The length of a rectangle is 2 ft longer than its width. if the perimeter of the rectangle is 32 ft , find its area.
Final answer:
To find the area of the rectangle, first solve for the width using the perimeter formula. The width is found to be 7 ft. Then calculate the length as w + 2, which is 9 ft. The area is the product of length and width, resulting in 63 square feet.
Explanation:
To solve this problem, we need to set up equations based on the information given about the rectangle's dimensions and the perimeter.
Step 1: Define Variables
Let w be the width of the rectangle in feet. Consequently, the length l will be w + 2 feet, since the length is 2 feet longer than the width.
Step 2: Perimeter Equation
The perimeter (P) of a rectangle is given by 2(l + w). We can use the perimeter given (32 ft) to create an equation: 2(w + w + 2) = 32.
Step 3: Solve for w
Combine like terms and divide both sides by 2 to find w:
4w + 4 = 32
w = 7 ft.
Step 4: Find l
The length is w + 2, which is 7 ft + 2 ft = 9 ft.
Step 5: Calculate Area
The area of a rectangle is l × w. Therefore, the area is 9 ft × 7 ft = 63 square feet.
A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange.Aminata chooses one piece of fruit at random.What is the probability that she chooses.
The probability of Aminata choosing a specific type of fruit is calculated by dividing the number of that fruit by the total number of fruits in the bowl. Different fruit types have different probabilities due to their varying quantities.
Explanation:The question asks about the probability of Aminata choosing a specific type of fruit from a bowl containing 3 apples, 4 bananas, 2 pears, and 1 orange. To find the probability of Aminata choosing any one type of fruit, we first need to determine the total number of fruit pieces in the bowl, which is 3 apples + 4 bananas + 2 pears + 1 orange = 10 pieces of fruit.
The probability of selecting any specific type of fruit is then calculated by dividing the number of that fruit type by the total number of pieces.
The probability of choosing an apple is 3/10.The probability of choosing a banana is 4/10 or simplified to 2/5.The probability of choosing a pear is 2/10 or simplified to 1/5.The probability of choosing an orange is 1/10.Each fruit type has a different probability of being chosen based on its quantity in the total mix of fruits.
Solve 3x - 4 ≤ 2 or 2x + 11 ≥ -1.
Answer:
[All reals]............
John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard.
a. What is the largest area that can be enclosed?
b. What dimensions will result in the largest yard?
In the figure, TU is tangent to the circle at point U. Use the figure to answer the questions.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT, and the tangent segment, TU. You may used words and/or an equation.
(b) Suppose RT = 9 in. and ST = 4 in. Is it possible to find the length of TU? If so, show how to find the length. If not, explain why not.
Thanks in advance. I appreciate the help. I'm still not that good at questions like this one.
The lengths of segments in the circle are determined by the tangent-secant theorem. Given RT = 9 inches and ST = 4 inches, we can use this theorem to find that TU will be approximately 8.06 inches.
Explanation:In this complex geometry problem involving circles and tangents, there are several relationships at play. You're looking at a circle that has a secant, RT, and a tangent, TU, creating several segments within the figure.
(a) According to the tangent-secant theorem, the squared length of the tangent segment is equal to the difference in the squared lengths of the entire secant and its external part. This can be expressed mathematically as TU² = RT² - ST².
(b) We can use this theorem with the given lengths for RT and ST to find the length of TU. Plugging in, we get TU² = 9² - 4² = 65. The length of TU is the square root of this, which is approximately 8.06 inches.
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Find the volume of a cone?
Bryan is paid $32 per hour and works 8 hours per day. He receives one paid day off for each 16 days that he works. What is his true hourly wage?
A. $40 per hour
B. $34 per hour
C. $32 per hour
D. $48 per hour
$40 per hour is his true hourly wage, option A is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Bryan works 8 hours per day, so he works 16 x 8 = 128 hours during the 16-day period.
His pay for the 16-day period is 16 x 8 x $32 = $5,120.
He receives one paid day off for each 16 days that he works, so he gets 16/1 = 16 paid days off for every 16 days worked.
Therefore, he actually works for 16 - 16/1 = 0 days during those 16 days.
His true hourly wage is his total pay divided by the actual number of hours he works:
True hourly wage = $5,120 / 128 hours = $40 per hour
Hence, $40 per hour is his true hourly wage, option A is correct.
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simple interest = P × r × t
Joe borrowed $900 from Sam for six months. How much will Sam earn if he charges Joe a simple interest rate of 4 percent?
Answer:
$18.
Step-by-step explanation:
We have been given that Joe borrowed $900 from Sam for six months. The interest rate charged by Sam is 4%.
We will use Simple interest formula to solve our given problem.
[tex]I=PrT[/tex], where,
[tex]I=\text{Simple interest}[/tex],
[tex]P=\text{Principal amount}[/tex],
[tex]r=\text{Interest rate in decimal form}[/tex],
[tex]T=\text{Time in years}[/tex].
Let us convert our given rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
12 months = 1 year.
1 month = 1/12 year.
6 months = 6/12 year = 1/2 year = 0.5 year.
Upon substituting our given values in simple interest formula we will get,
[tex]I=900*0.04*0.5[/tex]
[tex]I=900*0.02[/tex]
[tex]I=18[/tex]
Therefore, Sam will earn $18 if he charge Joe a simple interest rate of 4 percent.
FUNCTIONS! HELP! Math!
If dewayne answered 38 items correctly on a test, and received a score of 76%, How Many items were on the test?
to compute how one currency compared to another you must use the
1. negotiated rate
2.exchange rate
3. agreement rate
or 4.bartered rate
im guessing its the exchange rate right ?,
Help Please
Tamara needs to buy motor oil to fill the 3 empty cylindrical barrels at her oil service center each barrel is 7 ft deep and has a radius of 4 ft what is the volume of oil needed use 3.14 for the radius.
Answer:
1055.04 volume
Step-by-step explanation:
Please help me out! :)
Sam cut a flat wooden board into fourths. He used three of the pieces as backgrounds for posters. He used equal pieces of the leftover board as backgrounds for 5 photos. What fraction of the original board did he use for each photo background? Enter your answer in the boxes.
Jane and Ron have combined annual gross earnings of $31,850. What is the
maximum amount they should consider spending for the purchase of a
house?
a. $79,625
b. $53,000
c. $31,850
d. $63,700
ANSWER ASAP WITH EXPLANATION
Triangle ABC has vertices at A(3, 8) , B(11, 8) , and C(7, 12) . Triangle FGH has vertices at F(8, 4) , G(16, 4) , and H(12, 8) . Which sequence of transformations shows that triangle ABC and triangle FGH are congruent? Select each correct answer. Translate triangle ABC down 4 units, and then translate triangle ABC right 5 units. Translate triangle FGH down 4 units, and then translate triangle FGH left 5 units. Translate triangle FGH up 4 units, and then translate triangle FGH left 5 units. Translate triangle ABC down 4 units, and then translate triangle ABC left 5 units.
This the answer hope it helps!!
Medal to correct answer!!
A game of "Doubles-Doubles" is played with two dice. If a player rolls doubles, the player earns 3 points and gets another roll. If the player rolls doubles again, the player earns 9 more points. How many points should the player lose for not rolling doubles in order to make this a fair game?
3/5
27/35
9/10
1
The answer will be 27/35
Step-by-step explanation:Probability is the number of outcomes out of total outcomes present or the extent to which something is likely to happen. In the given problem there are two dices which means there are total 36 outcomes because each dice has 6 sides. So the probability of the given case will be
Probability of getting two doubles on both dice = 1/36
Probability of getting just one double = 5/36
Similarly
Probability of getting no doubles on both dice is = 5/6.
So in order to find the probability we add the products of the probabilities and solve:
12/36 + 5*(3-x)/36 - 5*x/6 = 0
x = 27/35
Which simply means the player should lose 27/35 points for not rolling a double.
the hoop rotates through qan angle of 3/2 pie radian in 1 second how many revolutions does the hoop make in 1 minute
A cell phone plan charges $15$15 per month for 300300 text messages. The plan charges $0.08$0.08 for each additional text message. You use 6060 additional texts this month. What is your bill for the month?
The company charges 15 dollars per month for first 300 text messages and thereafter 0.08 dollars for any additional text message.
It says that we used additional 60 text messages (after fair usage of first 300 messages in the plan).
Our bill for this month would be sum of charges for 300 messages and charges for additional 60 messages.
Total bill = 15 dollars + 60x0.08 dollars = (15 + 4.80) dollars.
Total bill = 19.80 dollars.
Hence, our bill this month would be 19.80 dollars.
how is the graph of y=-1/2(5)^x-3 translated from the graph of y=1/2(5)^x
The transformation of [tex]y = -\frac12(5)^{x-3[/tex] to [tex]y = \frac12(5)^{x[/tex] is reflection across the x-axis followed by a shift to the left by 3 units
Describing the transformation of f(x) to g(x).
From the question, we have the following parameters that can be used in our computation:
[tex]y = -\frac12(5)^{x-3[/tex]
[tex]y = \frac12(5)^{x[/tex]
Rewrite them as
[tex]f(x) = -\frac12(5)^{x-3[/tex]
[tex]g(x) = \frac12(5)^{x[/tex]
From the above, we have that
f(x) is first reflected across the x-axis
This is represented by the loss of negative factor in g(x)
Then f(x) is shifted left by 3 units
This is represented by the loss of -3 in g(x)
Hence, the transformation of f(x) to g(x) is reflection across the x-axis followed by a shift to the left by 3 units
Mrs. McDonnell is making 25 paper cones to fill with popcorn for her daughter's birthday party. 4 inches 7 inches Find the volume of one paper cone if the diameter is 4 inches and the height is 7 inches. Round your answer to the nearest cubic inch.
The volume of one paper cone if the diameter is 4 inches and the height, is 7 inches is equal to 29in³.
We have given that,
Mrs. McDonnell is making 25 paper cones to fill with popcorn for her daughter's birthday party.
The volume of one cone would be 29 in³.
What is the formula for the volume of a cone?The formula for the volume of a cone is V=(1/3)πr²h.
Substituting our information we have:
V=(1/3)(3.14)(4/2)²(7)
We divide the diameter by 2 because the radius is half of the diameter. This gives us:
V=1/3(3.14)(28)
V= 29.306
V≈ 29in³
Therefore the volume of one paper cone if the diameter is 4 inches and the height, is 7 inches is equal to 29in³.
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Megan predicts she will sell 42 glasses of lemonade this weekend. If Megan actually sold 58 glasses of lemonade, what was Megan's percent error? Round your answer to the nearest tenth of a percent.
Megan's percent error is approximately 27.6%.
Megan's percent error can be calculated by finding the absolute difference between her predicted value and actual value, dividing that by the actual value, and then multiplying by 100 to get a percentage.
Calculate the absolute difference:
|58 - 42| = 16.
Find the percent error:
(16 / 58) × 100 ≈ 27.6%.
What Is The Value Of n So That The Expression
X² + 12 x + n Is A Perfect Square Trinomial ?
( 1 Point )
A . 36
B . 36
C . 72
D . 144,
Given is the expression, x² + 12x + n
It says to find value of 'n' that converts it into a Perfect Square Trinomial.
A perfect square trinomial is a quadratic expression which has a single root with multiplicity 2. i.e. it is of the form :- x² + 2bx + b² = (x + b)²
On comparing it with the given expression, we get :-
So 2b = 12 and n = b²
b = 6
and so b² = 6² = 36.
⇒ n = 36
Hence, x² + 12x + 36 = (x + 6)² i.e. n = 36 is the final answer.
The amplitude of y = -3sin(x) is _____.
Which rigid transformation does NOT result in a reversed orientation of the original image? Justify your answer
D) T(x,y) = (x, y - 2); The transformation slides the original image a given distance in a given direction. Is the CORRECT answer
Arnold's company reimburses his expenses on food, lodging, and conveyance during business trips. The company pays $40 a day for food and lodging and $0.50 for each mile traveled. Arnold drove 400 miles and was reimbursed $2600. Part A: Create an equation that will determine the number of days x on the trip (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many days did Arnold spend on this trip? (1 points)
HELP!!! Which of the following completes the statements of proof?
A police officer earned $932 a week last year. What was his yearly salary?
A. $50,328
B. $49,396
C. $47,532
D. $48,464
Jenna is a professional typist.she can type 22,500 words in 5 hours of typing.in one hour how many words can she type?in one minute how many words can she types?
Which of the following represents a physical change to matter?
A. combustion of carbon to form carbon dioxide B. rusting C. melting a stick of butter D. separating hydrogen gas from water,