Final answer:
To maximize the enclosed area, each kennel should be in the shape of a square with dimensions of 52.5 feet by 52.5 feet.
Explanation:
To maximize the enclosed area, each kennel should be in the shape of a square. Let's assume that each side of the square kennel has a length of x feet.
Each kennel has four sides, so the total length of fencing required for all four kennels is 4x feet.
Given that there are 210 feet of fencing available, we can set up the equation 4x = 210 and solve for x to find the length of each side of the square kennel.
Dividing both sides of the equation by 4, we get x = 52.5 feet.
Therefore, each kennel should have dimensions of 52.5 feet by 52.5 feet to maximize the enclosed area.
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 4% of 70%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.
PLZ HELP ME FAST! Given that ∠MQL = 180° and ∠XQR = 180°, which equation could be used to solve problems involving the relationships between ∠MQR and ∠XQL?
A) (−5b + 115) = (125 − 10b)
B) (−5b + 115) + (125 − 10b) = 180
C) (−5b + 115) − (125 − 10b) = 180
D) (−5b + 115) − 180 = (125 − 10b)
Given
∠MQL=180°
∠XQR=180°
Hence ∠MQL=∠XQR
(We know that ∠MQL is the sum of ∠MQR and ∠RQL
and ∠XQR is the sum of ∠XQM and ∠MQR)
lets plug in these in our equation
∠MQL=∠XQR
∠MQR + ∠RQL = ∠XQM + ∠MQR
We can cancel out ∠MQR
hence ∠RQL = ∠XQM
hence we can infer that the opposite angles of intersecting lines are equal
similarly
∠MQR = ∠XQL
which is
125-10b = -5b+115
Hence the right option is A)
Find the radius and the circumference to the nearest hundredth when d ≈ 3.8 in. Use 3.14 for π.
The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.
We have,
If we let d be the diameter of a circle, then the radius of the circle, r, is half of the diameter.
Therefore, we can find the radius of the circle by dividing the diameter by 2:
r = d/2
In this problem,
d ≈ 3.8 in, so we have:
r = 3.8/2 = 1.9 in
To find the circumference of the circle, we can use the formula:
C = 2πr
where π is approximately equal to 3.14 and r is the radius we just found. Substituting in the values, we get:
C = 2 x 3.14 x 1.9 ≈ 11.94 in
Therefore,
The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.
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What is 4xy + xy -7x + x?
Final answer:
The expression 4xy + xy - 7x + x simplifies to 5xy - 6x by combining like terms, specifically combining 4xy and xy to get 5xy, and -7x and x to get -6x.
Explanation:
The expression 4xy + xy - 7x + x can be simplified by combining like terms. The terms 4xy and xy are like terms, as they both have the same variables x and y to the same power. Similarly, the terms -7x and x are like terms because they both contain the variable x to the same power. To simplify, we combine 4xy and xy to get 5xy and combine -7x and x to get -6x. Therefore, the simplified expression is 5xy - 6x.
Steps involved:
The expression is 4xy + xy - 7x + x.
Combine like terms: 4xy + xy = 5xy
Combine like terms: -7x + x = -6x
Therefore, the simplified expression is 5xy - 6x.
Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will be the value of the house after 10 years
compare 16 cups to 1 gallon
The length of a side of a rectangle is 2 units less than a number, and the width is 4 units more than the length. Which of the following expressions represents the area of the rectangle, in square units?
the sum of two numbers is 51 and the difference is 15 what are the numbers
HELP! GIVING BRAINLIEST AND POINTS!!!
1. Which mixed number is greater? 8 1/3 or 8 1/4?
2. Put the following mixed numbers in order from LEAST to GREATEST: 7 1/2, 7 1/5, 7 7/8.
when derek planted a tree it was 36 inches tall. the tree grew 1 1/4 inches per year the tree is now 44 3/4 inches tall. how many years ago did derek lant the tree?
If a canoe travels with a speed of A mph for 3 hours, and then with a speed of B mph for the rest of the journey, how long does it take to travel C miles
t = (C - 3*A)/B + 3
i dont know if its correct but hope it helps!
square root of -72 written in terms of i
Bob sells hats and scarves.
At the start of the day, he has : hats : scarves = 4 : 3
During the day he sells 25 hats.
At the end of the day, he has: hats : scarves = 7 : 9
How many scarves does Bob have in his store
Alexa buys 27 stamps, each stamp is of 1 square unit of area. She exchanges them for 8 sugar cubes, whose total volume is numerically (not dimensionally) equal to the total area of Alexa?s stamps. Which of the following represents the length of a cube of sugar
Alexa exchanges 27 stamps for 8 sugar cubes. To find the length of a sugar cube, we calculate the volume of each cube and then find the cube root of the total volume.
Explanation:In this scenario, Alexa buys 27 stamps, each with an area of 1 square unit. She exchanges them for 8 sugar cubes, whose total volume is equal to the total area of the stamps. To find the length of a single sugar cube, we need to calculate the volume of each sugar cube and then find the length of one side.
The total area of the stamps is 27 square units.Since each stamp has an area of 1 square unit, the total volume of the sugar cubes is also 27 cubic units.To find the length of a single sugar cube, we need to find the cube root of 27, which is approximately 3.Therefore, the length of a cube of sugar is approximately 3 units.
Ed is on a road trip. He has already traveled 220 miles and is driving at a rate of 64 miles per hour. Which equation could be used to find how many hours, x, Ed has left in his road trip if he is traveling 604 total miles
Measurement is the use of numbers according to a standard. true or False
Answer:
The given statement is true.
Step-by-step explanation:
Measurement is the use of numbers according to a standard.
This statement is true.
Measurements should always be taken with respect to a fixed standard.
For example- If we are weighing something, the measurements should be in pounds or kilograms or ounces etc. Otherwise, we can never know the weight of anything.
Rosa made 12 gallon of lemonade to sell at a lemonade stand.How many pints of leamonade did she make
how high off the ground is kite if the man flies a kite with 100 ft of string and angles at 52 degrees?
find x intercepts of y=-3^× + 2
the product of nine and x is greater than six more than the product of three and x...?
A 32 ft ladder leans against a building so that the top of the ladder touches the building at a point 23 ft above the ground. To the nearest tenth of a foot, how far from the bottom of the building is the bottom of the ladder? 39.4 ft 27.5 ft 22.2 ft 30.1 ft
The graph shows a system consisting of a linear equation and a quadratic equation.
What is the solution(s) to the system?
Question 10 options:
(3, 4) only
This system has no solution.
(3, 4) and (5, 12)
(0, 7) and (2, 0)
Answer:
(3, 4) and (5, 12)
Step-by-step explanation:
The points where the two curves intersect are the solutions to the system of equations:
(3, 4) and (5, 12)
Answer:
Step-by-step explanation:
The graph of the function g(x) is a transformation of the parent function f(x)=x2 .
Which equation describes the function g?
g(x)=(x−3)2
g(x)=x2−3
g(x)=x2+3
g(x)=(x+3)2
Lalasa and yasmin are designing a triangular banner to hang in the school gymnasiums. They first draw the design on paper. The triangle has a base of 5 inches and a height of 7 inches. If 1 inch on the drawing is equivalent to 1.5 feet on the actual banner, what will the area of the actual banner be?
A. 17.5 ft2(squared)
B. 52.5 ft2
C. 39.375 ft2
D. 78.75 ft2
The correct answer is C. 39.375 square feet.
The student's question pertains to finding the area of the actual banner when a scale transformation is applied to a triangular design. To calculate the area of the actual banner, we need to scale the base and the height of the triangle from the drawing size to the actual size and then use the formula for the area of a triangle.
First, we convert the measurements of the base and the height from inches to feet using the given scale of 1 inch = 1.5 feet:
Base in feet: 5 inches × 1.5 feet/inch = 7.5 feetHeight in feet: 7 inches × 1.5 feet/inch = 10.5 feetWe then apply the area formula for a triangle which is Area = (base × height) / 2:
Area = (7.5 feet × 10.5 feet) / 2 = 39.375 square feet
Therefore, the correct answer is C. 39.375 square feet.
Greg drew a pair of parallel lines and a line segment next to each other on a chalkboard. Which of these statements best compares the pair of parallel lines and the line segment? (1 point) Parallel lines and the line segment have no dimensions of measurement. The parallel lines and the line segment always meet at a common endpoint which is called the vertex. Parallel lines and a line segment cannot lie on the same plane at the same time because they do not overlap. The parallel lines extend infinitely in both directions, and the line segment has two endpoints.
Answer: If drew drew a pair of lines and draw the segment between them, in a way that the segment is delimited by both lines, then:
If two lines are parallel, then they will never overlap each other, and if you draw a segment between them, then the segment will have two endpoints (one at each intersection with the lines)
So the correct answer is that the parallel lines extend infinitely in both directions, and the line segment has two endpoints.
Classify each pair of labeled angles as complementary, supplementary, or neither. Drag and drop the choices into the boxes to correctly complete the table. Each pair of angles may belong to more than one category. complementary supplementary neither Two angles, on the left a fifty three degree angle and on the right a one hundred twenty seven degree angleTwo angles, on the top a thirty four degree angle and on the bottom a fifty six degree angleTwo lines intersect with an angle on the top left labeled sixty seven degrees and on the bottom right sixty seven degrees
Answer:
Step-by-step explanation:
Since it is given that when two lines intersect, the angle on the top left is 53° and 127°, thus they both form supplementary angles as the sum of both angles that is 53+127=180°.
Also, from the given information, the angle on the top is 34° and on the bottom is 56°, they both form a complementary angle pair, a sthe sum of both the two angles is 90° as 56+34=90°.
Also, the angle on the top left is =67° and the angle on the bottom right =67°, they both form vertical pair angles as both the angles are vertically opposite to each other.
What are the equivalent ratios shown in the table? Complete the statement.
24:2=_:3=_:5.5=108:_=_:15
Answer:
24:2=36:3=66:5.5=108:9=180:15
Step-by-step explanation:
24:2=36:3=66:5.5=108:9=180:15
The complete statement is -
24 : 2 = 36 : 3 = 66 : 5.5 = 108 : 9 = 180 : 15
What is a expression? What is a mathematical equation? What are ratios?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
We have the following statement -
24 : 2 = _ : 3 = _ : 5.5 = 108: _ = _ : 15
We have -
24 : 2 = x : 3 = y : 5.5 = 108 : z = k : 15
We can solve it partly -
24/2 = x/3
x = (24 x 3)/2
x = 36
Now, we have -
36/3 = y/5.5
(36 x 5.5)/3 = y
y = 12 x 5.5
y = 66
Moving further -
66/5.5 = 108/z
z = (108 x 5.5)/66
z = 9
Finally -
(108/9) = (k/15)
k = (108 x 15)/9
k = 12 x 15
k = 180
Therefore, the complete statement is -
24 : 2 = 36 : 3 = 66 : 5.5 = 108 : 9 = 180 : 15
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If you flip the coin five times what is the probability that it will be tail all five times
Which classification best describes the following system of equations?
12x+5y-3z=36
x-2y+4z=3
9x-10y+5z=27
inconsistent and dependent
consistent and dependent
consistent and independent
inconsistent and independent
Answer: These three planes are consistent and independent.
Explanation:
Since, if the system of planes has a solution then it is called Consistent, While, if it does not have any solution then it is called inconsistent.
Further, If the consistent system has infinite solution then it is dependent but if it has only a unique solution then it is called independent.
Here, given equations of planes are
12x+5y-3z=36 -------(1 )
x-2y+4z=3 -------(2)
9x-10y+5z=27 -------(3)
From equation (1), 3z=12x+5y-36⇒z=4x+5y/3-12 ------(4)
after putting this value in equation (2) and (3), we will get two equation in variables x and y
So, x-2y+4(4x+5y/3-12)=3 ⇒x-2y+16x+20y/3-48=3⇒3x-6y+48x+20y-144=9⇒51x+14y=153 --------(5)
And, 9x-10y+5(4x+5y/3-12)=27⇒ 9x-10y+20x+25y/3-60=27⇒ 27x-30y+60x+25y-180=81⇒87x-5y=261 --------(6)
after solving equation equation (5) and (6) we will get x=3 and y=0
substituting these values in equation (4) we will get z=0
Thus the solution of these three plane (1), (2) and (3) is x=3, y=0 and z=o
Which is the unique solution, Thus the given planes are consistent and independent.
The given system of equations is consistent and independent so, [tex]\fbox{\begin\\\ \bf option (3)\\\end{minispace}}[/tex] is correct.
Further explanation:
A system of equations is said to be a consistent system if the solution exists and if the solution does not exist then it is an inconsistent system.
If a consistent system has a unique solution then it is an independent system of equations but if the number of solutions is infinite then it is a dependent system of equations.
Label the given equations as shown below:
[tex]\boxed{x-2y+4z=3}[/tex] …… (1)
[tex]\boxed{12x+5y-3z=36}[/tex] …… (2)
[tex]\boxed{9x-10y+5z=27}[/tex] …… (3)
The augmented matrix for the above equations is, as follows:
[tex]\left[\begin{array}{ccc}1&-2&4\\12&5&-3\\9&-10&5\end{array}\Biggm\vert\begin{array}{c}3\\26\\27\end{array}\right][/tex]
Apply row transformation [tex]R_{2}\rightarrow R_{2}-12R_{1}[/tex] and [tex]R_{3}\rightarrow R_{3}-9R_{1}[/tex] as,
[tex]\left[\begin{array}{ccc}1&-2&4\\0&29&-51\\0&8&-31\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]
Now, apply row transformation [tex]R_{2}\rightarrow R_{2}-4R_{3}[/tex] and [tex]R_{3}\rightarrow R_{3}-3R_{2}[/tex] as,
[tex]\left[\begin{array}{ccc}1&-2&4\\0&-3&73\\0&-1&188\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]
Now, apply row transformations [tex]R_{2}\rightarrow -R_{2}+2R_{3}[/tex] and [tex]R_{3}\rightarrow R_{3}+R_{2}[/tex] as,
[tex]\left[\begin{array}{ccc}1&-2&4\\0&1&303\\0&0&491\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]
The equations obtained from the above augmented matrix are,
[tex]\begin{aligned}x-2y+4z&=3\\y+303z&=0\\491z&=0\end{aligned}[/tex]
The first equation is simplified to obtain the value of z as,
[tex]\begin{aligned}491z&=0\\z&=0\end{aligned}[/tex]
Substitute [tex]0[/tex] for [tex]z[/tex] in the equation [tex]y+303z=0[/tex] to obtain the value of [tex]y[/tex] as,
[tex]\begin{aligned}y+(303\cdot0)&=0\\y&=0\end{aligned}[/tex]
Now, substitute [tex]0[/tex] for [tex]z[/tex] and [tex]0[/tex] for [tex]y[/tex] in the equation [tex]x-2y+4z=3[/tex] to obtain the value of [tex]x[/tex] as,
[tex]\begin{aligned}x-(2\cdot0)+(4\cdot0)&=3\\x&=3\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]3[/tex], the value of [tex]y[/tex] is [tex]0[/tex] and the value of [tex]z[/tex] is [tex]0[/tex] and the system has a unique solution.
Thus, the given system of equations is consistent and independent.
Option (1)
Here, the first option is inconsistent and dependent.
There exists a solution of the given system of equations so it is consistent.
Therefore, option (1) is incorrect.
Option (2)
Here, the second option is consistent and dependent.
There exists a solution of the given system of equations so it is consistent.
Also, the solution is unique therefore the system of equations is independent.
Therefore, option (2) is incorrect.
Option (3)
Here, the third option is consistent and independent.
There exists a solution of the given system of equations so it is consistent.
Also, the solution is unique therefore the system of equations is independent.
Therefore, option (3) is correct.
Option (4)
Here, the fourth option is inconsistent and independent.
There exists a solution of the given system of equations so it is consistent.
Therefore, option (4) is incorrect.
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Answer details
Grade: High school
Subject: Mathematics
Chapter: System of linear equations
Keywords: Equations, unique solution, independent, dependent, consistent, inconsistent, infinite solutions, homogeneous equation, non- homogeneous equation, determinant.
Ethan has $1.25 in dimes, nickels, and pennies. He has twice as many dimes as pennies, and the number of nickels is one less thank the number of pennies. How many dimes, nickels, and pennies does he have?
Answer: 10 d /5 p/ 4 n
Step-by-step explanation: