The value of the sides, NM and OL are 16 and 8 respectively
How to determine the value
To determine the value of x, we have the note the properties of a parallelogram.
The properties of a parallelogram includes;
Opposite sides of a parallelogram are parallelOpposite sides of a parallelogram are congruentOpposite angles of a parallelogram are congruentInterior angles are supplementaryEach diagonal of a parallelogram divides it into two congruent trianglesThe diagonals of a parallelogram bisect each other at right angleThen, we have;
NM = OL
substitute the values
x + 12 = 2x + 8
Now, collect like terms
x = 4
NM = 4 + 12 = 16
OL = 16
Hence, the value are 4 and 16
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A plumber is cutting pieces of pipe that are 3.27 meters long. The pipe must be within 0.07 meters of the required length. Write and solve an absolute value inequality to find the range of the length of pipe.
The range of the length is 3.2 meters to 3.34 meters
How to determine the range of the lengthFrom the question, we have the following parameters that can be used in our computation:
Length of pipe = 3.27 meters
Relative error = 0.07 meters
Represent the range with x
So, we have
|x - Length| = Relative error
substitute the known values in the above equation, so, we have the following representation
|x - 3.27| = 0.07
Remove the bracket
x - 3.27 = 0.07 or x - 3.27 = -0.07
Evaluate
x = 3.2 or x = 3.34
Hence, the range is 3.2 meters to 3.34 meters
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2. a farmer has 2,000 feet of fencing to enclose a pasture area. the field will be in the shape of a rectangle and will be placed against a river where there is no fencing needed. what is the largest area field that can be created and what are its dimensions?
The correct answer is 500 yards. The largest area for the field will be when the cube is a forecourt. With 2000 yds. of fencing, each side would be 2000/4 = 500 yds.
Long, or 500 yds. If there were no swash also, the largest area would be given by a square configuration since adding the length and dwindling the range of a square by the same value, t will drop the area by a square with sides of length. Now add the swash on one side. The swash acts like a glass.
As we guard in a cube on one side of the swash, imagine an identical cube on the other side. The maximum area is given when the two blocks form a square, that's when we have a cube doubly as long as wide.
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The value of the largest area of the field will be 5000 sq. ft.
From the given data,
Total pasture area of fencing =2,000 feet
The shape of the field =rectangular
As the area of the rectangle = l*b
So, we can write it as;
2000=x+2y, (As the area of surrounded by a river from one side, so we need to only fence twice of width and only one length (Side) of the rectangle.
Now applying the formula of the area of the rectangle
we will get it as:
[tex]$$\begin{aligned}& A(x)=x\left(\frac{2000-x}{2}\right)=\frac{1}{2}\left[2000 x-x^2\right] \\& A^{\prime}(x)=\frac{1}{2}[2000-2 x]=0 \\\end{aligned}$$[/tex]
Solving the value,
We will get: x=100 ft y=50 ft
So, determining the value of the largest area,
We will get it as:
A_{max}=(100)(50)=5000 Sq. ft.
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Find the area of quadrilateral, if it's four sides are 27cm, 25cm, 28cm and 32cm and a diagonal is 30cm
The area of quadrilateral ABCD = 4√6314 sq cm. + 15√663 sq. cm
Define the features of quadrilateral?A polygon with four sides, 4 angles, and 4 vertices is called a quadrilateral. The Latin words quadri, which indicates four, and latus, which means side, were combined to form the English word quadrilateral.For this given question:
four sides are 27cm, 25cm, 28cm and 32cm. diagonal is 30cmIn ΔABD , using Heron's formula.
semi perimeter s = a + b + c / 2
s = 27 + 25 + 30 / 2
s = 41 cm
Now,
Area ( ΔABD ) = √s(s - a)(s - b)(s - c)
Area ( ΔABD ) = √41(41 - 27)(41 - 25)(41 - 30)
Area ( ΔABD ) = √41x14x16x11
Area ( ΔABD ) = 4√6314 sq cm.
Now,
In ΔBCD
semi perimeter s = a + b + c / 2
s = 32 + 28 + 30 / 2
s = 45cm
Area ( ΔBCD ) = √s(s - a)(s - b)(s - c)
Area ( ΔABD ) = √45(45 -32)(45 - 28)(45 - 30)
Area ( ΔABD ) = 15√663 sq. cm
Thus, the area of quadrilateral ABCD = 4√6314 sq cm. + 15√663 sq. cm
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What is the focus of the hyberbola shown ?
(0, -26) and (0,25 )is the focus of the hyberbola.
Locate the hyperbola's focus?Any point in a hyperbola has distances from the two foci that are fixedly different from each other.
Every hyperbola has two foci (plural for focus). The hyperbola's branches are encircling both of them.
(0,-26) is inside the lower branch (0,-24) is not inside the lower branch (0,25) is inside the upper branch (0,30) is inside the upper branch
Lower branch is our main focus. We must examine the image to determine which of two potential solutions is correct. From the maxima to the focus for the lower branch is one distance. The top branch needs the same, which we must discover. Distances between points (0,30) and (0.25) are 1 and 6, respectively.
(0, -26) and (0,25).
The complete question is,
What is the depicted hyperbola's point of focus? (0, −26) (0, −24) (0, 25) (0, 30) (0, 30) BRAINLIESTT.
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Plsss helppp!!!!!!!!
Answer: (7)^-2 and 1/49 are equivalent
Step-by-step explanation:
If the perimeter of triangle ABC is 27. 6cm, what is the perimeter, in centimeters of triangle BCD. AB = 9. 6cm BC = 6 cm
The perimeter of the triangle BCD is 17.25 centimeters.
A closed route that covers, encircles, or outlines a one-dimensional length or a two-dimensional form is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are several uses in real life for perimeter calculations.
so, perimeter of the triangle is the sum of all its side length.
Perimeter of one triangle / perimeter of another triangle= side of one triangle by side of another triangle.
let us suppose that the perimeter of triangle BCD is equal to X
27.6/x = 9.6/6
x = 17.25 cm
therefore, the perimeter of triangle BCD is equal to 17.25 centimeters.
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a train traveled at an average speed of 45 miles per hour for 40 minutes, and at an average speed of 60 miles per hour for 1 hour. what was the average speed of the train, in miles per hour, for the trip?
So, the average speed of the train is 54.09 miles per hour.
To calculate the average speed of the train for the entire trip, you need to find the total distance traveled and the total time traveled.
First, you can convert the time traveled at each speed to hours. 40 minutes is equal to 40/60=0.67 hours. So the total time traveled is 1+0.67=1.67 hours.
To find the total distance traveled, you can use the formula: distance = speed x time. At 45 mph, the distance traveled is 45 x 0.67 = 30.15 miles. At 60 mph, the distance traveled is 60 x 1 = 60 miles. Therefore, the total distance traveled is 30.15 + 60 = 90.15 miles.
Finally, you can use the formula: average speed = total distance / total time.
Average speed = 90.15 miles / 1.67 hours = 54.09 miles per hour.
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alma starts running and jacob starts running 7 seconds later. let t represent the number of seconds since alma started running. write an expression (in terms of t ) that represents the number of seconds jacob has been running.
The expression that represents the number of seconds Jacob has been running is t - 7.
A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. An expression's structure is as follows: (Math Operator, Number/Variable, Math Operator). The two integers are connected by a mathematical operator.
Since Jacob started running 7 seconds after Alma, the number of seconds Jacob has been running can be represented as t - 7. So the expression that represents the number of seconds Jacob has been running is: t - 7.
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Solve for a. a> a+4 ○ a > 21/1/20 O O a -7
The inequality expression has no solution for a
How to determine the solution of aFrom the question, we have the following parameters that can be used in our computation:
a > a + 4
Subtract the variable a from both sides of the equation
So, we have the following representation
a - a > a + 4 - a
Evaluate the difference
This gives
0 > 4
The above expression is false
hence, the inequality has no solution
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What is the area of the roof top garden?
Total area of the roof top garden is 272 ft² .
What is the garden's square foot size?Rooftop planters can have soil depths ranging from six inches at the very least, to allow for little groundcovers and shrubs, to three to four feet, which is necessary for huge shade and coniferous trees. Divide the length by the width of a rectangle or square to find its area.
The square footage of the area is calculated by multiplying the length and width. Please maintain the same unit size (feet or inches). For a rectangular garden area, multiply the length by the width to get the square footage. A suitable garden is often one that is roughly 10 feet by 10 feet, if your landscape permits it (3 x 3 meters).
Given, the figure comprises of triangle and rectangle,
Area of rectangle = length × breadth
= 12 ft × 20 ft
= 240 ft²
Area of triangle = 1/2 × base × height
= 1/2 × 8 × (20 - 12)
= 1/2 × 8 × 8
= 32 ft²
Total area of the figure = Area of rectangle + Area of triangle
= 240 + 32
= 272 ft²
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Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students: Exceeds the Speed Limit Does Not Exceed the Speed Limit Male 40 25 Female 10 25 Based on the analysis, what can be concluded?a. Driving behavior and gender are correlated. B. Driving behavior and gender are not related. C. Driving behavior and gender are related. D. No conclusion is possible
Based on the analysis, we can be conclude that (C) Driving behavior and gender are related.
The link between variables is described by correlation. It can be viewed positively or negatively, as well as strong or weak. A correlation does not prove a cause. When the variable on the x-axis rises as the variable on the y-axis rises, there is a positive linear association. An upward-sloping straight regression line illustrates this.
When one variable rises while the other falls, there is a negative linear correlation. A straight regression line with a falling slope illustrates this. When there is a relationship between variables, but the relationship is not linear, there is a non-linear correlation (straight).
Hence, according to correlation theory, Driving behavior and gender are related.
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A figure is rotated 180 degrees clockwise about the origin. Which statement is true about the rotated figure?
(a) It is a different shape and size from the figure.
(b) It is the same shape as the figure but is larger.
(c) It is the same shape and size as the figure.
(d) It is the same shape as the figure but is smaller.
The shape and size remains the same represents the correct alternative.
What is image rotation?A rotation is a type of transformation which is a turn.A figure can be turned clockwise or counterclockwise on the coordinate plane.In both transformations the size and shape of the figure stays exactly the same.Given is that a figure is rotated 180 degrees clockwise about the origin.
When a coordinate (x, y) is rotated by 180 degrees clockwise about the origin, the new coordinates become ( - x, - y). But only the coordinates change, the shape and size remains the same.
Therefore, the shape and size remains the same represents the correct alternative.
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The functions f(x)=−34x+2 and g(x)=(14)x+1 are shown in the graph. What are the solutions to −34x+2=(14)x+1? Select each correct answer. Responses −1 negative 1 0 0 1 1 2 2 3
The solutions to the equations is the point of intersection of graphs and the points are ( 0 , 2 ) and ( 1 , 1.25 )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the first equation be represented as A
Now , the value of A is
y = ( -3/4 )x + 2 be equation (1)
Let the second equation be represented as B
Now , the value of B is
y = ( 1/4 )ˣ + 1 be equation (2)
Now , to calculate the solutions to the equations , plot the equations in the graph
The point of intersection of equation of lines represents the solution to the equation
Substituting the values in the equation , we get
( -3/4 )x + 2 = ( 1/4 )ˣ + 1
The first point of intersection is ( 0 , 2 )
when x = 0 , y = 2
( -3/4 ) (0) + 2 = ( 1/4 )⁰ + 1
On simplifying the equation , we get
0 + 2 = 1 + 1
2 = 2
So , the solution is ( 0 , 2 )
Hence , the equations are solved
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Calculate the indicated length in the figure.
An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 875 drank alcohol regularly, 665 smoked cigarettes, 207 used illegal drugs, 422drank alcohol regularly and smoked cigarettes, 113 drank alcohol regularly and used illegal drugs,126 smoked cigarettes and used illegal drugs, 97 engaged in all three behaviors, and217 engaged in none of these behaviors.
a) How many students were surveyed?
nothing
According to the following Venn diagram, the number students surveyed is 2063
The term Venn diagram in math is defined as overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items
Here we have given that anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs.
While we looking into the Venn diagram we have identified that 875 drank alcohol regularly, 665 smoked cigarettes, 207 used illegal drugs, 422drank alcohol regularly and smoked cigarettes, 113 drank alcohol regularly and used illegal drugs,126 smoked cigarettes and used illegal drugs, 97 engaged in all three behaviors, and 217 engaged in none of these behaviors.
Then the number of students is calculated as,
=> 875 + 667 + 207 + 97 + 217
=> 2063
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Choose the two equations you would use to solve the absolute value equation below. Then solve the two equations.
|6x – 4| = 6
A.
6x + 4 = 6 and 6x – 4 = –6;
B.
6x + 4 = 6 and 6x – 4 = –6;
C.
6x – 4 = 6 and 6x – 4 = –6
D.
6x – 4 = 6 and 6x – 4 = –6;
The solution to the absolute value equation |6x – 4| = 6 is 6x - 4 = 6 and 6x - 4 = -6
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The absolute value of a real number x is the non-negative value of x without regard to its sign.
Given the absolute value equation:
|6x - 4| = 6
Therefore, the absolute equation can be represented by:
6x - 4 = 6 and -(6x - 4) = 6
Simplifying:
6x - 4 = 6 and 6x - 4 = -6
adding like terms:
6x = 10 and 6x = -2
x = 5/3 and x = -2/3
The solution to |6x – 4| = 6 is x = 5/3 and x = -2/3
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state the converse, contrapositive, and inverse of each of these conditional statements. a) if it snows today, i will ski tomorrow. b) i come to class whenever there is going to be a quiz. c) apositive integer is a prime only if it has no divisors other than 1 and itself.
a) If it snows today, I will ski tomorrow.
Converse: If I ski tomorrow, it snows today.
Contrapositive: If I don't ski tomorrow, it doesn't snow today.
Inverse: If it doesn't snow today, I won't ski tomorrow.
b) I come to class whenever there is going to be a quiz.
Converse: Whenever I come to class, there is going to be a quiz.
Contrapositive: Whenever I don't come to class, there isn't going to be a quiz.
Inverse: Whenever there isn't going to be a quiz, I don't come to class.
c) A positive integer is a prime only if it has no divisors other than 1 and itself.
Converse: If a positive integer has no divisors other than 1 and itself, then it is a prime.
Contrapositive: If a positive integer is not a prime, it has divisors other than 1 and itself.
Inverse: If a positive integer has divisors other than 1 and itself, it is not a prime.
A mathematical conditional statement is a statement that presents a relationship between two statements, where one statement (the "condition") is only true if the other statement (the "conclusion") is also true.
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the four longest rivers in the world are all named after types of monkeys the howler river is 230 Mi longer than the Barbary River the Gin river is 150 Mi longer than the Barbarian River the retinal river is 30 miles shorter than the Barbary River the rivers when combined have a total length of 19,230 Mi how long is each River?
Answer: We can set up a system of equations to represent the information given:
Let x = length of Barbary River
Howler River = x + 230
Gin River = x + 150
Retinal River = x - 30
Total length = x + (x + 230) + (x + 150) + (x - 30) = 19,230
We can then use substitution and the equations above to solve for the length of each river:
x + (x + 230) + (x + 150) + (x - 30) = 19,230
4x + 350 = 19,230
4x = 18,880
x = 4720 (length of Barbary River)
Howler River = x + 230 = 4720 + 230 = 4950 mi
Gin River = x + 150 = 4720 + 150 = 4870 mi
Retinal River = x - 30 = 4720 - 30 = 4690 mi
Step-by-step explanation:
What is the slope of the line ( 3 ,5 ) and (-6,-6)
HELPPPP
Sid has a baseball cap collection. 75% of his caps have sports team symbols. If 24 of the caps have the team symbols, how many total caps does Sid have?
32
52
98
173
Sid has a total of 32 caps.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign {%}.Given is that Sid has a baseball cap collection. 75% of his caps have sports team symbols. 24 of the caps have the team symbols.
Let the total number of caps be {x}. Then, we can write -
24 = 75% of {x}
24 = (75/100) {x}
24 = 3/4 {x}
{x} = 24 x 4/3
{x} = 32
Therefore, Sid has a total of 32 caps.
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Simplify the expression below.
12.8 - 3s + 15.5 + 8s
Answer: 5s + 28.3
Step-by-step explanation:
(/8-/+)+(/++/4) find the sum plsss
The sum of the fraction given for the sum of 7/8 and 1/4 will be 1 1/8.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
It should be noted that the sum of 7/8 and 1/4 will be:
= 7/8 + 1/4
= 7/8 + 2/8
= 9/8
= 1 1/8
Therefore, the sum is 1 1/8.
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Complete question
7/8 + 1/4. Find the sum.
Which set of side lengths can be used to form a triangle?
O 3 ft, 3 ft, 7 ft
O 5 ft, 9 ft, 3 ft
O 6 ft, 7 ft, 7 ft
O 9 ft, 7 ft, 2 ft
so we have hmmm 4 sets above, hmm let's check say the second set, the triangle with sides 5, 9, 3. Check the picture below.
we have three sides, let's look at the two smaller sides first, 5 and 3.
if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side? Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 5 - 3 = 2. However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle. So whatever the third side may be, it must be greater than 2.
Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 3 + 5 = 8. However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle. So whatever the third side may be, it must be less than 8.
so for those reasons the third side can't be 9, it won't work for a triangle, even 8 is not good, so it must be less.
Now, if we look at the 1st set and 4th set, we end up with the same dilemma, the longest side is too long.
If we take a looksie at the 3rd set however with small sides of 6 and 7, it gives us a third side that must be more than 1 but less than 13, so 7 fits just nicely, so that one works.
What 2 numbers are equivalent to 35%
35% can be represented in equivalent decimal form and fraction form 0.35 and 7/20
How is this calculated?35% is equivalent to 0.35 in decimal form. Divide the percentage by 100 to get the decimal equivalent. 35 / 100 = 0.35.
35% is equivalent to 7/20 as a fraction. A percentage must be multiplied by 100 before being simplified to become a fraction. 35/100 = 0.35, or 7/20, can be written more simply.
Although both forms are equal, they are employed in various contexts. The fraction form is more frequently used in probability and statistics while the decimal form is more frequently used in calculations.
It's also important to keep in mind that percentages are a technique to express numbers as fractions of 100. For example, 35% is the same as 35/100, or 7/20.
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Please help with question 11!!
“Given the functions f(x) = sqr x^2 - 3 and g(x) = sqr 36-x^2 what is the domain of f- g within the real set of numbers??
PLS HELP!!! THANK YOU!!
The domain of the function f(x) - g(x) is given as follows:
[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
For a square root, the inner term cannot be negative, hence the domain of f(x) is given as follows:
x² - 3 >= 0
|x| >= sqrt(3)
x <= -sqrt(3) or x >= sqrt(3).
For function g(x), the domain is given as follows:
36 - x² >= 0
x² <= 36
|x| <= square root (36)
|x| <= 6.
-6 <= x <= 6.
The domain of the subtraction function is the intersection of the domain of both functions, hence:
[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]
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the number of observations will always be the same as the group of answer choices number of variables. number of elements. population size. sample siz
In a data set, the number of observations will always be the same as the group of answer choices number of variables is the number of elements.
A data set is a collection of data. It is a set that corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.
The data set lists values for each of the variables, such as example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files.
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In four years' time, Imran's mother will be three times as old as Imran. Six years ago, his mother was seven times as old as him. Find
(i) Imran's present age,
(ii) the age of Imran's mother when he was born.
Answer:
(i) 11 years old
(ii) 30 years old
Step-by-step explanation:
K is x
In four years, he will be x+4 and his mother will therefore be 3(x+4)
Six years ago, he was x-6 and his mother was 7(x-6).
In 10 years his mother went from 7(x-6) to 3(x+4)
so their difference is 10
7x-42+10=3(x+4), since 7x-42 is 10 years less than 3x+12
7x-32=3x+12
4x=44
x=11 age of K now
in 4 years he will be 15 and his mother 45.
Six years ago he was 5 and his mother 35
Therefore, his mother was 30 when he was born.
She is now 41.
Imran is currently 10 years old. His mother's current age is 34 years old and she was 24 years old when Imran was born.
Explanation:The question involves a system of equations based on the relationship between Imran and his mother's ages. We can define Imran's current age as i and his mother's current age as m. From the problem we have the following two equations:
In four years' time, his mother will be three times as old as him: m + 4 = 3 * (i + 4)Six years ago, his mother was seven times as old as him: m - 6 = 7 * (i - 6)
By solving this system of equations, we can determine that Imran's current age (i) is 10 years old and his mother's current age (m) is 34 years old. To find the age of Imran's mother when he was born, we would subtract Imran's age from his mother's, i.e., 34 - 10, so Imran's mother was 24 years old when Imran was born.
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What are the domain and range of the function y=f(x) as shown on the graph?
For the graphed function we have:
The domain
D: {-3, -2, -1, 0, 1, 2}
And the range
R: {0.25, 0.5, 1, 2, 4, 8}
What are the domain and the range of the function?For a function y = f(x), we define the domain as the set of possible inputs and the range as the set of possible outputs.
Remember that the notation in point form is (input, output).
Now, the graphed points are:
(-3, 8), (-2, 4), (-1, 2), (0, 1), (1, 0.5), (2, 0.25)
The domain is the set of the first values:
D: {-3, -2, -1, 0, 1, 2}
And the range is the set of the second values:
R: {0.25, 0.5, 1, 2, 4, 8}
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How long does it take Emil to ride his skateboard
42 meters at 6 meter/minute?
7 hours
7 minutes
7 days
Answer:
42/6 = 7 Minutes
Step-by-step explanation:
Question: PartA Can you draw a Gaussian surface that offers a simple way to compute the electric field surrounding a charged dipole? O Yes O No
It is impossible to create a Gaussian surface that makes it easy to calculate the electric field around a charged dipole. Thus, the response is no.
According to Gauss's law, the enclosed electric charge directly affects how much an electric field's net flux is moving over a closed surface. This is given by, [tex]\phi=\frac{Q}{\epsilon_0}[/tex], where the electric flux is represented by Ф, the permittivity of free space is represented by [tex]\epsilon_0[/tex], and the enclosed charge is represented by Q.
Gauss's law must be applied for the symmetric charge distribution required for the given surface in the equation [tex]\frac{Q}{\epsilon_0}=\int\vec{E}\cdot d\vec{A}[/tex] to have a single value of the electric field.
The electric field surrounding a charged particle can be estimated using the Gaussian surface. Gauss' Law cannot be applied to the dipoles because electric dipoles lack a surface with a symmetric distribution of the electric field all around them.
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