Triangle KLM repreent a ection of a park et aide for picnic table. The picnic area will take up approximately 400 quare yard in the park. Triangle K L M i hown. The length of K M i 45 yard and the length of L M i 20 yard. Angle L K M i 25 degree. Trigonometric area formula: Area = One-half a b ine (C)
To the nearet yard, what amount of fencing i needed to urround the perimeter of the picnic area?
95 yard
107 yard
160 yard
190 yard
Answers
The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.
We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.
We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.
Using this in the given triangle KLM, we get:
Area = (1/2)(KL)(KM)(sin K),
or, 400 = (1/2)(KL)(45)(sin 25°),
or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.
Thus, we get KL = 42 yards.
Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.
Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
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Answer: b
Step-by-step explanation:
Related Questions
Find the average rate of change of the function f(x)=−2x2+5 between x=−1 and x=3.
Answers
The average rate of change of the function f(x)=−2x^2+5 between x=-1 and x=3 is -16.
The average rate of change of the function f(x)=−2x^2+5 between x=-1 and x=3 is -16.What is the average rate of change?The average rate of change of a function is the ratio of the change in the y value of the function over the change in the x value of the function within a certain interval.For a function f(x),
the average rate of change from x=a to x=b is given by the formula below;Average rate of change = (f(b) − f(a)) / (b − a)Substituting the values in the formula we get,Average rate of change= [-2(3)^2+5-{-2(-1)^2+5}]/ (3-(-1))= [-2(9)+5-{-2(1)+5}] / (3+1)= (-18+5+2-5)/4 =-16 Therefore, the average rate of change of the function f(x)=−2x^2+5 between x=-1 and x=3 is -16.
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using the digits 1, 2, 3, 4, 5, 6, 7, and 9, form 4 two-digit prime numbers, using each digit only once. what is the sum of the 4 prime numbers?
Answers
Using the given digits only once , the four 2 digit prime numbers are 23 , 41 , 59 , 67 and the the sum of the 4 prime numbers is 190 .
Prime Numbers can be defined as numbers that is greater than 1 and whose only factors are 1 and itself .
For Example : 2 is prime number , 11 is a prime number .
In the question ,
9 digits are given as 1, 2, 3, 4, 5, 6, 7, and 9
we have to form 4 two - digit prime numbers , using each digit only once ,
So , the prime numbers using the given digits using the digits only once is
(i) 23
(ii) 41
(iii) 59
(iv) 67
and the sum of the 4 prime numbers is = 23 + 41 + 59 + 67
= 190
Therefore , the 4 prime numbers are 23 , 41 , 59 , 67 and their sum is 190 .
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Keith and Toby want to get a pizza that costs $18.95. Keith has $11.18, and Toby has $5.87. How much more money do they need to buy the pizza?
Answers
Answer: $1.90
Step-by-step explanation:
Combine the radicals 9 x-3 x
6
6 x
-6 2x
-6
Answers
Answer:
6xStep-by-step explanation:
9x - 3x
[When like terms are combined then as per statement they get subtracted]
= 6x (Ans)
hope this helps!
if a polynomial is divided by x-5, the quotient is 2x^2 +8x-9 and the remainder is 3 what is the original polynomial?
Answers
Answer:
\(P(x)=2x^3-2x^2-49x+48\)
Step-by-step explanation:
Let the original polynomial be \(P(x)\).
We know that when it is divided by \((x-5)\), the quotient is \(2x^2+8x-9\) and we get a remainder of 3.
Therefore, this means that:
\(\frac{P(x)}{x-5}=2x^2+8x-9+\frac{3}{x-5}\)
Remember what it means when we have a remainder. Say we have 13 divided by 3. Our quotient will be 4 R1, or 4 1 over 3. We put the remainder over the divisor. This is the same thing for polynomials.
So, to find our original polynomial, multiply both sides by \((x-5)\):
\((x-5)\frac{P(x)}{x-5}=(x-5)(2x^2+8x-9+\frac{3}{x-5})\)
The left side will cancel. Distribute the right:
\(P(x)=2x^2(x-5)+8x(x-5)-9(x-5)+\frac{3}{(x-5)}(x-5)\)
Distribute:
\(P(x)=(2x^3-10x^2)+(8x^2-40x)+(-9x+45)+(3)\)
Combine like terms:
\(P(x)=(2x^3)+(-10x^2+8x^2)+(-40x-9x)+(45+3)\)
Evaluate:
\(P(x)=2x^3-2x^2-49x+48\)
And we're done!
Explanation:
Let a be the original polynomial
Where a/(x-5) = 2x^2 + 8x - 9 (remainder 3)
a = (2x^2 + 8x - 9)(x-5) + 3
a = 2x^3 - 10x^2 + 8x^2 - 40x - 9x + 45+3
a = 2x^3 - 2x^2 - 49x + 48
2. How deep is the water?
15 ft
6 ft
Answers
7 -14m = 2m - 5 multi step variables on both sides
Answers
7 - 14m = 2m - 5
+14m +14m (add 14 on both sides)
_____________
7 = 16m - 5
+5 + 5 (add 5 on both sides)
_____________
12 = 16m
__ ___ (divide 16 on both sides)
16 16
m = 0.75
Answer:
m = 3/4
Step-by-step explanation:
7 - 14m = 2m - 5 (given)
7 + 5 - 14m = 2m - 5 + 5 (addition poe)
*add 5 to both sides to cancel -5 out*
12 - 14m = 2m
12 - 14m + 14m = 2m + 14m (addition poe)
*add 14m to both sides to cancel -14m* out*
12 = 16m
12/16 = 16m/16 (division poe)
*divide by 16 on both sides to cancel out the coefficient*
12/16 = m
m = 12/16 (symmetric property)
*mirror to the other side*
m = 12÷4/16÷4 (division poe)
*divide the numerator and denominator by its greatest common factor*
m = 3/4
Q1. Convert the following LPs to standard form: minz=3x1+x2 s.t.
x1>=3
x1+x2<=4
2x1−x2=3
x1,x2>=0
minz=3x1+x2
s.t.
x1>=3
x1+x2<=4
2x1−x2=3
x2>=0,x1: unrestricted
Answers
The standard form of the LP is
min z = 3x1 + x2
s.t.
x1+ - 3 >= 0
x2 >= 0
x2 <= 4 - x1
2x1 - x2 + s = 3
x1+, x1, x2, s >= 0.
The problem is in standard form with all constraints as "≤" inequalities and all variables non-negative.
To convert the given linear programming problem (LP) into standard form, we need to make sure that all the constraints are of the form "≤" and the objective function is in the form of "minimize" or "maximize" with all variables on the right side.
1. Start by converting the objective function. The given objective function is already in the form of "minimize," so no changes are needed.
2. Next, convert the first constraint, x1 >= 3. Since it is already in the correct form, we can move on to the second constraint.
3. Convert the second constraint, x1 + x2 <= 4. To convert it to the "≤" form, subtract x1 from both sides: x2 <= 4 - x1.
4. Now, convert the third constraint, 2x1 - x2 = 3.
Since it is an equation, we need to introduce a slack variable to convert it into an inequality.
Add a new variable, s, and rewrite the constraint as follows: 2x1 - x2 + s = 3.
5. Finally, we need to ensure that all variables are non-negative.
The given constraint x2 >= 0 is already in the correct form, but x1 has no explicit lower bound.
To address this, we can introduce a new variable, x1+, and rewrite x1 as the difference between x1+ and 3: x1 = x1+ - 3.
The standard form of the LP is now:
min z = 3x1 + x2
s.t.
x1+ - 3 >= 0
x2 >= 0
x2 <= 4 - x1
2x1 - x2 + s = 3
x1+, x1, x2, s >= 0.
In summary, the LP is converted to standard form by rewriting the constraints and introducing additional variables as necessary to ensure all constraints are in the form of "≤" and the objective function is in the form of "minimize."
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need help with bellwork I will give brainiest
Answers
Answer:
3)
3.73 mph [miles per hour]
6 km/h [kilometers per hour]
1.67 m/s [meters per second]
4) Yes, because 1.67 m/s is faster than 1.5 m/s
in 5-8, find each reciprocal. 5/9 8 7/3 1/12
Answers
the answer
155
324
5/9 (87/3(1/12)= 155/324
Brian earns $5 per hour babysitting. He makes a graph and plots what he
earns for different numbers of hours. He places the number of hours he
works on the x-axis and his earnings on the y-axis. What is the slope of the
line that Brian graphs?
Answers
Answer:
The slope of the line is 5
Step-by-step explanation:
When we talk of the slope of a straight line graph, we refer to the rate at which the values on the y-axis changes as a ratio of the changes we have on the x-axis
Now, from the question, number of hours is placed on x-axis, while we have the amounts on the y-axis
having $5 per hour means the rate of change of what is earned to number of hours worked is 5 and this is the slope of the line
Complete the explanation of how you can use equations with variables on both sides to solve real-world problems. (PLEASE HELP I GOT SCAMMED SEVERAL TIMES D:)
You can (blank) the costs of service that charge hourly or weekly rates.
A. Separate
B. Match
C. Compare
Answers
You can "compare" the costs of services that charge hourly or weekly rates using equations with variables on both sides.
Equations with variables on both sides can be used to solve real-world problems, such as comparing the costs of services that charge hourly or weekly rates.
For example, if a car rental company charges a weekly rate of $200 plus $0.25 per mile and another company charges a weekly rate of $150 plus $0.30 per mile, you can use equations with variables on both sides to determine which company offers the better deal based on the number of miles driven.
Let x be the number of miles driven and y be the total cost, then we can write two equations for the two companies:
Company A: y = 0.25x + 200
Company B: y = 0.30x + 150
We can then solve for x by setting the two equations equal to each other:
0.25x + 200 = 0.30x + 150
0.05x = 50
x = 1000
So if the number of miles driven is less than 1000, Company A is the better deal; if it's more than 1000, Company B is the better deal. Equations with variables on both sides can be used in various real-world situations to compare costs, determine rates, and solve other practical problems.
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What are the terms in the expression 5y -x + 7? A. Sy, -X B. 3,-1,7 C. 5y, -x, 7 D. Sy, x, 7
Answers
The two factors means that the two value will equate with zero
A) 2x-6
They can be aslo simplified as :
2x-6=0
2x=6
x=3
Thus they gave only one values and cannot be expressed as the factors of two product
B) 2x+6
In this expression
we can simplify as :
2x+6
2x+6=0
2x=-6
x=-3
Thus , they are also not expressed as the factors of the two product
C) 2(x+6)
In this expression
we can simplify as :
2x+12
2x+12=0
2x=-12
x=-6
Thus , they are also not expressed as the factors of the two product
D) (2+x)÷(6+x)
They can express as fraction
\(\begin{gathered} (2+x)\div(6+x)=\frac{(2+x)}{(6+x)} \\ (2+x)\div(6+x)=(2+x)(6+x)^{-1} \end{gathered}\)Thus, They express as the product of the tewo factors
Answer : D) (2+x)÷(6+x)
What is the circumference of a circle with a radius of 80 inches?
Answers
Answer:
502.4 inches
Step-by-step explanation:
\(C = 2\pi \: r \\ = 2 \times 3.14 \times 80 \\ = 6.28 \times 80 \\ = 502.4 \: in \\ \)
A textbook is opened at random. What page numbers is the book opened to if the product of the opened page numbers is 132?
Answers
The book is opened to pages 11 and 12.
How to get the product of the page
So, we can write the equation:x * (x + 1) = 132
Expanding the equation, we get:
x² + x = 132
To solve for x, we need to rewrite the equation as a quadratic equation:
x²+ x - 132 = 0
Now, we can factor the quadratic equation:
(x - 11)(x + 12) = 0
This equation has two solutions for x:
x = 11
x = -12
Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.
So, the book is opened to pages 11 and 12.
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a five-foot prep casts a shadow that is 40 feet long while standing 200 feet from a streetlight. how high above the ground is the lamp?
Answers
30ft high above the ground is the lamp.
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
BC⊥AD and DE⊥AD
∠ABC = ∠ADE(=90°)
Also,∠A=∠A
ΔABC ΔADE (AA similarity)
AB/AD = BC/DE
40/(200 + 40) = 5ft/DE
DE = 5ft×6 = 30ft
Hence, 30ft high above the ground is the lamp.
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need help with vertical angles
Answers
Answer:
ok what is thepromblem
Step-by-step explanation:
Answer:
whats up? whats tha questionn :)
Step-by-step explanation:
please help, i also need m
Answers
Therefore, the measure of angle SQR is. \(156-6y=26\) degrees.
What is triangle?A triangle is a three-sided polygon, which means it is a flat shape with straight sides. Triangles are one of the basic shapes in geometry and can be identified by their three sides and three angles. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measurements, including equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are used in many areas of mathematics and science, as well as in everyday life, such as in construction and design.
To find the measure of angle SQR, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore:
Angle QRS + Angle RSQ + Angle SQR = 180
Substituting the given values, we get:
\((2y + 16) + (4y + 8) + Angle SQR = 180\)
Simplifying and solving for Angle SQR, we get:
\(Angle SQR = 180 - (2y + 16) - (4y + 8)\)
\(= 180 - 6y - 24\)
\(= 156 - 6y\)
\(= 26\)
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how many pattern block trapezoids would create 5 hexagons
Answers
The correct answer is "It takes 15 pattern block trapezoids to create 5 hexagons."
Pattern block trapezoids are a type of geometric shape commonly used in math education. They are one of several shapes that can be used to create tessellations, or repeating patterns, on a flat surface. Pattern block trapezoids come in different sizes and are made of different colored plastic or foam, with each color representing a different size and shape. In addition to their use in creating tessellations, pattern block trapezoids are often used to teach geometry concepts such as area, perimeter, and angles. They can also be used to help students develop spatial reasoning skills and problem-solving abilities. The most common set of pattern blocks includes six shapes: the trapezoid, hexagon, square, parallelogram, rhombus, and triangle. These shapes can be combined in a variety of ways to create different patterns and designs, making them a versatile and useful tool for math education.
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Find the tangent of the angle whose measure is negative pi. (-pi)
Answers
First convert the angle measure from radians to degrees using the formula
\(\theta\cdot\frac{180}{\pi}\)Were θ represents the angle of interest
So for this exercise the angle is pi, so:
\(\pi\cdot\frac{180}{\pi}=180\)Now using the calculator you can determine tha tangent of negative 180º
tan(-180º)=0
So the tangent of negative pi should also be zero
Inez and Joel work at a store that sells
cell phones. Inez worked for 7 hours
and 23 minutes. Joel worked for
4 hours and 51 minutes. How much
longer did Inez work than Joel?
2 hours 32 minutes
12 hours 14 minutes
3 hours 28 minutes
3 hours 32 minutes
Answers
Answer:
2 hours 32 minutes
Step-by-step explanation:
Subtract.
If you could subscribe to my friend penny_pg3d on YT, that would be great! :)
This is the answer I got so the first guy got it right
In the United States, how many children under age 11 studied a language other than English in school
Answers
Answer:
less than 5%
Step-by-step explanation:
In the USA less than 5% of children under the age of 11 study a language other than English at school
Hopefully this helped- have a good day)
An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes. a. Let X ¯ be the sample average lifetime of 100 Duracell batteries and Y ¯ be the sample average lifetime of 100 Eveready batteries. What is the mean value of X ¯ − Y ¯ (i.e., where is the distribution of X ¯ − Y ¯ centered)? How does your answer depend on the specified sample sizes? b. Suppose the population standard deviations of lifetime are 1.8 hours for Duracell batteries and 2.0 hours for Eveready batteries. With the sample sizes given in part (a), what is the variance of the statistic X ¯ − Y ¯ , and what is its standard deviation? c. For the sample sizes given in part (a), draw a picture of the approximate distribution curve of X ¯ − Y ¯ (include a measurement scale on the horizontal axis). Would the shape of the curve necessarily be the same for sample sizes of 10 batteries of each type? Explain.
Answers
thanks, this is a answer (:
1. Two crucial tasks inherent in the initial stage of group therapy are orientation and ______________.
2. Ambiguity and lack of a structured approach in groups often lead to:
Answers
Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.
Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.
It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.
Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.
Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.
Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.
To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.
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Mila buys 11/12 pounds of almonds and 5/6 pounds of pecans.
Which answer is the most accurate estimate for how many more pounds of almonds she buys than pounds of pecans?
0 pounds
1/2 pounds
1 pound
Answers
Answer: Check explanation.
Step-by-step explanation: I think its 0. Not sure. Hope this helped!
High population density can cause increases in competition for resources, such as food and shelter. The table shows the number of zebras living in four different regions.
A 3-column table has 4 rows. The first column has entries Region A, Region B, Region C, Region D. The second column is labeled Population of Zebras with entries 1,312, 630, 16,400, 17,800. The third column is labeled Area (kilometers squared) with entries 212, 314, 625, 902.
In which region is competition for resources most likely the greatest?
Region A
Region B
Region C
Region D
Answers
Answer: C. Region C
Step-by-step explanation: Done on edge! Hope this helps!
An architect designed an apartment building that was to be 196 ft. High. He made a model of the building using a scale of ½ inch = 1 foot. How high was the model?
Answers
Answer:
25feet
Step-by-step explanation:
Read each problem carefully and solve.
19. Ellie built 6/10 of a fort on Saturday and the rest on Sunday. How much of the fort did Ellie build on Sunday?
A. 1/100
B. 4/100
C. 60/100
D. 40/100
Answers
Is [1 -2 1] an eigenvector of [3 3 5 6 3 6 7 7 5]? If so, find the corresponding eigenvalue.
Answers
No, [1 -2 1] is not an eigenvector of [3 3 5; 6 3 6; 7 7 5].
To determine if [1 -2 1] is an eigenvector of [3 3 5; 6 3 6; 7 7 5], we need to check if the given matrix multiplied by the vector is equal to a scalar multiple of the vector.
Let's perform the calculation:
[3 3 5; 6 3 6; 7 7 5] * [1; -2; 1] = [3 + (-6) + 5; 6 + (-6) + 6; 7 + (-14) + 5] = [2; 6; -2].
Since the result is not equal to a scalar multiple of [1 -2 1], we can conclude that [1 -2 1] is not an eigenvector of [3 3 5; 6 3 6; 7 7 5].
There is no corresponding eigenvalue for [1 -2 1] in this case.
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The radius of the front wheel of Liz's bike is 54cm. Liz goes for a cycle and travels 54. 82km. How many full revolutions did Liz's front wheel complete?
Answers
The number of full revolutions that Liz's front wheel completed is 16,037 full revolutions.
First, we need to find the circumference of the wheel. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. In this case, the radius of the wheel is 54 cm, so we can plug that into the formula:
C = 2π(54 cm) = 108π cm
Next, we need to convert the total distance traveled from kilometers to centimeters, so that we can divide by the circumference of the wheel in centimeters.
There are 100,000 centimeters in a kilometer, so we can multiply the distance traveled in kilometers by 100,000 to get the distance in centimeters:
54.82 km * 100,000 cm/km = 5,482,000 cm
Now we can divide the total distance traveled by the circumference of the wheel to find the number of full revolutions:
5,482,000c m / 108π cm = 16,037.35
So, Liz's front wheel completed approximately 16,037 full revolutions.
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