Systems of equation that have the same solution are called equivalent systems.
Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.
In contrast, we can be sure that two systems of equations are not equivalent if we know that a solution of the one is not a solution of the other.
Note: This idea of equivalent systems of equations pops up again in linear algebra. However, the examples and explanations in this article are geared to a high school algebra 1 class.
Example 1
We're given two systems of equations and asked if they're equivalent.
System A
−12x+9y=7
9x−12y=6
system B
−12x+9y=7
3x−4y=2
If we multiply the second equation in System B by 3, we get:
3x−4y=2
3(3x−4y)= 3(2)
9x−12y=6
Replacing the second equation of System B with this new equation, we get an equivalent system:
−12x+9y=7
9x−12y=6
Whoa! Look at that! This system is the same as System A, which means system A is equivalent to System B
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Which ordered pairs make the open sentence true?
4x+y>9
Answer:
Step-by-step explanation:
let x = 5, y = 0
so the equation is 4x+y>9
and put the value of x and y in the equation
4 (5) + 0 > 9
20 + 0 > 9
20 > 9, therefore the order pair ( 5,0) satisfies the condition. true
Two shops rent kayaks for a rental fee plus a fee per hour. How many hours must a kayak be rented for the total costs to be the same? Shop A Rental fee: $8 Hourly fee: $3 Shop B Rental fee: $3 Hourly fee: $4 The total costs are the same when a kayak is rented for hours.
The total costs are the same when a kayak is rented for 5 hours
How do we determine the hours that both have the same costs?
The hours that both shops have the same cost is determined by equating the total cost in shop A to the total cost in shop B, in short, we need to first of all , model the total cost in each shop based on the straight-line equation formula shown below since the total cost is made of fixed charge and variable charge
y=a+bx
y=total cost
a=fixed charge for each shop
b=hourly fee
x=number of hours
Shop A:
total cost=8+3x
Shop B:
total cost=3+4x
8+3x=3+4x
8-3=4x-3x
5=x
At 5 hours both Shops A and B would have the same cost
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The hours when the cost of renting the kayaks would be the same is 5 hours.
The total cost of renting a kayak is $23.
When would the total cost be equal?The equation that can be used to represent the total cost of renting a kayak is a linear function. A linear equation is an equation whose graph is a straight line. A linear equation increases by a predetermined constant. An example of a linear equation is x + 2.
The form that the equation would be is:
Total cost = rental fee + (hourly fee x number of hours)
Total cost at Shop A = $8 + $3h
Total cost Shop B = $3 + $4h
Where h is the number of hours the kayak was rented.
When the total costs are equal, the two above equations would be equal.
$3 + $4h = $8 + $3h
Combine similar terms: $4h - $3h= $8 - $3
Add similar terms together: h = 5 hours
Total cost = $3 + $4(5)
$3 + $20 = $23
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Directions: Determine whether each relation is a function. Explain your answer.
7) No, y has two different values when x = -1.
8) Yes, each value of x maps onto only one value of y.
9) Yes, each value of x maps onto only one value of y.
Find how long it takes a person to drive 212 miles on a highway if she merges onto a highway at 6 p.m. and drives nonstop with her cruise control set on 80 mph.
Margo borrows $800 agreeing to pay it back with 8% annual interest after 8 months. how much interest will she pay?
Answer:
43
Step-by-step explanation:
800 × 8% × (8/12)
whats 9 and 4 exponent time negative 1/3 and 4 exponent?
1. 1.371742E−3
2. 256 .
What is an Exponent?
An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 2³) means: 2 x 2 x 2 = 8.
It is written as a small number to the right and above the base number.
Here in the question we find out (9)∧-3 and (4)∧4
1. (9)∧-3 =x∧n=9−1
x∧n=9-³
=1/9³
=1/9×9×9
=1/729
=0.0013717421124829
=1.371742E−3
2. (4)∧4 =x∧n=4∧4
=4×4×4×4
=256
The meaning of exponent is a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power.
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Tutorial D
If x = 0 and y < 0, where is the point (x, y)
located?
◄))
on the x-axis
on the y-axis
Verify that y=e^xy is an implicit solution of the differential equation (1-xy)y'=y^2
Yes, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
Here,
The differential equation (1-xy)y' = y^2
And, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2.
What is Differential equation?
A differential equation is a mathematical equation that relates some function with its derivatives.
Now,
To show y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2, we have to find the solution of differential equation.
The differential equation is;
[tex](1-xy)y'=y^2\\\\\\\\[/tex]
[tex](1-xy) \frac{dy}{dx} = y^2[/tex]
[tex]\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }[/tex]
It is form of [tex]\frac{dx}{dy} + Px = Qy[/tex],
Where, P is the function of y and Q is the function of x.
Hence, Integrating factor = [tex]e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y[/tex]
The solution is;
[tex]x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c[/tex]
[tex]xy = lny + c[/tex]
Take c = 0, we get;
[tex]xy = lny\\\\y = e^{xy}[/tex]
Hence, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
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square root method 5x+9=134
Answer:
Step-by-step explanation:
What are you trying to find? If you want to find x then:
5x = 134 - 9
5x = 125
x = 25
if you want square root then,
x = √625 or
x = 5^2
#12: m∠GKH = ____
need the answer
YALL IS ANYONE WILLING TO SOLVE MATH?
Answer:
A = 1160
B = 1160 is already in standard form.
C = 1200
6 minus a number minus 11
Answer:
In equation form it should be: (6-x) -11
Step-by-step explanation:
BOOM!!! Your Welcome
11. Suppose you write and solve an equation to determine the amount of money m you have in your bank
account after several weeks. You find that m = -36. Choose any of the following interpretations of this
value which are correct.
The bank owes you $36.
The account has a balance less than $0.
You overdrew on the account by $36.
The account has a positive balance.
Answer:It means you would have spent $36 below zero and now you owe the bank some money
Step-by-step explanation:
Givin g(x) = -x+4, solve for x when g(x)= 0
Answer:
x = 4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
I got you bro dont worry
point b is between A and C. if AC = 3x+3, BC = 2x-1, and AB = 11. Find the length of BC
==================================================
Work Shown:
AB+BC = AC
(11) + (2x-1) = 3x+3
2x+10 = 3x+3
2x-3x = 3-10
-x = -7
x = 7
which is then use to find:
BC = 2x-1 = 2*7-1 = 13AC = 3x+3 = 3*7+3 = 24As a check,
AB+BC = 11+13 = 24 = AC which confirms the answer.
A car travels 100 meters in 5 seconds. What is the speed of the car?
speed = distance over time; 1 mile = 1609 meters
Answer:
20 m/s
Step-by-step explanation:
speed = 100m /5s = 20 m/s
= 72 km/hr
= 72 km / hr * 1 mile / 1.609 km = 44.7 mph
Find the slope of the line passing through the points (7, -2) and (7,5).
slope:
Answer: the slope=0
Step-by-step explanation:
[tex]\displaystyle\\(7,-2)\ and\ (7,5)\\[/tex]
[tex]\displaystyle\\\boxed {the \ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]
[tex]x_1=7\ \ \ \ \ x_2=7\ \ \ \ y_1=-2\ \ \ \ \ y_2=5\\Hence,\\\displaystyle\\the slope=\frac{7-7}{5-(-2)} \\\\the\ slope=\frac{0}{5+2} \\\\the\ slope=\frac{0}{7}\\\\ the\ slope=0[/tex]
Jason is collecting coins from different countries around the world. He currently has coins from 99 countries and plans to add 4 new countries to his coin collection each week. At this rate how many weeks (w) will it take Jason to have coins from all 195 countries?
Equation:
Solution:
Final Answer:
???
The number of weeks that it will take Jason to have coins from all 195 countries is 24 weeks.
How to calculate the equation?It should be noted that an equation is simply used in Mathematics to show the relationship the exist between different variables.
Let the number of weeks be represented by w.
Therefore, based on the information, the appropriate equation will be:
99 + (4 × w) = 195
99 + 4w = 195
4w = 195 - 99
4w = 96
Divide
w = 96/4
w = 24
Therefore, based on the calculation illustrated above, the number of weeks that it will take Jason to have coins from all 195 countries is 24 weeks.
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The graph shows the relationship between miles and kilometres.
a)
Convert 20 miles
to km.
b)
Convert 64 km
to miles.
By cross multiplication, we have found the following results:
a) 20 miles are equal to 32.180 kilometers.
b) 64 kilometers are equal to 39.776 miles.
How to convert a distance value into another distance unit
In this problem we must convert a given value in a unit into its equivalent quantity in another unit of same kind. We must convert miles to kilometers and viceversa by using conversion rates and cross multiplication.
First, we must convert a distance of 20 miles to kilometers by cross multiplication:
x = 20 mi × (1.609 km / 1 mi)
x = 32.180 km
Second, we must convert a distance of 64 kilometers to miles by cross multiplication:
x = 64 km × (1 mi / 1.609 km)
x = 39.776 mi
RemarkThe graph is missing, but this question can resolved by using conversion rates, that is, a mile equal 1.609 kilometers.
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Answer:
here is the answer⬇️
If the equation ax = b is consistent, then its solution set is obtained by translating the solution set of ax = 0. true or false?
True, ax=b requires only one solution to be homogeneous. If ax=b is consistent, the ax=b solution set is acquired by translating the ax=0 solution set.
What is consistent?A two-linear equation system can have one solution, an infinite number of solutions, or even no solution. The number of solutions distinguishes equation systems.
Some key features regarding the consistent are-
A system is said to be consistent if it has at least one solution.A consistent system is independent if it has exactly one solution.It is dependent if a consistent system does have an infinite number of solutions. When the equations are graphed, they constitute the same line.A system is considered to be inconsistent if it has no solution. Because the line graphs do not intersect, the graphs are parallel, and that there is no solution.Therefore, if the equation ax=0 has a trivial solution, the columns of the a matrix A are linearly independent.
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Find the exact equation of the function graphed to the right. Show your work. Vertex: (-2,4) x intercepts:(-5,0) (1,0) y intercept (0,2)
The equation for the parabola Is; y = -²/₅[(x + 5)(x - 1)]
How to Interpret a Quadratic Graph?
We are given the following;
x-intercepts = (-5,0) and (1,0)
y - intercept = (0, 2)
We know that the x-intercepts are the roots of the quadratic equation while the y-intercept is the value of y when x is zero.
Thus;
(x + 5) and (x - 1) are factors of the given quadratic equation.
f(x) = a(x + 5)(x - 1)
At y-intercept of (0,2), we have;
a(0 + 5)(0 - 1) = 2
a = -2/5
Thus we can write the equation for the parabola as;
y = -²/₅[(x + 5)(x - 1)]
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one of the subsets of set n and set g is a Ø true or false?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
An empty set is subset of each and every possible set, as it has no elements in it, which is why the given statement is " True "
The graph of F(x), shown below, has the same shape as the graph of G(x) = x2, but it is shifted to the left 2 units. What is its equation? F(x) = _____ A. F(x) = (x - 2)2 B. F(x) = x2 + 2 C. F(x) = x2 - 2 D. F(x) = (x + 2)2
The transformed equation is:
F(x) = G(x + 2) = (x + 2)^2
So we can se that the correct option is D.
What is the equation?We know that the graph of F(x) has the same shape of G(x) = x^2, but shifted to the left 2 units.
Remember that for a random function f(x), a shift of 2 units to the left is written as:
h(x) = f(x + 2).
Then, in this case, we can write:
F(x) = G(x + 2)
Replacing G(x), we can get the transformed equation:
F(x) = G(x + 2) = (x + 2)^2
So we can se that the correct option is D.
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What is the surface area of a igloo with a 20 ft. diameter
The surface area of a igloo with a 20 ft. diameter is [tex]628ft^{2}[/tex]
According to question statement, we are supposed to find the surface area of an igloo with a 20ft. diameter.
Before solving this question, we should be aware of the fact that an igloo is of a Hemispherical shaped object usually made up of ice.
So for finding out area of igloo we find the surface area of of the hemisphere.
Curved Surface area : [tex]2\pi r^{2}[/tex]
Total Surface area: [tex]3\pi r^{2}[/tex]
where r is the radius of igloo.
Radius is half of the diameter therefore [tex]r=\frac{diameter}{2}[/tex]
[tex]r=\frac{20ft}{2} \\r=10ft[/tex]
Therefore radius is 10 ft.
Curved Surface Area: [tex]2*3.14*10^{2} =628ft^{2}[/tex]
Total Surface Area: [tex]3*3.14*10^{2} =942ft^{2}[/tex]
But as we are supposed to find the surface area therefore the answer is [tex]628ft^{2}[/tex].
Hemisphere: A hemisphere is a 3-Dimensional figure which is obtained by bisecting a sphere into two equal halves through its diameter.If you want to learn more about surface areas, click on the link given below:
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6/X + 9 if x = 3
pls help me
answer:
6/x + 9 = 11
explanation:
6 div. 3= 2
2+9=11
12. −7.5 • −2³/4
19
Answer:
-9.5
Step-by-step explanation:
X - 2(X + 10) = 12
What is this??!?!!?
Answer:
-32
Step-by-step explanation:
Pal, it's M A T H
Answer:
-32
Step-by-step explanation:
x-2x-20=12
-x=32
x=-32
.....................
A student increased in height from 1.52m to 1.68m, calculate the percentage increase (show your working)
The percentage increase in the student's height is 10.52%.
Here we are given that a student's height increases from 1.52m to 1.68m.
Thus, the absolute increase in the student's height will be-
1.68 - 1.52 = 0.16 meters.
Now, we need to find the percentage increase in the student's height.
The formula for calculating percentage increase is given by-
Percentage increase = change in value/ initial value * 100
Here, the change in value is 0.16 meters and the initial value is 1.52 meters.
Thus, percentage increase in height = 0.16 / 1.52 *100
= 1600/ 152
= 400/ 38
= 200/ 19
= 10.52%
Thus, the increase in the student's height is 10.52%.
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How many 1/2's are there in 6?
Answer:
12
Step-by-step explanation:
There are 12 1/2's in 6.
To find how many 1/2's there are in 6, you have to divide 6 by 1/2.
6 ÷ 1/2
To divide by a fraction, you have to multiply by the reciprocal (reverse the numerator and denominator of a fraction).
6/1 × 2/1
6 × 2
= 12
Have a lovely rest of your day! :)
4 less than a number n is −15 in eqation form
Answer:
n - 4 = - 15
Step-by-step explanation:
Hope this helps :)