To find the length and width of a rectangle given its area and the relationship between its dimensions, set up and solve an equation by following the step-by-step process.
Explanation:Given: The width of a rectangle is 3 inches less than its length and the area is 340 square inches.
To solve: Let the length be 'x' inches, then the width is 'x - 3' inches. Set up the equation 'x(x - 3) = 340', solve for 'x' to find the length and width.
Step-by-step:
Express the area as a product of the length and width: 'x(x - 3) = 340'.Expand and rearrange the equation: 'x^2 - 3x - 340 = 0'.Factor the quadratic equation: '(x + 17)(x - 20) = 0'.Solve for 'x': 'x = -17' or 'x = 20'. Since length cannot be negative, the length is 20 inches.Calculate the width: '20 - 3 = 17 inches'.the sum of the real numbers x and y is 15. their difference is 3. what is the value of xy?
The value of xy is such that the sum of the real numbers x and y is 15 and their difference is 3 is 54.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Given that sum of the x and y is 15
So,
x + y = 15
And difference
x - y = 3
By adding both equations,
2x = 18
x = 9 and y = 6
So their product 9 × 6 = 54.
Hence "The value of xy is such that the sum of the real numbers x and y is 15 and their difference is 3 is 54".
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beth owes 17,000 on her car loan. The interest rate on her loan is 4.25% She will be paying this loan off for 4 years. How much will she pay altogether?
To find the total payment Beth will make on her car loan, calculate the total cost using the loan formula. Beth will pay a total of $19,890 in total.
Explanation:Beth owes $17,000 on her car loan with a 4.25% interest rate, to be paid off over 4 years. To calculate the total amount she will pay, you use the formula for calculating the total cost of a loan: Total Payment = Principal + (Principal x Interest Rate x Time).
Principal = $17,000Interest Rate = 4.25% = 0.0425Time = 4 years.Plugging in the values:
Total Payment = $17,000 + ($17,000 x 0.0425 x 4)
Beth will pay a total of $17,000 + ($17,000 x 0.0425 x 4) = $17,000 + $2890 = $19,890 altogether.
Does a two-digit number exist such that the digits sum to 9 and when the digits are reversed the resulting number is 9 greater than the original number? Identify the system of equations that models the given scenario. t + u = 9 10t + u = 10u + t – 9 t + u = 9 10t + u = 10u + t t + u = 9 tu = ut + 9
The answer would be "t + u = 9 and 10t + u = 10u + t - 9". This can be found if you replaced t with 4 and u with 5. Adding the 2 digits would give you 9, and using the formula "10t + u = 10u + t - 9". Replace t and u with 4 and 5 then simplify. 10*4 + 5 = 10*5 + 4 - 9. Simplifying you'd get 45 = 54 - 9 or 45 = 45 which make the statement true. Thus making "t + u = 9 and 10t + u = 10u + t - 9" the answer.
I hope this helps!
The equations described in this problem are:
t + u = 9
10t + u = 10u + t - 9
When the two equations are substituted and solved, t = 4 and u = 5.
The original number described in the word problem is 45.
Help!! There are at least 3 slices of bread left in the bag how do I write an inequality for that?
Answer:
I need help on this question too but instead of 3 its 7!!! i also need to write both a inequality and a graph! pls respond as fast as possible.
Step-by-step explanation:
thanks
Theresa worked 9 hours on Monday and 7 hours on Wednesday. Her total pay was $156.00. What is her rate per hour?
What would be the radius of A= 530.66 square meter
Scott viewed 72 classic cars at a car show.Of the cars he viewed,3/8 were sports cars. How many sports cars did Scott view
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
Answer:
B on Edge 2020
Step-by-step explanation:
(-2,2)
What could be the length of the third side of the triangle if it is known that the first two sides are 15 and 27?
Please tell me the answer if you absoulutley know it
In the regular nonagon shown, what is the measure of angle x?
4/15 divided by 8/25
Anna is buying trim to go around her rug. Her rug measures 54 inches by 42 inches. How many inches of trim will Anna need to buy
What is the sum of the series? ∑ i=1 5 4i Enter your answer in the box.
Answer:
the answer IS 60
Step-by-step explanation:
The sum of the given series [tex]\sum 4i[/tex] is 60.
What do you mean by the sum of the series?A series can have a sum of each term of the series tends to zero but there are some series in which has each term tends to be zero and do not have a sum.
5
[tex]\sum 4i[/tex] = 4 × 1 + 4 × 2 + 4 × 3 + 4× 4 + 4 × 5
i=1 = 4 + 8 + 12 + 16 + 20
= 60
Hence, the sum of the series [tex]\sum 4i[/tex] is 60.
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A fresh cup of coffee is placed on a table to cool. The table below shows the relationship between the temperature of the coffee, y, as it relates to time in minutes, x.
Time (minutes), x 0 1 2 3
Temperature (F°), y 200 150 112.5 84.375
Which function can be used to represent the relationship shown in the table?
y = (0.75) x
y = 0.75(200) x
y = 200(-0.75) x
y = 200(0.75) x
y = 200 * (0.75) ^ x
The local sports shop has backpacks on sale for $28. The original price was $40. What is the percent decrease for the backpack price?
A company pays its commercial agents 5% of any deal. What should the value of a deal be for the agent to earn $2000?
Answer:
The value of the deal should be $40,000.
Step-by-step explanation:
remember that 5% as a decimal is .05.Let x = value of deal
The equation would be .05x = $2000
Divide both sides by 0.05.
x=40,000
What is the length of BB' ?
This picture shows a feeding trough that is shaped like a right prism 5,4,6. list each face of the feeding trough . What is the surface area of the trough?
Please help
Answer:
Step-by-step explanation:
Samantha works at a nursery where she pots plants. It takes her 1 1/2 hours to pot 12 plants. How many plants can Samantha pot in 1 hour? (Please give me the equation you used.)
Please help fast!
Final answer:
Samantha can pot 8 plants in 1 hour.
Explanation:
To find out how many plants Samantha can pot in 1 hour, we need to determine how many plants she can pot in 1 1/2 hours and then convert that to 1 hour.
If Samantha can pot 12 plants in 1 1/2 hours, we can set up a proportion to find out how many plants she can pot in 1 hour:
12 plants / 1.5 hours = x plants / 1 hour
To solve for x, we can cross multiply:
12 * 1 = 1.5 * x
12 = 1.5x
To isolate x, divide both sides of the equation by 1.5:
x = 12 / 1.5
Simplifying the equation, we get:
x = 8
Therefore, Samantha can pot 8 plants in 1 hour.
PLEASE HELP ASAP
Which polynomial is a quintic binomial? 3x^5+2 x^2+4x 5x^2−2x+1 x^4+2x^3−x^2+7x+11
Bonds from the city of Denver with a face value of $1,000 each are selling at 110.611. If Sean wishes to purchase three such bonds, how much can he expect to pay?
Answer:
The answer is C-3,318.33
Step-by-step explanation:
just took the test homie
The unit used to measure an angle is called
What is the slope of a line that is perpendicular to the line shown?
(3, 3) (-3, -1)
Answer:
-3/2
Step-by-step explanation:
The line shown has slope ...
... (y2 -y1)/(x2 -x1) = (-1 -3)/(-3 -3) = -4/-6 = 2/3
The slope of the perpendicular line is the opposite of the reciprocal of this:
... -1/(2/3) = -3/2
The price has changed from $120 to $75. by how many percent did it change?
The price has changed by 37.5% from $120 to $75.
Explanation:To find the percentage change, we can use the formula:
Percentage change = ((new value - old value) / old value) * 100
In this case, the old value is $120 and the new value is $75. Plugging these values into the formula, we get:
Percentage change = (($75 - $120) / $120) * 100 = (-$45 / $120) * 100 = -0.375 * 100 = -37.5%
Therefore, the price has changed by 37.5%.
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The percentage change in price from $120 to $75 is calculated by subtracting the initial price from the final price, dividing the result by the initial price, and then multiplying by 100. The price has decreased by 37.5%.
Explanation:The question involves calculating the percentage change in price. To do this, you start by subtracting the final price ($75) from the initial price ($120) to determine the difference. In this case, the difference is $120 - $75 = $45. This represents the total change in price.
To find out the percentage change represented by this difference, you divide the difference ($45) by the original price ($120) and then multiply the result by 100 to convert it to a percentage. This can be represented by the formula:
((Final Price - Initial Price) / Initial Price) x 100.
So, the percentage change would be calculated as follows: ((120 - 75) / 120) * 100 = 37.5%. Therefore, the price has decreased by 37.5%.
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a medication is supplied in a mixture that contains 7.5 mg of medication per millimeter of solution. the dosage rate is 10.0 mg of active ingredient per kilogram of body weight. calculate the number of millimeters of medication that should be given to a patient weighing 187 lb.
The length of the longer leg of a right triangle is 19ft more than five times the length of the shorter leg. the length of the hypotenuse is 20ft more than five times the length of the shorter leg. find the side lengths of the triangle.
This problem can be solved by creating and solving a quadratic equation based on the Pythagorean theorem. We denote the length of the shorter leg as 'x', and substitute '5x+19' and '5x+20' as lengths of the longer leg and hypotenuse in the theorem.
Explanation:The entire problem revolves around the application of the Pythagorean theorem, which in a right-angled triangle gives the relationship a² + b² = c², were a and b are the lengths of the shorter sides (legs) and c is the length of the longest side (hypotenuse).
Let's denote the length of the shorter leg as 'x'. From the problem, we know that the longer leg is 5x+19 and the hypotenuse is 5x+20. Using the Pythagorean theorem, we have:
((5x+19)² + x²) = (5x+20)².
You can solve this equation to find out the value of 'x', following which you can substitute this value back into 5x+19 and 5x+20 to find lengths of the longer leg and hypotenuse.
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3) Ashley uses the two points on the coordinate plane to represent the location of her house and the public library. Each unit on the graph represents 1 mi. How far is the public library from Ashley’s? Show your work.
Isabella jump rope is 2.03 meters long. Avery jump rope is 0.15 meters shorter than Idabellas jump rope. Measures in meters, what is the length of Averys jump rope?
What is the simplified form of the expression? x8 - 2y10 - 5x5
What is the constant of proportionality in the equation 2y=6x
The constant of proportionality in the equation 2y = 6x is [tex]\( \frac{1}{3} \)[/tex].
In the equation (2y = 6x), the constant of proportionality represents the relationship between x and y. To isolate it, divide both sides of the equation by (6x):
[tex]\[\frac{2y}{6x} = \frac{6x}{6x}\][/tex]
This simplifies to:
[tex]\[\frac{1}{3} = \frac{y}{x}\][/tex]
So, the constant of proportionality is [tex]\(1/3\)[/tex], indicating that for every unit increase in x, y increases by [tex]\(1/3\)[/tex].