Hence, in response to the provided question, we can say that As a result, equation A(1,2) and A'(5,12) are not dilations.
What is equation?An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.
To evaluate if the points A(1,2) and A'(5,12) reflect a dilation, we must first determine the dilation's scale factor.
Let's use the given points to compute the scale factor:
(length of A' A) / scale factor (length of A)
A's length A [tex]=\ sqrt[(5-1)2 + (12-2)2] = \sqrt[16^2 + 10^2] =\ sqrt(296) (296)[/tex]
A's length is one.
[tex](\sqrt(296)) / 1\\\sqrt(x) = scale factor (296)[/tex]
As a result, the scaling factor is not an integer. That is, the transformation from point A to point A' is not a dilation with a whole number scale factor.
As a result, A(1,2) and A'(5,12) are not dilations.
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Estimate the exact maximum in the exact minimum
The estimations for the given function are:
maximum ---> y ≈ 120minimum ---> y ≈ -175How to identify the maximum and minimum?For a function y = f(x) we define the maximum as the value of f(c) such that:
f(c) ≥ f(x) for any value of x.
And the minimum as:
f(k) ≤ f(x) for any value of x.
Usin the graph it is easier, just select the value at the top for the maximum and the value at the bottom for the minimum, we can see that:
maximum ---> y ≈ 120
minimum ---> y ≈ -175
Remember, these are estimations.
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The equations were multiplied by constants and added together to determine that the value of x in the system of
equations is -4.
What is the value of y?
0-6
O-3
O 3
06
As a result the system of equation , y has a value that is roughly 4.33.
SYSTEM OF EQUATIONS: WHAT IS IT?A group of two or more equations with the same variables is referred to as a system of equations. The collection of numbers that simultaneously make all the equations true is the system's solution.
For instance, take into account the equations below:
2x + y = 5
x - y = 1
There are two equations with two variables in this system (x and y). The collection of numbers that simultaneously satisfy both equations is the system's solution. The answer in this situation is x = 2 and y = 1.
We may solve for y by substituting the value of x in the system of equations, which is -4, into one of the equations.
Consider the following two equations:
axe + by = c
dx + ey = f
We can solve for y by substituting the value of x into one of the equations if we know it.
As an illustration, if x = -4, then we have:
2x + 3y = 5
4x - 3y = -16
We can change one of the equations to read x = -4:
2(-4) + 3y = 5
When we simplify this equation, we obtain:
-8 + 3y = 5
8 is added to both sides to get at:
3y = 13
When we multiply both sides by 3, we get:
y = 13/3
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It takes 32 pounds of seed to completely plant a 4 -acre field. How many acres can be planted per pound of seed?
Answer:
Step-by-step explanation:
To solve this problem, we need to find the number of acres that can be planted per pound of seed.
We know that it takes 32 pounds of seed to plant a 4-acre field. Therefore, the amount of seed needed to plant 1 acre is:
32 pounds / 4 acres = 8 pounds/acre
This means that for every pound of seed, we can plant:
1 acre / 8 pounds = 0.125 acres/pound
Therefore, we can plant 0.125 acres per pound of seed.
If a year has 52 weeks, what fraction of a century is 13 weeks?
Answer:
Step-by-step explanation:
There are different methods to approach this problem, but one possible way is:
First, find the number of weeks in a century: 100 years × 52 weeks/year = 5200 weeks
Then, find the fraction of a century that is 13 weeks by dividing 13 weeks by 5200 weeks: 13/5200 = 1/400
Therefore, 13 weeks is 1/400 of a century.
What is JL if KM=6?
Not really much context but that’s the whole question
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{x}{6}=\cfrac{6}{8}\implies \cfrac{x}{6}=\cfrac{3}{4}\implies x=\cfrac{18}{4}\implies x=\cfrac{9}{2} \\\\[-0.35em] ~\dotfill\\\\ 8+x\implies 8+\cfrac{9}{2}\implies \cfrac{25}{2}\implies 12\frac{1}{2}=JL[/tex]
Step-by-step explanation:
geometric mean theorem :
the height of a right-angled triangle to the Hypotenuse is the square root of the product of the parts of the Hypotenuse (as the height splits the Hypotenuse into 2 parts : JM and ML).
JL = JM + ML
in short
KM = sqrt(JM × ML)
6 = sqrt(8 × ML)
36 = 8 × ML
ML = 36/8 = 9/2 = 4.5
so,
JL = JM + ML = 8 + 4.5 = 12.5
Compute the cost assigned to ending inventory using (a) FIFO, (b) LIFO, (c) weighted average, and (d) specific identification. For specific identification, units sold include 70 units from beginning inventory, 200 units from the March 5 purchase, 50 units from the March 18 purchase, and 90 units from the March 25 purchase.
By calculating, the cost assigned to ending inventory using (a) FIFO is $12,272, (b) LIFO is $13,048, (c) weighted average is $0 (since all units were sold), and (d) specific identification is $9,772.
To compute the cost assigned to ending inventory using different inventory costing methods, we need to determine the cost of goods sold (COGS) and the cost of ending inventory based on the specific method. Here is the calculation for each method:
(a) FIFO (first-in, first-out) method:
We assume that the earliest inventory items purchased are the first ones sold. Therefore, the cost of goods sold is calculated using the cost of the earliest inventory items, while the cost of ending inventory is based on the cost of the most recent purchases. Here are the calculations:
COGS: 110 units x $51.20 + 200 units x $56.20 + 50 units x $86.20 + 70 units x $61.20 = $23,216
Ending inventory: 90 units x $61.20 + 160 units x $63.20 = $12,272
(b) LIFO (last-in, first-out) method:
We assume that the most recent inventory items purchased are the first ones sold. Therefore, the cost of goods sold is calculated using the cost of the most recent inventory items, while the cost of ending inventory is based on the cost of the earliest purchases. Here are the calculations:
COGS: 90 units x $61.20 + 270 units x $86.20 + 230 units x $56.20 = $43,104
Ending inventory: 110 units x $51.20 + 140 units x $96.20 + 50 units x $86.20 = $13,048
(c) Weighted average method:
We calculate the weighted average cost per unit for all the inventory purchased during the period, and use this average cost to determine the cost of goods sold and ending inventory. Here are the calculations:
Weighted average cost per unit = ($51.20 x 110) + ($56.20 x 230) + ($86.20 x 270) + ($61.20 x 90) + ($63.20 x 160) / (110 + 230 + 270 + 90 + 160) = $72.62
COGS: 590 units x $72.62 = $42,878.80
Ending inventory: 0 units (all units have been included in COGS)
(d) Specific identification method:
We identify the specific cost of each unit sold based on its purchase price. Here are the calculations:
COGS: 70 units x $51.20 + 200 units x $56.20 + 50 units x $86.20 + 90 units x $61.20 + 80 units x $63.20 + 20 units x $96.20 = $43,708
Ending inventory: 80 units x $63.20 + 70 units x $96.20 = $9,772
Therefore, the cost assigned to ending inventory using (a) FIFO is $12,272, (b) LIFO is $13,048, (c) weighted average is $0 (since all units were sold), and (d) specific identification is $9,772.
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Write an equation of the line that passes through the point (–4, 6) with slope –4.
A. y−6=−4(x+4)
B. y+4=−4(x−6)
C. y−6=4(x+4)
D. y+4=4(x−6)
Answer:
Answer is A
Step-by-step explanation:
General equation of a line is given by;
[tex]{ \boxed{ \rm{y = mx + c}}}[/tex]
m is gradientc is y-intercept.From the question, m = -4
[tex]{ \rm{y = - 4x + c}}[/tex]
For (-4, 6)
[tex]{ \rm{6 = ( - 4 \times - 4) + c}} \\ { \rm{6 = 16 + c}} \\ { \rm{c = - 10}}[/tex]
Therefore;
[tex]{ \rm{y = - 4x - 10}} \\ { \colorbox{silver}{subtract \: 6 \: from \: both \: sides}} \\ { \rm{y + ( - 6) = ( - 4x - 10) + ( - 6)}} \\ \\ { \rm{y - 6 = - 4x - 16}} \\ \\ { \rm{y - 6 = - 4(x + 4)}}[/tex]
Challenge) Solve for a. Answer as a mixed number. A=______
The value of the a in the mixed form is [tex]-1 \frac{5}{43}[/tex].
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To solve for a, we can begin by isolating the variable on one side of the equation.
First, we can subtract 3 from both sides to get:
-7/12 - 3 = 4/a
Next, we can simplify the left side by finding a common denominator of 12:
-7/12 - 3 * 12/12 = 4/a
-7/12 - 36/12 = 4/a
-43/12 = 4/a
To solve for a, we can multiply both sides by a/4:
(-43/12) * (a/4) = 1
Multiplying the left side gives:
-43a/48 = 1
Dividing both sides by -43/48 gives:
a = -48/43
To express this as a mixed number, we can divide the numerator by the denominator:
-48 ÷ 43 = -1 with a remainder of 5
Therefore, the value of the a in the mixed form is [tex]-1 \frac{5}{43}[/tex].
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Complete question:
Challenge) Solve for a. Answer as a mixed number. A=?
-7/12 = 4/a+3.
HELP A construction company takes 1 7/8 hours to remove 2 3/4 of dirt what is the hit rate metrics ton per hour
Answer: To calculate the hit rate metric in tons per hour, we need to first calculate how many tons of dirt the construction company can remove in one hour.
To do this, we'll convert the given time and amount of dirt into a rate of dirt removal in tons per hour:
The company takes 1 7/8 hours to remove 2 3/4 tons of dirt
We can convert 1 7/8 hours to an improper fraction: 15/8 hours
We can convert 2 3/4 tons to an improper fraction: 11/4 tons
We can calculate the rate of dirt removal as the amount of dirt divided by the time: (11/4 tons) / (15/8 hours) = (11/4) ÷ (15/8) = (11/4) x (8/15) = 22/15 tons per hour
Therefore, the construction company has a hit rate metric of 22/15 tons per hour, which simplifies to 1.47 tons per hour (rounded to two decimal places).
Step-by-step explanation:
Find the common ratio of 1,3,9,-27 and the next three terms
Answer:
Step-by-step explanation:
The common ratio of this sequence is 3. Next 3 terms are -81, -243, and -729.
Each child has 34 stickers and 9 bottle If there are 9 children how many stickers are in total
Answer: 306
Step-by-step explanation:
Each child has 34 stickers and 9 bottles. To find the total number of stickers, we need to multiply the number of stickers per child by the number of children.
34 stickers x 9 children = 306 stickers
So there are 306 stickers in total.
how many teams completed the escape room in 45 minutes or less !! PLS I NEED IT BEFORE 10:00 PM!!!!!!
Find the L.C.M. and H.C.F of 84 and 56.
[tex] \mathbb{ANSWER:}[/tex]
LCM: 168
Multiples of 84: 84, 168…Multiples of 56: 56, 112, 168…HCF: 28
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84what is this?????????????????????????????
PLSS i NEED help :/ Can u show me the method too? I'm really stuck
IS IT RIGHT??? OR I MISSED SOMETHING
pls help due tmrw i want a good grade
My folks really want me to succeed in class and gave me the goal of getting an 80. I know that my classwork grade is the easiest to change, so I wonder if I can meet my goal by only changing my classwork grade. If both my homework score and my assessments score stays the same, how low can I go in classwork to reach the goal of an 80? Show all work.
My assessments grade: 91.5%
My classwork grade: 100%
My homework grade: 97.2%
Grading System:
Assessments are worth 40%
Classwork is worth 40%
Homework is worth 20%
Therefore, if your percentage test scores and homework grades remain the same, you can submit classwork with a grade as low as 71.4% and still receive an overall grade of 80%.
Describe percentages.In statistics, a percentage is a figure or an integer that is expressed as a fraction of 100. Additionally, the words "pct.," "pct," but also "pc" are rarely used. The "%" symbol, however, is commonly used to denote it. There are no dimensions; the percentage total is flat. Percentages are really just numbers because the numerator is 100. To indicate that a number is a percentage, either the percent character (%) or the text "percent" must appear before it.
Here,
Using the following formula, we can determine how little classwork you need to complete to receive an overall score of 80%:
Tests account for 40% of the final grade, classwork for 40%, and homework for 20%.
=> 80% = (91.5%) x (40%) + (40%) for classwork + (97.2%) x (20%)
When the numbers are multiplied by the corresponding weights:
=> (0.4 times classwork) + (0.32) + (0.1944) = 0.8
Simplifying:
=> 0.8 - 0.32 - 0.1944 = 0.4 x Classwork
=> 4. times classwork equals 0.2856
=> multiplying by 0.4
=> Work in class = 0.714
Therefore, if your test scores and homework grades remain the same, you can submit classwork with a grade as low as 71.4% and still receive an overall grade of 80%.
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One hour later the right triangle is 15 inches long and 13 inches high and the base and height are changing at the same rate is there hypotenuse increasing or decreasing now?
The hypotenuse of the new triangle is increasing.
What theorem can be used to determine the triangle?The Pythagorean Theorem can be used to determine the new right triangle's hypotenuse length:
[tex]c^2 = a^2 + b^2\\c^2 = 13^2 + 15^2\\c^2 = 169 + 225\\c^2 = 394\\c ≈ 19.85[/tex]
Hence, the hypotenuse of the new right triangle measures roughly 19.85 inches in length.
Let h be the height of the triangle, and let b be the base of the triangle, both as functions of time t. We know that the base and height are changing at the same rate, so we can express this as:
dh/dt = db/dt = k, where k is a constant rate of change.
We can use the Pythagorean Theorem to express the length of the hypotenuse c as a function of h and b:
[tex]c^2 = h^2 + b^2[/tex]
Taking the derivative of both sides with respect to time t using the chain rule, we get:
2c(dc/dt) = 2h(dh/dt) + 2b(db/dt)
Simplifying and substituting the values for h, b, and c at time t = 0 (when the original triangle was given):
2c(dc/dt) = 2(7)(k) + 2(x)(k)
2c(dc/dt) = 14k + 10k
2c(dc/dt) = 24k
adding 2c to both sides' sums:
(12k/c) = (dc/dt)
For the new triangle, substitute the value of c as follows:
(dc/dt) = 12k/19.85
The sign of (dc/dt) will be decided by the sign of 1/c because k is positive and constant. Since we know that 1/c is positive and that c is positive, we can infer that (dc/dt) will also be positive because it will have the same sign as k. As a result, the new triangle's hypotenuse is growing.
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What is the equation for this graph?
Answer:
[tex]y=\frac{5}{2} x[/tex]
Step-by-step explanation:
Notice is a line, The equation for a line can be found as the following:
[tex]y-yo=m(x-xo)[/tex]
We need to find the slope.
First take two points of the graph
(0,0) the origin and (4,10) for example. Notice i do assume the X value is 4 for Y=10, since the cropping for the picture doesn't show the exact values for X .
Then the slope is given by equation:
[tex]m=(y-yo)/(x-xo)\\[/tex]
[tex]m=\frac{10-0}{4-0} =5/2[/tex]
then the equation is
[tex]y-0=\frac{5}{2} m(x-0)[/tex]
[tex]y=\frac{5}{2} x[/tex]
Answer:
y=5/2x or y=2.5x
Step-by-step explanation:
Simplify (2x3y2 − 8x2y + 4y) − (5x3y2 − 4x2y − 4y). −3x3y2 − 4x2y −3x3y2 + 12x2y −3x3y2 − 4x2y + 8y −3x3y2 − 12x2y + 8y
The simplified expressiοn is [tex]-3x^3y^2 - 4x^2y + 8y[/tex].
What is expressiοn ?Mathematical statements are called expressiοns when they cοntain at least twο terms that are cοnnected by an οperatοr and cοntain either numbers, variables, οr bοth. The mathematical οperatοrs can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn. Fοr instance, the expressiοn x + y is an expressiοn where x and y are terms with an additiοn οperatοr in between.
In mathematics, there are twο types οf expressiοns: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables.
Tο simplify [tex](2x^3y^2-8x^2y+4y) − (5x^3y^2-4x^2y - 4y)[/tex], we need tο distribute the negative sign in frοnt οf the secοnd set οf parentheses, and then cοmbine like terms. This gives:
[tex]2x^3y^2 - 8x^2y + 4y -5x^3y^2 + 4x^2y + 4y[/tex]
[tex]= (2x^3y^2 - 5x^3y^2) + (-8x^2y + 4x^2y) + (4y + 4y)[/tex]
[tex]= -3x^3y^2 - 4x^2y + 8y[/tex]
Therefοre, the simplified expressiοn is [tex]-3x^3y^2 - 4x^2y + 8y[/tex].
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Answer:
its C −3x3y2 − 4x2y + 8y
Step-by-step explanation:
Which linear function represents a slope of 1/4?
Answer:
The second answer choice represents a slope of 1/4.
Step-by-step explanation:
Using the coordinates (8,5) and (0,3) you can do point slope form (y2-y1/x2-x1). In this problem that would translate to 5-3/8-0 which is 2/8 and can be simplified to 1/4.
Find the 8th term of 27,9,3,1
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1. They each walk 500 units to school. Who walks 500 feet, and who walks 500 yards? Explain your reasoning
Answer:
Below
Step-by-step explanation:
If they each walk in straight lines to the school Lin is closer than Elena
so Lin walks 500 ft and Elena walks 500 yards ( which is 1500 ft)
Alice drew two game boards. These game boards are the same shape and the same size. She said that
1/2
of each game board is shaded.
Is Alice correct or incorrect? Choose the text to complete the statement.
Alice is _________ because _____________________________________________________.
(do not delete this question nor reporting this question)
Answer:
Alice is correct because area of shaded region of both the gameboards are equal.
Step-by-step explanation:
Here it is given that both the gameboards are of same shape and size and Alice stated that the area of shaded regions of both the gameboards are same.
Let us take the length of the board be "l" and its breadth be "b" .
Initial area of the gameboard will be lb since it is a rectangle.
1st case :-
breadth of the shaded region= b
length of the shaded region = l/2 (since the length becomes half )
Area of the shaded region = b*l/2 = lb/2 .
2nd case :-
breadth of the shaded region = b/2 ( since breadth becomes half. )
length of the shaded region = l
Area of the shaded region = l/2
Area of the shaded region = b/2*l = lb/2 .
As we can see that the area of shaded region in both shaded region in both cases are equal also it is half of the total area of the rectangle. Hence Alice was correct.
Hence the area of the shaded regions in both the cases are similar and half of board in case is shaded .
The area of a square whose sides are (x+8)cm is 64cm², then what is x?
Answer:
Step-by-step explanation:
area of square=side ×side
we have, side=x+8
also we have area of square=64cm²
∴ (x+8)cm×(x+8)cm=64cm²
⇒x²+16x+64=64 ∵( a+b )²=a²+b²+2ab
⇒x²+16x=0
⇒x(x+16)=0
∴x=0 or x=-16
Ashley measured the total snow in her yard every 30 minutes after a snowstorm started. The graph below shows her findings. Using the points (1,6) and (3, 9) which equation of the line best fits this data shown? Total Snow (inches) 10 Hours
The equation of the line of best fit is given as follows:
y = 1.5x + 4.5.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.Two points on the line for this problem are given as follows:
(1,6) and (3,9).
When x increases by 2, y increases by 3, hence the slope m of the line is given as follows:
m = 3/2
m = 1.5.
Hence:
y = 1.5x + b.
When x = 3, y = 9, hence the intercept b of the line is obtained as follows:
9 = 1.5(3) + b
b = 9 - 4.5
b = 4.5.
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5. Jasmyn plays in the outfield on her softball team. She throws a softball at a rate of 2(t-2) (t + 5). How much time will the softball spend in the air? (Hint) Find the x-intercepts.
The time the softball will spend in the air is 2 seconds
How much time will the softball spend in the air?From the question, we have the following parameters that can be used in our computation:
Rate = 2(t - 2)(t + 5)
To determine the time, we set the rate to 0
So, we have
2(t - 2)(t + 5) = 0
Divide by 2
(t - 2)(t + 5) = 0
The above means that
t - 2 = 0 or t + 5 = 0
Evaluate
t = 2 or t = -5
Time cannot be negative
So, we have
t = 2
Hence, the time is 2 seconds
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The Rodriguez family and the Barnes family each used their sprinklers last summer. The Rodriguez family's sprinkler was used for 15 hours. The Barnes family's sprinkler was used for 35 hours. There was a combined total output of 1050 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour?
Rodriguez family's sprinkler:
Barnes family's sprinkler:
The water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35) by solving the expression formed.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that are written in a certain order. Expressions can be evaluated or simplified by following the rules of arithmetic or algebra. Examples of expressions include "2x + 3", "(a + b) / c", and "5^2 - 3".
According to given information :
Let's use the variable "r" to represent the water output rate for the Rodriguez family's sprinkler.
Then, the water output rate for the Barnes family's sprinkler can be represented as "50 - r", since the sum of the two rates is 50 L per hour.
Using the formula:
rate x time = amount of output, we can set up two equations:
r x 15 = amount of water output for the Rodriguez family
(50 - r) x 35 = amount of water output for the Barnes family
We also know that the total amount of water output is 1050 L, so we can set up a third equation:
r x 15 + (50 - r) x 35 = 1050
Now we can solve for "r".
First, simplify the third equation
15r + 1750 - 35r = 1050-20r = -700r = 35
Therefore, the water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35).
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Write a system of equations to solve the following scenario. Twins Jon and Ron together earned $96,000 last year. Ron earned $8,000 more than three times what Jon earned. How much did each of the twins earn? Use the variable j to represent the amount Jon earned. Use the variable r to represent the amount Ron earned.
The amount Jon and Ron earn are $22,000 and $ 74,000 respectively.
What is word problem?Word problem is a mathematical problem expressed entirely in words typically used as an educational tool.This word problem is interpreted into mathematical equation or expression.
Represent the amount Jon earn by j and Ron earn by r
j+r = 96000 equation 1
r = 8000+ 3j equation 2
from equation 1
r = 96000-j
substitute 96000-j for r in equation 2
96000-j = 8000 +3j
collect like terms
96000-8000 = 3j +j
88,000 = 4j
j = 88000/4
j = $22,000
from equation 1
22000+r = 96000
r = 96000-22000
r = 74,000
Therefore the amount Jon and Ron earn are $22,000 and $ 74,000 respectively.
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mr.jones decided to invest in the stock market, but the market declined by an average of 2.5% each month during the first 6 months of his investment. If mr.jones initially invested $1,500, how much does he have remaining?
Step-by-step explanation:
If the stock market declined by an average of 2.5% each month during the first 6 months of Mr. Jones' investment, we can calculate the total percentage decrease using the following formula:
(1 - 0.025)^6 = 0.8938
This means that after 6 months, Mr. Jones' investment would have decreased by approximately 10.62% (1 - 0.8938 = 0.1062).
To calculate how much money Mr. Jones has remaining, we need to multiply his initial investment of $1,500 by the percentage decrease:
$1,500 x 0.1062 = $159.30
Therefore, Mr. Jones would have $1,500 - $159.30 = $1,340.70 remaining after the first 6 months of his investment in the stock market with an average decline of 2.5% each month.