/2`
Now we have:
`f(x) = x^2 - 7/2x + 3/2`
This is the quadratic function in standard form that has zeros of 3 and 1/2.
Describe how it is possible to calculate the enthalpy of formation for a compound that cannot be synthesized directly from the constituent elements.
The enthalpy change of each step in the cycle must be added together to obtain the enthalpy of formation of the desired compound.
The enthalpy of formation of a compound that cannot be synthesized directly from the constituent elements can be calculated using the Hess's Law. Hess's Law states that the enthalpy change of a reaction is independent of the route taken from reactants to products. This law allows for the enthalpy of formation of a compound to be determined by summing the enthalpy changes of a series of known reactions, referred to as a ‘thermochemical cycle’, which lead to the compound of interest. To use this law, the enthalpy of formation of the intermediate species formed during the reaction must be known.
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What is p(8 or less than 7) write answer as a whole number
The expression "p(8 or less than 7)" suggests that we are looking for the probability of an event that satisfies one of two conditions: either the outcome is 8 or the outcome is less than 7. However, we need to know the specific probability distribution or situation in which this function p is being used to calculate a meaningful answer.
For example, if p represents the probability of rolling a certain number on a fair six-sided die, then p(8 or less than 7) would be 0, because 8 is not a possible outcome and all outcomes less than 7 are equally likely. However, if p represents the probability of a certain event occurring in a particular situation, then we would need more information about the nature of the event to calculate the probability.
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What is the solution to the system of equations?
A.(7,9)
B.(9,7)
C.(-5,11)
D(11,-5)
Answer:
Step-by-step explanation:
4x - 5y = -17
-4x - 24y = -244
-29y = -261
y = 9
x + 54 = 61
x = 7
(9,7) Option B
An office building casts a shadow that is 15 feet long. A nearby tree casts a showdown that is 2/5 feet long. If the tree is 5 feet tall how tall is the office building.
The height of the office building is 187.5 feet.
What are some other names for height?It is typically measured horizontally along the X-axis. Height is defined as the distance between the bottom and top of an object. In Geometry, it is sometimes referred to as altitude.
Let's call the office building's height h. We can use a proportion to find h:
height of office building / length of shadow cast by office building = height of tree / length of shadow cast by tree
h / 15 = 5 / (2/5)
The right side of the equation can be simplified as follows:
5/(2/5) = 5 * 5/2 = 12.5
When we plug this into the proportion and solve for h, we get:
h / 15 = 5 / (2/5)
h / 15 = 12.5 \sh = 15 * 12.5 \sh = 187.5
As a result, the office building's height is 187.5 feet.
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What is the value of k?
127.3°
at 3:25 p.m., two trains left kalamazoo, michigan. one train traveled westward at a constant rate of
When they are 111 miles apart, the current time is 4:10 p.m.
If the time taken for two trains to be apart by 111 miles by "t" time.
Then at that time, t, the train which is at 82 mph, should have traveled a distance of 82T miles.
d1 = 82t
At the same time, t, the train which is at 66 mph, should have traveled a distance of 66T miles.
d2= 66t
The total distance traveled by both trains is d1 + d2 = D
D = 82t + 66t
D = 148t
From the given data, D = 111
Hence, 148t = 111
Solving the equation, the time t
t = 111÷148
t = 0.75
Converting it into minutes,
t = 0.75*60
t = 45 mins.
The current time ( T ) = the time at which both the trains left ( t1 ) + 45 mins.
T = t1+t
T = 3:25 + 45 min.
T =4:10 pm
Therefore, the current time is 4:10 p.m
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The complete question is-
At 3:25 p.m., two trains left Kalamazoo, Michigan. one train traveled westward at a constant rate of 82 miles per hour, while the other traveled eastward at a constant rate of 66 miles per hour. if they are now 111 miles apart, what time is it now? show your work on how you solved this situation.
Find x and y to these two congruent triangles
Answer:
the whole is always 180 so take away the x and y and add up the remaining problems and whatever is left after that is your answer.
Step-by-step explanation:
claire invests £200000 in a saving account foe 4 years .the account pays compound interest at a rate of 1.6% per annum
calculate the total amount of interest claire will get at the end of four years
Answer:
We can use the compound interest formula to find the total amount of interest Claire will get at the end of four years:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of money in the account at the end of the four years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = £200000
r = 0.016 (1.6% expressed as a decimal)
n = 1 (compounded annually)
t = 4
So, the formula becomes:
A = £200000(1 + 0.016/1)^(1*4)
= £200000(1.016)^4
= £219,463.18
To find the total amount of interest Claire will get, we need to subtract the principal amount from the total amount of money in the account at the end of four years:
Total interest = £219,463.18 - £200,000
= £19,463.18
Therefore, Claire will get £19,463.18 in total interest at the end of four years.
Larger values of r^2
imply that the observations are more closely grouped about the:
a. average value of the independent variables.
b. average value of the dependent variable.
c. least-squares line.
d. origin.
e. None of the above answers is correct.
Larger the value of r² (R²) imply that the observations are more closely grouped about the least squares line (regression line) option C.
The dependent variables on the y-axis and the independent variables on the x-axis are shown as a linear connection by a regression line. By examining the data pattern the variables' effects have created, the correlation is established.
As the (R2) is large therefore, the model is a good fit or bounded close to regression line least squares line (regression line).
In a regression graph, the regression line that is closest to the data points is shown. By changing the value of x in the regression equation, this statistical tool helps study how a dependant variable y behaves when the independent variable x changes.
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Complete question:
Larger values of r2 (R2) imply that the observations are more closely grouped about the
Group of answer choices:
average value of the dependent variableoriginleast squares line (regression line)average value of the independent variablessuppose that for a particular distribution of scores, the mean is 6 with a standard deviation of 3. what is the z score for a raw score of 12?
The z-score for a raw score of 12 in a distribution with a mean of 6 and a standard deviation of 3 is 2.
The z-score is a measure of how many standard deviations a raw score is above or below the mean of a distribution. It is calculated by subtracting the mean from the raw score and then dividing the result by the standard deviation.
In this case, we have a mean of 6 and a standard deviation of 3. To find the z-score for a raw score of 12, we can use the formula:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the values we have, we get:
z = (12 - 6) / 3 = 2
Therefore, the z-score for a raw score of 12 in this distribution is 2. This means that the raw score of 12 is 2 standard deviations above the mean of 6. The z-score can be used to compare scores from different distributions, and to calculate probabilities and percentiles.
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Edwin drives his car at a speed of 70km per hour how much distance will he cover in 3 hour and 30 minutes
The total distance covered by Edwin in duration of 3 hours and 30 minutes at a speed of 70km per hour is equal to 245 kilometers.
Use the formula,
distance = speed x time
To find the distance Edwin covers in 3 hours and 30 minutes.
First, convert 3 hours and 30 minutes to hours.
1 hour is equal to 60 minutes, so,
This implies,
3 hours and 30 minutes
= 3 + 30/60
= 3.5 hours
Now apply the formula we have,
distance = speed x time
⇒ distance = 70 km/h x 3.5 h
⇒ distance = 245 kilometers
Therefore, distance covered by Edwin will be 245 kilometers in 3 hours and 30 minutes, if he drives at a speed of 70 km/h.
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Cameron packed two pairs of shorts and three shirts for a trip. What are some combinations of shirts and shorts. How many days will he have a different outfit to wear?
As per the combination method, Cameron can wear a different outfit for 6 days.
If we want to find the number of different combinations of shirts that Cameron can wear with a pair of shorts, we need to calculate the value of 3C1 (which means choosing 1 shirt out of 3). Using the formula above, we get:
³C₁ = 3! / (1! x (3-1)!) = 3
So there are 3 possible combinations of shirts that Cameron can wear with a pair of shorts.
Since Cameron has 2 pairs of shorts, he can wear each combination twice (once with each pair of shorts). Therefore, the total number of different outfits he can wear is:
3 (number of shirt combinations) x 2 (number of pairs of shorts) = 6
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Down below are the coordinates after dilation but it says its wrong
Answer:
For the original triangle:
A is at (-3, 6), B is at (1, 2), C is at (-5, 1).
For the new triangle:
A' will be at (-3 - 3, -(6 + 2)) = (-6, -8)
B' will be at (1 - 3, -(2 + 2)) = (-2, -4)
C' will be at (-5 - 3, -(1 + 2)) = (-8, -3)
Marissa needs 4 cups of olive oil to make a recipe if olive oil cost two dollars a cup how much money will she need to buy the olive oil
Marissa will need 4 cups of olive oil for a recipe. If olive oil costs two dollars per cup, she will need 4 x 2 = 8 dollars to buy the olive oil.
To make a recipe, Marissa needs 4 cups of olive oil. At a cost of $2 per cup, she would need to spend a total of 4 x $2 = $8 to buy the necessary amount of olive oil. This is a straightforward multiplication problem where the quantity of olive oil required is multiplied by the cost per cup. By using the multiplication operator, we can find the total cost needed to purchase the olive oil. Therefore, the total cost of the olive oil is directly proportional to the quantity of olive oil needed, with the cost per unit remaining constant at $2 per cup.
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which variables are basic and which variables are nonbasic in this tableau? what basic variables are associated with rows 1, 2, and 3 of this tableau? what are the values of all the variables associated with this basic feasible solution?
In this simplex tableau, x₄, x₅, and z are the basic variables, while x₁, x₂, x₃, x₆, x₇, and x₈ are the nonbasic variables. The values of all the variables associated with this basic feasible solution are x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, and z = 620.
In this tableau, the basic variables are x₄, x₅, and z, while the nonbasic variables are x₁, x₂, x₃, x₆, x₇, and x₈.
The basic variable associated with row 1 is x₄, the basic variable associated with row 2 is x₅, and the basic variable associated with row 3 is z.
The values of all the variables associated with this basic feasible solution are:
x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, z = 620.
Note that these values correspond to the entries in the tableau in the "BV" column.
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The missing tableau is in the image attached below
Ben Weatherstaff has a flower garden that is 9 m wide and 13 m long. He wants to increase the area to 221m² by increasing the width and the length the same amount. What will be the length (greater dimension) of the new flower garden?
A: 4m
B: 26m
C: 13m
D: 17m
Using area of the rectangle, we can find that the new flower garden will be 13m in length (greater dimension).
What do you mean by area?The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter. Multiplying the length by the width yields the area of a rectangle (breadth).
As a result, the following formula can be used to determine the area of a rectangle whose length and breadth are "l" and "w," respectively. The rectangle's area is L × W. A rectangle's area is therefore equal to length * width.
Now here the dimensions of the rectangle are, l = 13m and b, = 9m.
Area of the rectangle is 13 × 9 = 117m².
Now the area of the rectangle is increased to 221m².
So, when we increase the length from 13 m to 17m and the breadth from 9m to 13m, we get area = 17 × 13 = 221m².
Therefore, length of the new garden will be 17m long.
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The hypotenuse of a right triangular plot of land has a ratio of 16:65 with the shorter leg. The longer leg is
exactly 189 feet long. Find the perimeter of the plot of land.
Using Pythagorean theorem, the perimeter of the plot of land is 1783/16 feet.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental mathematical concept that outlines the relationship between a right triangle's three sides. It states that the square of the hypotenuse's (triangle's longest side) length equals the sum of the squares of the other two sides (the legs).
The Pythagorean theorem can be expressed numerically as follows:
a² + b² = c²
Let x= length of the shorter leg. Then, using the given ratio, the length of the hypotenuse can be expressed as 16x/65.
By the Pythagorean theorem, we have:
x² + 189² = (16x/65)²
Simplifying this equation, we get:
4225x² + 189² * 65² = 16² * x²
Solving for x, we get:
x = 315/4
Therefore, the perimeter is
189 + 315/4 + √(189² + (16/65)² * 315²/16)
Simplifying this expression, we get:
189 + 315/4 + 243/4 = 207/4 + √(2134441/256)
207/4 + 1463/16 = 1783/16
Therefore, the perimeter of the plot of land will be 1783/16 feet.
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The length of a rectangular porch is (x + 7) feet. The area of the porch is (x² + 9x + 14) square feet. Factor the expression for the area in order to find an expression for the width of the porch.
We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
area of a rectangle
Area = length x width
To do this, we can factor the expression for the area, which gives us:
x² + 9x + 14 = (x + 2)(x + 7)
Area = length x width
(x + 2)(x + 7) = (x + 7) x width
x + 2 = width
Therefore, the expression for the width of the porch is x + 2 feet.
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How long is each side of the box if the volume is 1,000,000?
Step-by-step explanation:
[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]