ALGEBRA 2/ TRIG QUESTION ATTACHED Please help ❤️❤️
The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?
omgggg please help guys
The number of yards of string lights the manager needs to enclose in this area is 26 yards.
Given that the stage manager of a school play creates a rectangular acting area of 42 square yards.
What is the perimeter of the rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
The number of yards of string lights that the manager needs to enclose the area is given by the perimeter of the rectangular area.
Let the length of the rectangular acting area be x, then the width is given by 42 / x.
Recall that the perimeter of a rectangle is given by
P = 2(length + width) = 2(x + 42/x) = 2x + 84/x
The perimeter is minimum when the differentiation of 2x + 84/x is equal to 0.
2-84/x² = 0
⇒2x²-84=0
⇒2x²=84
⇒x²=42
⇒x=√42
⇒x=6.48≈6.5
Now, perimeter = 2(6.5) + 84/6.5
=13+12.92
=25.92≈26
Therefore, the number of yards of string lights the manager needs to enclose in this area is 26 yards.
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Simplify (-2) ^2 + |-15| ÷ 3
he Mitchell family is renting a boat for the day. The boat rental has a flat fee of $100 plus $20 for each hour. They have to pay for a whole hour even if they are not out on the lake for a whole hour. For example, if they rent the boat for 3 and one-half hours, they have to pay for 4 hours. If they want to spend $250 or less on the boat rental for the day, how many hours can they rent the boat? Write an inequality and solve.
250-100 = 150
150/20 = 7.5
7 hours
inequality: 100+20x <=250
They can rent the boat for 7 hours for $ 240 in total.
Since the Mitchell family is renting a boat for the day, and the boat rental has a flat fee of $ 100 plus $ 20 for each hour, and they have to pay for a whole hour even if they are not out on the lake for a whole hour, to determine, if they want to spend $ 250 or less on the boat rental for the day, how many hours can they rent the boat, the following calculation must be performed:
Fixed cost + Variable cost multiplied by the number of hours = Final cost 100 + 20X = 250 20X = 150 X = 150/20 X = 7.5 100 + 20 x 8 = 100 + 160 = 260 100 + 20 x 7 = 100 + 140 = 240
So they can rent the boat for 7 hours for $ 240 in total.
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Which numbers should be multiplied to obtain 175^2 − 124^2?
A. 51 and 299
B. 51 and 51
C. 2601 and 2601
D. 30501 and 30749
The numbers that should be multiplied to obtain 175² - 124² are 51 and 299. This is due to the algebraic concept of a difference of squares.
Explanation:The mathematical expression 175² - 124² can be represented as the difference of squares. The difference of squares is a special case in algebra where a² - b² can be factored into (a + b)(a - b). So, in this case, we can represent 175² - 124² as (175 + 124)(175 - 124).
Hence, the numbers that should be multiplied in this case are 51 and 299. Therefore, the correct answer is option A: 51 and 299.
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If two lines intersect, then they intersect in exactly _____.
two points
one point
one line
one plane
Answer:
The correct answer is one point.
Step-by-step explanation:
In geometry, if two lines cross each other, they will do so at an exact point.
Imagine that the lines are formed by thousands of points located next to each other, which makes us see a line, therefore if they cross, they will do so at a single point that will have a coordinate in (x, y) format.
When the two lines are on the same plane, the following situations may occur:
if they match they have an unlimited number of points in common if they are different but they have the same slope they are parallel and they do not have points in common if the above does not happen, they have a single point of intersection.write 1.08 X 10^4 in standard form
The required standard form for 1.08 X 10^4 is 10800.
Given that,
To write 1.08 X 10^4 in standard form.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
1.08 * 10⁴ = 1.08 * 10000 = 10800
Thus, the required standard form for 1.08 X 10^4 is 10800.
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What is the point of intersection when the system of equations below is graphed on the coordinate plane?
x-y=1
y-x=1
A) no intersection point
B)infinite intersection points
C)(1, 0)
D)(–1, 0)
Answer with explanation:
The two system of equation which are graphed on coordinate plane :
→x -y =1
y=x-1
→y-x=1
y=x+1
⇒Comparing with Slope intercept form of Line which is y= m x +c,
→m=1 for both the lines
As, the two lines has same slope , so they are parallel.Parallel lines never Intersect.
⇒The two system of equation have no solution as:
[tex]\frac{1}{-1}= \frac{-1}{1}\neq \frac{1}{1}[/tex]
Option A:→ No Intersection Point
What is the measure of angle S?
SOLVE Janet piano teacher charged $12.50 for a 30-minute lesson if Janet has a 4 lesson per month how much will she owe her piano teacher a year
A vineyard has 165 acres of chardonnay grapes. a particular soil supplement requires 6.00 grams for every square meter of vineyard. how many kilograms of the soil supplement are required for the entire vineyard? (recall that 1 km2 = 247 acres)
Answer:
4008.10 kg
Step-by-step explanation:
We have been given that a vineyard has 165 acres of chardonnay grapes. a particular soil supplement requires 6.00 grams for every square meter of vineyard.
We know that 1 squared km equals 247 acres.
[tex]\text{165 acres}\times\frac{\text{1 km}^2}{\text{247 acres}}[/tex]
[tex]165\times\frac{\text{1 km}^2}{247}[/tex]
[tex]0.6680161943319838\text{ km}^2[/tex]
We know 1 square km equals 1000000 meters.
[tex]0.6680161943319838\text{ km}^2\times \frac{1000000\text{ m}^2}{\text{ km}^2}[/tex]
[tex]0.6680161943319838\times 1000000\text{ m}^2[/tex]
[tex]668016.1943319838\text{ m}^2[/tex]
Now, we will multiply 6 by [tex]668016.1943319838\text{ m}^2[/tex].
[tex]668016.1943319838\text{ m}^2\times \frac{\text{6 grams}}{\text{m}^2}[/tex]
[tex]668016.1943319838\times \text{6 grams}[/tex]
[tex]4008097.1659919028\text{ grams}[/tex]
[tex]4008097.1659919028\text{ grams}\times \frac{1\text{ kg}}{\text{1000 grams}}[/tex]
[tex]4008.09716599190281\text{ kg}[/tex]
[tex]4008.10\text{ kg}[/tex]
Therefore, 4008.10 kg of the soil supplement are required for the entire vineyard.
What is the total cost of a pair of jeans that are priced $50.00 if there is 7 1/2% sales tax
.help me please thannks
What is the answer to this equation y=4x+8x for x
least common multiple of 8 and 12
12⋅1=12
This is not divisible by 8.
12⋅2=24
This is divisible by 8.
8⋅3 =24
the least common multiple is 24
In which quadrant is the point (5,-2) located?
Answer: Quadrant 4
Step-by-step explanation: Since the rules for Quadrant 4 is (+, -) than it will be there because 5 is a positive number and -2 is a negative number.
After finishing his shift, a security guard wrote 6.75 under "hours worked" on his time card. how long did he work ?
The security guard worked for 6 hours and 45 minutes, this is because 0.75 of an hour is equivalent to 45 minutes.
Explanation:In the context of this question, the security guard logged 6.75 hours on his shift. This figure is given in decimal format. To convert this into hours and minutes, you need to understand that .75 of an hour is three quarters of 60 minutes. So, 0.75 x 60 minutes is 45 minutes. Therefore, the security guard worked for 6 hours and 45 minutes.
This is equivalent to 6 hours and 45 minutes. In decimal form, 0.75 represents three-quarters of an hour, which is 45 minutes. So, he worked for 6 hours and 45 minutes.
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Allie has $20 to spend to take some friends bowling. The bowling alley rents a pair of shoes for $4 & each game costs $1 for up to & including eight players. If Allie & her friends want to play three games, how many pairs of shoes can they rent?
PLEASE HELP ASAP!!! Will give brainliest!
What is the relationship between 8.76×106 and 8.76×102 ?
Select from the drop-down menus to correctly complete the statement.
8.76×10^6 is ___ times ___ than 8.76×10^2 .
1) 1000, 10,000, 100,000, or 1,000,000.
2) Greater or Less.
10^6 = 1,000,000
10^2 = 100
1,000,000 / 100 = 10,000
so 8.76x10^6 is 10,000 times greater than
Subtract your scores for questions 6,10,14, and 17 from the number 6 explain
According to the U.S. Geological Survey, the Mississippi River is 200 mi shorter than the Missouri River. Together, they cover a total of 4880 mi. Find the lengths of each river.
What is x-7/4 = 5/6
Amaya's test scores in algebra 1 are 78 and 91. She has one more test left and wants to earn a B for the course, which is from 80-89 inclusive
Answer:
Amaya must get marks between 71 and 98 in order to get B grade
Step-by-step explanation:
Amaya's test scores in algebra 1 are 78 and 91.
Let she got x marks in third test
The average all the three test must be 80-89
i.e. [tex]80\leq\dfrac{78+91+x}{3}\leq 89[/tex]
Multiplying all sides by 3, we get
240≤ 78+91+x≤ 267
240≤ 169+x≤ 267
Subtracting all sides by 169, we get
71≤ x≤ 98
Hence, Amaya must get marks between 71 and 98 in order to get B grade
Grace and jack Share £140 in the ratio 3:4 work out the amout that jack gets
The amount of money that Jack gets between the money shared is £80
What is the ratio?In mathematics, the ratio is a relation that gives a quantitative measure between two expressions in a way that tells us how A is contained in B.
Given that:
The total amount shared by Grace and Jack = £140The total ratio = 3+4 = 7The amount that Jack get is:
= (4/7) × £140
= £80
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Which point of concurrency can lie outside the triangle?
A.
incenter
B.
median
C.
orthocenter
D.
centroid
Please select the best answer from the choices provided
A
B
C
D
Divide these polynomial a (27x 4 - 18x 3 + 9x 2) ÷ 3x
The pitcher for the robins throws a baseball at 90.0 miles per hour. The pitcher on the bluebirds throws a baseball 121 feet per second. Which pitcher throws a baseball faster?
Answer:
The pitcher of robins throws a baseball faster.
Step-by-step explanation:
Speed of base ball thrown by the pitcher for the robins = 90.0 mile/hour
1 mile = 5280 feets
1 hour = 3600 seconds
[tex]90.0 mile/hour=\frac{90.0\times 5280 feet}{3600 s}=132 feet/s[/tex]
Speed of base ball thrown by the pitcher for the bluebirds= 121 feet/s
132 feet/s > 121 feet/s
The pitcher of robins throws a baseball faster.
A patio floor is shaped like a rectangle with a
width of w cm and a length of 21 ft.
Find an expression that represents the area of
the floor.
A fair coin is tossed 5 times in a row the exact probability of the coin landing heads exactly 2 times is what
Answer:
The probability is [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
Given is that a fair coin is tossed 5 times in a row.
This gives total number of outcomes as = [tex]2\times2\times2\times2\times2=32[/tex]
As its needed that heads comes exactly 2 times, so favorable outcomes are = 5C2
[tex]\frac{5!}{2!(5-2)!}[/tex]
Solving this we get 10
Therefore, the probability of getting heads exactly 2 times is =
[tex]\frac{10}{32}[/tex] or
[tex]\frac{5}{16}[/tex]
Answer:
See image
Step-by-step explanation:
Plato
Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total employee benefits are _____% of his gross pay.