The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).
We have,
Matrix A becomes singular (i.e., its determinant is zero).
The given matrix A is:
A = | 3x -6 |
| -4 x |
Using the determinant formula for a 2x2 matrix, we have:
det(A) = (3x * x) - (-6 * -4)
Simplifying the expression:
det(A) = 3x^2 - 24
To find the value of x for which det(A) = 0, we set the determinant equal to zero:
3x^2 - 24 = 0
Now, we can solve this quadratic equation for x:
3x^2 = 24
x^2 = 8
x = ±√8
Therefore,
The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).
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A track-and-field coach recorded the length of each student's standing long jump. The data is summarized in the box plot.
Standing Long Jumps
0
+
2
4
+
Feet
6
8
10
Choose all of the statements that can be concluded from this data.
A. The median jump length is 5 feet, which is the average length of a standing long jump for the students represented in the box plot.
B. The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of
their long jump.
C. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 4 feet of the
median.
D. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 2 feet of the
median.
A
Answer:
A because of the average length showed
What is the square root of pi?
Pi is a Greek number that plagues mathematics, physics, and circles to the point where pi-fatigue is actually a thing. Pi is an infinite number, however it will henceforth only be written as 3.14159.
I have two solutions to your problem.
The first, and probably less appealing answer, but most used everywhere, would be to use a calculator.
But if you find yourself without a calculator at the ready, I hope you’re prepared to math quite dubiously.
Finding the square power, inverse of a radical, or whatever is multiplied by itself to equal 3.14159, is the second step. We must start someplace to start our attempt, and that place is 3.14159. Since 1 squared equals 1 and 2 squared equals 4, our result, expressed in decimal form, is larger than 1 but less than 2. After that, we just start divising and multiplying the decimals again until we have calculated the square root of pi.
TL;DR
1.7724531 is the approximate square root of pi.
Answer:
1.77245385091
Step-by-step explanation:
A rectangle is 8 feet longer than it is wide. find the dimensions of the rectangle if its area is 345 sq-feet.
The width of rectangle is 15 feet and the length of rectangle is 23 feet.
According to the statement
Width of rectangle = x
Length of rectangle = x+10
Area of rectangle = 345 sq-feet.
we know that the area of rectangle is
Area of rectangle = L*W
Substitute the values in it then
345 = (x) (x+8)
345= (x)^2 + 8x
(x)^2 + 8x - 345 = 0
By factorisation
(x-15) (x+23) = 0
So, width of rectangle is 15 feet and the length of rectangle is 23 feet.
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Find the area of the figure
Answer:
36 in.
Step-by-step explanation:
find the area of the rectangle and triangle first
area of rectangle = length x height
aR = (6 + 6) x 5
aR = 12 x 5
aR = 60
area of triangle = base x height x 1/2
aT = (6 + 6) x 4 x 1/2
aT = 12 x 4 x 1/2
aT = 24
now, to find the area of the shaded area subtract the triangle from the rectangle
area = rectangle - triangle
a = 60 - 24
a = 36
Find and compare the growth rates in the weekly number of specialty items produced at each factory.
Show your work.
0.129 is the change in the growth rate of company.
According to statement
we have to find and compare the growth rate of the company weekly.
we use the growth rate formula is
GROWTH RATE = present - past / present
Substitute the values in this formula
1st week = 220-190 / 220
1st week = 0.136
2nd week = 252-220 / 252
2nd week = 32 / 252
2nd week = 0.126
3rd week = 290-252 / 290
3rd week = 0.131
4th week = 337 - 290 / 337
4th week = 0.139
5th week = 380 - 337 / 380
5th week = 0.113
6th week = 440 - 380 / 440
6th week = 0.136
7th week = 505 - 440 / 505
7th week = 0.128
Now we find the average value of growth rate
Average = 0.136 + 0.126+0.131+0.139+0.113+0.136+0.128 /7
Average = 0.909/7
Average = 0.129
So, 0.129 is the change in the growth rate of company.
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Consider an unstructured overlay network in which each node randomly chooses c neighbors. If P and Q are both neighbors of R, what is the probability that they are also neighbors of each other
The probability value become is 2c/(N-1).
According to the statement
we have given that If P and Q are both neighbors of R, and by considering unstructured network in which each node randomly chooses c neighbors.
we have to find that the probability of neighbors that they are also neighbors of each other.
So, For this purpose to find the probability is
Consider a network of N nodes unstructured and let
If each node chooses c neighbors at random,
then the probability that P will become by choose Q, or Q chooses P is roughly 2c/(N-1).
And the probability outcomes value become is 2c/(N-1).
So, The probability value become is 2c/(N-1).
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Solve for this equation:
x(x+3)(x+3)=0
Answer:
x^3+6x^2+9x
if you are trying to find the original function
if not, and you are trying to find the zeros is
x=-3
x=0
Step-by-step explanation:
multiply x(x+3)
x^2+3x
then multiply that by x+3 and that should give you the answer
Answer:
x = 0 or x = -3 or x = -3
Step-by-step explanation:
set up factors as:
x = 0
x + 3 = 0
x + 3 = 0
the first will remain as x = 0 while the others become x = -3 once subtracted
i hope this helped!
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The solution to the inequality is x > 3
The number line that represent the solution set will be:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. The correct option is the second option
Linear InequalitiesFrom the question, we are to determine the number line that represents the solution set for the given inequality
The given inequality is
3(8 – 4x) < 6(x – 5)
First, we will solve the inequality
3(8 – 4x) < 6(x – 5)
Clear the brackets
24 - 12x < 6x - 30
Collect like terms
24 + 30 < 6x + 12x
54 < 18x
Divide both sides by 18
3 < x
∴ x > 3
Hence, the number line that represent the solution set will be:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. The correct option is the second option
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What is another way to name angle 3?
O Angle MVK
O Angle LVM
O Angle LVK
O Angle KVM
Answer:
intimately there are three types of angles a cute angle and angle between zero and 90° right angle and angle 90 degree angle of two angle and angle between 90 and 180 degree
The length of a rectangle is 5 5/3 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68
(question and answers attached)
The perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The perimeter of any object is the total sum length of its boundary.
The perimeter of a rectangle with length l units and width w units is given as:
Perimeter = 2(l + w) units.
In the question, we are given that the length of a rectangle is 5 3/5 inches and its width is half of its length. We are asked to find the perimeter of the rectangle.
The length of the given rectangle (l) = 5 3/5 inches = 28/5 inches.
The width of the given rectangle (w) = Half of length = 1/2 * 28/5 inches = 14/5 inches.
Thus, the perimeter of the rectangle = 2(l + b) = 2(28/5 + 14/5) inches,
or, the perimeter = 2(42/5) inches,
or, the perimeter = 84/5 inches,
or, the perimeter = 16.8 inches.
Thus, the perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The given question is incorrect. The correct question is:
"The length of a rectangle is 5 3/5 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68"
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There are 500 passengers on a train. 7/20 are men and 40% are women. the rest are children
On the train, there are a total of 125 children.
Calculating the number of childrenTotal number of passengers = 500
Out of 500 passengers, men =7/20
So, the number of men= 500* 7/20 = 175
Out of 500 passengers, women = 40%
So, the number of women passengers = 500*40/100 = 200
Therefore, the total number of men and women passengers= 175+200 = 375.
There are also children on the train. So, the rest number should be those children.
The rest number =children= 500- 375 = 125.
So, it is concluded from the above equation that there are 125 children on the train.
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20 points!
i need help with these rational numbers
The rational numbers are explained below.
What are rational numbers?The complete question can't he found. Therefore, an overview will be given. Rational numbers are the numbers that can be represented by the quotient p/q of two integers.
In this case, p and q are integers and p isn't equal to 0.
The examples include 1/5, 1/3, -2, 5, etc.
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Given a polynomial function f(x) = 2x2 – 3x 5 and an exponential function g(x) = 2x – 5, what key features do f(x) and g(x) have in common? both f(x) and g(x) have the same domain of ([infinity], -[infinity]). both f(x) and g(x) have the same range of [0, -[infinity]). both f(x) and g(x) have the same x-intercept of (2, 0). both f(x) and g(x) increase over the interval of [-4 , [infinity]).
Both f(x) and g(x) have the same domain of (9,-infinity).
What is a function?A function is an expression that shows the relationship between two or more numbers and variables.
Plotting the functions f(x) = 2x² – 3x + 5 and g(x) = 2ˣ - 5:
Both f(x) and g(x) have the same domain of (9,-infinity).
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please help! this is the last one i need and i forgot how to do it!
Based on the information, Christian would have $5525.5 of annuity.
How to calculate the annuity?According to given information, the number of coffees per week is 3 then, per month is 3x4 = 12
For each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54
Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133
n = number of payments = 8 x 12 = 96
We can use the formula for finding the future value as below
FV = C x [ ( 1 + r )n-1 ] / ( r )
FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)
= 54 x [ (1.13609 - 1)] / (0.00133)
= 54 x 0.13609 / (0.00133)
= 54 x 102.3233
= 5525.5
Therefore Christian would have $5525.5 of annuity.
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Find two consecutive numbers such that sum of four times the first and triple the second is 157. (Linear Function)
Step-by-step explanation:
Set up a system of equations,
Consective numbers appear before and after so we need two number such that
[tex]x + 1 = y[/tex]
or
[tex]x - y = - 1[/tex]
Likewise, we also know that
[tex]4x + 3y = 157[/tex]
Let multiply the top equation by 3.
We get
[tex]3x - 3y = - 3[/tex]
Then we add the bottom equation to that
[tex]4x + 3y = 157[/tex]
[tex]7x = 154[/tex]
[tex]x = 22[/tex]
Then we plug in x for the original equation,
[tex]22 + 1 = 23[/tex]
So the two numbers are 22,23.
WILL MAKE BRAINLIEST!!
Solve for x.
Answer:
8
Step-by-step explanation:
51 + 4x + 7 = 90 - combine like terms
58 + 4x = 90 - subtract 58 from each side
4x = 32 - divide both sides by 4
x = 8
Answer:
x = 8
Step-by-step explanation:
The red square indicates that there is a right triangle. All right triangles have angles equal to 90°. Therefore, we can find the value of "x" by setting the sum of both the interior angles to 90°.
(4x + 7) + 51° = 90° <----- Sum of both angles is 90°
4x + 58 = 90° <----- Combine 58 and 7
4x = 32 <----- Subtract 58 from both sides
x = 8 <----- Divide both sides by 4
Lola wins $240
She spends $48 on a dress.
What percentage of the $240 has she spent?
Answer:
Step-by-step explanation:
$240 = 100
$48 = X
100 * 48 = 240X
4800 / 240 = 240X / 240
X = 20
She spent 20% on the dress
Irene knows her blood type is A, but William does not know his blood type. However, William knows that his mother and father both had blood type B. Irene and William's first child is a boy with type O blood. Based on this information, William's blood type could be
Based on this information, William's blood type could be either B or O.
What is Segregation of alleles?
Allele pairs (several features of the same gene) are segregated during meiosis so that they can be transferred selectively to different gametes.During meiosis, maternal and paternal alleles separate.What is genotype vs phenotype ?
Genotype: An organism's genetic makeup. Phenotype. physical characteristic that arises within an organism as a result of its genotype. Probability law.Genotype - the set of alleles that make up an organism.How does genotype influence phenotype ?
The alleles you have for a specific gene or collection of genes are referred to as your genotype. The physical attribute itself, or phenotype, can be affected by both genotype and environmental variables.Learn more about Genotype
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A square has a perimeter of 12x 52 units. which expression represents the side length of the square in units?
Answer:
X
Step-by-step explanation:
KHAN ACADEMY
35. A can of popcorn is to be packed in a box for shipping as shown. The can is 18 inches tall and has a radius of 7 inches. The box is 19 inches tall and has a square base with sides of length 15 inches. All empty space around the can is to be filled with packing material. How many cubic inches of packing material will be needed?
The amount of packing material is 1506 cubic inches
How to determine the amount of packing material?The given parameters are:
Can
Radius, r = 7 inches
Height, h = 18 inches
Box
Base dimension, l = 15 inches
Height, h = 19 inches
The volume of the can is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]V_1 = 3.14 * 7^2 * 18[/tex]
[tex]V_1 = 2769[/tex]
The volume of the box is
[tex]V =l^2h[/tex]
So, we have:
[tex]V_2 =15^2 * 19[/tex]
[tex]V_2 =4275[/tex]
The amount of packing material is;
Amount = V2 - V1
This gives
Amount = 4275 - 2769
Evaluate
Amount = 1506
Hence, the amount of packing material is 1506 cubic inches
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Suppose the probability that a Wide Receiver catches a ball thrown to him is 0.9. Let X model the number of catches he has if he is targeted 8 times in a game. What is the mean number of balls you would expect him to catch
Using the binomial distribution, the mean number of balls you would expect him to catch is of 7.2.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are:
n = 8, p = 0.9.
Hence the mean is:
E(X) = np = 8 x 0.9 = 7.2.
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Using the equation y = 2x - 3, what would the input need to be for an output of 7?
00
O 11
05
08
Several friends bought flowers to make table centerpieces. write the ratios of purple flowers to white flowers for each friend. bouquets of flowers purple flowers white flowers rowan 8 2 marcia 10 1 jillian 10 2 lulua 18 3 who has the smallest ratio of purple to white flowers? rowan marcia jillian lulua
The ratio for Rowan = 4:1.
The ratio for Marcia = 10:1.
The ratio for Jillian = 5:1.
The ratio for Lulua = 6:1.
The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.
Ratios are fractions in the simplest form representing the relationship between two quantities.
The ratio of purple to white flowers for each friend can be shown as:-
Rowan:
The number of purple flowers = 8
The number of white flowers = 2
Thus, the fraction of purple to white flowers = 8/2 = 4/1.
Thus, the ratio for Rowan = 4:1.
Marcia:
The number of purple flowers = 10
The number of white flowers = 1
Thus, the fraction of purple to white flowers = 10/1.
Thus, the ratio for Marcia = 10:1.
Jillian:
The number of purple flowers = 10
The number of white flowers = 2
Thus, the fraction of purple to white flowers = 10/2 = 5/1.
Thus, the ratio for Jillian = 5:1.
Lulua:
The number of purple flowers = 18
The number of white flowers = 3
Thus, the fraction of purple to white flowers = 18/3 = 6/1.
Thus, the ratio for Lulua = 6:1.
The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.
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Answer:Its rowan
Step-by-step explanation:Mark me brainliest need award
The equation y=ax^2 describes a parabola. If the value of a is positive, which way does the parabola open?
A.Up
B.Right
C.Left
D.Down
A. Up
Step-by-step explanation:Parabolas are graphs that make U-shapes and are formed from quadratic equations.
Vertical Parabolas
There are 2 different types of parabolas: vertical and horizontal.
Vertical parabolas have a vertical axis of symmetry. So, they open up or down.Horizontal parabolas have a horizontal axis of symmetry. So, they open left or right.If the x-value is squared, then the parabola is vertical. So, this graph must open up or down.
Positive A-Value
The a-value is the coefficient before the squared term. In a vertical parabola, the graph opens up if the a-value is positive. On the other hand, the graph opens down when the a-value is negative.
In this case, the graph is a vertical parabola that opens up. This means that the range will have a minimum value but no maximum.
Solve the equation. -9×+1==×+17 O x=-8 O x = -2 O x=2 © ) x=8
WILL MAKE BRAINLIEST!! What type of angle is angle A?
PLEASE HELP 80 POINTS !!!!!!!!
Answer:
Step-by-step explanation:
a) it is a reflection
b) it is vertex B"
Carson buys eggs and lemons at the store. he pays a total of $39.62. he pays $6.74 for the eggs. he buys 8 bags of lemons that each cost the same amount.
The algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74
According to the question,
Cost of 1 bag of lemons = $x
Cost of 8 bags of lemons = 8*x = 8x
Cost of 8 bags of lemons = Total cost - cost of the egg
8x = $39.62 - $6.74
Hence, the algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74.
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Which of the following systems of linear inequalities is represented by the
solution graphed below?
O A. y>2 and ys x
O B. y22 and rex
O C. x> 2 and y2 x
O D. x22 and y > x
The solution graphed below represents the y>2 and [tex]y\leq x[/tex] system of linear inequalities.
When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.
Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities.
Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities.
Equivalent inequality refers to linear inequalities with the same solution.
From the given graph, it can be seen that the line parallel to the x-axis represents y>2 and the other inclined line represents [tex]y\leq x[/tex] .
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Find a 49 of the sequence 70, 63, 56, 49,
Answer:
- 226
Step-by-step explanation:
ARITHMETIC SEQUENCE.
Number of term of an Arithmetic progressions has the formular.
Tn = a + ( n - 1 ) d
From the question,
First term ( a ) = 70
common difference = T2 - T1 = 63 - 70 = -7
For the 49th term
T49 = a + 48d
= 70 + 48 ( -7 )
= 70 - 336 = - 226