a) The numeric values of each function at x = 3 are given as follows:
f(3) = 50.g(3) = 10.b) The division is given as follows: f(3)/g(3) = 5.
c) The domain of f(x)/g(x) is given as all real values except x = -7, as the function g(x), which is the denominator of the division, assumes a value of 0 at x = -7.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
Hence the numeric values are found replacing the lone instance of x by 3 in each function, as follows:
f(3) = 5(3) + 35 = 15 + 35 = 50.g(3) = 3 + 7 = 10.Hence the division is given as follows:
(f/g)(3) = f(3)/g(3) = 50/10 = 5.
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An airline ticket costs $260 without the tax if the tax raise 8% what's the total bill for the ticket
Question2_=) 6th grade math please help (only answer if you know the answer don't guess PELASEE) Marking brainlist!! QUESTION WORTH 60 POINT!!
Which of the following is the distance between the two points shown?
A graph with the x-axis starting at negative 4, with tick marks every one-half unit up to 4. The y-axis starts at negative 4, with tick marks every one-half unit up to 4. A point is plotted at negative 3, 0 and at 0.5, 0.
2.5 units
3.5 units
−3.5 units
−2.5 units
Answer:
see below
Step-by-step explanation:
the direct distance between the 2 points should be √9.25 = 3.04, but there's no such answer, so I guess they are making you count the units. By definition the distance cannot be negative. so it should be 3.5.
However, if this 6th grade math question is testing you on your understanding of the direction of x axis then because a point is plotted at -3 on the axis (cause it's Y value =0), then its distance to (0,0) is -3, and then you go up 0.5 to the next point. With that said, whether you should add the -3+0.5 = -2.5 that'll depend on the teacher or the textbook - not exactly sure what they are trying to test you on. it's a very vague question.
8 piglets are evenly sharing 5 liters of milk.
How much milk should each piglet get?
Each piglet will receive 0.625 L of milk.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Left to Right
We have 8 piglets that only have 5 liters of milk to share in between them. We need to split the milk between the 8 piglets.
We can divide the amount of milk we have already by the amount of piglets total:
5 liters of milk ÷ 8 piglets
Evaluating this, we should get 0.625 L of milk per piglet, assuming we don't lose a single drop while splitting the milk.
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c=1/30x^2-2x+1530 what is the minimum cost
The minimum cost is $1500.
What is Vertex form?
The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants of the parabola is at (h, k).
Given:
y =1/30 x²-2x+1530
y= 1/30 x² - 2x + 1530
comparing the above equation with y ax²+ bx +c we get
a = 1/30
b = -2
c = 1530
Now, the the x coordinate of the vertex
h = -b/(2a)
h = -(-2)/(2x(1/30))
h = 2/(2/30)
h = (2/1) x (30/2)
h = (2 x 30)/(1 x 2)
h = 60/2
h = 30
So, The x coordinate of the vertex is 30.
Now, we plug in x = 30 to find the y coordinate of the vertex.
y =1/30 x²-2x+1530
y =1/30 (30)²-2(30)+1530
y =1/30 (900)-60+1530
y= 1500
Thus, the minimum cost is $1500
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1. which of the following initializes an 8 x 10 matrix with integer values that are perfect squares? (0 is a perfect square.) int[][] mat
B. II only. This initializes an 8 X 10 matrix with integer values that are perfect squares by looping through the rows and columns of the matrix and setting each element equal to the row number multiplied by itself.
II initializes an 8 X 10 matrix with integer values that are perfect squares. The initialization starts by declaring the matrix with the line int [][] mat = new int [8][10]; which creates the 8 X 10 matrix. The next step is to use a nested for loop to loop through the rows and columns of the matrix. The first loop, for(int r=0; r<mat.length; r++), begins by setting an integer variable r to 0 and looping through all of the rows in the matrix. The second loop, for(int c=0; c<mat[r].length; c++), begins by setting an integer variable c to 0 and looping through all of the columns in the matrix. Finally, the last line, mat[r][c] = r*r;, sets each element of the matrix equal to the row number multiplied by itself. This ensures that the values in the matrix are all perfect squares.
The complete question : Which of the following initializes an 8 X 10 matrix with integer values that are perfect squares? (0 is a perfect square.)
I. int [][] mat = new int [8][10];
II. int [][] mat = new int [8][10];
for (int r=0; r<mat.length; r++){
for(int c=0; c<mat[r].length; c++){
mat[r][c] = r*r; }}
III. int [][] mat = new int [8][10];
for (int c=0; c<mat[r].length; c++){
for(int r=0; r<mat.length; r++){
mat[r][c] = c*c; }}
A. I only
B. II only
C. III only
D. I and II
E. I, II, and III
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s) a real number is repeatedly selected uniformly over the interval [0, 1] until the sum of all numbers chosen exceeds 1. what is the expected value of the count of numbers that are select
Since the sum of the numbers selected must exceed 1, we know that n must be at least 1. Therefore, the expected value of X is finite and is equal to 2.
The expected value of the count of numbers that are selected can be found using the geometric distribution, since it models the number of trials until a success occurs.
Let X be the number of numbers that are selected until the sum of all numbers exceeds 1. Then X has a geometric distribution with parameter p, where p is the probability of success on each trial, i.e. the probability that the sum of all numbers selected does not exceed 1.
Since the numbers are selected uniformly over [0, 1], the probability of success on each trial is given by the area under the curve between 0 and 1 after the first number is selected.
On the first trial, the probability of success is 1. On the second trial, the probability of success is the area under the curve between 0 and (1 - the first number selected).
On the third trial, the probability of success is the area under the curve between 0 and (1 - the sum of the first two numbers selected), and so on.
The expected value of X can be found using the formula for the expected value of a geometric distribution:
E(X) = 1/p
Since the expected value of the sum of n independent and identically distributed uniform [0, 1] random variables is n/2, we can use this to find p:
E(X_1 + X_2 + ... + X_n) = n/2
where X_1, X_2, ..., X_n are the n numbers selected.
So, p = 1 / (1 + n/2).
Finally, we can substitute this into the formula for E(X) to find the expected value of X:
E(X) = 1 / (1 - n/2) = 2 / (2 - n)
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A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section.
A rectangle is shown. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters. A vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. Lines are drawn from the bottom left point to the top of the vertical line and from the bottom right point to the top of the vertical line.
What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines?
21.2 m
27.5 m
32.5 m
38.2 m
Answer:
Option D) 38.2
Solution
1) The square section
The side length of the square is 15m.
You can use Pythagoras's theorem to find the length of the diagonal:
Diagonal ^2 = (15m)^2 + (15m^2) = 450 m^2
=> Diagonal = √(450m^2) = 21.21m
2) The small rectangle section
The sides of this rectangle are 23 - 15 = 8 m and 15 m
Now use the Pythagoras's theorem:
diagonal^2 = (8m)^2 + (15m)^2 = 289 m^2 =>
diagonal = √(289m^2) = 17 m
3) Then the sum of the lengths of the diagonals of the two sections is 17m + 21.21 m = 38.21
Answer: 38.21 m
find the volume of the solid formed by rotating the function about the x-axis. round to four decimal places.
The volume of the solid formed by rotating the function f(x)=x about the x-axis from x=0 to x=1 is equal to the integral of the area of the cross-section of the solid from x=0 to x=1. The area of the cross-section is equal to the area of a circle with radius x, which is equal to πx. Thus, the volume of the solid is equal to the integral of πx from x=0 to x=1.
This integral can be solved using the formula for the area of a circle, which is equal to πr. Thus, the volume of the solid is equal to π∫x dx from x=0 to x=1. After solving the integral, the volume of the solid is equal to π/3. Thus, the volume of the solid formed by rotating the function f(x)=x about the x-axis from x=0 to x=1 is equal to 0.3333.
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using a scale of 1 inch = 2 feet and wing of airplane is 24 feet how long is the wing
The length of the wing is, 12 inches.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The scale is,
⇒ 1 inch = 2 feet
And, Wing of airplane is 24 feet.
Now, We have;
The scale is,
⇒ 1 inch = 2 feet
Hence, The length of wing is,
⇒ 24 / 2 inches
⇒ 12 inches
Thus, The length of the wing is, 12 inches.
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(Systems of Linear Equations MC)
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $4, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 4 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $12 to send the box, represented by the equation y = 12.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A package that weighs 4 pounds will cost $12 for both options.
A package that weighs 8 pounds will cost $12 for both options.
A package that weighs 12 pounds will cost $20 for both options.
A package that weighs 12 pounds will cost $28 for both options.
Based on the graph of the system of equations, the cost of the two shipping options would be the same when: A. A package that weighs 4 pounds will cost $12 for both options.
How to determine when the cost of the two shipping options would be the same?Based on the information provided above, the customer sent a package for $4 with an additional $2 per pound. The total cost, y, can be represented by this equation:
y = 4 + 2x ....equation 1.
where:
x represents the amount of pounds of the package.
For the second option, the total cost can be represented by this equation:
y = 12 ....equation 1.
By equating equation 1 and equation 2, we have the following:
12 = 4 + 2x
2x = 12 - 4
2x = 8
x = 4.
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Answer:
A. A package that weighs 4 pounds will cost $12 for both options.
Step-by-step explanation:
(50 POINTS AND BRAINLYEST GURANTEE)
Find the area of the following shape. Make sure to indicate what shapes were used, by sketching on the image, listing
formulas, and show work listed for each shape. (5 total points – 2 for accurate shapes, 2 for accurate work, 1 for total
area answer)
Answer:
53.137 (sq.units).
Step-by-step explanation:
1. to draw red line in order to divide the given shape by two figures;
2. the required area consists of two: green - area of semicircle with radius r= 3 and blue - area of trapezoid with bases 8 and 5 and height 6. Then
3. the required area is
A=A(semicircle)+A(trapezoid);
A≈0.5*3.1415*3²+0.5*(8+5)*6=0.5*(28,274+78)=53.137
Answer:
53.137 sq.units also its a explanation for this answer
Step-by-step explanation:
the sq.untits would be a 53.137 hope this helps!
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 12 10 17 39
Female 2 19 3 24
Total 14 29 20 63
If one student was chosen at random,
find the probability that the student got a B.
the grpah displays the distance Wes;ey was from home s he rain in preparation for his cross - country meet. Describe the change in distance over time
The description of the change in distance over time is;
He ran further away from home, then sped up and went further. He then
slowed down, still going further from home. He then turned
around and headed home.
How to Interpret a Distance Time Graph?A distance-time graph is defined as a graph that shows how far an object has travelled in a given time. It is a simple line graph that denotes distance versus time findings on the graph. Distance is plotted on the y-axis. Time is plotted on the x-axis.
From the attached graph, we see that Wesley ran further away from home, and then he sped up and went further in the journey. He then
slowed down, and still going further from home. Finally, he turned
around and headed home.
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a box of candy hearts contains 52 hearts, of which 19 are white, 10 are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orange, and 6 are green. if you select nine pieces20 chapter 1 probability of candy randomly from the box, without replacement, give the probability that (a) three of the hearts are white. (b) three are white, two are tan, one is pink, one is yellow, and two are green.
(a) Probability(3 white) = (19/52) * (18/51) * (17/50) = 0.027
(b) P(3 white, 2 tan, 1 pink, 1 yellow, 2 green) = (19/52) * (18/51) * (17/50) * (10/49) * (9/48) * (7/47) * (5/46) * (6/45) * (6/44) = 0.00004
(a) The probability of selecting three white hearts is calculated by multiplying the probability of selecting each heart. The probability of selecting one white heart is 19/52. The probability of selecting two white hearts is 18/51, and the probability of selecting three white hearts is 17/50. When multiplied together, the overall probability is 0.027.
(b) The probability of selecting three white hearts, two tan hearts, one pink heart, one yellow heart, and two green hearts is calculated by multiplying the individual probabilities for each heart. The probability of selecting one white heart is 19/52, the probability of selecting two tan hearts is 10/49, the probability of selecting one pink heart is 7/47, the probability of selecting one yellow heart is 5/46, and the probability of selecting two green hearts is 6/45. When multiplied together, the overall probability is 0.00004.
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Game Over Electronics has made $18,500 in profit so far this year. The company expects the
profit during the rest of the year to be 19% of its revenue. You can use a function to estimate
the total profit this year if the revenue from now through the end of the year is x dollars.
Write an equation for the function. If it is linear, write it in the form h(x) = mx + b. If it is
exponential, write it in the form h(x) = a(b)*.
An equation for the profit function is expressed as; h(x) = 0.19x + b
How to solve Function Word Problems?The parameters in the given problem are;
Amount of profit made so far this year = $18500
The revenue from now through the end of the year = $x
Percentage profit for the rest of the year = 19%
Since profit made so far is $18500, then that will be regarded as the y-intercept from the linear equation form;
y = mx + b
Now, 19% profit will be regarded as the slope. Thus, the equation for the function is;
h(x) = 0.19x + b
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to make sure you understand the derivation based on the five assumptions (a-e), select the correct order in which the assumptions were used in the derivation above.
The correct order of the assumptions used in the derivation is: A, B, C, D, E. A states that the population is large, B: random, C: representative, D: large, and E states that the sampling is done without replacement.
The derivation of the Central Limit Theorem was based on five assumptions: (a) The population is large, (b) The sample is random, (c) The sample is representative, (d) The sample size is large, and (e) The sampling is done without replacement. The first assumption used in the derivation is that the population is large, which means that the number of individuals in the population is much greater than the sample size. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases. The second assumption used is that the sample is random, which means that each individual in the population has an equal chance of being selected for the sample. This helps to ensure that the sample is representative of the population as a whole. The third assumption is that the sample is representative, which means that the characteristics of the sample are similar to those of the population. This is important because it allows us to make generalizations about the population based on the sample. The fourth assumption is that the sample size is large. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases.
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You can use the equation A =(HW/3600)^1/2
to approximate a person's body surface area A (in square meters), where H
is height (in centimeters) and W is weight (in kilograms). Approximate the body surface area of a person with a height
of 160 centimeters and a weight of 64 kilograms.
Body surface area:______
m²
The body surface area is given by the equation A = 1.6865 m²
What is an 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.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the body surface area be represented as A
Now , the equation will be
A = ( HW / 3600 )^1/2
A = √( HW / 3600 ) be equation (1)
where H is the height in centimeters and W is the weight in kilograms
Now , the value of H = 160 cm
The value of W = 64 kg
Substituting the values in the equation , we get
A = √ [ ( 160 x 64 ) / 3600 ]
On simplifying the equation , we get
A = √ ( 10240/3600 )
A = √ ( 2.8444 )
A = 1.6865 m²
Therefore , the body surface area is 1.6865 m²
Hence , the equation is A = 1.6865 m²
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Indefinite integral of cos(x) sin(x) dx
The solution of the indefinite integral ∫ sin x cos x dx is (1 / 2) · sin² x + C.
How to determine the indefinite integral by algebraic substitution
There are integrals that can be solved by means of algebraic substitutions, which simplifies the expression and allow a quicker solution. Now we proceed to find the solution. First, define algebraic subtitution:
u = sin x
du = cos x dx
Second, simplify the integral by formulae defined in the previous step:
∫ sin x cos x dx
∫ u du
Third, integrate the resulting expression:
(1 / 2) · u² + C, where C is the integration constant.
Fourth, reverse the algebraic substitution:
(1 / 2) · sin² x + C
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run the strongly connected components algorithm on the following directed graphs g. when doing dfs on gr: whenever there is a choice of vertices to explore, always pick the one that is alphabetically first.
The strongly connected components of graph g are then determined to be the set of vertices {A, B, C, D, E}. This is because each vertex is reachable from every other vertex in the graph.
Graph g:
A→B
B→C
C→D
D→E
E→A
The strongly connected components algorithm is used to determine the strongly connected components of a directed graph. A strongly connected component is a subgraph of a directed graph in which every vertex is reachable from every other vertex.
The algorithm begins by running a depth-first search (DFS) on the graph. When running DFS on graph g, we start at vertex A and explore all its adjacent vertices before moving to the next vertex. In this case, we explore vertex B first. We then explore vertex C, followed by D and E. Finally, we explore vertex A again before finishing the DFS.
Once the DFS is complete, the algorithm then computes the transpose of the graph. The transpose of a graph is the graph with all the edges reversed. For graph g, this would be A←B, B←C, C←D, D←E, and E←A.
Finally, the algorithm runs a second DFS on the transpose of the graph. Since the edges are reversed, we start at vertex A and explore its adjacent vertices in reverse order. In this case, we explore vertex E first, followed by D, C, B, and finally A.
The strongly connected components of graph g are then determined to be the set of vertices {A, B, C, D, E}. This is because each vertex is reachable from every other vertex in the graph.
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Evaluate
a*b= a+b -2ab
(2*3)*5
The solution to the algebraic expression (2*3)*5 using a*b= a+b -2ab is; 68
How to solve Algebraic Expressions?Algebraic expressions are defined as the idea of expressing numbers using letters or alphabets without truly specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as a, b, c etc. These letters are usually referred to as variables.
We are given the format for the algebraic expression as;
a*b = a + b - 2ab
Thus, we can solve the expression (2*3)*5 as;
(2*3) = 2 + 3 - 2(2*3)
= -7
(-7 * 5) = -7 + 5 - 2(-7 * 5)
= -2 + 70
= 68
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Suppose the probability that an individual has blue eyes is 0.41. Four people are randomly selected Find the probability P that exactly tYpo have blue eyes Round your answer to four decimal places.
The probability P that exactly has blue eyes is P = 0.1887
The probability of exactly t people having blue eyes can be calculated using the binomial distribution formula. The binomial distribution models the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
In this case, the number of trials is 4, the probability of success is 0.41 (the probability of an individual having blue eyes), and the number of successes is the number of people with blue eyes. Plugging in these values into the binomial distribution formula gives us the probability of exactly t people having blue eyes.
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$g$ is the centroid of equilateral $\triangle abc.$ $d$, $e$, and $f$ are midpoints of the sides as shown. $p$, $q$, and $r$ are the midpoints of $\overline {ag}$, $\overline {bg}$, and $\overline {cg}$, respectively. if $ab
The coordinates of the centroid of the given triangle can be found by using the midpoint formula to calculate the coordinates of points P, Q, and R, and then taking the average of the x-coordinates and y-coordinates of these points.
The centroid of a equilateral triangle can be found by drawing the medians of the triangle. The median of a triangle is a line segment connecting a vertex of the triangle to the midpoint of the opposite side. The three medians of an equilateral triangle intersect at the centroid. In this scenario, the centroid of the given triangle is point G.
The midpoints of the sides of the triangle are points D, E, and F. The midpoints of the medians of the triangle are points P, Q, and R. The coordinates of the points can be found using the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates of the endpoints of the line segment.
The coordinates of the centroid, G, can be found by taking the average of the x-coordinates and y-coordinates of the midpoints of the medians. The x-coordinate of G is the average of the x-coordinates of P,Q, and R, and the y-coordinate of G is the average of the y-coordinates of P,Q, and R.
Finally, the coordinates of the centroid of the given triangle can be found by using the midpoint formula to calculate the coordinates of points P, Q, and R, and then taking the average of the x-coordinates and y-coordinates of these points.
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Complete question:
What is the area of the square with vertices [tex]$d$, $p$, $q$[/tex] ?
Nate's weekly pay, in dollars, when he works x hours is represented by this expression.
16. 50 x
24.75 (a
How much is Nate paid for each hour he works over 40?
0≤x≤ 40
40) + 660 x > 40
Nate is paid 16.50 dollars for each hour he works over 40.
How to calculate?We have that Nate's weekly pay is represented by the expression 16.50x + 24.75(a),
where x is the number of hours worked and a is a value such that 0 <= x <= 40.
We know that a mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
If x > 40, the pay for each additional hour worked is given by the rate of change of the expression, which has it at 16.50 dollars per hour.
We therefor ca conclude that Nate is paid 16.50 dollars for each hour he works over 40.
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math. please. help. me. quickly.
Answer:
no clue
Step-by-step explanation i cant help you with this and i just tying to get points
Answer the questions
The triangles ∆ABC and ∆BMK are similar triangles, and ∆ABC ≅ ∆BMK. The perimeter of the quadrilateral ACKB is equal to 74 feet.
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
We have that line AC of the triangle ∆ABC is parallel to line BK of the triangle ∆BMK and also line CB of the triangle ∆ABC is parallel to line KM of the triangle ∆BMK which implies that lines AB and BM are of equal distance. Given that B is the midpoint of AM. We can conclude that triangles ∆ABC and ∆BMK are similar triangles.
Since ∆ABC is an equilateral triangle, then all the sides of the quadrilateral ACKB are equal and its perimeter is calculated as:
18.5 feet × 4 sides of the quadrilateral = 74 feet.
In conclusion, the triangles ∆ABC and ∆BMK are similar triangles, and ∆ABC ≅ ∆BMK. The perimeter of the quadrilateral ACKB is equal to 74 feet.
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Find the length of the three missing sides in the rhombus below.
x=
y=
z=
The length of the three missing sides in the rhombus are x=75,y=75,z=75
What is rhombus and some of its properties?Rhombus is a parallelogram whose all sides are of equal lengths.
Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).
Its vertex angles are bisected by its diagonals.
The triangles on either side of the diagonals are isosceles and congruent.
Given;
One side of rhombus= 75
Now, as we know that all sides of rhombus are equal
x=y=z=75
Therefore, the sides of rhombus will be x=75,y=75,z=75.
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80 figs are kept in a container. Each fig weighs 0.02 kg. What is the
total weight of the figs?
the Total weight of the container that kept figs is 1.6 kg.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, 80 figs are kept in a container. Each fig weighs 0.02 kg.
Since,
One fig is weighing = 0.02 kg
So,
80 figs will weigh = 0.02 * 80
80 figs will weigh = 1.6 kg
Therefore, the Total weight of the container that kept figs is 1.6 kg.
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2. a) b) 5 3 c) d) a What is 258 plus 329? What is 258 plus-319? What is 1 023 minus 648? What is 648 minus 1 023? 3
Answer:
A=587
B=-61
C=375
D=-375
Step-by-step explanation:
Determine the matrix equation for:
x1 + 2x₂ = 11
3x1 + 4x2 = 25
A. [ 1 2 3 4 ] = [11 25] [x1 x2]
B. [ 1 2 3 4 ] [x1 x2] = [11 25]
The matrix equation for the given is [tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex] and option B is the correct answer.
What is matrix?A matrix, sometimes known as matrices, is a rectangular array or table of letters, numbers, or other symbols organized in rows and columns that is used to represent a mathematical object or a characteristic of one.
Matrix representations of linear mappings without additional details enable explicit computations in linear algebra. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices.
The given equation is:
x1 + 2x₂ = 11
3x1 + 4x2 = 25
The equation is represented in matrix form as follows:
[tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex]
Hence, the matrix equation for the given is [tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex] and option B is the correct answer.
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(4) In 2018, Apple had the largest profit of any company in the United States. They made
$48,351,000,000. One of the largest losses of any company during one year was AOL Time Warner in
2002, which lost $123,160,000,000. Write and evaluate a subtraction expression to find the difference
between Apple's 2019 profits and AOL Time Warner's 2002 losses.
I
I
I
I
1
The value of the equation is A = - $ 74,80,90,00,000
What is an 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.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The profit of Apple in 2018 P = $ 48,351,000,000
The loss of AOL Time Warner in 2002 L = $ 123,160,000,000
So , the difference between between Apple's 2019 profits and AOL Time Warner's 2002 losses is A
A = P - L
Substituting the values in the equation , we get
A = $ 48,351,000,000 - $ 123,160,000,000
On simplifying the equation , we get
A = - $ 74,80,90,00,000
Hence , the equation is A = - $ 74,80,90,00,000
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