7. A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Can such a system have a unique solution? Explain. Choices: a. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If there is a free variable, the solution set contains a unique solution. b. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains infinitely many solutions. If the linear system is inconsistent, there is no solution. c. Yes, it can have a unique solution. Because there are more equations than variables, there are no free variables. If the system is consistent and there are no free variables, the solution set contains a unique solution. If the system is inconsistent, there is no solution. d. Yes, it can have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains either a unique solution or infinitely many solutions. If the linear system is inconsistent, there is no solution.
The correct answer is b. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains infinitely many solutions. If the linear system is inconsistent, there is no solution.
A linear system is a set of linear equations that can be expressed in the form Ax = b, where A is a matrix of coefficients, x is a vector of unknowns, and b is a vector of constants. Linear systems can be solved using a variety of methods, such as matrix inversion, Gaussian elimination, or the LU decomposition. In addition, linear systems can be used to model a variety of real-world problems, such as linear programming, optimization problems, and electrical networks.
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Solve the given initial-value problem. dy + 2(t + 1)y2 = 0, y(0) dt 1 15 1 y(t) = 2 + 2t + 15 x Give the largest interval I on which the solution is defined. (Enter your answer using interval notation.)
The Largest interval in which the solution of the differential equation is defined is (-5, 3).
dy/dt + 2(t + 1)y² = 0 and y(0) = -1/15
Now, dy/dt + 2(t + 1)y² = 0
dy/dt = -2(t + 1)y²
By separating variables
dy/y² = -2(t + 1) dt
Integrating both sides
∫dy/y² = -∫(t + 1) dt
-1/y = -(t²+2t) + c
y(t) = /(t²+2t - c)
We know, y(0) = -1/15
So, -1/15 = 1/(0+0-c)
c = 15
∴ y(t) = 1/(t² + 2t - 15)
Now, y(t) is defined if t² + 2t - 15 ≠ 0
Let t² + 5t - 3t - 15 = 0
(t + 5)(t - 3) = 0
t = -5, 3
So, the intervals are (-∞ , -5), (-5, 3) and (3, ∞)
As t = 0 lies in between (-5, 3) hence the interval in which the solution is defined is (-5, 3)
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In Exercises 1-4, determine if the system has a nontrivial solution. Try to use as few row operations as possible. (1). 2 x1 - 5 x2 + 8 x3 = 0 -2 x1 - 7 x2 + x3 = 0 4 x1 - 2 x2 + 7 x3 = 0 (2). x1- 3 x2 + 7 x3 = 0 -2 x1 - x2 + 4 x3 = 0 x1 - 2 x2 + 9 x3 = 0 (3). -3 x1 - 5 x2 + 7 x3 = 0 -6 x1 - 7 x2 + x3 = 0 (4). -5 x1 - 7 x2 + 9 x3 = 0 x1 - 2 x2 + 6 x3 = 0
(1). 2 x1 - 5 x2 + 8 x3 = 0
-2 x1 - 7 x2 + x3 = 0
4 x1 - 2 x2 + 7 x3 = 0
Add the first and second equation:
0 x1 - 12 x2 + 9 x3 = 0
Add the third equation:
4 x1 - 2 x2 + 7 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(2). x1- 3 x2 + 7 x3 = 0
-2 x1 - x2 + 4 x3 = 0
x1 - 2 x2 + 9 x3 = 0
Add the first and second equation:
-x1 - 4 x2 + 11 x3 = 0
Add the third equation:
0 x1 - 6 x2 + 16 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(3). -3 x1 - 5 x2 + 7 x3 = 0
-6 x1 - 7 x2 + x3 = 0
Add the first and second equation:
-9 x1 - 12 x2 + 8 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(4). -5 x1 - 7 x2 + 9 x3 = 0
x1 - 2 x2 + 6 x3 = 0
Add the two equations:
-4 x1 - 5 x2 + 15 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
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You are a marketing manager and need to summarize recent spending on advertisements. You have placed 2 small advertisements that cost $325 each, 5 WILL FAST!! MARK BRAINLYIST IF RIGHT ANSWER
medium-sized advertisements that cost $750 each, and 12 large advertisements that cost $1,300 each. Which expression shows how to calculate the mean cost per advertisement?
A: 325 + 750 + 1,300 / 3
B: 325 + 750 + 1,300 / 19
C: 2 X 325 + 5 X 750 + 12 X 1,300 / 3
D: 2 X 325 + 5 X 750 + 12 X 1.300 / 120
The required expression used to calculate the mean cost per advertisement is 325 + 750 + 1,300 / 3. Option A is correct.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
Here,
Mean cost of each type of advertisement
= the sum of the cost of small. medium and large advertisement / 3
= 325 + 750 + 1,300 / 3
Thus, the required expression used to calculate the mean cost per advertisement is 325 + 750 + 1,300 / 3. Option A is correct.
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In radiation protection, which of the following is a measure of the probabilistic health effect on an individual as a result of an intake of radioactive material into the body?
A. TEDE
B. Gyt
C. Gya
D. CEDE
The correct answer is A. TEDE, which stands for Total Effective Dose Equivalent.
This is a measure of the effective dose equivalent to an individual resulting from an intake of radioactive material. It takes into account the type of material ingested and the radiation dose received.
It takes into account the type of material ingested and the radiation dose received. TEDE is generally used in radiation protection to estimate the probabilistic health effect on an individual as a result of an intake of radioactive material.
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Help Please I have 7 of these to do within 30 minutes and i dont get them
Answer:
angle JKL is 22°
Step-by-step explanation:
You want the measure of exterior angle JKL represented by (5x-3)°, given that the remote interior angles of ∆IJK are I = (2x +8)° and J = (x -1)°.
Exterior angleThe exterior angle is equal to the sum of the remote interior angles:
angle JKL = angle I + angle J
5x -3 = (2x +8) +(x -1)
5x -3 = 3x +7 . . . . . . . . . simplify
2x = 10 . . . . . . . . . . . add 3-3x
x = 5 . . . . . . . divide by 2
5x -3 = 5(5) -3 = 22 . . . . . degrees
Angle JKL is 22 degrees.
__
Additional comment
It is helpful to draw a figure. The attached figure is not to scale, but the angle measures are appropriately labeled.
The unlabeled interior angle at K is supplementary to the labeled exterior angle there. That same interior angle is also supplementary to the sum of the other two interior angles, since the sum of all the angles is 180°. Two angles supplementary to the same angle are congruent. This means the exterior angle JKL is congruent to the sum of the two marked interior angles. It's a simple relation, easy to derive, and useful to remember.
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A sector of a circle has an area of 20 square feet. Find the central angle which forms the sector if the radius is 5 feet. The central angle of the sector isradians. (Type an integer or a simplified fraction.)
The area of a sector of a circle is equal to the central angle multiplied by the radius squared, divided by 2. In this case, the sector of the circle has an area of 20 square feet, the radius is 5 feet, and we need to find the central angle.
The central angle will be 6.28 radians.
To find the central angle, we can rearrange the equation to solve for the angle:
Central Angle = (2 * Area) / (Radius^2)
Substituting the given values, we get:
Central Angle = (2 * 20) / (5^2)
Simplifying, we find that the Central Angle equals 6.28 radians.
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A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares fromthe four corners and turning up the sides. Find the side of the square cutout that gives the box the largest possible volume.
a) 0 in.
b) 6 in.
c) 5/3 in.
d) 2450/27 in.
The side of the square cutout that gives the box the largest possible volume
Therefore the answer is d) 2450/27 in.
To find the side length of the square cutouts that give the box the largest volume, we need to find an expression for the volume of the box in terms of the side length of the square cutouts. We can start by subtracting four times the area of one square cutout from the total area of the tin sheet to find the area of the box sides. The volume of the box will then be equal to the area of the box sides multiplied by the height.
The side length of the square cutouts can be represented by x. The area of one square cutout is x^2, so the total area of the four cutouts is
4x^2
The area of the tin sheet is 8 * 15 = 120. The area of the box sides is then
120 - 4x^2
The volume of the box is then (120 - 4x^2) * 8, which we want to maximize. To do this, we can differentiate the expression for the volume with respect to x and set it equal to zero, then solve for x. The solution to this optimization problem is
x = 2450/27, which is the side length of the square cutouts that gives the box the largest volume.
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A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 3 comma 7
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The y-intercept is at (27/2 ,9) in the Slope Intercept Form .
What is a line's Slope Intercept Form?
A line with m as its slope, m as its y-intercept, and c as its coefficient makes up the graph of the linear equation y = mx + c. The values of m and c in this version of the linear equation known as the slope-intercept form are real numbers.
The graph of the line passes through (0,9) and (3,7) .
Slope of the line = (7 - 9)÷(3 - 0) = -2/3
Hence the line will have the equation:
y - 9 = -2/3 ( x - 0 )
or, y - 9 = -2x/3
or, 3y - 27 = -2x
2x + 3y = 27
Now from the real world situation at y = 0, x = 27/2
and at x = 0, y = 9
Hence the y-intercept is at (27/2 ,9)
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qualitive or quantitive .tHE NUMBER OF CARS SOLD by a car dealer last month
What is the name of the segment inside the large triangle?
Answer:
Altitude: Segment from a vertex of a triangle that is perpendicular to the opposite side. This segment may be inside the triangle, on the triangle, or outside the triangle. Pictured below are the altitudes (represented as black segments) of acute, right, and obtuse triangles.
Step-by-step explanation:
I have a triangle with a measure of 15 cm, what will be its perimeter?
Answer: Its perimeter is 45 cm.
Step by step explanation:
Data :
We have a triangle with a measure of 15 cm
We must simplify taking into account that it is an equilateral triangle, all its sides are equal, therefore the perimeter is the sum of its sides:
P = Sum of its sides[tex]\bf P= 15 + 15 + 15[/tex]
[tex]\boxed{\bf \: P = 45 \: cm}[/tex]
Rpt: Its perimeter is 45 cm.
jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. if m represents the number of ounces of mango juice in the blend and p represents the number of ounces of papaya juice in the blend, which of the following inequalities represents this scenario? A m - p< 32 m - p2 32 C m+p<32 D m+p2 32
jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. So, m + p ≤ 32 inequalities represents this scenario.
What is an inequality?A relationship that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. Less than, larger than, less than or equal to, and more than or equal to are the four fundamental inequalities. A mathematical connection between two expressions is known as an inequality, and it is shown using one of the following: "≤" , "≥" , "<" and ">".
Given that,
Number of mango = m
Number of papaya = p
The limit of juices should be less than or equal to 32 ounces
Thus, the sum of mass of mangoes and papaya should be less than or equal to 32 ounces.
So, m + p ≤ 32
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The complete question is as follows:
{100 points} Shown is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work W is done by the force in moving an object a distance of 8 m?
W = _______ J
The work done by the force in moving an object a distance of 8 m is; 144 J
How to solve a Force Distance Graph?A force-displacement graph will have force (in N) on the vertical axis and displacement (in m) on the horizontal axis. The area of the graph is = Fs. This quantity represents the work done on the object.
The area of the given graph is gotten by using the area of a trapezium which is;
Area = ¹/₂(sum of parallel sides) * height
Plugging in the relevant values gives;
Area = ¹/₂(8 + 4) * 24
Area = 144 J
This area represents the work done
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Which of the following is a factor of 9x^2+21+10
Answer: 3x+5
Step-by-step explanation:
trust me i had that question for home work
Calculate the average speed of a cyclist who travels 30 km in 3 hr
Given:-
[tex] \rm{Distance= \bold{ 30km}}[/tex][tex] \: [/tex]
[tex] \rm{Time = \bold{3hr}}[/tex][tex] \: [/tex]
To Find:-
[tex] \rm{Speed \: of \: a \: cyclist = ?}[/tex][tex] \: [/tex]
By using formula:-
[tex] \boxed{ \bold{ \rm{ \color{skyblue}Speed = \frac{Distance}{Time} }}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{Speed = \frac{Distance}{time} }\\ = \rm{\cancel\frac{30}{3}} \\ \: \:\: \: \: \: \: \: \: \underline {\boxed{\rm \red{= 10km/hr}}}[/tex]
[tex] \: [/tex]
hope it helps!:)
The average speed of the cyclist is 10 km/hr.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
As per the question,
Given that the distance is 30 km and the time is 3 hours.
To calculate the average speed of a cyclist, we can use the formula:
average speed = distance/time
Substitute the given values in the above formula,
average speed = 30 km / 3 hr
average speed = 10 km/hr
Therefore, the average speed of the cyclist is 10 km/hr.
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PLEASE ANSWER
The perimeter of the rectangle below is 120 units. Find the length of side VY .
Write your answer without variables.
The length of side VY is 25.
What is a regular figure and its perimeter?A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).
Suppose that length of each side of that figure be of u units, then we have the perimeter as:
P=u+u+...+u (n times) = n xu
units.
Given;
The perimeter of the rectangle below is 120 units
The two sides of rectangle are 2y+3 and3y+2
Now,
2l+2b=120
2(2y+3)+2(3y+2)=120
4y+6+6y+4=120
10y+10=120
y+1=12
y=11
VY=2y+3
VY=2*11+3
VY=25
Therefore, the length according to given perimeter will be 25units.
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Describe at least two similarities between constructing a perpendicular line through a point on a line and constructing a perpendicular through a point off a line
Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The following are the two similarities between drawing a perpendicular line through a point on a line and drawing one through a point of a line:
Both of these procedures start by drawing two arcs to the sides of the point. They both have six angles.Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.
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A video game system and several games are sold for $668. The cost of the games is 3 times as much as the cost of the system. Find the cost of the
system and the cost of the games.
Cost of the video game system:
URGENT
the cost of the system and the cost of the games is: $501. This can be solved using the concept of equation.
What is an equation?The connection between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
The total cost of the video game system and the several game = $668
Let, the cost of several game = x and
The cost of video game system = 3x
To find the cost of the system and the games
According to the problem,
or, x + 3x = 668
or, 4x = 668
or, x = $167
Hence, the cost of several game = $167 and
The cost of video game system = $3 × 167 = $501
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Divide R60 in the ratio 1:2
In order to divide the amount Rs.60 in the ratio 1:2
We take x as the variable that replicates the 1st amount + 2nd amount = Rs.60
Putting the values into a equation we get
1x + 2x = 60
3x = 60
x = [tex]\frac{60}{3}[/tex]
x = 20
Hence the amounts are ,
1x = 20
2x = 2 x 20 = 40
please answer quickly, question from ixl.
Answer:
5x>20 and 4
Step-by-step explanation:
x is how many packs Dave bought
5x>20 because he went over the 20 dollar budget
5(4) = 20
Buying 4 packs of cards wouldn't go above the budget, so he must've bought more than 4 packs of cards.
Simple Question what is 100 plus 100
Answer: 200 because 100 plus 100 equal 200
estimate the following sum: 2 1/3 + 5 5/16 + 2/7=
The of sum of the fraction 2 1/3 + 5 5/16 + 2/7 is 7 313/336
How to estimate the sum of fractions?
Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing
We want the of sum 2 1/3 + 5 5/16 + 2/7 =
For convenience sake, we can convert the mixed fractions to improper fractions. That is:
2 1/3 = 7/3
5 5/16 = 85/16
2 1/3 + 5 5/16 + 2/7 = 7/3 + 85/16 + 2/7
The LCM of 3, 16 and 7 is 336
= (7*112 + 85*21 + 2*48)/336
= (784 + 1785 + 96)/336
= 2665/336
= 7 313/336
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Graham volunteers each Saturday at a veterinarian's office.
He spends 3 hours cleaning.
He walks dogs for 15 minutes (0.25 hours) each.
• He walks 1 dog at a time.
He volunteers no more than a total of 5 hours each Saturday.
The inequality 3+0.25x ≤5 describes the situation, where x represents the number of dogs he walks. Which of the following is a
reasonable solution to this inequality?
A. 7
B. 11
C. 9
D. -5
Question 3 Mutiple Choice Worth 4 points)
(05.02 MC)
Two families went to a baseball game. The first family bought 3 pretzels and 5 sodas, which totaled $23. The second family bought 4 pretzels and 6 sodas, which totaled $28. How much did one soda cost?
O $3
O$4
O $5
O $6
Answer:
B) $4--------------------------------
Let the cost of a pretzel be p and cost of a soda be s.
The first family bought 3 pretzels and 5 sodas, which totaled $23:
3p + 5s = 23The second family bought 4 pretzels and 6 sodas, which totaled $28:
4p + 6s = 28Divide the second equation by 4 to get:
p + 1.5s = 7p = 7 - 1.5sSubstitute this into first equation and solve for s:
3(7 - 1.5s) + 5s = 2321 - 4.5s + 5s = 230.5s = 23 - 210.5s = 2s = 2/0.5s = 4Cost of a soda is $4, this is option B.
Answer:
B is the answer
Step-by-step explanation:
I took the test and I got 100 percent.
Blake flips a fair coin and stops flipping once he gets a head. He gets the minimum of $16 and $2 n, where n is the total number of Blake's flips. For example, if Blake flips a head on the first try, then n=1. What is the fair value of this game?
If Blake flips a fair coin , and stops flipping once he get head , then the fair value of the game is 7 .
The Fair Value /Expected value is a mathematical definition that refers to the average outcome of a random process, such as a game or an investment. It is calculated by taking into account all the possible outcomes of the process, weighting each outcome by its probability of occurrence, and summing up the results.
We know that every coin flip has a equal chance of being heads or tails.
So, the probability of getting a head on each flip = 0.5 ;
The expected value is calculated as :
⇒ P(n=1)×(2¹) + P(n=2)×(2²) + P(n=3)×(2³) + P(n=4)×(2⁴) + P(n=5)×(2⁵) + P(n≥6)×(2⁶) ;
⇒ (0.5¹)×2 + (0.5²)×4 + (0.5³)×8 + (0.5⁴)×16 + (0.5⁵)×32 + (1-0.5-0.25-0.125-0.0625 - 0.03125)×64 ;
⇒ 5 + 0.03125 × 64 ;
⇒ 5 + 2
⇒ 7
Therefore , The Fair Value of this game is 7 .
The given question is incomplete , the complete question is
Blake flips a fair coin and stops flipping once he gets a head. He gets the minimum of $16 and $2ⁿ , where n is the total number of Blake's flips. For example, if Blake flips a head on the first try, then n=1. What is the fair value of this game?
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Cleatus owns a large number of goats and relies on them to make his living. He
wakes up one morning to find half of his flock dead in the field. Cleatus cannot see
any evidence of a predator and is at a loss as to what happened to his goats Local
scientist Alcmaeon asks if he can take a few of the dead goats with him to attempt to
figure it out. How will Alcmaeon MOST likely attempt to solve this mystery of sudden
goat death that decimated Cleatus's flock?
The most likely way Alcmaeon will try to solve this mystery about the sudden death of the goats would be by taking blood samples to analyze a possible disease or epidemic in the goat herd.
What would be the best option to decipher the cause of death of the Cleatus goats?The best option to decipher the cause of death of the Cleatus goats is to take a sample from one of the goats to do an autopsy and identify the possible cause of death. Additionally, you can take blood samples to analyze a possible disease or infection that has caused the death of the sheep.
This would be the most effective way of detecting a possible cause of death as it allows Cleatus to know if the goats left alive are sick or at risk of dying from a disease.
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What is the solution to the square root equation?
x+3 = √2x−1 +5
Answer: x - √2x = 1
Step-by-step explanation:
An athlete wants to supplement his daily diet with beef and plant proteins. The content of iron, calcium, and vitamins (in milligrams per spoonful) is given in the table:
Product Iron Calcium Vitamins
Beef Protein 6 3 2
Plant Protein 2 3 4
Which graph shows the number of spoonfuls of beef protein and plant protein he needs to include in his diet to receive at least 18 milligrams of iron, 21 milligrams of calcium, and 16 milligrams of vitamins?
The correct graph for the supplements is attached below.
What is the bar chart?A bar chart is a graph that uses bars to represent and compare data. The length of the bar represents the magnitude of the data being displayed, with longer bars indicating larger values.
Bar charts can be used to display data for one or more categories, and can be either vertical or horizontal. They are commonly used to compare and visualize the distribution of categorical data.
The correct bar graph that shows the distribution of the supplements have been shown in the image that is attached to the answer that we have here.
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Can someone help me please
I have to do this maze for Geometry and it’s due tomorrow.
X has to equal 11 and all I have to work with is “the measure of angle 2 = 3x+5” and a random 64.
These are isosceles triangles. I don’t understand.
Help :’)
The measure of angle 2 is 38° and the value of x is 11
How to find the measure of angle 2?Geometry is a branch of mathematics concerned with the study of space, shapes, sizes, and positions of objects. It covers topics such as points, lines, angles, surfaces, and solids.
Check the attached image for labelling. From the figure:
u = 64° (base angles of an isosceles triangle are equal)
t = 180 - 64 - 64 = 52° (Sum of angles in a triangle)
y = 90 - t
y = 90 -52 = 38°
y = m∠2 (base angles of an isosceles triangle are equal)
m∠2 = 38°
m∠2 = 3x + 5
3x + 5 = 38°
3x = 38 - 5
3x = 33
x = 33/3
x = 11
Therefore, the value of x is 11
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