The slope of the original line is 3/5.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line.
To find the slope of the original line, we need to convert the equation to the slope-intercept form (y = mx + b), where m is the slope.
To convert, we'll isolate y:
-3x + 5y = 20
5y = 3x + 20
y = (3/5)x + 4
The slope of the original line is 3/5. The slope of the line perpendicular to this line would be the negative reciprocal of this slope, or -5/3.
Hence, The slope of the original line is 3/5.
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please solve for area and perimeter
The area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.
What is area and perimeter?
The area of a shape or figure is its area, whereas the perimeter of a shape is its outer boundary over a given distance. Area is measured in square units or unit2 while perimeter is measured in the same unit.
The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to determine a rectangle's or square's perimeter.
Radius, r = 8 cm
Perimeter of a circle = 2πr
Perimeter of s quarter circle = 2πr/4 = 1/2πr
Perimeter of Shaded part = 1/2 * 2πr
= 1/2 × 2 × π × 8
= 8πcm.
Area of a circle = 2πr²
Area of quarter circle = 2πr²/4 = 1/2πr²
Area of a square = length ²
Area of Shaded part = Area of Quarter-circle - Area of Square
= 0.5π(8)² - 8²
= 0.5π(64) - 64
Area of Shaded part = 36.53 cm^2
Hence, the area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.
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Maddox has 21 to spend on souverniers as gift for his friends. He wants to buy each friend a keychain and a pin. The equation 3f + 4f =21 can be used to find f, the number of friends for which he can buy souvenirs
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{3f + 4f = 21}[/tex]
[tex]\textbf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(3f + 4f) = 21}[/tex]
[tex]\mathsf{3f + 4f = 21}[/tex]
[tex]\mathsf{7f = 21}[/tex]
[tex]\textbf{DIVIDE 7 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{7f}{7} = \dfrac{21}{7}}[/tex]
[tex]\textbf{SIMPLIFY it!}[/tex]
[tex]\mathsf{f = \dfrac{21}{7}}[/tex]
[tex]\mathsf{f = 3}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{f = 3}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
Which of the following is equivalent to the quadratic equation below after completing the square?
x² +6x-3=12
A. (x+6)² = 12
B. (x+3)² = 24
C. (x+6)² =9
D. (x+3)² = 9
What is the volume of the composite solid? Use 3.14 for pie and round your answer to the nearest cm3. cylinder height is 2.5 radius : 3 inches, cone is height of 3 inches and radius of inches.
(A) 471 cm3
(B) 733 cm3
(c) 707 cm3
(D) 1099cm3
The volume of the composite solid, given the dimensions for the cylinder and cone, is D. 1, 099 cm ³
How to find the volume ?First, find the volume of the cone which can be found by the formula:
= π x radius ² x ( height / 3 )
Height = 3 inches
Radius = 3 inches
The volume is:
= π x radius ² x ( height / 3 )
= π x 3 ² x ( 2.5 / 3 )
= 28.27 inches ³
The volume of the cylinder is :
= π x radius ² x height
= π x 3² x 2. 5
= 70. 69 inch ³
The volume of the composite solid is:
= 28. 27 + 70. 69
= 98.96 inch³
In cm³, this is:
= 98. 96 x 16.3871
= 1, 099 cm ³
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a teacher offers gift cards as a reward for classroom participation. the teacher places the gift cards from four different stores into a bag and mixes them well. a student gets to select two gift cards at random (one at a time and without replacement). each outcome in the sample space for the random selection of two gift cards is equally likely. what is the probability of each outcome in the sample space? startfraction 1 over 16 endfraction one-sixth one-fourth one-half
The probability of each outcome is 1/12 or 0.083.
The probability of each outcome in the sample space can be calculated using the formula for permutations. The formula for permutations is nPk = n!/(n-k)!. In this case n is the number of gift cards (4) and k is the number of gift cards to be selected (2). In this example, the sample space consists of 16 possible outcomes, and each outcome is equally likely. Thus, the probability of each outcome is 1/16. To calculate this, divide 1 by the total number of outcomes (16). This results in the probability of each outcome being 1/16.Therefore, nPk = 4P2 = 4!/2! = 12. Since each outcome is equally likely, the probability of each outcome is 1/12 or 0.083. This can be written as a fraction as 1/12 or as a decimal as 0.083.
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A billiard ball starts 86\,\text{cm}86cm86, start text, c, m, end text from the corner pocket, as shown. The ball rolls 120\,\text{cm}120cm120, start text, c, m, end text in another direction, hits a rail, and rolls another 100\, \text{cm}100cm100, start text, c, m, end text into the pocket.
The angle is 45 degrees between the trajectories the ball takes before and after hitting the rail.
What are equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value
To determine the value A statement is not an equation if it has no "equal to" sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Hence, The angle is 45 degrees between the trajectories the ball takes before and after hitting the rail.
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consider an undirected graph with n vertices and m edges. what are the minimum and maximum number of connected components that the graph could have, respectively?
The maximum is N*(N-1)/2 and the minimum is N-1 if there are N vertices.
Proof:
Consider an adjacency matrix where each entry is either 1 (to denote the presence of an edge) or 0 (to indicate the absence of an edge) (to indicate the absence of an edge). Each row of the upper triangle must have at least one "1" in order for a graph to be connected.
By merely placing one 1 in each row of the upper triangle, the minimum is reached. Now, if the adjacency matrix is N by N, the first row will have N-1 elements in the upper triangle, the second row will have N-2 elements, the third row will have N, the fourth row will have N, and so on until the last row will have 0 items. Consequently, there are N total rows "with an upper triangle", each with only one 1. Hence, the number of edges in N-1.
The maximum occurs if every element of the upper triangle has one. Now, the number of elements in the upper triangle of the whole matrix is
1 + 2 + ... + (N-2) + (N-1) = N*(N-1)/2.
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There are several sets of three different numbers whose sum is 15 which can be chosen from {1,2,3,4,5,6,7,8,9}. How many of these sets contain a 5 ?
Answer is 4 of these sets contain a 5 in sets of three different numbers whose sum is 15
These problems are really brute force, there is no real clever way. I only just listed all possible combinations
HOWEVER, notice in answer.
5 1 9
5 2 8
5 3 7
5 4 6
Since ALL the sets contain a 5, we just subtract 5 from 15.
So we need TWO terms in a set and they add up to 10, and also are unique.
This is quite easy.
1 9
2 8
3 7
4 6
5 5 (does not work because cannot repeat digit)
thus , answer is 4 of these sets contain a 5 in sets of three different numbers whose sum is 15
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Which of these formulas describes the sequence 4, 5, 6, 7,...? (1) 22 n an =+ (3) 3 n an =+(2) 2 21 n ann =++ (4) 31 n an =+
The formula describes the sequence will be aₙ = n + 3. Then the correct option is 3.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The sequence is given below.
4, 5, 6, 7, ....
The first term is 4 and the common difference is given as,
d = 5 - 4
d = 1
Then the formula is given as,
aₙ = 4 + (n - 1) × 1
aₙ = 4 + n - 1
aₙ = n + 3
The formula describes the sequence will be aₙ = n + 3. Then the correct option is 3.
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Which of these is a correct step in constructing congruent angles?
A. Use a straightedge and draw an arc across the first arc from a leg of the given angle
B. Use a straightedge to measure the width between the points where the first arc cuts both legs of the given angle
C. Use a compass and draw an arc across both the legs of the given angle
D. Use a compass and join points to make the new leg of the congruent angle
Answer:
C. Use a compass and draw an arc across both the legs of the given angle.
Step-by-step explanation:
PLEASE HELP ASAP TYSM
Answer:
77 cups
Step-by-step explanation:
88 ounces/ day = 11 cups/ day
A week = 7 days
=> 11 x 7 = 77 cups/week
Which best describes the offspring of protists?
always genetically identical to one parent
always genetically identical to both parents
never genetically identical to one parent
sometimes genetically different than both parents
The best description of the offspring of Protists is D. sometimes genetically different than both parents
How do Protists reproduce ?Asexual reproduction in protists includes methods such as binary fission, budding and fragmentation, in these methods the offspring are always genetically identical to one parent.
Sexual reproduction in protists can be through conjugation, meiosis, or syngamy, in this case the offspring are not always genetically identical to one or both parents. It is possible for the offspring to be genetically different from both parents due to the genetic recombination that occurs during sexual reproduction.
So, the statement that best describes the offspring of protists is "sometimes genetically different than both parents" as it depends on the type of reproduction method used.
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The five-number summary for the number of years of experience for each teacher at Carlson High School is shown in the following table. Min 2
Q1 5
Median 8
Q3 11
Max 16
The five-number summary suggests that about 25% of Carlson High School teachers have fewer than how many years of experience?
Answer: 5
Step-by-step explanation:
We are looking for the number of years below the 25th percentile, which is given by the first quartile.
Since the first quartile is 5, we know that about 25% of Carlson High School teachers have fewer than 5 years of experience.
Write the coordinates of the vertices after a reflection over the x-axis.
The coordinate of the vertices (x,y) after a reflection over the x-axis is (x, -y). It is also known as a rule.
What are coordinates?
Coordinates are two numbers (Cartesian coordinates) or a letter and a number that point to a specific point on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical).
A reflection of a point, line, or figure in the x-axis entailed mirroring the image over the x-axis. In this case, the x-axis is referred to as the axis of reflection.
The rule for reflecting over the x-axis is to negate the value of each point's y-coordinate while keeping the x-value constant.
For instance, when point P with coordinates (7,3) is reflected across the x-axis and mapped onto point P', P"s coordinates are (7,-3). The x-coordinate for both points remained unchanged, but the y-coordinate changed from 3 to -3.
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a board that is 12 feet long must be cut into two pieces that have lengths in a ratio of 3 to 2. find the legnths of the two pieces.
The first piece is 7.2 feet long, and the second piece is 12- 7.2 = 4.8 feet long.
The ratio of the two pieces is 3 to 2. This means that the length of the first piece is 3/5 of the total length, and the length of the second piece is 2/5 of the total length.
If we let x be the length of the first piece, the length of the second piece is:
12 - x
Since the ratio of the two pieces is 3 to 2, we can set up the equation:
(3/5) * 12 = x
Solving for x:
x = 7.2
So, the first piece is 7.2 feet long, and the second piece is 12- 7.2 = 4.8 feet long
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Evaluate. 9^2+2⋅4−5
Please help (40 points)
Answer: 84
Step-by-step explanation:
9^2+2*4-5
Let's solve according to PEMDAS and calculate the exponent first.
That leaves us with
81+2*4-5
Next, it's time to multiply.
81+8-5
From then on, we can just add and subtract to get the final answer:
84
The length of a rectangle is twice its width.
The perimeter of the rectangle is 42 cm.
Label the diagram with the correct length and width for the rectangle.
cm
cm
દ
Answer: W = 7, L = 14
Step-by-step explanation: L = 2W. 2L + 2W = 42. Plug in L and we get 4W + 2W = 42. 6W = 42. W = 7. L = 14
The perimeter of a rectangle pool is 332m, if the length of the pool is 89m, what is its width?
Answer: 77m
Step-by-step explanation:
The equation for the perimeter of a rectangle is: p = 2(length) + 2(width). We are given both perimeter and the length, so we can plug in these values to solve for what is missing.
332m = 2(89) + 2(width)
332m = 178 + 2(width)
154 = 2(width)
width = 77
Just combine like terms and get the variable (width) by itself on one side of the equation to solve. Hope this helps!
Answer:
width = 77 m
Step-by-step explanation:
Perimeter = sum of all sides
As a rectangle has 2 lengths and 2 widths making a total of four sides;
P = 2 ( l + w)
332 = 2 ( 89 + w)
332/2 = 89 + w
166 = 89 + w
166 - 89 = w
77 = w
Therefore, the width of the pool is 77 m
plsss helppppppppppppppppp
Answer:
hard
Step-by-step explanation:
ybfhf
(15 + y ) - (a+ u) }{3 ^ {2} -x}
After simplification, the value of expression is,
⇒ 15 + y - 9a + ax - 9u + ux
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (15 + y) - (a + u) (3² - x)
Now, Simplify the expression as;
⇒ (15 + y) - (a + u) (3² - x)
⇒ (15 + y) - (a + u) (9 - x)
⇒ (15 + y) - (9a - ax + 9u - ux)
⇒ 15 + y - 9a + ax - 9u + ux
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Which of the following graphs does NOT describe y as a function of x?
The second graph does not represent the y as a function of x.
What is the function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
The x value of a point where a vertical line intersects a function represents the input for that output y value.
If we can draw any horizontal line that intersects a graph more than once, then the graph does not represent a function because that y value has more than one input.
If we draw a line parallel to the y-axis it cuts the graph in more than one point.
So, that does not represent a function.
Here, we have given four graphs
Among this, the second graph intersects the x-axis two times,
Hence, the second graph does not represent y as a function of x.
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The area of the shaded region shown below is 214 units^2.
What's the value of x?
The value of x, considering the area of the rectangular regions, is given as follows:
x = 12.
How to obtain the area of a rectangle?The area of a rectangle is given by the multiplication of the two dimensions of the rectangle.
The area of the shaded region is obtained subtracting the area of the entire rectangle by the area of the inner white rectangle.
The area of the entire rectangle is given as follows:
(x + 8)(x + 5) = x² + 13x + 40.
The area of the white region is given as follows:
(x + 2)(x - 3) = x² - x - 6.
Hence the area of the shaded region is given as follows:
x² + 13x + 40 - (x² - x - 6)
x² + 13x + 40 - x² + x + 6
14x + 46.
As the area of the shaded region is of 214 units squared, the value of x is obtained as follows:
14x + 46 = 214
14x = 168
x = 168/14
x = 12.
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Residents in a city are charged for water usage every three months. the water bill is computed from a common fee,
along with the amount of water the customers use. the last water bills for 40 residents from two different
neighborhoods are displayed in the histograms.
The interval that contains the median water bill is D: $200 - $225.
The data in tabular form is as follows: ata :
Class interval ------- Frequency -------- Cummulative frequency
100 to 125, ----------- 1 --------------------1
125 to 150 -----------2--------------------3
150 to 175----------- 5 --------------------8
175 to 200----------- 10 ------------------18
200 to 225-----------13------------------ 31
225 to 250 ------------8 -----------------40
Median class = Cumulative frequency / 2
Cumulative frequency= 40
So
Median class = 40 / 2
Median class = 20
The class interval containing the 20th frequency is "200 - 225"
Therefore it is concluded that the interval which contains the median water bill is $200 - $225.
"
Complete question
A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8.
Which interval contains the median water bill?
$150–$175
$175–$200
$200–$225
$225–$250
"
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Help me out pleasereeeee
Answer:
90°
Step-by-step explanation:
So we know that ∠PRM is 120° and that line m would be 180°, we would subtract 120 from 180 to get 60°.
So ∠PRQ is 60°.
All the angles of a triangle equals to 180°.
∠PQR is given as 30°. So we will need to add 60+30=90.
180-90=90. So ∠QPR is 90°.
Convert 46.1031 to Four significant figures
The required converted number is 46.10 which is 46.1031 rounded to four significant figures.
What is the place value strategy?Place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, using your place values, such as tens and hundreds.
To convert 46.1031 to four significant figures, we must first identify the four most significant digits. In this case, the four most significant digits are 46.10.
To express 46.1031 in four significant figures, we round it to 46.10.
Therefore, 46.1031 rounded to four significant figures is 46.10.
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A company has 120 people who assemble toys. If 60% of these people assemble yoyo's, how
many more workers must transfered from other departments so that 70% of the people are assembling yo-yo's?
Answer:
12 people
Step-by-step explanation:
Total people in the company = 120
No. of People who assemble yo- yo's = 120 × (60/100
= 72
Now, we need 70% of the total people to assemble yoyo = 120 × (70/100)
= 84
We already have 72 people assembling yoyo,
No. of more people needed = 84 - 72 = 12
Hence, if we have 12 more people from other departments, 70% of the total people would be assembling yo-yo's.
Hint: Find the value of x first, then substitute the answer into 2x - 24.
The measure of angle BFG is
The measure of the value of corresponding angle is found as : ∠BFG = 76.
Define the term corresponding angles?Corresponding angles refer to the angles on the similar corners of two lines, which are often parallel and are crossed with another line (referred to as the transversal). The angles created when a transversal intersects two parallel lines have been known as corresponding angles. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, as well as endless parallel railroad tracks.For the given question:
Given values:
∠BCD = x + 26∠BFG = 2x - 24∠BCD = ∠BFG (Corresponding angles)
x + 26 = 2x - 24
2x - x = 26 + 24
x = 50
Then,
∠BFG = 2*50 - 24
∠BFG = 100 - 24
∠BFG = 76
Thus, the measure of the value of corresponding angle is found as : ∠BFG = 76.
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the complete question is-
Hint: Find the value of x first, then substitute the answer into 2x - 24.
The measure of angle BFG is ___.
∠BCD = x + 26
∠BFG = 2x - 24
What are the two types of graphs?
A Graph comprise of nodes and edges. The nodes are sometimes also denoted to as vertices and the edges are lines or arcs that joins any two nodes in the graph.
1. Finite Graphs: A graph is said to be limited if it has a finite number of vertices and a finite number of edges.
2. Infinite Graphs: A graph is said to be infinite if it has an unlimited number of vertices as well as an unlimited number of edges.
3. Trivial Graph: A graph is said to be trivial if a finite graph consists of only one vertex and no edge.
4. Regular Graph: A simple graph is called to be regular if all vertices of graph G are of equal degree.
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Georgina had total stock earnings of $395.50 and a real return of $275.80. The difference is (5 points) due to a sudden drop in the stock market investments due to taxes, inflation, and fees due to a payout to the stockholders due to property taxes and fees charged on gains
The difference between Georgina's total stock earnings and her real return is $119.70. he difference between Georgina's total stock earnings and her real return is $119.70.
What is the difference?
The term "difference" refers to the amount by which one quantity is greater or less than another.
The difference between Georgina's total stock earnings and her real return can be calculated as follows:
Difference = Total stock earnings - Real return
Difference = $395.50 - $275.80
Difference = $119.70
Hence, the difference between Georgina's total stock earnings and her real return is $119.70.
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. An integer a is said to be a type 0 integer if there exists an integer n such that a3n. An integer a is said to be a type 1 integer if there exists an integer n such that a-3n 1. An integer a is said to be a type 2 integer if there exists an integer m such that a - 3m + 2. * (a) Give examples of at least four different integers that are type 1 integers (b) Give examples of at least four different integers that are type 2 integers (c) By multiplying pairs of integers from the list in Exercise (9a), does it appear that the following statement is true or false? If a and b are both type 1 integers, then a b is a type 1 integer.
When n is known to be an integer, the formula for m also produces an integer. The assumption is confirmed once the necessary integer m was located.
what is integer ?Positive, negative, and zero are all examples of integers. As a result, integers include numbers like 0, 1, 2, 3, as well as -1, -2, and 3. There are no additional parts, such as fractions or decimals, in integers. As a result, fractional values like 3 1/2 and decimal numbers like -7.5 are NOT integers. All positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity are included in the category of integers. The fundamental arithmetic operations are included in integer operations (addition, subtraction, multiplication and division). In mathematics, integers are any numbers that are either positive, negative, or zero, with the exception of fractions. As a result, operations on integers are simple.
given
Any whole number that is a multiple of 3 is a type 0 integer. Examples are 3, 6, 9, and 12.
n=1: 3(1)=3
n=2: 3(2)=6
n=3: 3(3)=9
n=4: 3(4)=12
When n is known to be an integer, the formula for m also produces an integer.
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