A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x−2)=48 x(x-2)=48 What is the length, x, of the garden? The length is _____ feet.
Answer:
The length is [tex]8[/tex] feet.
Step-by-step explanation:
we know that
the area of the rectangle is equal to
[tex]A=xy[/tex]
where
x is the length side of rectangle
y is the width side of rectangle
In this problem we have
[tex]A=48\ ft^{2}[/tex]
so
[tex]48=xy[/tex] ----> equation A
[tex]y=x-2[/tex] ------> equation B
substitute equation B in equation A
[tex]48=x(x-2)[/tex]
[tex]x^{2}-2x-48=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2}-2x-48=0[/tex]
so
[tex]a=1\\b=-2\\c=-48[/tex]
substitute in the formula
[tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-48)}} {2(1)}[/tex]
[tex]x=\frac{2(+/-)\sqrt{4+192}} {2}[/tex]
[tex]x=\frac{2(+/-)14} {2}[/tex]
[tex]x=\frac{2+14} {2}=8\ ft[/tex] -----> the solution
[tex]x=\frac{2-14} {2}=-6[/tex]
If the actual length of the bridge is 4200 feet, then what is the scale of the diagram of the bridge?
Xy=30
3x-y=-9
Solve by the substitution method
Write a multiplication problem in which the product is between 0.05 and 0.75
Find the x-intercepts of the parabola with vertex (-3,-18) and y-intercept at (0,0)
To find the x-intercepts of the parabola given its vertex and y-intercept, we can first determine the equation of the parabola. Then, we set y equal to zero and solve for x. In this case, the x-intercepts are 0 and -6.
Explanation:The x-intercepts of a parabola can be found by setting the y-coordinate to zero and solving for x. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex. In this case, the vertex is (-3, -18), so the equation of the parabola is y = a(x + 3)^2 - 18. Since the y-intercept is at (0, 0), we can substitute these values into the equation to solve for a. Plugging in the values gives: 0 = a(0 + 3)^2 - 18. Solving for a, we get a = 2. Therefore, the equation of the parabola is y = 2(x + 3)^2 - 18. To find the x-intercepts, we set y equal to zero and solve for x: 0 = 2(x + 3)^2 - 18. Simplifying, we have 2(x + 3)^2 = 18. Dividing both sides by 2 gives (x + 3)^2 = 9. Taking the square root of both sides, we get x + 3 = ±3. Solving for x gives the x-intercepts as x = 0 and x = -6.
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In a survey, 480 people, or 75%, said they attended a movie at least once a month. How many people were surveyed?
36% of a number is 9. What is the number
Answer:
25
Step-by-step explanation:
0.36 × (a number) = 9
9/0.36 = (a number) = 25 . . . . . divide by the coefficient of the variable
The number is 25.
Someone came into my shop and stole $100.00 from the register without my knowledge. The person came back in with the same $100.00 five minutes later and he bought $70.00 worth of items and gave him back $30.00 in change. How much money did I lose?
what is the nearest tenth of 47.5?
A rectangle has a length of 32 yards less than 3 times its width. If the area of the rectangle is 748 square yards, find the length of the rectangle.
The length of the rectangle will be 34 yards.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The two-dimensional space occupied by the rectangle is called the area of the rectangle.
Given that A rectangle has a length of 32 yards less than 3 times its width. If the area of the rectangle is 748 square yards. The length and the width will be calculated by forming an expression.
Area = L x W
Area = W ( 3W - 32 )
748 = 3W² - 32W
3W² -32W -748 = 0
W = 22 and W = -11
The width will be 22 yards put W in the expression of L to get L.
L= ( 3W - 32 )
L = ( 3 x 22 - 32 ) = 34 yards
Therefore, the length of the rectangle will be 34 yards.
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Please help ASAP
Kevin and randy muise have a jar containing 39 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $ 7.15 . How many of each type of coin do they have?
The jar contains how many quarters and nickels ?
One student is selected at random from group of 12 freshmen, 16 sophomores, 20 juniors, and 2 seniors. Find the probability that the person selected is
The price of a DVD is $19 . The price is 12% lower than last week.
What was the price of the DVD last week?
Round your answer to the nearest cent.
Need answer in less than 10 mins. plz
Solve in terms of x and Y
if the area of the triangle is 84 inches squared what is the value of x
[tex]84[/tex]
[tex] \sqrt{84} [/tex]
Question Help
The bank statement included bank charges. On the bank reconciliation, this item is:
A.
a deduction from the balance per company books.
B.
a deduction from the balance per bank statement.
C.
an addition to the balance per bank statement.
D.
an addition to the balance per company books.
Since bank charges are deductions from the bank statement balance, the correct answer is:
B. a deduction from the balance per bank statement.
When reconciling a bank statement with the company's books, bank charges are typically deducted from the balance per bank statement.
Let's break down the process:
1. Balance per bank statement: This is the ending balance reported by the bank on the statement.
2. Additions to the bank statement balance: These are items such as deposits in transit (deposits made but not yet recorded by the bank), interest earned, or other credits.
3. Deductions from the bank statement balance: These are items such as outstanding checks (checks issued by the company but not yet cleared by the bank), bank fees or charges, and NSF (non-sufficient funds) fees.
The employees from maintenance go for coffee together every day at 9 a.m. On Monday, Hector paid $5.35 for three cartons of milk, six cups of coffee, a seven doughnuts. On Tuesday, Guillermo paid 4.80 for four milks, two coffees, and eight doughnuts. On Wednesday, Anna paid $4.40 for two milks, five coffees, and six doughnuts. On Thursday, Alphonse had to pay for two milks, five coffees, and seven doughnuts. How much change did he get back from his $10bill?
I'm pretty sure its D.
the product of two consecutive even positive integers is 782 more than the sum of the two integers. Find the integers
To find the consecutive even positive integers, we set up an equation based on the given information and solve for the variables.
Explanation:Let's assume the first even positive integer is x. Therefore, the next consecutive even positive integer will be x + 2. According to the problem, the product of these two integers is 782 more than their sum. We can set up the equation as x(x + 2) = x + x + 2 + 782.
Simplifying the equation, we get x^2 + 2x = 2x + 784.
By solving this quadratic equation, we find that the value of x is 26. Therefore, the consecutive even positive integers are 26 and 28.
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The interest on 6000 at 6% compounded semiannually for eight years is?
Is one period a complete cycle of a graph?
A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving?
Use a linear approximation (or differentials) to estimate the given number.
e^−0.01
The approximate value of e^-0.01 is 0.99
Given :
we use linear approximation to estimate the given number
[tex]e^{-0.01}[/tex]
For linear approximation we use equation
[tex]L(x)=f(a)+f'(a)(x-a)[/tex]
Lets assume some value for 'a' that is close to -0.01
Lets assume a=0
[tex]f(x)=e^x\\f(0)=e^0\\f'(x)=e^x\\f'(0)=e^0[/tex]
Lets plug in all the values
[tex]L(x)=f(a)+f'(a)(x-a)\\L(x)=e^0+e^0(x-0)\\L(x)=1+1(x-0)\\L(x)=1+1x[/tex]
Now we estimate e^-0.01
the value of x is -0.01
[tex]L(x)=1+x\\L(-0.01)=1-0.01\\L(-0.01)=0.99[/tex]
The approximate value is 0.99
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To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x. Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.
Explanation:To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x.
Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.
Let's use the point x = 0 as our approximation point.
The linear equation is given by y = f'(a)(x - a) + f(a), where y represents the value of e^x, f'(a) represents the derivative of e^a at x = a, and f(a) represents the value of e^a at x = a.
Since the derivative of e^x is simply e^x, we have f'(0) = e^0 = 1.
Plugging in the values, we get y = 1(x - 0) + e^0 = x + 1. Therefore, substituting x = -0.01 into the equation, we estimate that e^−0.01 ≈ -0.01 + 1 = 0.99.
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If Cade shoots 275 free throw baskets in 2 hours, about how many can he shoot in 5 hours.
A scientist is working with 0.9m of gold wire. How long is the wire in millimeters?
Answer:
The length of the wire in millimeters is 9 × 10² mm.
Step-by-step explanation:
1 meter is equal to 1000 millimeters. This is the ratio that we use to convert a length in meters to one in millimeters. A scientist is working with 0.9 m of gold wire. We will use a conversion fraction to express this number in millimeters.
0.9 m × (1000 mm/ 1 m) = 900 mm = 9 × 10² mm (we round off to 1 significant figure)
The length of the wire in millimeters is 9 × 10² mm.
A wheel of radius 1.9 feet is moving forward at 12 feet per second. How fast is the wheel turning?
At his grandfather's funeral, rick cries, "grandpa's not coming back." approximately how old is rick?
Rick's age cannot be determined based on his statement at his grandfather's funeral.
Explanation:Rick's age cannot be determined based solely on his statement at his grandfather's funeral. Crying and expressing grief at a funeral is a normal response regardless of age. It is important to remember that people of all ages experience loss and express their emotions in different ways. Age is a complex and multifaceted characteristic influenced by a variety of factors. Therefore, it is not possible to accurately determine Rick's age based on the given information.
The Harper family is traveling to visit friends. The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.
Rate is found by dividing distance by time.
What is the rate for the family’s trip in miles per hour?
need now plz
Answer: 47.5 miles per hour
Step-by-step explanation:
We know that ,
[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Given : The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.
i.e. Distance = 276.45 miles
Time = 5.82 hours
Then, the rate(speed) for the family’s trip in miles per hour will be :-
[tex]\text{Speed}=\dfrac{276.45}{5.82}=47.5\text{ miles per hour}[/tex]
Hence, the rate for the family’s trip = 47.5 miles per hour
1.enter a quadratic polynomial which has zeros at 11 and 3
2.enter a quadratic polynomial which has zeros at -2 and 6
3.enter a quadratic polynomial which has a double root at -6
An equation with zeroes at r1 and r2 factors to (x-r1)(x-r2).
double root at r1 just means (x-r1)^2
We have given that,
enter a quadratic polynomial which has zeros at 11 and 3
What is the quadratic polynomial?A quadratic polynomial is a second-degree polynomial where the value of the highest degree term is equal to 2. The general form of a quadratic equation is given ax^2+bx+C=0
1. f(x)=(x-11)(x-3)
2. f(x)=(x-(-2))(x-6) or f(x)=(x+2)(x-6)
3. f(x)=(x-(-6))^2 or f(x)=(x+6)^2
if you wanted an expanded form
1. f(x)=x²-14x+33
2. f(x)=x²-4x-12
3. f(x)=x²+12x+36
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Janelle bought a pair of sneakers for $75.65. There was a 15% discount. What was the original price of the sneakers?
To determine the original price of Janelle's sneakers, we calculate the inverse of the 15% discount that left her with a final price of $75.65, revealing the original price to be $89.00.
To find the original price of the sneakers that Janelle bought with a 15% discount, we need to understand that the final price after the discount represents 85% of the original price. This is because a 15% discount reduces the original price by 15%, leaving us with 100% - 15% = 85% of the original price. Janelle's sneakers cost her $75.65 after the discount.
Let's denote the original price by x. Therefore, 85% of x is equal to $75.65. We can set up an equation to represent this relationship:
0.85x = $75.65
To find x, we divide both sides of the equation by 0.85:
X = $75.65 / 0.85
x = $89.00
Thus, the original price of the sneakers was $89.00 before the 15% discount.