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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What is x-7/4 = 5/6
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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
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.
This diagram of airport runway intersections shows two parallel runways. A taxi way crosses both runways. How are 6 and 2 related?
a)corresponding angles
b) alternate interior angles
c)same side interior angles
d) none of these
Answer: a)corresponding angles
Step-by-step explanation:
When two lines are intersected by a transversal line then the non adjacent angles in the matching corners are known as pair of Corresponding Angles.In the given figure angle 6 and angle 2 are the two non adjacent angles in the matching corners , which we called as a pair of Corresponding Angles. {By definition}
Therefore, angle 2 and angle are related by corresponding angles .
In the given diagram, angles 6 and 2 are corresponding angles.
To determine how 6 and 2 are related, we will define each of the terms in the option.
Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines. They are found at different intersections but on the same side of each parallel line and the same side of the transversal line.Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal. The angles are positioned at the inner corners of the intersections and lie on opposite sides of the transversal.Same side interior angles are two angles that are on the interior of two lines and specifically on the same side of the transversal
Angles 6 and 2 are found at different intersections but on the same side of the parallel lines and the same side of the transversal line.
Hence, angles 6 and 2 are corresponding angles.
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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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Point M is the midpoint of AB . AM=3x+3, and AB=8x−6.
What is the length of AM?
The length of AM is 21.
Given that,
Point M should be the midpoint of the AB.AM = 3x + 3.AB = 8x - 6.Now
We can say that
AB = 2AM
And,
AM = [tex]\frac{AB}{2}[/tex]
AM [tex]=\frac{(8x-6)}{2}[/tex]
= 4x - 3
Now
3x + 3 = 4x - 3
4x - 3x = 3 + 3
x = 6
Finally,
AM = 3x + 3
= 3(6) + 3
= 18 + 3
= 21
Therefore we can conclude that The length of AM is 21.
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The length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas of the squares is 269 in squared . in2. find the lengths of the sides of the two squares.
The length of the side of the big square is 13 in. while that of the smaller square is 10 in.
Square
Square is a quadrilateral in which all the sides are equal to each other. Also opposite sides are parallel to each other and all angles measure 90 degrees.
Let a represent the length of the bigger square side and b represent the length of each side of the smaller square, hence:
a = b + 3 (1)
Also:
a² + b² = 269
(b + 3)² + b² = 269
2b² + 6b - 260 = 0
b = -13 or 10. Since b cannot be negative hence b = 10.
a = b + 3 = 10 + 3 = 13
The length of the side of the big square is 13 in. while that of the smaller square is 10 in.
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To find the lengths of the sides of the two squares with a combined area of 269 square inches, where the larger square has sides 3 inches longer than the smaller square, we set up a quadratic equation based on the areas. Solving the equation gives us 10 inches for the smaller square and 13 inches for the larger square.
Explanation:Finding the Lengths of the Sides of the Two Squares
We are given that the larger square has sides that are 3 inches longer than the sides of the smaller square and that the sum of their areas is 269 square inches. Let's denote the side length of the smaller square as s inches. Then, the side length of the larger square is (s + 3) inches.
The area of the smaller square is s^2, and the area of the larger square is (s + 3)^2. The sum of their areas is given by:
s^2 + (s + 3)^2 = 269
Expanding the equation gives us:
s^2 + s^2 + 6s + 9 = 269
Combining like terms, we get:
s^2 + s^2 + 6s + 9 - 269 = 0
2s^2 + 6s - 260 = 0
Dividing the entire equation by 2, we simplify to:
s^2 + 3s - 130 = 0
This is a quadratic equation that can be factored:
(s + 13)(s - 10) = 0
Setting each factor equal to zero gives us two possible solutions for s:
s + 13 = 0s - 10 = 0The negative solution is not physically meaningful for the length of a side, so we discard s = -13 and take s = 10 inches as the side length of the smaller square. The larger square, therefore, has sides of 13 inches.
So, the side lengths of the two squares are 10 inches and 13 inches respectively.
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?
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.What is the answer to this equation y=4x+8x for x
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.
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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Why do we never accept the null hypothesis or the research hypothesis? (instead we either reject or fail to reject)?
Write an equation for the description. Ten times the sum of half a number x and 5 is 7.
ALGEBRA 2/ TRIG QUESTION ATTACHED Please help ❤️❤️
Divide these polynomial a (27x 4 - 18x 3 + 9x 2) ÷ 3x
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
.help me please thannks
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
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The area of a rectangle is 60 square inches. The length of the rectangle is 7 inches longer than the width. Which equation models this situation?
A: w + 7= 60
B: 7w = 60
C: w(w+7) = 60
D: w + 7w = 60
The answer is (c)
As the width is w , length becomes w + 7
Hence:
Area = l × b
60 = w(w+7)
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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The total cost C( in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take
a. Solving the equation for x gives x = (C - 60)/85.
b. The number of ski trips that you would take if you spend a total of $315 is 3 ski trips.
The number of ski trips that you would take if you spend a total of $315 is 5 ski trips.
In Mathematics and Geometry, a linear equation is a type of function with a constant slope and whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.
Part a.
By making x the subject of formula in the given equation, we have:
C = 85x + 60
85x = C - 60
x = (C - 60)/85
Part b.
When the value of C is 315, number of ski trips (x) is given by;
x = (315 - 60)/85
x = 3 ski trips.
When the value of C is 485, number of ski trips (x) is given by;
x = (485 - 60)/85
x = 5 ski trips.
Complete Question:
The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take.
a. Solve the equation for x.
b. How many ski trips do you take if you spend a total of $315? $485?
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
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.
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
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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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
Find the distance between a and b. a = 14/5 , b = 112/65
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.