The vectors to be linearly independent, this equation must have only the trivial solution x1 = x2 = x3 = 0. This is true if and only if a is not equal to 2 or -2. Thus, the answer is (a) a = 1, -4.
To determine the values of a for which the given vectors are linearly independent, we need to set up the equation Ax = 0, where A is the matrix formed by taking the given vectors as its columns and x = (x1, x2, x3) is a vector of coefficients. If the only solution to this equation is the trivial solution x = (0, 0, 0), then the vectors are linearly independent.
Writing out the matrix and setting up the equation, we have:
| 0 a 4 | | x1 | | 1.a |
| 1 0 1 | | x2 | = | 4 |
| 3 2 2 | | x3 | | 0 |
To solve for x1, we eliminate the first column by subtracting 3 times the first row from the third row, and then subtracting the first row from the second row:
| 0 a 4 | | x1 | | 1.a |
| 1 0 1 | | x2 | = | 4 |
| 0 -3 -10| | x3 | | -3a |
We can now solve for x2 and x3 in terms of x1:
x2 = 4 - x1
x3 = (-3a + 3x1 - 10x2)/3
If the only solution to this equation is x1 = x2 = x3 = 0, then the vectors are linearly independent.
Substituting the values of x2 and x3 into the first equation, we get:
0x1 + ax2 + 4x3 = a(4 - x1) + 4((-3a + 3x1 - 10(4 - x1))/3) = -26a + 16x1 + 16.
For such more questions on Trivial solution:
https://brainly.com/question/13252722
#SPJ11
Find the equation of the line with slope = 6 and passing through (2,20). write your equation in the form y = mx + b.
Answer:
y = 6x + 8
Step-by-step explanation:
y = mx + b
20 = 6(2) + b
b = 8
y = 6x + 8
Dion is 4 years older than Agustina. In 3 years the sum of their ages will be 46. How old is Dion now?
Answer:
22
Step-by-step explanation:
Dion (d) is 4 years older than Agustina (a)
d=a+4
In 3 years the sum of their ages will be 46
d+3+a+3=46
d+a+6=46
d+a=40
d=40-a
d=a+4
a+4=40-a
2a=36
a=18
Plug a back in
18+4=d
22=d
d=22
Sorry if this was a little long.
Below is the market for funnel cakes at a small community fair.
a) what is the equilibrium price and quantity of the funnel cakes?
b) What is the total consumer spending on funnel cakes at the equilibrium point?
c) Calculate the producer surplus and consumer surplus at equilibrium. Show your work.
d) What would be the result if the suppliers charged $6? Explain.
e) Cheese pretzels are substitute good for funnel cakes at the same fair. Draw a correctly labeled graph of the market for cheese pretzels. Shade the area of consumer surplus.
f) A large number of new guests enter the fair. Illustrate the effect of this change on the same graph from part E.
g) does the consumer surplus increase, decrease, or stay the same as a result of the change from part F? Explain.
h) A new cheese pretzel stand opens at the same fair. On a new graph, illustrate the market for cheese pretzels at this fair before and after the new stand opened.
i) if the large number of new guests entering the fair happened at the same time that the new cheese pretzel stand open how would the equilibrium price and quantity for cheese pretzels change? Explain.
From the graph given, the equilibrium price and quantities are given respectively as;
Price = $5Quantity = 6 units of funnel cakes.What is the total consumer spending on funnel cakes at the equilibrium point?The total consumer spending(TCS) is achieved by finding the product of the price and the quantities at the equilibrium point.
Hence,
TCS = 5 * 6
= 60
A) The producer surplus is the area of the triangle shaded yellow in the attached image.
Recall that he area of triangle is:
1/2 b * h
b = 4
h = 6
Hence Area of the RA-Triangle (Producer Surplus) =
1/2 * 4 * 6
= 12
B) The Consumer surplus is the area of the triangle shaded Green in the attached image.
Recall that the area of triangle is:
1/2 b * h
b = 4
h = 6
Hence Area of the RA-Triangle (Consumer Surplus) =
1/2 * 4 * 6
= 12
What would be the result if the suppliers charged $6?
If the suppliers charged $6, then the quantity demanded would drop to 4 units of funnel cakes. It is demonstrated graphically. Recall that the law of demand and supply indicates that when prices goes up, demand comes down and vice versa.
Graph II illustrates what would happen if a large number of guests entered the fair. It would result to a right-ward shift in the demand curve.
Does the consumer surplus increase, decrease, or stay the same as a result of the change from part F?Yes, there is an increase in the consumer surplus. Now there are more consumers hence the total amount they are willing to pay as an aggregate sum has increased from what was.
Learn more about Equilibrium market conditions:
https://brainly.com/question/12252562
#SPJ1
The diagonals of a rectangle measure x+5 feet and 2x+1 feet what is the value of x?
The value of x is 4.
Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.
The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.
In the given figure ABCD is a rectangle.
OA=2x+1 and OD=x+5 [Given]
AC and BD are diagonals of a rectangle.
As we know that the diagonals of a rectangle are always equal.
So, AC = BD
We can also write it as,
2×OA=2×OD
2×(2x+1) =2×(x+5)
Apply the distributive property a(b+c)=ab+ac, we get
4x+2=2x+10
Subtract 2x from both sides, we get
4x+2-2x=2x+10-2x
2x+2=10
Subtract 2 from both sides, we get
2x+2-2=10-2
2x=8
Divide both sides by 2, we get
2x/x=8/2
x=4
Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.
Learn more about rectangles from here brainly.com/question/1549055.
#SPJ4
Function the graphic below:
The graph is a decreasing exponential graph.
How to illustrate the information?Part A: The given graph is decreasing the exponential graph since the graph is decreasing rapidly as the value of x is increasing and the value of y is decreasing rapidly.
Part B: The graph shown here is maybe the case of any electric appliance which is of cheap quality. The time when it is brought then its performance and its life is awesome after that its life is decreasing rapidly.
Learn more about graph on:
https://brainly.com/question/19040584
#SPJ1
Complete question:
Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship. Identify and interpret the key features of the function in the context of the situation you described in part A.
What is the total probability of rolling a single die twice, and having it land on 3 the
first roll, and a number greater than 3 the second roll?
er:
Answer:
0,5*0,5=0,25
Step-by-step explanation:
assuming a die of 6 faces
25
0,5 for < 4; 0,5 for < 3
Shara is building a birdhouse. She cuts a 6-foot-long board into sections that are each 1/3 foot long. How many sections of the board will Shara have when she is finished cutting?
A 2
B 6 1/3
C 10 1/3
D 18
Answer:
D
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by its reciprocal.
6 ÷ 1/3
= 6 x 3/1
= 6 x 3
= 18
The number of sections of the board Shara has when she is finished cutting is 18 sections.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Length of the board = 6 feet
Length of the section = 1/3 feet
The number of 1/3 feet sections.
= 6 ÷ 1/3
= 6 x 3
= 18
Thus,
Shara when she is finished cutting will have 18 sections.
Learn more about fractions here:
https://brainly.com/question/24370499
#SPJ2
The geometry students have designed a hexagonal flowerbed for the Homes for
Humanity landscaping project. The shape indicates the color of the flowers. The
design is composed of two congruent rhombuses (blue), four congruent parallelograms
(red and white), and four congruent trapezoids (red and white). The circular area
surrounding the design is an existing rock bed.
The students have determined the following measurements of each figure:
the bases of the trapezoids are 6 ft and 8 ft,
• the heights of the trapezoid and the parallelogram are 3.5 ft each, and
• the horizontal distances between the left and right vertices of each rhombus is 2
ft.
Trapezoid
[tex]A=\frac{1}{2}(3.5)(6+8)=24.5[/tex]
Parallelogram
[tex]A=(3.5)(6)=21[/tex]
Rhombus
[tex]A=\frac{1}{2}(7 \cdot 2)=7[/tex]
Red Area
[tex]2(21)+2(24.5)=91[/tex]
White Area
[tex]2(21)+2(24.5)=91[/tex]
The circular area surrounding the design is an existing rock bed are 24.5, 21, 27, 91 and 91 ft sq.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
It is given the bases of the trapezoids are 6 ft and 8 ft,
The heights of the trapezoid and the parallelogram are 3.5 ft each, and the horizontal distances between the left and right vertices of each rhombus is 2 ft.
Trapezoid
Area = 1/2(3.5)(6 + 8)
Area = 24.5
Parallelogram
Area = 1/2(3.5)(6)
Area = 21
Rhombus
Area = 1/2(7)(2)
Area = 7
Red Area
Area = 2(21) + 2(2.4)
Area = 91
White Area
Area = 2(21) + 2(2.4)
Area = 91
Learn more about area here:
https://brainly.com/question/13522634
#SPJ2
15-point question. Pls help
Answer:
44
Step-by-step explanation:
x + (22 - 13) = 53
x + 9 = 53
x = 44
Answer:
44
Step-by-step explanation:
x+(22-13)=53
x+22-13=53
x+9=53
x=44
The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s in the $n^{\rm{th}}$ block. What is the sum of the first $1234$ terms of this sequence
Consider the lengths of consecutive 1-2 blocks.
block 1 - 1, 2 - length 2
block 2 - 1, 2, 2 - length 3
block 3 - 1, 2, 2, 2 - length 4
block 4 - 1, 2, 2, 2, 2 - length 5
and so on.
Recall the formula for the sum of consecutive positive integers,
[tex]\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2[/tex]
Now,
[tex]1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016[/tex]
which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.
In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of
[tex]\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224[/tex]
numbers, and their sum is
[tex]\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400[/tex]
This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of [tex]1+9\times2=19[/tex].
So, the sum of the first 1234 terms in the sequence is 2419.
The official height to width ratio of the United States flag is 1:1.9 If a United States flag is 6 feet high, how wide is it?
Answer:
11.4 feet
Step-by-step explanation:
1/1.9 = h/w (h= height, w=width)
Solving for w, gives you the formula
w = (1.9)h
This means the width is 1.9 times the height.
Use the formula to find the width where the height is 6 feet.
h = 6
w = (1.9)(6) = 11.4
The width is 11.4 feet.
The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are _____. Group of answer choices B0 and B1 y and x a and b a and B
B0 AND B1 are the parameters which describes the intercept and slope of the lines.
According to statement
we have to find the parameters which describes the intercept and slopes.
Simple linear regression is a model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
So, B0 AND B1 are the parameters which describes the intercept and slope of the lines.
Learn more about SLOPES here https://brainly.com/question/3493733
#SPJ4
Consider the function f(x) = one-third(6)x. what is the value of the growth factor of the function?
6 is the growth factor in the function f(x) = (1/3)(6ˣ).
The rate at which a quantity multiplies itself over the independent factor, to increase the value of the function exponentially is known as its growth factor.
In the question, we are given a function f(x) = (1/3)(6ˣ) and are asked to identify the growth factor of the function.
We know that the rate at which a quantity multiplies itself over the independent factor, to increase the value of the function exponentially is known as its growth factor.
In the given function, f(x) = (1/3)(6ˣ), (1/3) remains unaffected with the change in the independent factor x, but 6 is exponentially increasing with x.
Thus, 6 is the growth factor in the function f(x) = (1/3)(6ˣ).
Learn more about growth factor at
https://brainly.com/question/26296863
#SPJ4
Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
A
B
F
D
C
E AC = BC
ZAZB
Answer:
ASA
Step-by-step explanation:
Answer the question please!!!!!!
[tex]Simplify \: \: \\ ( \: a \: ) \: 287 \: \times \: 90 \\ ( \: b \: ) \: 105 \: \times 95[/tex]
Answer:
a) 25830
b)9975
Step-by-step explanation:
a) 287
x 90
25830
b) 105
x 95
9975
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A shaded polygon A B C D is graphed in an x y plane, where x axis ranges from 0 to 7 in increments of 1 and y axis ranges from 0 to 6 in increments of 1. The vertices are as follows: A (1, 1), B (2, 3), C (5, 4), and D (4, 2). Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′. The slope of C'D' is___ .
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
Find out more on transformation at: brainly.com/question/4289712
Factor x4 + xy3 + x3 + y3 completely. Show your work. Hint: First factor out a monomial. x4 + xy3 + x3 + y3 =
Answer:
[tex]x^{3} ( x + 1 ) + y^{3} (x+1)\\= (x+1)(x^{3} + y^{3})[/tex]
Answer:
Step-by-step explanation:
YOU PLUS ALL OF THEM
can someone please help me with 17a
Answer:
r=8.74038744 m
and surface area=1303.76211 m2
Step-by-step explanation:
The Bay announced it would open a 9000-plus square metre freestanding store in the new West Grand Promenade. This would be the largest store on the promenade, with other smaller stores selling food, tires, and shoes. How else can this particular Bay store be described
This Bay store can also be described as a big box retailer store.
Big Box Retailer
A big box retailer is a physically enormous retail store that is typically a component of a chain of stores (also known as a hyper store, supercenter, superstore, or megastore). By extension, the phrase, big box retailer can also refer to the business that runs the store.
The Bay Store as a Big Box
There are numerous retail chains that only operate in Canada, aside from the large American big box retailer stores like Walmart Canada and the formerly-existent Target Canada. These include places like Hudson's Bay by Home Outfitters, Loblaws by Real Canadian Superstore, Rona, Winners by HomeSense, Canadian Tire by Mark's & Sport Chek, Shoppers Drug Mart, Chapters by Indigo Books and Music, Sobeys, and several others.
Learn more about big box retailers here:
https://brainly.com/question/16236924
#SPJ4
solve -9 2/7 - (-10 3/7)
A star is estimated to be 150,000,000,000,000 km away from Earth. Write this distance in scientific notation. [?] × 10 km
Answer:
[tex](1*10^{15} )(5*10^{14})[/tex] or 1.5×10^14
Step-by-step explanation:
The answer is [tex](1*10^{15} )(5*10^{14})[/tex] or 1.5×10^14.
Hope this helps!
Total area=
Help me please, thankss
The Area of given figure is 341.6 square.
According to the statement
we have to find the total area of given figure.
Here a= 10 and h= 11
So, we use the formula is A = a(a + √((a)^2 + 4(h)^2))
where the a represent the base of given solid or sides of the equilateral triangle
And h represent the slant height of the solid.
So, Substitute the values in above formula then
A = 10(10 + √((10)^2 + 4(11)^2))
A = 10(10 + √((100 + 4(121))
A = 10(10 + √(100 + 484)
A = 10(10 + √(584)
A = 10(10 + 24.16)
A = 10(34.16)
A= 341.6
So, The Area of given figure is 341.6 square.
Learn more about AREA here https://brainly.com/question/10090807
#SPJ1
Which of these numbers is irrational?
-3.5
3.5
ОО
35
√5 help
Answer:
√5 is irrational
Step-by-step explanation:
A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.
ApplicationUsually, a number that can only be expressed exactly using a symbol will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.
The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.
__
Additional comment
A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.
Solve each system by elimination
Answer:
system of equation by elimination
1 write both equation in standard form
2 make the coefficient of one variable opposites
3 add the questions relating from step to eliminate one variable
4 solve for the remaining variable
5 substitute the solution from step for into one of the original equation
Let k be the largest integer such that 343/7^k is an integer. What is the remainder when 343/7^k is divided by 7
Answer:
1
Step-by-step explanation:
The given ratio will be the remaining factor of 343 after factors of 7 have been removed. The value of interest is that factor, modulo 7.
Factors of 343343 = 7·7·7 = 7³
RatioThe value of k is the power of 7 in the factorization of 343, so we have ...
k = 3
and ...
343/7³ = 1
RemainderThe remainder when this ratio is divided by 7 is ...
1 mod 7 = 1
The remainder when 343/7^k is divided by 7 is 1.
Find the equation of a circle with center at (5, 6) and radius 8.
Answer:
(x - 5)^2 + (y - 6)^2 = 64
Step-by-step explanation:
Every circumference is in the form:
(x - xc)^2 + (y - yc)^2 = r^2
Where xc is the x of the center. Yc is the y of the center. r is the radius. We just plug in the values and we're done.
Answer:
[tex](x-5)^2+(y-6)^2=64[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
center = (a, b)radius = rGiven:
center = (5, 6)radius = 8 unitsSubstitute the given values into the formula:
[tex]\implies (x-5)^2+(y-6)^2=8^2[/tex]
[tex]\implies (x-5)^2+(y-6)^2=64[/tex]
Therefore, the equation of a circle with the given values is:
[tex](x-5)^2+(y-6)^2=64[/tex]
Learn more about equations of circles at:
https://brainly.com/question/27955619
https://brainly.com/question/27783217
A teacher knows that 80% of her students will score no more than 5 points above or below the class average, 85%, on the test. Which inequality represents the test scores of 80% of her students?
Answer:
[tex]|x-85| \leq 5[/tex]
Step-by-step explanation:
|x-85| represents the 'distance' of the test score than 85, and this distance must be less than or equal to 5.
Find the missing segment in the image below.
Answer:
10.
Step-by-step explanation:
6/9 = x/15
9x = 6*15
9x = 90
x = 10.
Answer:
10
Step-by-step explanation:
[tex]\frac{6}{15} =\frac{x}{x+15}[/tex]
[tex]6(x+15)=15x[/tex]
[tex]6x+90=15x[/tex]
[tex]90=15-6x[/tex]
[tex]90=9x[/tex]
[tex]x=90/9= 10[/tex]
Hope this helps
If my savings of $x grows 10% each year. how much will I have in: 2 years
The amount I'll have in two years at the growth rate described is; $1.21x.
How much will I have in 2 years?Since it follows that the savings grow by 10% each year, it can be concluded that the growth factor is; 110% = 1.1
Hence, in two years, we have;
= $x × (1.1)²
= $1.21x.
Read more on growth factor;
https://brainly.com/question/3451703
#SPJ1
Answer:
1.21x
Step-by-step explanation:
on rsm it says its correct
4. For a camping trip, each person packs 1.5 lb of food per day. Let p represent the number of people on the trip, and let f represent the total weight of food packed for each day. What is the independent variable in this relationship? Explain. I need this with explanation please:(