Two augmented matrices for two linear systems in the variables x, y, and I are given below.
The augmented matrices are in reduced row-echelon form.
For each system, choose the best description of its solution.
If applicable, give the solution.
(a)
10-1
01 1
100 0
5
100 2
0011 4
000-2
OThe system has no solution.
O The system has a unique solution.
(x,x.) - D
O The system has infinitely many solutions.
O (1.7.²) = (1.D
(1.7.2) -..D
(x,y,z) ==)
O The system has no solution.
O The system has a unique solution.
(x,y) - D
O The system has infinitely many solutions.
(x, y, z)=(xD
(2.3.²) -..D
(..)-:)
8
X
Answers
a) The system has infinitely many solutions in the following format:
(2 + z, 5 - z, z).
b) The system has no solution.
How to obtain the number of solutions of each system?To obtain the number of solutions of each system, the equations are built from the augmented matrix presented.
For item a, both sides of the matrix have one zero row, hence the system has infinitely many solutions, and the equations are given as follows:
x - z = 2.y + z = 5.Hence the solutions in terms of z are given as follows:
x = 2 + z.y = 5 - z.Thus the format of the solutions is of:
(2 + z, 5 - z, z).
For item b, the right side has three non-zero rows, while the left-side has two, meaning that it has no solutions.
This can be verified from the last line, as the equation would be of:
0z = -2.
Which has no solution.
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Related Questions
eighty-seven and seven hundred twenty-eight thousandths in  Decimal form help plssss
Answers
Eighty-seven and Seven hundred twenty-eight thousandths in decimal form is 87.728.
How to change in decimal form?
Given the unclear wording, there are various ways to respond to this question, depending on exactly what you mean.The answer is 338.14 if you meant "three hundred and thirty-eight and seven hundred divided by five thousand."The answer is 338.705 if you mean "three hundred and thirty eight and seven hundred five divided by one thousand."The two solutions are 0.0676 and 0.14 if you meant "three hundred thirty eight divided by five thousand AND seven hundred divided by five thousand."Eighty-seven and Seven hundred twenty-eight thousandths in decimal form:
= 87 + 728/1000
= 87 + 0.728
= 87.728
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In a company, 90% of the workers are woman. If 430 people work for the company who aren’t woman, how many workers are there in all? Use pencil and papare. Show two different ways that you can solve this problem
Answers
4300 workers are there in all.
What is algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Here, we have
In a company, 90% of the workers are women.
430 people work for the company who aren’t women.
% of male = 10%
Now,
10% of x = 430
10÷100 × x = 430
x = 4300
Hence, 4300 workers are there in all.
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-7(8x + 5) = 5x+10
Solve for x simplify
(No solution, Infinitely many solutions, One solution)
Answers
The equation -7(8x + 5) = 5x+10 has one solution of x which satisfies the equation. The solution is x = -45/61.
What is solution of system of equation?
A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system.
According to the given question:
Given equations is -7(8x + 5) = 5x+10
Simplifying both sides to get value of x
-7(8x + 5) = 5x+10
-56x - 35 = 5x + 10
-61x = 45
x = -45/61
Therefore x has one solution which is -45/61
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A store is having a 12-hour sale. The total number of shoppers who have entered the store thours after it begins is modeled by the function S defined by [tex]S(t)=0.5 t^4-16 t^3+144 t^2[/tex] for [tex]0 \leq t \leq 12[/tex]. At time [tex]t=0[/tex], when the sale begins, there are no shoppers in the store. The rate at which shopper's leave the store, measured in shoppers per hour, is modeled by the function [tex]L[/tex] defined by [tex]L(t)=-80+\frac{4400}{t^2-14 t+55}[/tex] for [tex]0 \leq t \leq 12[/tex]. According to the model, how many shoppers are in the store at the end of the sale (time [tex]t=12[/tex] )? Give your answer to the nearest whole number.
Answers
At the end of the sale, there were a total of 196 customers in the store for the given function.
What is a function?The earliest known attempt to the notion of function may be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity.
The total number of shoppers in the store is the number of shoppers present at the start of the sale Plus the number of shoppers who entered the store minus the number of shoppers who left.
Given that there were no shoppers in the store before the sale began, the number of shoppers in the store at the start of the sale is 0.
It is assumed that the number of customers who have entered the store is represented by S(t)=0.5t⁴-16t³+144t².
So, at t=12, the number of shoppers in the store is S(12)=
0.5(12)⁴-16(12)³+144(12)²
S(12)=3456 shoppers.
L(t)= -80+(4400/t²-14t+55)
At t=12,
[tex]\int\limits^{12}_0 {L(t)} \, dt[/tex]=[tex]\int\limits^{12}_0[/tex]( -80+(4400/t²-14t+55))dt
At the end of the sale, there were a total of 196 customers in the store.
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50 Points!!! Are RHS and HL triangles the same? Yes or no? Explain.
Answers
Answer:
Yes------------------
RHS and HL refer to same thing.
A right angled triangle has one hypotenuse and two sides.
If the hypotenuse and one side of one triangle is congruent to hypotenuse and one side of another triangle, then the two triangles are congruent.
We know sides of a right triangle are also called the hypotenuse and legs. RHS is also called HL because they both refer to hypotenuse and one side or leg.
The F distribution's curve is positively skewed.
T/F
Answers
Answer: True
Step-by-step explanation:
-The f-distribution curve is positively skewed towards the right with a range of 0 and ∞
The value of F is always positive or zero. It never has negative values.
Select the values that make the inequality h<3h<3 true. (Numbers written in order from least to greatest going across.) -5 -2 0 2 2.9 2.99 2.999 3 3.001 3.01 3.1 4 6 8 11
Answers
The values that make the inequality, h < 3h < 3, true are the values of h in the range 0 < h < 1. The values -5, -2, 0, 2, 2.9, 2.99, 2.999, 3, 3.001, 3.01, 3.1, 4, 6, 8, 11, are larger or smaller than the values make the inequality true.
What is an inequality in mathematics?An is a comparison between two expressions, using non equal expressions, such as ≥, >, ≠, <, or ≤ symbols.
The specified inequality is; h < 3·h < 3
When h < 3·h, we get;
h is a positive number larger than 0, such that we get;
When h < 0, 3·h < h
Therefore; h > 0
The inequality, 3·h < 3, indicates;
3·h < 3
h < 3/3 = 1
h < 1
Which indicates that we get;
0 < h < 1
Therefore, non of the values make the inequality, h < 3·h < 3
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On a number line, point d is at -6, and point e is at 8. point f lies between points d and e. if is , where does point f lie on the number line? point f is at on the number line.
Answers
The point F lies on 4.5 in the number line.
What is the number line?
The number line is a One dimensional representation of point referring by a number only.
We know that if a point divides a line joining the points at x, y in the number line respectively in m:n ratio then that point lies on
= (my+nx)/(m+n) in the number line.
Here in the given problem that,
Point D lies on -6 in the number lin
Point E lies on 8 in the number line
And F lies between D and E points and DE:EF = 3:1
So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.
So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5
Hence, the point F lies on 4.5 in the number line.
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Please Help me With this ASAP (20 Points)
Answers
Answer:
200*1-0.95-0.95+0.9025
200*1-1.9+0.9025
200*0.0025
0.5
evaluate the sum of 4.2 and 466.99
Answers
The sum of decimals 4.2 and 466.99 evaluates to 471.19
How to evaluate the sum of decimals?
Decimals are numbers that consist of two parts namely, a whole number part and a fractional part separated by a decimal point e.g 2.35
Given: 4.2 and 466.99
To evaluate the sum of 4.2 and 466.99, you simply need to add the two numbers. Arrange the numbers as shown below and add as you would add other numbers.
4.2
466.99
.................
471.19
................
Therefore, the sum 4.2 and 466.99 is 471.19
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An electronic manufacturer determine that the profit P (in dollar) obtained by producing x unit of a DVD player and y unit of a DVD recorder i approximated by the model P(x, y) = 8x 10y − (0. 001)(x2 xy y2) − 10, 000. Find the production level that a maximum profit. What i the maximum profit?
Answers
The production level that a maximum profit is 186000 and the maximum profit will at the points of (200, -4000) , under the concept of absolute maximum value.
The P(x, y) = 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000, the first partial differentiate of the given equation with respect to x and y,
Px= ( 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000) = 8-0.001(2x-y) ....2
Py= 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000) = 10-0.001(x-2y) ... 3
Considering the above equation to be equal to zero :
=>8-0.001(2x-y) =0 =>0.001(2x-y) =8 .....4
=>10-0.001(x-2y) =0 =>0.001(x-2y) = 10 ...5
Solving the equations 4 and 5 we get the lues of x and y we get are :
x= 2000, and y = -4000 , Now the partial differentiate for the equations 2 ad 3 are with respect to x and y :
pxx(x,y)=-0.002
pyy(x,y)= 0.002
pxy(x,y) =-1
The discriminant of the function wil be at (2000,-4000):
D = 0.002*-0.002 -(-1)^2 =-1.0004 ,here D <0, so the critical values (200, -4000) reaches the maximum value .So the production level will be :
P(2000, -4000) = 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000 = 186000
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At a football stadium, 5% of the fans in attendance were teenagers. If there were 340 teenagers at the football stadium, what was the total number of people at the stadium?.
Answers
The total number of people at the stadium was 6800 people .
A Percent in mathematics is defined as a number or ratio that is expressed as a fraction of 100 , it is denoted by sign "%" .
For Example : 2% is = 2/100 .
In the question ,
it is given that ,
percent of teenagers fans in the stadium is = 5%
number of teenagers present at the football stadium is = 340
which means 5% represents 340 people ,
So , 1% will be 340/5 = 68 people .
the total percent of people present in the stadium is = 100% ,
multiplying both sides by 100 ,
we get ,
So , 100% = 68 × 100 = 6800 people
Therefore , The total attendance at the football stadium was 6800 people .
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PLEASE HELP ME
What is the y-intercept of this line?
I keep getting confused someone please help me and explain it better to me
Answers
Answer:
2
Step-by-step explanation:
The y-intercept is the point at which the graph crosses the y-axis.
(I have marked it in blue on the attached graph).
From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Sample Mean car 1: 250.3 mi/ 10 gal
Sample mean car 2: 246.1 mi/10 gal
Question: Find the medians for Car 2 and Car 2
Answers
Answers in bold
Median of car 1: 249
Median of car 2: 251
====================================================
Explanation:
This is the data set for car 1
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5}202 & 247 & 241 & 223 & 246\\\cline{1-5}253 & 271 & 241 & 291 & 249\\\cline{1-5}259 & 257 & 261 & 246 & 268\\\cline{1-5}\end{array}[/tex]
Which when written out as a single long line, we have this:
202, 247, 241, 223, 246, 253, 271, 241, 291, 249, 259, 257, 261, 246, 268
Sort those values from smallest to largest to get this set
202, 223, 241, 241, 246, 246, 247, 249, 253, 257, 259, 261, 268, 271, 291
There are n = 15 items in that set.
n/2 = 15/2 = 7.5 which rounds to 8
The middle-most item, aka median, is in slot 8.
There are 7 items below the median, and 7 items above it. Giving us 7+1+7 = 15 items total.
Start at "202" and count 8 slots to the right until you arrive at 249 which is the median of the car 1 data set. Make sure you are looking at the sorted data set.
Follow similar steps for the car 2 data set. You should get 251 as the median of the car 2 data set.
What is the sum of the infinite geometric series?
Answers
first of all, let's find the common ratio in this geometric sequence, by simply dividing a any of the terms by the term right behind it, hmmm say -12 and 16
[tex]16~~,~~-12~~,~~9~~,~~-\cfrac{27}{4}~\hfill \stackrel{\textit{\LARGE common ratio}}{\cfrac{-12}{16}\implies -\cfrac{3}{4}} \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \textit{sum of an infinite geometric sequence} \\\\ \displaystyle S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^i\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\textit{first term}\\ r=\textit{common ratio}\\ \qquad -1 < r < 1\\[-0.5em] \hrulefill\\ a_1=16\\[1em] r=-\frac{3}{4} \end{cases}[/tex]
[tex]S=\cfrac{16}{ ~~ 1-\left( -\frac{3}{4} \right) ~~ }\implies S=\cfrac{16}{ ~~ 1 + \frac{3}{4} ~~ }\implies S=\cfrac{16}{~~ \frac{ 7}{ 4} ~~}\implies S=\cfrac{64}{7}[/tex]
show that if f is a function from s to t, where s and t are finite sets with |s| > |t|, then there are elements s1 and s2 in s such that f(s1)
Answers
T|=|S|⟹ there is bijection F:S→T.
What are bijection function?A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.
In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.
No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.
One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.
According to our question-
The function f:ST |S||T| has an injective and not a surjective nature.
Assume an injective function exists: g:TS|T||S|. |T|=|S|
(this follow from the Cantor-Bernstein theorem).
|T|=|S|⟹ F:S:T has a bijection.
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a 36 year old woman on chronic cyclosporine treatment for bilateral lung transplantation visits the emergency department complaining of extreme headache, nausea and vomiting. her exam is notable for bp 239/165, normal cardiac exam, bibasilar pulmonary rales, and 1 lower extremity edema. ekg showed asymmetric inverted t-waves in i, avl, and v4-6. in an effort to acutely control her blood pressure, which of the following is true?
Answers
The best treatment for this patient's acute blood pressure control is to administer an intravenous (IV) antihypertensive medication such as labetalol or nitroprusside. Additionally, it is important to assess for underlying causes of her elevated blood pressure such as infection, kidney disease, or heart failure.
What is blood pressure?
Blood pressure (BP) is indeed the force exerted by moving blood against blood vessel walls. The heart's action of trying to pump blood through the blood vessels is largely responsible for this pressure. The pressure in the major arteries is meant when the term "blood pressure" is used without qualification. Systolic pressure, or the highest pressure during one heartbeat, is typically expressed as the ratio of diastolic pressure, or the lowest pressure between two heartbeats, in blood pressure measurements. It is expressed as a millimetre of mercury (mmHg) just above atmospheric pressure in the immediate vicinity. Along with respiratory rate, pulse rate, oxygen levels, and body temperature, blood pressure is among the vital signs that medical professionals consider when assessing a patient's health.
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What is the answer?? please and thank you
Answers
Answer:
the answer is no
Step-by-step explanation:
О
A
13x + 13
7x+7
60°
с
B
Answers
Answer:
x = 9
Step-by-step explanation:
(7x + 7) + 60 = 13x + 13 (exterior angle)
7x + 67 = 13x + 13
6x = 54
x = 9
7. A tour guide charges $28 to take four people on a tour. How much does the tour guide charge per person?
Answers
Answer: $7
Step-by-step explanation:
We know that $28 for four people.
So we take 28 divided by 4 and we get $7 per people
The ale tax on a car that old for $13,500 i $910. At thi rate, how much higher i the tax on a car that ell for $16,500
Answers
The tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
What is the percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
We have,
First car price is = $13,500
and tax of the first car is = $910
Second car price is = $16,500
and tax of the second car is = ?
so,
$13,500 ----- 100,
$910 ----- x
x = 910 * 100 / 13500
x = 6.7
therefore, the rate of tax is 6.7%
so, we will calculate the tax for the second car,
$16,500 ----- 100,
y ----- 6.7
y = 6.7 * 16,500 / 100
y = $1105.5
difference of tax price between two cars = $1105.5 - $910 = $195.5
Hence, the tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
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Solve the inequality. 2x + 13 < 35
Answers
Answer:
x < 11
Step-by-step explanation:
there you go :)
Find only the margin of error to construct a 98% confidence interval for p1 - P2. Assume the samples are random and independent. Do not construct a confidence interval. Sample statistics: nâ = 1000, x1 = 250, and n2 = 1200, x2 = 195
Answers
The required margin of error construct a 98% confidence interval for p1 - P2 is 0.0403.
What is margin of error?Margin of errors, in statistics, is the level of blunder in results got from irregular examining overviews. A higher wiggle room in measurements shows less probability of depending on the consequences of a review or survey, for example the certainty on the outcomes will be lower to address a populace.
According to question:given data
n1 =1 000 x1 = 250
pˆ1 = x1n1 = 2501000 = 0.250
n2 = 1200 x2 = 195
pˆ2 = x2n2 = 1951200 = 0.1625
We have given confidence interval ,
98% ci for p1−p2.
Then,
α = 1 - 0.98 = 0.02
[tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.01}[/tex] = 2.326
Again,
E = [tex]Z\sqrt{\frac{p1(1-p1)}{n1}+ \frac{p2(1-p2)}{n2} }[/tex]
E = [tex]2.326\sqrt{\frac{0.250(1-0.250)}{1000}+ \frac{0.1625(1-0.1625)}{1200} }[/tex]
E = 0.0403
Thus, required margin of error is 0.0403.
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pls help right now I need help
giving brainliest
this is reading btw
Answers
Answer:
The answer is A
Step-by-step explanation: I'm so smart
If Jodie works on the computer for 6 hours every 2 days how many hours will she work on the computer in 14 days?
Answers
[tex]\begin{array}{ccll} hours&days\\ \cline{1-2} 6 & 2\\ x& 14 \end{array} \implies \cfrac{6}{x}~~=~~\cfrac{2}{14} \implies \cfrac{6}{x}=\cfrac{1}{7}\implies 42=x[/tex]
Answer: 42 hours
add 6 every 2 days
the hudson valley renegades stadium hold a maximum of 4,505 people. During the height of their popularity, they sold out 219 consecutive games. how many tickets were sold during this time?
Answers
Answer:
Step-by-step explanation:
4,505 tickets were sold 219 times.
4,505 x 219
The answer is 986,595
If the bag of fertilizer cost $11.75 what is the cost of nitrogen per pound?
Answers
Answer: 40 cents
Step-by-step explanation: Cost per lb of N in 1 ton of 28% UAN = $225 ÷ 560 lbs N = 40 cents per lb N.
A. Ue Pythagora’ Theorem to find the altitude of the triangle hown. B. Write the trigonometric ratio for a 60° angle. C. Write the trigonometric ratio for a 30° angle
Answers
The Trigonometric ratios are:
P/H = Sinθ
B/H = Cosθ
P/B = Tanθ
H/P = Cosecθ
H/B = Secθ
B/P = Cotθ
Where,
'P' represents the perpendicular
'B' represents the base
'H' = represents the hypotenuse
P/H = Sinθ
B/H = Cosθ
P/B = Tanθ
A. As the values of p, b or h are not given.
Pythagoras Theorem states that:
h² = p² + b² or h = [tex]\sqrt{p^2 + b^2}[/tex]
Altitude of a triangle is usually given by the perpendicular,
So,
h² = p² + b²
h² - b² = p²
p² = h² - b²
p = [tex]\sqrt{h^2 - b^2}[/tex]
B. The trigonometric ratios for θ = 60°
Sin 60 = √3/2
Cos 60 = 1/2
Tan 60 = √3
C. The trigonometric ratios for θ = 30°
Sin 30 = 1/2
Cos 30 = √3/2
Tan 30 = 1/√3
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A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also
a sphere with a radius of 0.78 inches. Select all the true statements.
The volume of the tennis ball is exactly 2 times the volume of the squash
ball.
The volume of the tennis ball is approximately 3 times the volume of the
squash ball.
The volume of both the tennis ball and squash ball is proportionate to the
scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
The volume of the tennis ball is 5.067 cubic inches and the volume of the
squash ball is about 0.63 cubic inches.
Answers
The two true statements about these are,
The volume of both the tennis ball and squash ball is proportionate to the
the scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
What is a sphere?
In geometry, a sphere is a three-dimensional solid figure, which is round in shape.
The surface area is 4πr².
The volume is (4/3)πr³.
The diameter is 2×radius of the sphere.
Given, A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also a sphere with a radius of 0.78 inches.
So, The volume of the tennis ball is (4/3)π(1.56)³ = 16 cubic inches.
The volume of the squash ball is (4/3)π(0.78)³ = 2 cubic inches.
The volume of both the tennis ball and squash ball is proportionate to the
the scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
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Can someone please help me
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]n^{4}[/tex]
This is already simplified.
[tex]\frac{1}{n^{-5}}[/tex]
This is already simplified.
[tex]n^6 . n^{-8}[/tex]
= [tex]n^{6 - 8}[/tex]
= [tex]n^{-2}[/tex]
[tex]n^7 . p^8[/tex]
= [tex]n^{7 + 8}[/tex]
= [tex]n^{15}[/tex]
[tex]\frac{1}{n^3}[/tex]
This is already in simplified form.
Thus,
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
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