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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of the 60 seeds you plant, 80% germinated. How many seeds germinated?
-For 11 points
Answer:
48 seeds germinated
Step-by-step explanation:
you have 60 seeds, and 80% of them germinated
80% = 0.80
[tex]60* 0.80 = 48[/tex]
48 seeds
Answer: 48 seeds germinated
Step-by-step explanation:
60/100= 0.6
0.6x80=48
Your friend
participates in a 3.1-mile race. She
walks for 1.4 miles of the race and runs
the rest. About how many miles does
your friend run
1.7 miles, just do the total amount of what can be considered distance, then minus what she walked, resulting in the answer to be the amount of time ran.
You roll two (standard, six-sided) dice. What is the probability that you do not roll "double sixes"?
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working alone, stefan can tar a roof in 17
hours. jaidee can tar the same roof in 18
hours. find how long it would take them
if they worked together.
round your answer to the nearest hundredth and include your units.
Stefan take 17 hours and Jaidee 18hours ,time taken by both of them if they work together is equal to 8.74 hours.
As given,
Time taken by Stefan 17 hours
work in 1 hour = 1/ 17
Time taken by Jaidee = 18 hours
work in 1 hour = 1/18
If worked together:
Work complete in 1 hour = (1/17) + (1/18)
= 35 / (17)(18)
Time taken to complete 1 work= (17)(18) /35
= 8.74 hours
Therefore, ,time taken by both of them if they work together is equal to 8.74 hours.
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answer plsss rn !!!
an equation will not pass through the origin if:
Answer:An equation will not pass through the origin if the points are 0,0.
Summarize the three conditions that must be checked before carrying out significance tests.
We introduced three conditions that should be met before we construct a confidence interval for an unknown population proportion: Random, Normal, and Independent.
What is random, normal and independent conditions?There are three crucial requirements that must be met in order to establish a confidence interval. These are Independent, Random, and Normal.
Any survey is carried out objectively.
It is required to assure randomness. An independent choice is equally likely to be made in a random sample. Similar to how the confidence interval is built, normal is used to confirm which phenomena are being employed or to correct the approach if necessary. In a similar vein, independent is crucial because it contains the facts to be analyzed. For the purpose of calculating the standard deviation, independent is used.
Therefore, it's crucial to consider the Random, Normal, and Independent criteria while building a confidence interval.
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Write a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.
Float rate_of_pay a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.
What is float rate_of_pay?
In contrast to fixed (or unchangeable) interest rates, floating interest rates change on a regular basis. Companies that offer credit cards and mortgages frequently use floating rates. Floating rates follow the market, a benchmark interest rate, an index, or both.Is a fixed or floating rate preferable?
In a rising rate environment, banks offer fixed rate loans at a higher rate than variable rate loans in order to profit more from the latter when rates rise. Fixed rate loans may have interest rates that are 300–350 basis points higher than floating rate loans.float rate_of_pay
rate_of_pay = 11.50, 12.75;
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Someone please help for 15 points!!!
Answer:
With what nothing there
Step-by-step explanation:
Lola has 4 1 2 cups of rice. she uses 3 4 of the rice to make sushi rolls for dinner. she uses the rest of the rice to make rice pudding for dessert. how much rice does lola use for the rice pudding?
Lola used 15/4 or [tex]3 \frac{3}{4} [/tex] cups of rice for pudding.
Amount of rice Lola has = [tex]4 \frac{1}{2} [/tex] cups
Converting from mixed fraction to improper fraction
Amount of rice Lola has = (2×4 + 1)/2
Amount of rice Lola has = 9/2 cups
Now, to find the amount of rice used for rice pudding, we will simply subtract the rice left with her after being used for sushi rolls.
Amount of rice used for pudding = Amount of rice Lola has - Amount of rice used to make sushi rolls
Amount of rice used for pudding = 9/2 - 3/4
Performing subtraction to find the amount of rice used for pudding
Taking LCM we get 4
Amount of rice used for pudding = (9×2 - 3)/4
Amount of rice used for pudding = (18 - 3)/4
Amount of rice used for pudding = 15/4
In mixed fraction, the amount of rice used for pudding = [tex]3 \frac{3}{4} [/tex]
Hence, Lola used 15/4 or [tex]3 \frac{3}{4} [/tex] cups of rice for pudding.
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When you divide an even number by an even number, is the result always an even number
Answer: No, for example, 50/2=25, 25 isn't even
Step-by-step explanation:
Answer:
No, it's not
Step-by-step explanation:
when u divide an even number with even number,the ans maybe appear in even as well as odd number also
For e.g:
1. 36/12=3
2. 12/6=2
3. 30/6=5
4. 60/10=6
(-5a+6)(-4a+3)
Cannot be a fraction
Hey there!
To solve this problem, we will take a look at the FOIL Method.
What is "FOIL"?FOIL is a simple acronym that can be used to multiply binomials. It stands for:
F - Front
O - Outer
I - Inner
L - Last
See the image below for an example of how to use this in the given situation.
ApplyFront: Multiply the two terms out in the front.
[tex](-5a)(-4a) = 20a^2[/tex]
Outer: Multiply the two terms on the outsides.
[tex](-5a)(3)=-15a[/tex]
Inner: Multiply the two terms on the insides.
[tex](6)(-4a)=-24a[/tex]
Last: Multiply the two terms in the back.
[tex](6)(3)=18[/tex]
AddNow, we add all of our answers from above:
[tex]20a^2-15a-24a+18[/tex]
SimplifySimplify by combining like terms:
[tex]20a^2-39a+18[/tex]
There's our answer!
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help me with my little sister's homework I forgot how to do this.
Answer:
3
Step-by-step explanation:
9/3 = 3
b is 3 times more than a
a farmer places beehives containing bees in her orchard to pollinate the plants. The table below shows the ratio of the number of beehives to the number of acres in the orchard if the bees pollinate the plants at a constant rate, how many acres will be pollinated by the bees in 18 beehives
I don't know helpp me with the mathhh pleaseee
Step-by-step explanation:
T=CB-6, for C what is the answer pls my homework is due in 39 minutes
Step-by-step explanation:
if you did not leave anything out, all we can do is
T = CB - 6
T + 6 = CB
C = (T + 6)/B
Find the value of each variable.
2(5x − 5)°
20yº
(5y + 5)
(3x - 5)°
Answer:
The answer is 10 for your math equation
Step-by-step explanation:
The values of each variable are x = 15° and y = 7°.
Given are two lines, intersecting each other at a point to make angles,
2(5x − 5)°, 20y°, (5y + 5)° and (3x - 5)°.
We need to find the values of the variables.
The lines are intersected in such a way that the angles 2(5x − 5)°, (3x - 5)°and (5y + 5)°, 20y° are making linear pairs.
We know that the linear pair angles sum up to make 180°.
So,
2(5x − 5)° + (3x - 5)° = 180°
10x - 10 + 3x - 5 = 180°
13x - 15 = 180°
13x = 195°
x = 15°
Similarly,
(5y + 5)° + 20y° = 180°
5y + 5 + 20y = 180°
25y = 175°
y = 7°
Hence the values of each variable are x = 15° and y = 7°.
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Five Spanish friends are playing in a house. Cammy, Ann, Rake, Dora, Stephen. Cammy and Ann are playing Chess, while Rake and Dora are playing together. Then Stephen is playing by himself, which would mean he is playing One player games. Can you figure out which game they are playing?
Answer:
Step-by-step explanation:A. Solution:
So we know that Ann and Cammy are playing Chess, and Stephen is playing by himself, which would mean he is playing -ONE-player games. So we have Rake and Dora, when you see their names, it creates a word. Cammy, Ann, Rake, Dora, and Stephen.
C A R D S
So Rake and Dora are playing cards. But what kind of cards? The ONE is spotlighted for clues, we have Spanish. So -ONE- in Spanish is UNO. If you search UNO, its a card game, TAAAAADDDDDDDDDAAAAAAAAA.
A hiker first hiked down into a canyon 1,345 feet below sea level. She then hiked 950 feet up the side of a mountain. What was the final altitude of the hiker? Please explain
The final altitude of the hiker 395 feet.
How to compute the value?From the information, the hiker first hiked down into a canyon 1,345 feet below sea level and she then hiked 950 feet up the side of a mountain.
This will be:
= -1345 + 950
= 395
Therefore, the final altitude of the hiker 395 feet.
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(Crys) Im in 11 grade and in applied geometry I need help crys and how do you show
ur work for it ( crys)
Answer:
1. -2/3 3. -5/4 5. 3/2 FOR THE REST OF THE PARTS LOOK THROUGH THE EXPLANATIONS
Step-by-step explanation:
Before I start the workings, I'll give a little explanation on this topic.
So, the equation of a straight line is
y = mx + c
where x and y are any coordinates of any point on the line.
m is the gradient or slope
m can be calculated using 2 formulas,
formula 1: Rise/Run
where rise is the how much a graph goes upwards or downwards, if its upwards use positive integer and if its downwards use negative integer.
Run is how much a graph moves to the right or to the left, if it moves to the right is is positive, if it moves to the left it is negative.
Formula 2: (y2-y1)/(x2-x1)
the values of these are taken through any 2 coordinates on the line.
and c is the y-intercept(the point where the line crosses the y-axis.
MOVING TO ANSWERING NOW
1. Dotted points on the line are (1,0) and (4,-2)
Formula of slope,
U can use any of the 2 formulas given above
I'll show both for this question
m = (y2-y1)/(x2-x1) = (-2-0)/(4-1) = -2/3
OR
m = rise/run = where rise is -2 and run is 3 so -2/3
2. TRY DOING THIS ONE YOURSELF
For the next part I'll do 3 and 5 for your understanding, try doing 2 and 4 on your own to understand.
3. Coordinates given (13,1) and (1,16)
m = (y2-y1)/(x2-x1) = (16-1)/(1-13) = 15/-12 simplify this and it becomes -5/4
5. (-8,-14) and (-10,-17)
m = (y2-y1)/(x2-x1) = (-17-(-14))/(-10-(-8)) = -3/-2 = 3/2
FOR THE NEXT PART I'LL DO 7,8 AND 10 FOR YOU, TRY DOING 9 ON YOUR OWN FOR PRACTICE.
I WILL ALSO ATTACH FILES FOR THE NEXT PARTS IN ORDER OF QUESTIONS SO SEE THEM.
7. y = x + 3 this means y = 1x +3 which means:
1 is the gradient
3 is the y-intercept
so 1 as a fraction is 1/1 which means rise is one upwards and run is 1 to the right.
Now go to the graph on the y-axis and plot the point 3, (0,3) is your y-intercept. From their rise by one and run by one this will lead u to point (1,4)
Mark both these points and make a line through them.
8. x = -5
now look at this equation in the form of y = mx + c
0 = 1x + 5 the means y is 0 and it is already told in the question that x = -5
if u rearrange 0 = 1x + 5 it will give you x = -5
now when y is 0 x = -5 put a point on the coordinate (-5,0) and draw a vertical straight line.
10. y = (1/4)x - 1
slope is 1/4 which means rise is 1 and run is 4
y-intercept is -1
now go to y=-1 which is the coordinate (0,-1) and rise by one and run by 4, this will take u to the coordinate (4,0) now put a dot on both coordinates, connect them and put a line through them.
You are dealt one card from a standard 52-card deck. find the probability of being dealt in a queen? quiizlet
The probability of being dealt in a queen is 1/13.
What is probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.To find the probability:
Total number of cards = 52Number of cards om 52 deck of cards = 4So, P = favourable events / total number of eventsThen, P = 4/52Probability = 1/13Therefore, the probability of being dealt in a queen is 1/13.
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Which relation(s) is/are not a function?
A (-4, 6), (0, 6), (7, 6), (4, 6), (-3, 6)
B (6,-4), (6, 0), (6, 7), (6, 4), (6, -3)
C (4, 1), (8, 2), (12, 3), (16, 4), (20, 4)
D (1, 4), (2, 8), (3, 12), (4, 16), (4, 20)
Answer:
B.
Step-by-step explanation:
B is not a function because it has a duplicate x value. Any function that has the same x value makes it automatically not a function.
A triangle has sides measuring 2.5x cm, 3x cm, and (2x+3) cm. the perimeter measures 60 cm.
The value of x is 7.6cm and the sides of the triangle are 19cm, 22.8cm and 18.2cm
Perimeter of triangle
The perimeter of a triangle is defined as the total length of its boundary.
The formula for the perimeter of a scalene triangle is
Perimeter = a + b + c,
where
"a", "b", and "c" are the three different sides.
Given,
A triangle has sides measuring 2.5x cm, 3x cm, and (2x+3) cm.
The perimeter measures 60 cm.
Here we need to find the value of x and the sides of the triangle.
Let the values of
a = 2.5x cm
b = 3x cm
and
c = (2x+3) cm
Then,
Apply the values on the formula for perimeter,
Then we get,
=> P = (2.5x) + (3x) + (2x +3)
=> P = 7.5x + 3
Now, apply the value of perimeter,
As P= 60,
Then.
=> 60 = 7.5x + 3
=> 7.5x = 60 - 3
=> 7.5x = 57
=> x = 57/7.5
=> x = 7.6
So, the sides of the triangle are,
a = 2.5x => 2.5 (7.6) = 19
b = 3x => 3(7.6) = 22.8
c = (2x+3) => 2(7.6) +3 = 15.2 + 3 = 18.2
Therefore, the sides of the triangle are 19, 22.8 and 18.2.
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Givien h(x)= 3x+1, solve for x when h(x) = 4
The value of x = 1 when the value of the function h(x) = 4.
What is a function?The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
Given that,
h(x)= 3x+1
The value of h(x) = 4:
4 = 3x + 1
4 - 1 = 3x
3x = 3
x = 1
Hence, the value of x = 1 when the value of the function h(x) = 4.
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Simplify by combining like terms. Write the answer with the variables in alphabetical order and any constant term last.
a+ ab^3 + ab^3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. a+ ab^3 + ab^3 simplifies to [ ]
O B. The expression cannot be simplified.
a+ ab³ + ab³ simplifies to 2ab³+a.
For simplifying the terms first we have to add Like Terms.
Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.
In Algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
So hence we will add ab³ + ab³= 2ab³
For any given term, we almost always list the variables in alphabetical order and any constant terms last — this is helpful in identifying common terms, a topic discussed in the next section. So, for example, it is simply not cool to write 15yx, 15 y x , we want to stay alphabetical and write 15xy. Exponents play no role in this decision.
Therefore a+ ab³ + ab³ simplifies to 2ab³+a.
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below is a list of volume of lava rates from four volcanoes. Which of the following is true of the rates at which lava flows? Choose all that apply.
Is the following sentence true?
Changing 3x + 6 into 3(x + 2) is
an
example of reverse distributing
Answer:
true
Step-by-step explanation:
21 = 3p - 6.
O A) 5
O в) 9
O C) 13
O D) 24
Answer: b) 9
Step-by-step explanation: if you take 3 * 9 it = 27 take that minus 6 that = 21
factorise completely m^2n-mn^2
Answer: nm(m-n)
Step-by-step explanation:
m^2n-mn^2=
n*m(m)-m*n(n)=
n*m(m-n)=nm(m-n)
help. Solve for x and show work
Answer: i belive x=1
27-28=1
2x-x
x
Step-by-step explanation: hope this helps
BIG IDEAS MATH
#14 i
MODELING REAL LIFE You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must
you leave the money in the account to earn $500 in interest?
(answer is in years)
Answer:
6.25years
Step-by-step explanation:
2000*4% = 80
500/80 = 6.25
6 years and 3 months
what is this answer because i have no idea and plus i need the answer ASAP
Step-by-step explanation:
option b is the correct answer
