The system of equations will have no solutions if the two lines are parallel, then one example can be:
5x - 2y = 1
15x - 6y = 0
For which values of a and b the system has no solutions?Here we have the following system of equations:
5x - 2y = 1
a*x - 6y = b
The system will have no solutions only if the two equations are parallel. You can see that the coefficient of y on the second equation is 3 times the coefficient on the first equation.
Then a should also be 3 times the coefficient of x on the first equation:
a = 3*5
a = 15
And b should be any number but 3 times the constant on the other equation:
b ≠ 3*1
So we can take b = 0, for example.
So the system with no solutions will be:
5x - 2y = 1
15x - 6y = 0
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4) You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2? ________
6% of the salary is $366
The total amount that would in the retirement account in the account each month is $732.
The amount that would be in the retirement account when you retire is $345,418.50.
The amount of money that you put in the account is $162,504.
The amount of money that the employer put in the account is $162,504.
The interest that was gained over the years is $20,410.50.
3% of the salary is $183.
The total amount that would in the retirement account in the account each month is $366.
The amount that would be in the retirement account when you retire is $172,709.25.
The amount of money that you put in the account is $81,252
The amount of money that the employer put in the account is $81,252
The interest that was gained over the years is $10,205.25.
How much would be in the retirement account?6% of the salary = salary x percentage
6% of the salary = 6% x $6,100
6% of the salary = 0.06 x $6,100 = $366
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $366 + $366 = $732
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $732 x 12 x (62 -25)
$732 x 12 x 37 = $325,008
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $345,418.50
Amount the employer put in the account = $325,008 \ 2 = $162,504
Interest earned = $345,418.50 - $325,008 = $20,410.50
3% of the salary = salary x percentage
3% of the salary = 3% x $6,100
3% of the salary = 0.03 x $6,100 = $183
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $183 + $183 = $366
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $366 x 12 x (62 -25)
$366 x 12 x 37 = $162,504
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $172,709.25
Amount the employer put in the account = $162,504 \ 2 = $81,252
Interest earned = $172,709.25 - $162,504 = $10,205.25
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identify the part of following expression 4x-2y + 6/ 2x
Coefficients:
Constants:
Variable Terms:
Like Terms:
identification of the expression 4x- 2y + 6 = 2x is
Coefficient: 4, -2, 2Constant: 6Variable term: 4x, -2yLike terms: 4x and 2xWhat is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, a linear expression 4x-2y + 6 = 2x
Coefficient:
Coefficients are the numbers by which the variables in an equation are multiplied
Thus, the Coefficient terms for this equation = 4x, -2y, 2x
Constants:
the constant is the part of the expression that does not vary with the value of x and y.
Thus, constant terms for this equation = 6
variable terms:
These are the terms that vary at the different values of x and y.
Thus, variable terms for this equation = 4x, -2y
Like terms:
Terms that have identical variable parts (same variable(s) and same exponent(s))
thus, Like terms for this expression = 4x, 2x
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Please Click The Screenshot.
Answer:
Step-by-step explanation:
70%=0.7
90 X 0.7 = 63
ANSWER IS 63
in the xy-plane what is the y-intercept of the graph of the equation y=(x-2)^2?
As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
what is equation ?The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two collinear and an equal marker in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). An identity holds true regardless of the value given to the variables.
given
Equation as given:
y = 6 (x - 1/2)(x+3)
To identify the equation's graph's y-intercept
Put x = 0 in place of it in the equation.
y = 6 (0 - 1/2)(0+3)
Apply the math operation, then find y.
y = -9
As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
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Which of these ratios are equivalent? Choose all that apply.
1) 16:4
2) 2:1
3) 32:2
4) 480:120
5) 4:16
6) 4:1
The ratios which are equivalent are as follows:
1) 16:4
4) 480:120
6) 4:1
Step-by-step solution:
1) 16:4
[tex]=\frac{16}{4}[/tex]
[tex]=\frac{4}{1}[/tex]
4:1
2) 2:1
[tex]=\frac{2}{1}[/tex]
2:1
3) 32:2
[tex]=\frac{32}{2}[/tex]
[tex]=\frac{16}{1}[/tex]
=16:1
4) 480:120
[tex]=\frac{480}{120}[/tex]
[tex]=\frac{4}{1}[/tex]
=4:1
5) 4:16
[tex]=\frac{4}{16}[/tex]
[tex]=\frac{1}{4}[/tex]
=1:4
6) 4:1
[tex]=\frac{4}{1}[/tex]
=4:1
Therefore, the correct solution to this question is:
1) 16:4
4) 480:120
6) 4:1
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Answer:
16:4 and 480:120 and 4:1 are equivalent.
Step-by-step explanation:
Nina uses 2/3 cup peanuts, 1/2 cup cashews, 3/4 cups pecans, and some raisins in a recipe that makes 2 1/4 cups of trail mix. How many cups of cashews are there per cup of trail mix?
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
1/2 ÷ 2 1/4
1/2 ÷ 9/4
1/2 x 4/9 = 4/18 = 2/9
question 12 to find the shaded portion
12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.
9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,
= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].
= [8×8 - 4×4] cm².
= 64 - 16 cm².
= 48 cm².
10. Similarly the figure in (10) is twice the area of the two trapezoids.
11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.
12. The total area is the sum of the areas of the trapezoid and the parallelogram.
13. The larger figure is a rectangle with a right-angle triangle on top.
We have to subtract two rectangles from this to obtain the area of the shaded region.
14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.
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ASAP! PLEASE HELPP!!
SHOW ALL WORK PLS
Answer:
(a, b, c) = (-3, -2, -4)
Step-by-step explanation:
You want to solve the system of 3 equations in 3 variables shown in the attached figure.
SolutionThe easiest solution is one provided by a suitable calculator (attached). It tells you ...
a = -3b = -2c = -4The "work" is entering the problem into the calculator.
Ad hocWe notice the sum of 'a' coefficients is zero, so we can add the three equations to get ...
(4a +5b -6c) +(-3a -2b +7c) +(-a +4b +2c) = (2) +(-15) +(-13)
7b +3c = -26 . . . . . simplify
Multiplying the third equation by 4 and adding that to the first equation gives ...
4(-a +4b +2c) +(4a +5b -6c) = 4(-13) +(2)
21b +2c = -50 . . . . . simplify
Now, we have two equations in two unknowns.
Multiplying the first equation above by 3 and subtracting this last equation eliminates the b term to give ...
3(7b +3c) -(21b +2c) = 3(-26) -(-50)
7c = -28 . . . . . simplify
c = -4 . . . . . . . divide by 7
Using this in the first "ad hoc" equation, we can find b:
7b +3(-4) = -26
7b = -14 . . . . . . . . add 12
b = -2 . . . . . . . . divide by 7
And the values of b and c can go into the last of the original equations to give ...
-a +4(-2) +2(-4) = -13
-a = 3 . . . . . add 16
a = -3 . . . . . multiply by -1
The solution is (a, b, c) = (-3, -2, -4).
__
Additional comment
The given solution is "ad hoc" because we decide how we're going to approach the solution based on the coefficients we see. Here, we are solving by "elimination," performing as little arithmetic as possible.
The third equation suggests we could make a substitution for 'a':
a = 4b +2c +13
That substitution would give a different set of equations in 'b' and 'c' than the ones shown above.
The second attachment shows a graphical solution to the system. It shows (a, b, c) = (-3, -2, -4). The graphing program requires the use of x and y instead of 'a' and 'b' for the variables.
Four methods of solving the system have been described. Take your pick. The calculator solution was the easiest, requiring each number to be entered once.
3 ratios that are equivalent to 15/40
Answer:
3.8 ,6.16 , 9.24
Step-by-step explanation:
What is statistics. Explain?
The science of statistics focuses on creating and researching strategies for gathering, analysing, interpreting, and presenting empirical data.
Research in statistics finds application in almost all scientific domains, and research concerns in the various scientific fields inspire the creation of new statistical methods and theories. Statistics is a very interdisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the theory that supports such methods. Uncertainty and variation are two key concepts in the study of statistics. In science, as well as more generally in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air. Probability is a mathematical language that is used to talk about uncertain events, and it is crucial to statistics. There are numerous causes of variance that can affect any measurement or data collection attempt. By this, we indicate that the result would probably alter if the same measurement was repeated. The goal of statisticians is to comprehend and, whenever feasible, manage the sources of variation.
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Someone HELPPppp for tmr
Answer:
y=1x-6
Step-by-step explanation:
First we find the slope by using rise over run. So you can either count up and over(rise/run) or use the slope formula y2-y1/x2-x1. You will find that the slope is 1, so plug that into the equation for mx. So we have y=1x so far. Then we find the y-intercept by looking where the graph intersects the y-axis. As you can see it intersects at -6, so plug -6 into the equation for b. No we have our full equation of y=1x-6.
-Hope this helped
I have a question which says:
Increase 32 by 4.4%
Answer:
increase amount = 32× 4.4%
= 32 × 4.4 ÷ 100
= 32 × 44 ÷ 1000
= 1.408
32 increased by 4.4% = 32 + 1.408 = 33.408
A chef makes small and large snacks to sell at a local art show. He cannot make more than 30
snacks before the show, with no more than 6 large snacks. The chef must make at least 10 small snacks to
earn a profit.
Part A
Let x represent the number of small snacks and y represent the number of large snacks. Given x ≥ 0 and
y 20, select all the inequalities that represent the situation.
0 x≤6
O y ≥ 10
Ox+y≤ 30
O 10x+6y≤ 30
0y≤6
0 x ≥ 10
-01:25
the inequalities that represent the situation are,
Ox+y≤ 30
0y≤6
0 x ≥ 10
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
Here, given that,
A chef makes small and large snacks to sell at a local art show.
He cannot make more than 30
snacks before the show, with no more than 6 large snacks.
The chef must make at least 10 small snacks to earn a profit.
Let,
x represent the number of small snacks
and y represent the number of large snacks.
Given x ≥ 0 and y 20
So, we get,
the inequalities that represent the situation are,
Ox+y≤ 30
0y≤6
0 x ≥ 10
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Does the table below represent a proportional relationship? DUE PLSS
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
Answer: The answer to your question is the letter B. May want to assess it before answering.
Identify each angle pair as Complementary, Supplementary, Adjacent, or Vertical. Select from the drop
down menu. Select the most specific choice.
Answer:
A. Adjacent
B. Complementary
C. Complementary
Step-by-step explanation:
Let a = (2, 1, 0), b = (3, -1, 2), c = (4, 0, 3).
Calculate the angle between a and the plane containing b and c.
Extra effort to show working will be awarded the brainliest.
The volume of the parallelopiped is 14 cubic units
What is the volume of a parallelopiped?The volume of a parallelopiped with vector sides a, b and c is given by
V = (a × b).c
We know that the parallelopiped has sides
a = (2, 1, 0)b = (3, - 1, 2) and c = (4, 0, 3)Thus, we proceed as follows
(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k
Since
i × i = 0, j × j = 0, k × k = 0, i × j = k, j × i = -k, j × k = i, k × j = -i, k × i = j, i × k = -j,So, we have
(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0
= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0
= 5i -7j - 2k
= (5, -7, -2)
Since (a × b) = (5, -7, -2)
Thus, the volume of the parallelopiped is
V = (a × b).c
= (5, -7, -2).(4, 0, 3)
= 5 × 4 + (-7 × 0) + (-2 × 3)
= 20 - 0 - 6
= 14
So, the volume is 14 cubic units
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9x+12y=-108 Please solve this, but it cannot be in fraction form!!!
All you have to do is solve this by using substitution or elimination. or in this case, because we don’t have a second equation, we would solve the x-intercept and y-intercept
X=-12
Y=-9
please help!
Use the Fundamental Counting Principle to determine how many kinds of teddy bears you can build if you must choose one of each category.
1) Choose the bear.
2) Choose an accessory.
3) Choose sound option.
Answer:
Step-by-step explanation:
33
"what is the median of the following values 9,9,2,8,11,6,4"
Answer: 8
Step-by-step explanation:
Arrange the data in ascending order, and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
Rearrange 9, 9, 2, 8, 11, 6, 4 in ascending order:
2, 4, 6, 8, 9, 9, 11
The number eight appears to be in the very middle, therefore it is the median.
Tell whether the angles are complementary or supplementary. Then find the value of x.
The angles add up to 180° so the angles are supplementary.
The value of x is 31.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
From the figure,
Two angles:
3x + 25 and 2x
These two angles form a straight angle.
Now,
3x + 25 + 2x = 180
5x = 180 - 25
5x = 155
x = 31
When the sum of two angles is 90°, then the angles are known as complementary angles.
When the sum of two angles is 180°, then the angles are known as supplementary angles.
Now,
3x + 25
= 3 x 31 + 25
= 93 + 25
= 118
2x
=2 x 31
= 62
Now,
118 + 62 = 180
Thus,
The angles are supplementary.
The value of x is 31.
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Victoria needs to earn at least an 85 in College Algebra. Only exam scores are used to calculate her grade. Currently she has scored an 82, 81, and 90 this semester. All that remains is the semester exam, which counts twice (counts as two exam grades). She hopes to make an 85 or higher in the class.
She would need to make two extra grades of 86 each.
What is the average?Here we can see that the average of the scores that Victoria would need to make is an average score of 85 so as to be able to pull through. In this case, we can see that we have the scores; 82, 81, and 90
Let the scores tat we have to count twice be p each and then we have;
85 = 82 + 81 + 90 + p + p/5
85 = 253 + 2p/5
5(85) = 253 + 2p
p = 5(85) - 253/2
p = 86
Hence, the twice scores that need to be earned for Victoria are both 86.
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least common number
( sorry i forgot what its called )
of 598 and 45
The least common multiple of 598 and 45 is 26, 910
How to find the least common multiple ?To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.
This gives:
598 prime factorization :
2 x 13 x 23 = 598
45 prime factorization :
3 x 3 x 5 = 45
The least common multiple is;
= 2 x 13 x 23 x 3 x 3 x 5
= 26, 910
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renee spent 1/8 of the day landscaping around the house. she spent 1/2 of that time pulling weeds. what fractions of the day did renee spend pulling the weed? PLS HELP IM HAVING A UNIT TEST ON MONDAY
Answer:
Renee spent 1/2 of the time she spent landscaping pulling weeds, which is 1/2 * 1/8 = 1/16 of the day. Therefore, Renee spent 1/16 of the day pulling weeds.
Britney bought 4 apples, 5 bananas, and 8 oranges at the grocery store.
Which is the ratio of apples to oranges written as a decimal?
A.
1.6
B.
0.4
C.
0.8
D.
0.5
Answer:
Step-by-step explanation:
The question asks for apples to oranges.
So put the number of apples as a numerator and the number of oranges as a denominator. Simply put 4 on top and 8 on the bottom:
4/8 then divide: 4 divided by 8 = .5
There is the ratio as a decimal.
0.5
Option D
An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
To summarize the situation, a worker writes the inequality:
10c+20s≤4,000 where c is the number of ounces of copper material and s is the number of ounces of silver material.
Which graph's shaded region shows the possible combinations of raw materials the company can buy?
The given graph's shaded region shows the possible combinations of raw materials the company can buy.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
An electronics company can spend no more than $4,000 on raw materials for circuit boards.
And, The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
Here, The inequality for the given condition is,
⇒ 10c + 20s ≤ 4,000
Where, c is the number of ounces of copper material and s is the number of ounces of silver material.
So, The given graph's shaded region shows the possible combinations of raw materials the company can buy.
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A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. Write and solve a system of equations to find the family’s paddling speed in still water. Let s equal the families paddling speed and c represent the current
a.
s + c = 2.75
s - c = 1.5
2.125 mi/h
c.
s + c = 2.75
c - s = 1.5
.60 mi/h
b.
2.75s = c
1.5s = c
1.725 mi/h
d.
2.75c = s
1.5c = s
30 mi/h
On solving the provided question, we can say that In still water, a family must paddle at a speed of 2.125 miles per hour.
What is speed?Speed is the amount of distance traveled by an object in one unit of time when it is in motion.
Given that, a family is paddling a boat (with the current). Their average speed in relation to the riverbanks is 2.75 miles per hour. On the way back, they paddle upstream (against the current), moving toward the riverbank at an average speed of 1.5 miles per hour.
Here, Let the family's speed on still water be x and the current's speed be y. Upstream speed is calculated using the formula 1.5 = x - y - - - - (1)
2.75 downstream speed = x + y - - - - (1)
Equations 1 and 2 are solved as follows: 2x = 4.25 and x = 2.125 miles per hour In still water, a family must paddle at a speed of 2.125 miles per hour.
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A pet shelter has 5 cats and 9 dogs.
Enter the ratios in the boxes.
ratio of cats to all animals:
ratio of dogs to cats:
The ratio of cats to all animals is 5:14
the ratio of dogs to cats is 9:5
Given-
Cats = 5
Dogs = 9
Total animals = cats+ Dogs
5+9=14
so the ratio of cats to all animals = 5: 14
and dogs to the cats= 9:5
Ratio give the relation between quantities of to identies.
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Find the measure of angle A,
The value of the Angle A is 74.3°.
What is Relation between angle and Side of a triangle?The longest side is in opposition to the longest angle, and the shortest side is in opposition to the smallest angle, respectively.
The opposite of the longest side is the greatest angle, while the opposite of the shortest side is the smallest angle. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.
The comparable sides are proportionate and the angles are same. The sides that are opposite the same angle are the corresponding sides. For instance, if two triangles have a 90-degree angle on each side, Triangle A's opposing side will match Triangle B's opposite side.
We know:-AB/sin(c)=AC/sin(a)=BC/sin(b)
8/sin(a)=5/Sin37°
Angle= 74.3°.
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Solve the following mentally 65% of 100
Answer: 65
Step-by-step explanation:
Kana tried to solve the system of equations below. She says there are no solutions. Is Kana correct? Explain your reasoning.
The solution for the given system of equations:
x = 6 and y = 6.
Kana is incorrect about the solutions of the given equations.
What are algebraic properties?Algebraic expressions and equations follow the same set of rules as numerical expressions and equations. The order of operations is preserved, and the laws governing addition and multiplication still apply.
Associative: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c
Identity: a + 0 = a , a ⋅ 1 = a
Inverse: a + ( − a ) = 0 , a ⋅ 1 a = 1
Distributive: a ( b + c ) = a b + a c
Given equations,
4x-2y=12 -----(a)
2x+2y=24 -----(b)
Multiplying -2 to the equation (b) like kana solution
-2 (2x+2y=24 )
By Distributive property
-2(2x+2y) = -2(24)
- 4x - 4y = - 48 ---------(c)
Now adding equation (a) and equation(c)
4x - 2y = 12
- 4x - 4y = - 48
__+___+____+__
- 6y = -36
⇒ y = 36/6 = 6.
Putting value of y in equation (b).
2(x) + 2(6) = 24
2x + 12 = 24
2x = 24 - 12
2x = 12
x =12/2 = 6
By the above calculation,
Value of x = 6 and
value of y = 6.
Hence, for the system of equations given
the solutions are:
x = 6 and y = 6
which proves that Kana is incorrect that there are no solutions.
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