The augmented matrix is [tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex].
What is a matrix?
A rectangular array or table containing numbers, symbols, or phrases that are arranged in rows and columns is known as a matrix.
The given system of equations is:
9y - 5 +9z = 0
7x = -3y +7 + z
5x + 7y = 5
Rewrite the equations as:
0x + 9y + 9z = 5
7x +3y -1z = 7
5x + 7y + 0z= 5
Therefore, the augmented matrix for the system of equations is:
[tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex]
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Determine the probability of occurence of the following single eventsA "4" appears in a single toss of a die
SOLUTION
The probability of an event occuring is found using the formula
[tex]\frac{possible\text{ outcome}}{\text{total possible outcome }}[/tex]There is only "one" 4, in a die, out of a total of "six" numbers labelled 1 to 6.
So, possible outcome = 1
Total possible outcome = 6, since the die was tossed once.
Probability becomes
[tex]\frac{1}{6}[/tex]Hence the answer is
[tex]\frac{1}{6}[/tex]A fan in a baseball stadium is sitting in a seat withtheir eye level is a vertical distance of 350 ftabove level.A) When the fan is looking at home plate, theangle of depression is 30°. What is the horizontaldistance from the fan to home plate? Round to thenearest 10th. Explain two different ways todetermine this distanceB) The same fan makes eye contact with a secondfan in the stands that is seated at a lower row inthe stadium. The straight-line distance betweenthe eyes of the two fans is 300 ft and the angle ofdepression is 48°. What is the vertical distancebetween field level and the eyes of the secondfan? Round to the nearest tenth.
GIVEN:
We are told that a baseball fan is sitting at a point where his eyes are 350 feet vertical distance from the ground. When the fan is looking at the home plate the angle of depression is 30 degrees.
Required;
Find the horizontal distance from the fan to the home plate.
Step-by-step solution;
We begin by making a sketch of the scene to determine the shape and angles formed. This is shown below;
From the sketch above we can see the that the baseball fan has effectively formed a right triangle with the home plate from his position and the dimensions, that is, angles and sides, have been labeled.
We have the reference angle given as 60 degrees and the opposite is x (horizontal distance from the fan to home plate). That means the adjacent side is 350.
We can now use the following trig ratio;
[tex]tan\theta=\frac{opposite}{adjacent}[/tex][tex]tan60\degree=\frac{x}{350}[/tex]We now cross multiply;
[tex]\begin{gathered} tan60\degree\times350=x \\ \\ 1.73205080757\times350=x \\ \\ 606.217782649=x \\ \\ x=606.2ft\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth) \end{gathered}[/tex]A second way to determine this distance is by using the triangle formed by the angle 30 degrees, in which case the horizontal distance will be the green line as shown in the sketch above. In that case, the vertical distance of 350 feet will be the opposite while the horizontal distance will be the adjacent while the reference angle will be 30 degrees.
For the second scenario, the straight line distance between both sets of eyes is 300 feet, and the angle of depression is 48 degrees. Note that the second fan is being watched at an angle of depression of 48 degrees which means he is at a lower level.
Now we are required to determine the vertical distance between the field level and the eyes of the second fan.
Let us begin by calculating the value of x as indicated in the triangle.
We shall use the trig ratio of;
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex][tex]cos42\degree=\frac{x}{300}[/tex]Now we cross multiply;
[tex]\begin{gathered} cos42\degree\times300=x \\ \\ 0.743144825477\times300=x \\ \\ 222.943447643=x \\ \\ x=222.9ft\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth) \end{gathered}[/tex]Observe carefully that the distance calculated as x (222.9 ft) is the vertical distance between both fans. If we subtract this value from 350 feet we will now derive the vertical distance from the second fan to the field level.
[tex]\begin{gathered} Vertical\text{ }distance=350-222.9 \\ Vertical\text{ }distance=127.1ft \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} (A)\text{ }606.2ft \\ \\ (B)\text{ }127.1ft \end{gathered}[/tex]Which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3x(2x8) + 7 ?
7 + 3 × (2 × 8) is the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 × (2 × 8) + 7.
Given, 3 × (2 × 8) + 7
Following the application of the Commutative property of addition, which stipulates that altering the order of addends does not affect the result.
The expression will be,
7 + (2 × 8) × 3
Then, using the associative principle of multiplication, which states that how elements are arranged in a multiplication issue does not affect the product.
The expression will be,
7 + 3 × (2 × 8)
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The next nine births at a hospital all being girls
Answer:
There is a chance it could happen. Rare occurrence though.
Step-by-step explanation:
Your lunch in the hospital cadet cost $6.50. Based on working 50weeks per year , how much will you spend on your lunch per year?
Answer:
Step-by-step explanation:
if they are working 7 days a week, lunch will cost $2,275
hope this helped :)
20Which equation, when paired with the equation below, will create a system of equations with infinitelymany solutions?3x - 8y = -5A. 3x+ 8y = -5B.6x+ 16y = -10C.6x- 16y = -10D. -8x+ 3y = 5
ANSWER
C. 6x - 16y = -10
EXPLANATION
An equation or a pair of equations has infinite solutions when all numbers are solutions of the equation(s).
The left and right hand side of the equation(s) are the same.
So, we have to look for the equation such that the case happens.
To do that, we have to simply look for an equation that is identical to the given equation:
3x - 8y = -5
By observing keenly, we see that the identical one is:
6x - 16y = -10
Divide both sides by 2, we have that:
3x - 8y = -5
Let us try to solve these equations:
3x - 8y = -5
3x - 8y = -5
Subtract the second from the first:
3x - 8y = -5
- (3x - 8y = -5)
0 + 0 = 0
=> 0 = 0
We see that both sides are identical.
So, the answer is option C.
Store A charges $10.00 for a pack of hotdogs and $8.00 for a pack of hotdog buns. Store B charges $11.00 for a pack of hotdogs and $7.50 for a pack of hotdog buns. Suppose you buy x packs of hotdogs and y packs of hotdog buns at both stores. You end up spend $80.00 at store A and $81.50 at store B. Which system of equations represents the total amount of money you spent on hotdogs and hotdog buns at each store?
Taking into account the definition of a system of linear equations, the system of equations that represents the total amount of money you spent on hotdogs and hotdog buns at each store is
10x + 8y= 80
11x + 7.50y= 81.50
System of linear equationsA system of linear equations is a set of linear equations that have more than one unknown, appear in several but not necessarily all of the equations, and are related by the equations.
In the systems of equations, the values of the unknowns must be found, with which when replacing, they must give the solution proposed in both equations.
System of equation in this caseIn this case, a system of linear equations must be proposed taking into account that:
"x" is the packs of hotdogs buns at both stores."y" is the packs of hotdog buns at both stores.You know that:
Store A charges $10.00 for a pack of hotdogs and $8.00 for a pack of hotdog buns. You end up spend $80.00 at store A.Store B charges $11.00 for a pack of hotdogs and $7.50 for a pack of hotdog buns.You end up spend $81.50 at store B.The system of equations to be solved is
10x + 8y= 80
11x + 7.50y= 81.50
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Given g(-2) = -4 and g'(-2) = 5, find the value of h'(-2) based on the function below.
h(x) = (-2x + 6) • g(x)
Step-by-step explanation:
so,
h(x) = f(x) × g(x)
h'(x) = f'(x) × g(x) + f(x)×g'(x)
with f(x) = -2x + 6
f'(x) = -2
so,
h'(-2) = -2 × g(-2) + (-2×-2 + 6) × g'(x) =
= -2 × -4 + 2 × 5 = 8 + 10 = 18
The question is below:
If function f(x) = √(x + 1) - 5 is translated three (3) units to the right and two (2) units up, the equation which represents g(x) is: D. f(x) = √(x - 2) - 3
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
Translating f(x) = √(x + 1) - 5 three (3) units to the right and two (2) units up, we have:
f(x) = √(x + 1) - 5
f(x) = √(x + 1 - 3) - 5 + 2
f(x) = √(x - 2) - 3
In Geometry, g(x - 3) simply means shifting a graph three (3) units to the right while adding two (2) to the function simply means moving the graph up.
In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 3 units to the right and 2 units up.
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15. In circle A, SQ = 12 and AT = 8. Find AR.AR =AR
We have to find the length of AR.
It will be the same as the length of AS, as they are both radius of the circle:
[tex]AR=AS[/tex]AS is the hypotenuse of a right triangle with legs AT and TS.
Also, TS has half the length of SQ, so we have:
[tex]TS=\frac{1}{2}SQ=\frac{1}{2}\cdot12=6[/tex]We then can calculate AS as:
[tex]\begin{gathered} AS^2=TS^2+AT^2 \\ AS^2=6^2+8^2 \\ AS^2=36+64 \\ AS^2=100 \\ AS=\sqrt[]{100} \\ AS=10 \\ \Rightarrow AR=10 \end{gathered}[/tex]Answer: AR = 10
O POLYNOMIAL AND RATIONAL FUNCTIONSFinding the maximum or minimum of a quadratic function
Given
The function,
[tex]g(x)=x^2+4x[/tex]To find:
The maximum or minimum value of the function, and where does it occur.
Explanation:
It is given that,
[tex]g(x)=x^2+4x[/tex]That implies,
Set g(x)=y.
Then,
[tex]\begin{gathered} y=x^2+4x \\ y=(x+2)^2-4 \\ y+4=(x+2)^2 \end{gathered}[/tex]Here, a=1>0.
Then, the parabola opens up.
And, k is the minimum functional value, it occurs when x = h.
Therefore,
1) g(x) has a minimum value.
2) g(x)'s minimum value is -4.
3) And it occurs at x = -2.
what's the perimeter of 3x2-1x2-4x+3 for parallelogram?
Answer:
The perimeter of the parallelogram is;
[tex]8x^2-8x+4[/tex]Explanation:
Given the figure of a parallelogram in the attached image.
With sides;
[tex]\begin{gathered} a=x^2-4x+3 \\ b=3x^2-1 \end{gathered}[/tex]The perimeter of a parallelogram can be calculated using the formula;
[tex]P=2(a+b)[/tex]substituting the given sides;
[tex]\begin{gathered} P=2(a+b) \\ P=2(x^2-4x+3+3x^2-1) \\ P=2(x^2+3x^2-4x+3-1) \\ P=2(4x^2-4x+2) \\ P=8x^2-8x+4 \end{gathered}[/tex]Therefore, the perimeter of the parallelogram is;
[tex]8x^2-8x+4[/tex]
Find the y-intercept of line on the graph.
Answer:
the y intercept is -3. it is -3 because it goes through the point (0,-3)
Describe the slope of the line.AY|(-3, 1)2|-22X-25(2,-2)
A = (-3, 1)
B = (2, -2)
First we will calculate the slope of the line
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{-2-1}{2-(-3)}=\frac{-3}{5}_{}[/tex]The slope is negative
Now, we are gonna calculate the equation, with (2, -2)
[tex]b=y-mx[/tex][tex]b=-2-(-\frac{3}{5})\cdot2[/tex][tex]b=-\frac{4}{5}[/tex]Which of (3, 5), (4, 6), (5, 7), and (6, 8) are solutions to y = x + 2?
O(3, 5) and (4, 6)
O(4, 6) and (5, 7)
Onone
O all
All of them would be the answer.
What is the basic component of solving an equation?The left side and right side of every equation should be equal. It is essential that both parties are on an even playing field. An equation must contain the following elements: coefficients, variables, operators, constants, terms, expressions, and an equals sign. Any one, some, or all of these terms may circle the equal sign in an equation.
Rule of Thumb for Equation Solving:
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.Here, we will put the values of x and y coordinates in the equations:
5=3+2
6=4+2
7=5+2
8=6+2
Hence, the right and left side of the equation is equal.
Thus, all of them are correct answers. It would just be all of them.
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please break down 145 + 216 with the hundreds tens and ones.
Step 1:
Sum the numbers
[tex]145+216=361[/tex]Step 2:
Express the number in Hundreds, Tens, and Ones
3 has a value of 300
6 has a value of 60
1 has a value of 1
Therefore, to express 361 in hundreds, tens and ones
A combined total of $41,000 is invested in two bonds that pay 6% and 7% simple interest. The annual interest is $2,700.00. How much is invested in each bond?
Answer
Amount invested at 6% interest = 17,000
Explanation
The simple interest on an invested principal (P), at a rate, R, for a period of time, T, is given by
Simple Interest = (PRT/100)
Let the amount invested at 6% be x
Let the amount invested at 7% be y
Sum of these amounts is $41,000
x + y = 41000
Simple Interest on x for 1 year
SI = (x × 6 × 1/100) = 0.06x
Simple interest on y for 1 year
SI = (y × 7 × 1/10) = 0.07y
Sum of annual interest = $2,700
0.06x + 0.07y = 2700
Now, we have a simultaneous equation
x + y = 41000
0.06x + 0.07y = 2700
Solving this simultaneously,
x = 17,000
y = 24,000
Hope this Helps!!!
Which equation represents a proportional relationship between x and y?
A.y=0.25x+1.25
B.y=4x
C.y=14x−2
D.y=23x−23
y=4x equation represents a proportional relationship between x and y.
Form the question
Only B doesn't have constant
y=4x
x=y/4
So option 2 is correct.
The formula y=kx y = k x can be used to describe a proportional relationship, where k is the constant ratio.
y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, diagrams, and equations can all be used to depict proportional relationships.
The graph of a straight line through the origin with a slope equal to the unit rate can be used to depict a relationship where two quantities are related proportionally. is equal to k, where k is the unit rate, for each point (x, y) on the graph.
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Please help me!! The question is in the attachment!!
Using it's concept, the probabilities are given as follows:
b) P(B|C) = 0.1429.
c) P(not A|B) = 0.8.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For item b, the conditional probability can be written as follows:
P(B|C) = P(B and C)/P(C).
From the diagram, we have that:
P(B and C) = P(5) = 0.05.P(C) = P(5) + P(6) = 0.05 + 0.3 = 0.35.Hence:
P(B|C) = 0.05/0.35 = 0.1429.
For item c, the conditional probability is:
P(not A|B) = P(not A and B)/P(B).
From the diagram, these probabilities are:
P(not A and B) = P(4) + P(5) = 0.15 + 0.05 = 0.20.P(B) = P(3) + P(4) + P(5) = 0.05 + 0.15 + 0.05 = 0.25.Hence:
P(not A|B) = 0.20/0.25 = 0.8.
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is when you multiply with any number with a negative or possitive the asnwer is also suppossd to also have a negative and possitive . Also will i get the answer wrong if i dont put any of the sighn ?
If we mutiply a positive number with a positive or negative sign we get the answer as number with sign.
[tex]eg\colon5\times(+1)=5,5\times(-1)=-5[/tex]If we mutiply a negative number with sign the answer will be,
[tex]eg\colon(-5)\times(+1)=-5,)-5\times(-1)=5_{}[/tex]Thus, if we mutiply a negative to a positive number the sign gets reversed.
Find the solution of each equation if the replacement set is 10 11 12 13
If we replace with 10:
[tex]\frac{10}{5}=2[/tex][tex]2=2[/tex]10 is a solution.
Let's try with 11:
[tex]\frac{11}{5}=2[/tex][tex]2.2\ne2[/tex]11 is not a solution.
WIth 12:
[tex]\frac{12}{5}=2[/tex][tex]2.4\ne2[/tex]12 is not a solution
WIth 13
[tex]\frac{13}{5}=2[/tex][tex]2.6\ne2[/tex]13 is not a solution.
Therefore, the solution to this equation is 10
- The simple interest equation is I = Prt, where I is the interest
-
earned, P is the principal investment, and t is the amount of time
(in years).
Use the formula to solve the problem: If a $5,000 investment earns
$1,57 interest over 18 years, what is the annual interest rate?
% (enter your answer as a percent and do not round)
T=
The rate of the given amount 0.001744%
What is Simple Interest?
Simple interest is a quick and easy way to calculate interest on a loan. Simple interest is the daily interest rate multiplied by the principal multiplied by the number of days until the next payment.
Given,
Principal = $5000
Interest = $157
Time = 18years
The formula for simple interest:
I = P x R x T
157 = 5000 x R x 18
R = 157 / 5000 x 18
R =0.001744%
Hence, the annual rate of interest is 0.001744%
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Select all of the answer choices that are solutions to the equation2x+2y=0.Ox=0y = -1O x = 1, y = -1Ox= -2O x = -2, y = -2O x = 0, y = 0
If the sum of two terms = 0, then the 2 terms must have the same value but different signs
That means x and y must have the same value but different signs
Look at the given answers
The 1st, 2nd, and 4th answers are wrong because the solution of this equation must have a value of x and a value of y together
In the 3rd answer
x = 1 and y = -1
Both have the same value and different signs
Then 3rd answer is a solution
In the 5th answer
x = -2 and y = -2
They have the same value with the same signs
The 5th answer is not a solution
In the last answer
x = 0 and y = 0
They have the same value but the zero has no sign
Then substitute them in the equation to check if it is solution or not
2(0)+2(0) = 0
0 + 0 = 0
The 2 sides of the equation are equal, then
The last answer is a solution
The answer is the 3rd and last answers
Most cars depreciate in value as they age. A specific model car purchased for $14 995depreciates by 28% per year. The function that models it value over time
(a)
Graphing the function from x = 0 to x = 10:
b)
Evaluate the function for x = 5
[tex]\begin{gathered} V\left(5\right)=14995\left(0.72\right)^5 \\ V\left(5\right)\approx2901.41 \end{gathered}[/tex]Answer:
$2901.41
c)
Let's solve the following inequality:
[tex]V\left(x\right)<1000[/tex]so:
[tex]\begin{gathered} \left(0.72\right)^x<\frac{1000}{14995} \\ x<\frac{1}{ln\left(0.72\right)}*ln\left(\frac{1000}{14995}\right? \\ x>8.2 \end{gathered}[/tex]Approximately after 8.2 years.
d)
[tex]4300=14995\left(y\right)^5[/tex]Let's solve the previous equation in order to find the rate y:
[tex]\begin{gathered} y^5=\frac{4300}{14995} \\ y=\sqrt[5]{\frac{4300}{14995}} \\ y\approx0.78 \end{gathered}[/tex]The depreciation rate is approximately:
[tex]0.78[/tex]It depreciates 22% per year
16. In Barry's state, the weekly unemployment compensation is 58% of the 26-week average forthe two highest-salaried quarters. A quarter is three consecutive months. For July, August, andSeptember, Ben earned a total of $17,500. In October, November, and December, he earned atotal of $18,300. Determine Barry's weekly unemployment compensation.
~ 399.3 $ / w
. The average for the 2 highest-salaried quarters:
(17 500 $ + 18 300 $ ) / 2 = 35 800 $ / 2 = 17 900$
. The 58% compensation representing the total amount Barry will be compensated:
17 900 * 58 / 100 = 10 382 $
. The weekly compensation:
10 382 $ / 26 week ~= 399.307692 $ / w
If a linear function has no restrictions, the domain of the function is
The Domain of the linear function with no restriction is (-∞,∞)
What is a linear function?A linear function is of the form f(x) = ax+ b, where a and b are constants , x is independent variable and the graph of such function is a straight line.
Domain of f is the set of all values of x for which function f is defined.
Given that the linear function has no restrictions , means the values of the function can be from anywhere of real line.
-∞ < f(x) < ∞
⇒ -∞ < ax+ b < ∞ , where a≠0
⇒ -∞- b < ax+ b-b < ∞ -b
⇒ -∞ < ax < ∞ ( adding or subtracting anything from infinity does not
make any difference)
⇒ -∞ < x < ∞
Thus the domain of the linear function which has no restriction is (-∞,∞)
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2. Invasive weed species can grow quickly. One variety grows up to 1.65 ft per day.
I NEED HELP .How fast in inches per minute can this weed grow? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
Invasive weed grows at a rate of 0.0011 ft per minute a day
In the above question, it is given as
Invasive weed grows really fast and the rate of its growth is being provided as follows
The rate at which the weed is growing a day is = 1.65 ft
We need to find the, rate at which this weed is growing per minute
So, to do this, we'll find the growth in 1 min
In 24 hours growth is = 1.65 ft
Conversion factors
We know, 1 hour = 60 minutes
In 1 min growth is = [tex]\frac{1.65}{24 . 60}[/tex]
Here, we have multiplied with 60 in the denominator to convert hours into minutes
After solving the fraction we'll get
Growth in 1 min of the weed = 0.0011 ft
Hence, Invasive weed grows at a rate of 0.0011 ft per minute a day
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.As the operations manager of the post-sales department, you need to estimate the average duration of an on-site visit by your technical staff. Based on the information in the service call log shown, what is the average time needed for an on-site visit? Service Call Duration 45 min 55 min 1 hr 35 min 1 hr 15 min 50 min O A 40 minutes O В. 1 hour 4 minutes O С. 1 hour 20 minutes D 4 hours O E 5 hours 20 minutes
The mean (or average) is given as:
[tex]\frac{\sum ^{}_{}x_i}{n}[/tex]where xi is the value of each data and n is the total number of data. In this case we have:
[tex]\frac{45+55+95+75+50}{5}=64[/tex]Therefore the average is 1 hour 4 minutes and the answer is B.
Gina's books has 349 fewer pages than terri's. if Gina's books has 597 pages, how many pages does Terri's books have?
Gina's books has 349 fewer pages than Terri's, if Gina's books has 597 pages, Terri's books have 946 pages. In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.
What is mathematical operations?In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.
The most commonly studied operations are the binary operations (i.e., the operations of arity 2), such as addition and multiplication, and the unary operations (i.e., the operations of arity 1), such as additive inverse and the multiplicative inverse. An operation of arity zero, or nullary operation, is constant. The mixed product is example of operation of arity 3, also called ternary operation.
Generally, arity is taken to be finite. However, the infinitary operations are sometimes considered, in which case "usual" operations of finite arity are called finitary operations.
A partial operation is defined similarly to operation, but with partial function in place of a function.
Gina's book = 597 pages
Terri's book= (597+349) pages
= 946 pages
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For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the
day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from
the mound. At the end of the day, the mound has 1,200 pounds of gravel.
The value of g for the given conditions is obtained from linear equations as 2000.
What is a linear equation?A linear equation in one variable has only one variable of order 1. It has the formula ax + b = 0, where x is a variable. There is only one solution to this equation.
The initial amount is given as g.
400 pounds is added.
2 times 600 pounds is taken out.
The remaining amount is 1200 pounds.
Form a linear equation from the given constraints.
g+400-2(600)=1200
Solve the linear equation using basic mathematical functions.
g+400-1200=1200
g=2400-400
g=2000
So, the value of g is obtained using the linear equation as 2000.
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