The system is inconsistent and has no solution. Therefore, the answer is "inconsistent".Since the last row is of the form [0 0 0 | b], where b is nonzero (b=7
To determine whether the system of equations represented by the given matrix has a solution, we can use row operations to put the matrix into reduced row echelon form. If the resulting matrix has a row of the form [0 0 ... 0 | b], where b is nonzero, then the system is inconsistent and has no solution. If there are any free variables in the reduced row echelon form, then the system has infinitely many solutions and is dependent. If there are no free variables and no rows of the form [0 0 ... 0 | b], then the system has a unique solution and is independent.
Using row operations, we can put the given matrix into reduced row echelon form as follows:
[tex][1 -3 1 4 | 4] (R1)[3 2 1 | 3] (R2)[-6 -4 -2 | 1] (R3)[/tex]
([tex]R2 - 3*R1) - > R2:[/tex]
[tex][1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[-6 -4 -2 | 1] (R3)(R3 + 6*R1) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 -22 4 | 25] (R3)(R3 + 2*R2) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 0 0 | 7] (R3)[/tex]
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A fruitier had 300 oranges and apples at first.20%of apples were sold in the morning.the fruitier then stocked up another 35 oranges.the total numbers of oranges and apple became 298.how many apples were there at first?
Answer:
185 apples
Step-by-step explanation:
We have to work in reverse to find the original number of apples.
298-35= 263 apples and oranges after 20% apples sold
300-263 = 37 apples
37 apples = 20%
For total apples:
37 apples x 5 = 20% x 5
185 apples = 100% of apples
There were 185 apples at first
Hope that helps :)
BONUS SECTION
This section is optional. Each correct answer will receive 2 points (12 points total)
which will be added to your test's raw score. Clearly indicate the necessary steps,
including appropriate formula substitutions, diagrams, graphs, charts, etc. For all
questions in this part, correct numerical answers without work shown or an
explanation will not receive any credit.
1. Shanika has a dilemma. She has five choices for future employment but does not
know which job opportunity to take. Calculate the annual income for each option
and let her know which job would earn her the most money.
Option 1: Keeping her present job at $15,000 per
year plus a 20% year-end bonus.
Option 2: Taking a job that pays $1,250 per month
Answer:
A
Step-by-step explanation:
A square wrestling mat has a perimeter of (12x−32)
feet. Write an expression in simplest form that represents the side length (in feet) of the mat.
Answer:
The perimeter of a square is given by the formula P = 4s, where s is the side length. In this case, we are given that the perimeter is (12x - 32) feet, so we can set up an equation:
P = 4s
(12x - 32) = 4s
To solve for s, we can divide both sides by 4:
(12x - 32)/4 = s
Simplifying the expression on the left:
3x - 8 = s
Therefore, the expression in simplest form that represents the side length of the square wrestling mat is 3x - 8 feet.
Answer:
Step-by-step explanation:
the answer would be 3 x − 8 3x-8 3x−8 ft
2. The ratio of boys to girls in the school
choir is 3:4. If there are 12 girls in the
choir, how many boys are in the choir?
Answer:
9 Boys
Step-by-step explanation:
As we Know, 12 ÷ 4 is 3
3 x 3 is 9
therefore, it's 9
What is the image of the point (-3 , 14) after a counterclockwise rotation about the origin through an angle of 90 degrees?
I need help with my homework
The average rate of change representing the state whose temperature is decreasing slower is given as follows:
-1.5ºF/day.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For Maine, in 9 days, the temperature fell by 13.5ºF, hence the rate is given as follows:
-13.5/9 = -1.5ºF/day.
For Connecticut, in 2.5 days, the temperature fell by 6.25ºF, hence the rate is given as follows:
-6.25/2.5 = -2.25 ºF/day.
A slower decline is in Maine, as it has a lower rate of change.
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Mrs. Rinaldi bought 5 pounds of apples. She used of that amount to make pies. How many pounds of apples did she use for the pies?
Determine the rage of the following graph
The range of function is values on the y-axis: R=[-7,2].
What is function?A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.
Here,
To find the range of a function, you need to determine all possible output values of the function. Start by identifying the function's domain, which is the set of all possible input values of the function. Once you know the domain, apply the function to each input value in the domain and record the corresponding output values. Once you have a list of output values, identify the smallest and largest values in the list. These values represent the range of the function. For example, consider the function f(x) = 2x + 1. The domain of this function is all real numbers.
To find the range, apply the function to several input values in the domain:
f(-3) = -5
f(-2) = -3
f(-1) = -1
f(0) = 1
f(1) = 3
f(2) = 5
f(3) = 7
These output values give us a set of possible output values, which are {-5, -3, -1, 1, 3, 5, 7}. The smallest value in the set is -5 and the largest value is 7, so the range of the function is [-5, 7].
Note that for some functions, it may be difficult or impossible to find the exact range. In such cases, you can use techniques such as graphing or calculus to estimate the range.
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Fill in the table of value for the equation y = 2x + 1
Answer:
To fill in the table of values for the equation y = 2x + 1, we can choose different values of x and substitute them into the equation to find the corresponding values of y. For example:
x y
0 1
1 3
2 5
3 7
4 9
To get the value of y, we substitute each value of x into the equation and simplify:
When x = 0:
y = 2(0) + 1 = 1
When x = 1:
y = 2(1) + 1 = 3
When x = 2:
y = 2(2) + 1 = 5
When x = 3:
y = 2(3) + 1 = 7
When x = 4:
y = 2(4) + 1 = 9
Therefore, the table of values for the equation y = 2x + 1 is:
x y
0 1
1 3
2 5
3 7
4 9
Answer the questions about the graph shown below.
Therefore, all values of x that are less than or equal to -3 make up the inequality's solution set.
what is inequality ?An inequality in mathematics is a claim that two values or expressions are not equivalent to one another. A relationship between two values, where one value is larger than, less than, or not equal to the other, is expressed by an inequality. The inequality marks "" (less than), ">" (greater than), "=" (less than or equal to), ">=" (greater than or equal to), and "" can be used to denote an inequality (not equal to).
given
The disparity is as follows:
-3x + 2 ≥ 11
By subtracting 2 from both sides of the inequality and then dividing the result by -3, we can separate x on one side of the inequality .
-3x + 2 - 2 ≥ 11 - 2
-3x ≥ 9
x ≤ -3
Therefore, all values of x that are less than or equal to -3 make up the inequality's solution set.
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how do i get it to stop making me watch a ad.
Answer:
Brainly Plus.
Step-by-step explanation:
You have to pay money. Otherwise, I don't think you can.
Maybe you could try just installing a bunch of ad-blockers.
But pretty much the only way is Brainly Plus.
An employee is 10 years from retirement and has decided to begin making $2,000 annual contributions into an IRA. The employee is currently in the 33% tax bracket but expects to be in the
15% tax bracket at retirement.
Which of the following contains the better choice with the correct reasoning?
O The Traditional IRA is the better choice because the employee will be taxed at a lower rate on lower earnings in retirement than during employment.
O The Roth IRA is the better choice because the employee will be taxed at a lower rate on lower eamings during employment than in retirement
O The Traditional IRA is the better choice because the employee will be taxed at a higher rate on lower earnings in retirement than during employment.
O The Roth IRA is the better choice because the employee will be taxed at a higher rate on lower eamings during employment than in retirement.
Based on the employee contribution, the Traditional IRA is the better choice because the employee will be taxed at a lower rate on lower earnings in retirement than during employment. The Option A is correct.
Why is Traditional IRA the best choice for the employee?The Traditional IRA allows the employee to make contributions on a pre-tax basis, which reduces the taxable income during the years of contribution. This reduces the tax liability during employment years in the 33% tax bracket. During retirement, the employee will be in the 15% tax bracket, which means they will pay a lower tax rate on the withdrawals from the Traditional IRA.
In contrast, the Roth IRA contributions are made with after-tax dollars, and the withdrawals during retirement are tax-free. Since the employee is currently in the 33% tax bracket, they will pay a higher tax rate on their current income than they would in retirement. Therefore, the Traditional IRA is a better choice for the employee in this scenario.
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Solve ( 5 5 6 + 1 3 4 ) − 4 7 12 . Select the correct solution. A. ( 5 + 1 + 5 6 + 3 4 ) − 4 7 12 = ( 6 + 8 10 ) − 4 7 12 = 6 8 10 − 4 7 12 = ( 6 − 4 ) + ( 8 10 − 7 12 ) = 2 1 12 B. ( 5 + 1 + 10 12 + 9 12 ) − 4 7 12 = ( 6 + 19 12 ) − 4 7 12 = 7 7 12 − 4 7 12 = 11 C. ( 5 + 1 − 4 ) + ( 10 12 + 9 12 − 7 12 ) = 2 + 12 12 = 2 + 1 = 3 D. ( 5 + 1 − 4 ) + ( 5 6 + 3 4 − 7 12 ) = 2 + 5 + 3 − 7 6 + 4 − 12 = 2 + 1 2 = 2 1 2
The correct solution of given expression is C. (5 + 1 - 4) + (10/12 + 9/12 - 7/12) = 2 + 1 = 3.
What is expression?
In mathematics, an expression is a combination of symbols, numbers, and operators that represents a value or a relationship between values. Expressions can be composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.
We can simplify the expression inside the parentheses first and then subtract the fraction.
(5 5/6 + 1 3/4) - 4 7/12
= (33/6 + 7/4) - 55/12
= (11/2 + 7/4) - 55/12
= 22/4 + 7/4 - 55/12
= 29/4 - 55/12
To subtract these fractions, we need a common denominator of 12:
= (329)/(34) - (555)/(512)
= 87/12 - 275/60
= 87/12 - 11/4
= (29/4) - (33/12)
= (29/4) - (11/3)
To find the correct solution, we can simplify this expression:
(29/4) - (11/3) = (87/12) - (44/12) = 43/12
Therefore, the correct solution is C. (5 + 1 - 4) + (10/12 + 9/12 - 7/12) = 2 + 1 = 3.
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Angela, Breanna, Christine, Debbie, and Esther are in a club and they need to pick two people to go to a
meeting. They write each person’s name on equally sized pieces of paper, put them in a hat, and mix the
papers thoroughly. Find the probability model for this chance process and use it to determine the probability
that Angela gets to go to the meeting.
So the probability that Angela gets to go to the meeting is 2/5.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.
Here,
There are a total of 5 people in the club, so there are 10 possible pairs of people that could be chosen to go to the meeting. Since each pair is equally likely to be chosen, the probability of any particular pair being chosen is 1/10.
To determine the probability that Angela gets to go to the meeting, we need to count the number of pairs that include Angela. There are 4 other people in the club, so there are 4 possible pairs that include Angela. Therefore, the probability that Angela gets to go to the meeting is:
P(Angela) = number of pairs that include Angela / total number of pairs
= 4 / 10
= 2 / 5
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ASAP NEED ANSWER !! Thank You! :>
The size of angle y in the quadrilateral is 130 degrees.
How to find the angle of a quadrilateral?A quadrilateral is a polygon with 4 sides and angles. The quadrilateral above is a kite. The sum of angles in a quadrilateral is 360 degrees.
Therefore, let's find the angles in the quadrilaterals as follows:
y + y + 70 + 30 = 360(sum of angles in a quadrilateral)
2y + 100 = 360
2y = 360 - 100
2y = 260
divide both sides by 2
y = 260 / 2
y = 130 degrees
Therefore, the size of y is 130 degrees.
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Janelys has a points card for a movie theater.
She receives 20 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
She needs at least 165 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Janelys can make to earn her first free movie ticket.
Answer: 12 times
Step-by-step explanation:
165-20=145
12.5x11=137.5
12.5x12=150
Answer: 12.5x+20≥165
x≥11.6
Step-by-step explanation:
Use the distributive property to multiply the expression 9(7m+2)
Answer:
63m+18
Step-by-step explanation:
9*7m is 63m and 9*2 is 18
Combine them and you get 63m+18!
Please help asap, will give brainliest if correct. What is the constant of proportionality of this table?
Show your work.
The constant of proportionality of this table is: k = 1/7.
Explain about the constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional.Proportional relationships appear as straight lines that go through the origin on a graph. The slope of a graph is equal to the constant of proportionality in the equation, and it refers to how steep a line is relative to other lines.When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.
Thus, using the x and its respective y values.
As the values are in direct proportion.
The constant of proportionality is:
k = 1/7
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why does this series [tex]tan(2^{-n} )[/tex] converge?
*its a series from 2 to infinity, but there is no symbol for that.
The series [tex]\tan(2^{-n})[/tex] is convergent.
What is convergence of series?In mathematics, the cοnvergence οf a series refers tο the behaviοr οf the series' partial sums as mοre terms are added. A series cοnverges if its sequence οf partial sums apprοaches a finite limit, which is called the sum οf the series. If the sequence οf partial sums dοes nοt apprοach a finite limit, the series diverges.
The series [tex]\tan(2^{-n})[/tex] converges because of the following reasons:
As n increases, [tex]2^{-n}[/tex] becomes very small, which makes [tex]\tan(2^{-n})[/tex] close to its linear approximation. Therefore, we can use the linear approximation of [tex]\tan(2^{-n})[/tex] to estimate its value.
The linear approximation of [tex]\tan(2^{-n})[/tex] is [tex]2^{-n}[/tex], which means that [tex]\tan(2^{-n})[/tex] ≈ [tex]2^{-n}[/tex] when [tex]2^{-n}[/tex] is small.
Since the series [tex]2^{-n}[/tex] is convergent, by comparison test, the series [tex]\tan(2^{-n})[/tex] is also convergent.
Alternatively, we can also use the fact that the series tan(x) is convergent for x ∈ (0, π/2), and since [tex]2^{-n}[/tex] → 0 as n → ∞, we have [tex]\tan(2^{-n})[/tex] → tan(0) = 0, which implies that the series [tex]\tan(2^{-n})[/tex] is convergent.
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Use the information given below to find tan(a + B)
cos a = 3/5, with a in quadrant IV
tan B = 4/3, with B in quadrant I I I
Give the exact answer, not a decimal approximation.
tan(a + B) = ?
let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said
[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]
Third Rock Ventures sells all its merchandise on credit. It has a profit margin of 8%, days sales outstanding were 60 days based on 360 days in a year, receivables of R180 000, total assets of R4000 000, and a debt ratio of 0,75. What is the company's return on equity (ROE)?
Answer:
Step-by-step explanation:
First, we need to calculate the company's credit sales for the year:
Credit Sales = Receivables / (Days Sales Outstanding / 360)
Credit Sales = R180,000 / (60/360) = R1,080,000
Next, we need to calculate the company's net income:
Net Income = Profit Margin x Credit Sales
Net Income = 0.08 x R1,080,000 = R86,400
We can calculate the company's total equity as follows:
Total Equity = Total Assets x (1 - Debt Ratio)
Total Equity = R4,000,000 x (1 - 0.75) = R1,000,000
Finally, we can calculate the ROE:
ROE = Net Income / Total Equity
ROE = R86,400 / R1,000,000 = 0.0864 or 8.64%
Therefore, Third Rock Ventures' return on equity is 8.64%.
Zoe has 7/3 of an ounce of children’s ibuprofen. A full dose for Zoe’s one-year-old is 2/5 of an ounce. To figure out exactly how many doses she has left, she drew the diagram below. But she realized that her diagram shows how many 1/5-ounce doses are in 7/3 of an ounce. How can she use her diagram to figure out how many 2/5-ounce doses she has? Explain using words and diagrams.
It should be noted that to use the diagram to figure out how many 2/5-ounce doses Zoe has, she can divide the 7/3-ounce amount into equal parts of 2/5 ounce.
How to explain the word problemOne way to do this is to divide 2/5 by 1/5 to get the number of 1/5-ounce portions that make up a 2/5-ounce dose, which is 2. Then, divide 7/3 by 2/5 to get the total number of 2/5-ounce doses she has.
So, using the diagram, Zoe can count the number of 1/5-ounce portions she has, and then divide that number by 2 to find out how many 2/5-ounce doses she has.
Alternatively, Zoe could redraw the diagram to show 2/5-ounce portions instead of 1/5-ounce portions, and then count the number of 2/5-ounce portions she has. She would need to divide the original diagram into equal parts of 2/5 ounce by drawing lines to divide each square into two parts. Then she can count the number of squares that represent a 2/5-ounce dose.
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5 times 100 times 105
Answer:
52500
Step-by-step explanation:
first do 5*105 to get 525 then mutiply by 100 to get 52500
pls help. grades due today. teacher hasnt taught me this
Answer:
5624.22 feet
Step-by-step explanation:
You want to know the distance from a skyscraper 1465 ft tall to a point where the angle of elevation to its top is 14.6°.
TangentThe tangent relation tells you ...
Tan = Opposite/Adjacent
ApplicationThe distance between buildings is the side of the right triangle adjacent to the angle of elevation. The height of skyscraper B is the side opposite the angle of elevation. Using the tangent relationship, we can find the distance d between the buildings as ...
tan(14.6°) = 1465/d
c = 1465/tan(14.6°) ≈ 5624.22 . . . ft
The distance from A to B is about 5624.22 feet.
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if 1 kg is equal to 1,000 G how many grams are in 7.28 kg explain how you found your answer
Answer:
here is your answer attached
Step-by-step explanation:
Rapunzel was sitting in her tower and waiting for the prince to come for tea. “He’s coming in 15 1/2 minutes, so I had better hurry and tidy up. Rapunzel started cleaning and finished with 55 seconds to spare. How long did it take to clean her room
It took Rapunzel approximately 14.58 minutes to clean her room.
What is cleaning ?
Cleaning refers to the process of removing dirt, dust, and other unwanted substances from a surface or an object.
Let's start by converting the time to minutes.
15 1/2 minutes = 15.5 minutes
Let's now subtract the time she finished cleaning from the time she started cleaning:
15.5 - 0.92 = 14.58 minutes
Therefore, it took Rapunzel approximately 14.58 minutes to clean her room.
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Tashaun drove 74 miles in 2 hours. Kamari drove 153 miles in 3 hours. If the speed limit is 50 miles per hour, who was speeding?
Group of answer choices
Neither
Tashaun
Both
Kamari
Answer:
kamari
Step-by-step explanation:
Tashaun: [tex]\frac{74}{2}[/tex]= 32mph
kamari: 153/3=51mph
so we can see that kamari is speeding the speed limit is 50 and 51>50 brainliest?
robbie had 5.00 to spend on lunch.He bought a hamburger for 1.26 potato chips for 65 cents and 2 drinks for 85 cents each how much money did he get back
Answer:
$1.39
Step-by-step explanation:
Robbie had 5.00 to start out with. The hamburger he bought was $1.26. The potato chips were $0.65 and the total of the 2 drinks would be $1.70. $0.85 x 2 = $1.70. If we add $1.26 + $0.65+ $1.70 it will equal = $3.61. Now if we take Robbies $5.00 and minues that by $3.61 (total of all food and drinks) we would get $1.39. So, Robbie only had $1.39 left.
Hopefullly that helps you !
Find the probability of winning second prize in a 5/45 lottery. That is, picking 4 of the 5 winning numbers
Answer:
The probability of winning second prize in a 5/45 lottery is 1 in 8,145. This is calculated by taking the total number of possible combinations (8,145) and dividing it by the total number of possible outcomes (1).
please help me for both please, asap :)) thank you!
Answer:
The correct answer is the third one
Step-by-step explanation:
[tex]8x + \frac{15}{x} = 26[/tex]
[tex]8 {x}^{2} + 15 - 26x = 0[/tex]
a = 8, b = -26, c = 15
[tex]d = {b}^{2} - 4ac = ( { - 26})^{2} - 4 \times 8 \times 15 = 676 - 480 = 196 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{26 - 14}{2 \times 8} = \frac{12}{16} = \frac{3}{4} [/tex]
[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{26 + 14}{16} = \frac{40}{16} = \frac{5}{2}[/tex]