The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).
Linear equation:
Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.
Given,
Here we have the following system of linear equations.
2x + 3y = 6
-3x + 5y = 10
Now, we need to find the solution for the equations.
Here we have to use the substitution method to solve this one,
To do the substitution method we have to follow the following steps:
Step 1) Solve anyone of the equations either for the variable x or y
Step 2) Now, substitute the value obtained from step 1 to the other equation
Step 3) Finally, solve the equation to find the value of the remaining variable.
Here we have to take the equation (2), and we have to solve it for the value of y,
For that we have to rewrite the equation as,
5y = 10 + 3x
y = (10 + 3x)/5
Apply the value of y on the equation (1), in order to get the value of x,
So,
2x + 3(10 +3x)/5 = 6
2x + (30 + 9x)/5 = 6
(10x + 9x + 30)/5 = 6
19x + 30 = 30
19x = 0
x = 0
Now, apply the value of x on the equation in order to get the value of y,
y = (10 + 3(0))/5
y = 10/5
y = 2.
Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).
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The total weight of three bean bags is 6.8 kg. Bag A weighs 1.5 kg more than Bag B. Bag C weighs 500 g more than Bag A. Calculate the weight of Bag B (will give brainliest and 50 points
Answer: 1.6 kg
Step-by-step explanation:
Let the weight of bag B in kg be B.
Then, Bag A weights B+1.5 and bag C weighs B+0.5.
[tex]B+1.5+B+0.5+B=6.8\\\\3B+2=6.8\\ \\ 3B=4.8\\\\B=1.6[/tex]
how many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
The number of ways to plan her schedule of menus for the 20 school days is 10^20.
How to many number of ways to plan her schedule?To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.
For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.
The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.
How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
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María compro dos boletos para una rifa con dis números
rosa compró 4 boletos calcular la
probabilidad de cada una de ganar
Answer:
translate to eng
Step-by-step explanation:
Determine if the equation is linear,quadratic,exponential, or absolute value Y=x² -5x+6
Explanations:
Note that any expression of the form:
[tex]ax^2\text{ + bx + c}[/tex]is a quadratic polynomial.
The given equation in the question is:
[tex]Y=x^2\text{ - 5x + 6}[/tex]Comparing the given equation with the general expression I wrote above:
a = 1, b = -5 and c = 6.
Since the given equation takes the form of the general expression, it is therefore quadratic.
PLEASE HELP ASAPPP!!!!
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.
What is the standard form of the equation of f(x)?
f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7
Answer:
f(x)= -x^2-6x+7
Step-by-step explanation:
Since the graph opens downward the function for the parabola is going to be negative. This leaves us with two answers.
Now use the remaining possible equations and solve for the vertex.
Using x= -b/2a to solve for the x value of the vertex plug in the values to solve.
a= -1 b= -6 c=7 so, since -6 is already negative plugging it in makes it positive -(-6)/2(-1) = 6/-2 = -3. So x equals negative 3.
Then plug in -3 into the equation to get the y-value.
- (-3)^2 - 6(-3) + 7 = -9 + 18 + 7 = 16 so this confirms the vertex for this equation is (-3,16) so the answer is -x^2-6x+7.
Hope this helped! :)
according to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
About twice as likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers.A 16 or 17-year-old driver has a higher risk of dying every mile they drive compared to operating a vehicle alone. increases by 44% when one of the passengers is under the age of 21. while transporting two passengers who are under 21 in doubles.
Are 16 year olds more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.To learn more about crash with two passengers refer to:
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16-year-old driver to crash with two passengers as opposed to with no passengers is about twice as likely.
Are 16 year old's more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.The complete question is,
According to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
just as likely
about twice as likely
about three times more likely
about four times more likely
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You have discovered another alien. Find the correct rescue path before answering this question.
When the spaceship starts from a point on the y axis, what is the y-intercept of the line of travel?
the x-coordinate of the spaceship
the y-coordinate of the spaceship
the y-coordinate of the alien
the distance from the spaceship to the alien
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
Given,
You have discovered another alien. Find the correct rescue path .
When the spaceship starts from a point on the y axis, we have to find the y intercept of the line of travel.
y-intercept;
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
Here,
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
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Let g be a group with normal subgroups m and n. furthermore, assume n is a subste of m. use the first isomorphic theorem to prove that (g/n)/(m/n) is isomorphic to g/m.
The proof of (g/n)/(g/m) isomorphic to g/m from the first isomorphism theorem is as shown below.
Let a group g with normal subgroups m and n. Furthermore, n is a subset of m.
Proof: We have to prove (g/n)/(m/n) ≅ g/m (1)
g/m and g/n are valid because m and n are normal in g. As normality satisfies the intermediate subgroup condition, n is normal in m. because normality is image-closed m/n is a normal subgroup in g/n. Under the quotient map by n, the normal subgroup m of g is sent to a normal subgroup m/n of g/n. Thus the L.H.S of the statement to prove makes sense.
To describe the isomorphism from the left side to the right side
φ: g/n \to g/m
ψ(gn) = gm
So, a coset of n is taken by the map and it gives the corresponding coset of m. This is well-defined, because if h∈ n, thus h∈ m, hence (gh)m = g(hm) = gm.
The map is a homomorphism. So we observe that it maps the identity element to the identity element, keeps group multiplication preserved, and also preserves the inverse map.
Also, the map is surjective because any coset gm is present as the image of gn under ψ.
Lastly, we need to find the kernel of the map which is given by the set of gn such that gm = m. This is those cosets of n that are in m, and this is the same as the coset space m/n. Thus the kernel of the map is exactly g/m. Thus, the surjective homomorphism ψ: g/n → g/m has kernel m/n. And now by the first isomorphism theorem
(g/n)/(m/n)≅g/m where ≅ shows isomorphism
another problem to prove whether f is an isomorphism:
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Anna is computing 266 - 39. To do so, she first says that 266 is close to 270 and 39 is
close to 40, so she starts out computing 270 - 40 = 230. She then computes 230 - 3 =
227, and declares that 227 is her final answer. Is Anna's strategy correct? If yes, explain
why. If no, explain why not. Be mathematically specific, and support your reasoning
with a number-line model.
Yes, her strategy was correct.
What is BODMAS?When compared to operations involving just two numbers, solving an arithmetic expression that includes multiple operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how do you work out an expression with brackets as well as multiple operations, as well as how to make a bracket simpler? Let's review the BODMAS rule as well as discover how brackets can be made simpler. For Bracket, Order, Division, Multiplication, Addition, and Subtraction, the acronym BODMAS is used. The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, as well as Subtraction, is also known as BODMAS in some areas. Thus, the following figure illustrates the order in which BODMAS and PEMDAS operate.
Simplification is done following BODMAS rule.
266-39 gives 227.
Hence, her strategy was correct.
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HELP MATH SUCKSSSSSS 7 and 8
Answer:
Step-by-step explanation:
Morgan can make 4 cupcakes with 1 cup of flour. How many cupcakes can she make with 18 cups of flour?
Answer: She can make 72 cupcakes.
Step-by-step explanation:
Use the order of operations to evaluate.[tex]16.5 + ({62 }^{2} - 15.6) - 2[/tex]
Thus, the final answer is 34.9.
2.
[tex]16.5+(6^2-15.6)-3=16.5+(36-15.6)-3[/tex]Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
Answer:
The answer is D
Step-by-step explanation:
Check to see when the graph is increasing and decreasing from left to right.
It is decreasing from x = -5 to x = -3 or (-5,-3) These look like a points but are not. They are intervals.
Then, it increases from x = -3 to x = 0 or (-3,0)
Then, it stays constant from x = 0 to x = 2 or (0,2)
Lastly, it decreases from x - 2 to x = 5 or (2,5)
To summarize, the graph is increasing from (-3,0). Decreasing on (-5,-3) and (2,5). and constant on (0,2)
The only option that fits these conditions is D.
Which number sentence is true? A. |10| < 1.0 B. |0| = 0 C. |-47| < |-30| D. |-100| < |0|
The second option (B) that is I0I = 0 is true.
This is a question of modulus.
Let us check all the options to find which one is true.
Let us check for A.
A. I10I < 0
We know that,
I10I = 10 > 0
Hence, this option is false.
Let us check for B.
B. I0I < 0
We know that,
I0I = 0 = 0
Hence, this option is true.
C. I-47I < I-30I
We know that,
I-47I = 47 and I-30I = 30
47 > 30
Hence,
I-47I > I-30I
Hence, this option is false.
D. I-100I < I0I
We know that,
I-100I = 100 and I0I = 0
100 >0
Hence,
I-100I > I0I
Hence, this option is false.
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1 billion, 1 million compare and give the factor
Answer:
1000000
Step-by-step explanation:
100000000: 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5
100000: 2 2 2 2 2 5 5 5 5 5
GCF: 2 2 2 2 2 5 5 5 5 5
The Greates Common Factor (GCF) is: 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 = 100000
can you help mw with my work?
In this problem the function that models the hight is:
[tex]h(t)=-5t^2+14t+3[/tex]So when the water hits the grownd h=0 so we replace that and solve for t so:
[tex]0=-5t^2+4t+3[/tex]To solve this expression we can use the cuadratic equation:
[tex]x=\frac{-4\pm\sqrt[]{16-4(-5)(3)}}{-10}[/tex]and we operate so:
[tex]\begin{gathered} x=\frac{-4\pm\sqrt[]{76}}{-10} \\ x=\frac{-4\pm8.7}{-10} \end{gathered}[/tex]Now we solve bout of the equation so:
[tex]\begin{gathered} x_1=\frac{-4+8.7}{-10}=-0.47 \\ x_2=\frac{-4-8.7}{-10}=1.27_{} \end{gathered}[/tex]So the answer that have sense is the secon one so the water hits the ground after 1.27 seconds
Write an exponential function in the form y and (2,171). ab that goes through points (0,19)
The exponential function has the following form:
[tex]y=a\cdot b^x[/tex]The function goes through the points ( 0, 19) and ( 2, 171 )
We will use the points to find the values of a and b
[tex]\begin{gathered} x=0\rightarrow y=19 \\ \\ 19=a\cdot b^0 \\ b^0=1 \\ a=19 \end{gathered}[/tex]Substitute with the point ( 2, 171 ) and the value of a to find b
[tex]\begin{gathered} x=2\rightarrow y=171 \\ a=19 \\ \\ 171=19\cdot b^2 \\ \\ b^2=\frac{171}{19}=9 \\ \\ b=\sqrt[]{9}=3 \end{gathered}[/tex]So, the answer will be:
[tex]y=19\cdot3^x[/tex]when the sun is 5 degrees above the horizon, how long will the shadow nof a 35ft tree be ?
tan 5 = x / 35
0.0874 = x / 35
cross- mulltiply
x = 35 x 0.0874
x = 3 . 059 = 3. 06 feet
a television program director has 14 shows available for monday night but can choose only 5 shows. how many different possible combinations are there?
There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.
What is permutation?
In mathematics, it is the number of ways in which given number of items can be arranged in different orders.
Here, we need to select 5 iteams from the given 14 iteams.
[tex]P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240[/tex]
Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.
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What is the exchange rate? Show your work.
1 US dollar = _________ euro.
The exchange rate is 1 USD = 0.992714 EURO
What is Conversion of unit?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm).
Given:
1 US dollar = _________ euro.
As, the exchange rate between US dollar to Euros
1 USD = 0.992714 EURO
1 USD = 1 EURO
So, if we have to find 5 US dollar into EURO then
5 US dollar = 5.02 EURO = 5 EURO
Hence, the exchange rate is 1 USD = 0.992714 EURO
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Do You Like Guns N' Roses, If So, What Is Your Favorite Song?
Answer:golden hour by JVKE
Step-by-step explanation:
6. There were a total of 139 points scored in the basketballgame. The Falcons scored (9x+22) and the Mavericks scored(16x - 8). What was the Falcons score for the game?
The total score in the basket game = 139
Falcons score = 9x + 22
Maverick score = 16x - 8
Therefore,
139 = 9x + 22 + 16x - 8
collect like term
139 - 22 + 8 = 9x + 16x
125 = 25x
divide both sides by 25
x = 125/25
x = 5
Falcons score = 9x + 22
Falcons score = 9(5) + 22
Falcons score = 45 + 22
Falcons score = 67
Evaluate without any table 3log2 +log20 - log 1.6
The value of 3log2 +log20 - log 1.6 is 2.
What is logarithm?
A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. or
logarithm is the exponent or power to which the base must be raised to be raised to yield a given number.
Given,
3log2 +log20 - log 1.6
we can write it as
log[tex]2^{3}[/tex]+log20 - (log 1.6)
= log 8+ log20 - (log 1.6) (property of logarithm)
= log (8×20/1.6)
=log 100
=2
Hence, the value of 3log2 +log20 - log 1.6 = 2
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Jennifer is thinking about getting an MBA. She will give up making $27,500 a year for the two years it takes to complete the MBA. She will also pay $45,000 in total costs to get the degree. Assume she will make $67,500 a year after she gets her MBA. How long will it take for Jennifer to recover her investment?
Answer:
un year
Step-by-step explanation:
8. 6w — 8z = 16
3w — 4z = 8
Substation
Let the two equations be 6w — 8z = 16 and 3w — 4z = 8
Then the equation be
[tex]$6 \cdot w-(8 \cdot z)-16=0$[/tex]
To estimate the value of w, we get
[tex]$6 \cdot w=-(-8 \cdot z-16)=6$[/tex]
simplifying the above equation, we get
[tex]$w=\frac{(-(-8 \cdot z-16))}{6}$[/tex]
[tex]$w=\frac{(16-(-8 \cdot z))}{6}$[/tex]
We insert the solution into one of the initial equations of our system of equations We get a system of equations:
[tex]$3 \cdot\left(\frac{(16-(-8 \cdot z))}{6}\right)-(4 \cdot z)-8=0 \\[/tex]
Therefore, the value of
[tex]$w=\frac{(16-(-8 \cdot z))}{6}[/tex]
If the two equations be 6w — 8z = 16 and 3w — 4z = 8 then the system of equations has infinitely many solutions.
How to estimate the value of w?Let the two equations be 6w — 8z = 16 and 3w — 4z = 8
Then the equation be
[tex]$6 \cdot w-(8 \cdot z)-16=0$[/tex]
To estimate the value of w, we get
[tex]$6 \cdot w=-(-8 \cdot z-16)=6$[/tex]
simplifying the above equation, we get
[tex]$w=\frac{(-(-8 \cdot z-16))}{6}$[/tex]
[tex]$w=\frac{(16-(-8 \cdot z))}{6}$[/tex]
We insert the solution into one of the initial equations of our system of equations We get a system of equations:
[tex]$3 \cdot\left(\frac{(16-(-8 \cdot z))}{6}\right)-(4 \cdot z)-8=0 \\[/tex]
Therefore, the value of
[tex]$w=\frac{(16-(-8 \cdot z))}{6}[/tex]
[tex]$&\frac{(3 \cdot(8 \cdot z+16))}{6}-4 \cdot z-8=0 \\[/tex]
simplifying the above equation, we get
8 - 8 = 0
0 = 0
The system of equations has infinitely many solutions.
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help pls sos help sos help
Answer:
Step-by-step explanation:
Up 6 right 4: (4,6)
Right 4 up 6: (4,6)
Left 4 up 6: (-4, 6)
Down 4 right 6: (6, -4)
Right 6 down 4: (6, -4)
Answer: Right 4 up 6 is (4,6), left 4 up 6 is (-4,6), and right 6 down 4 is (6, -4).
Step-by-step explanation: Since you're starting from the origin, it's mainly counting. For (4,6), you are moving 4 places from 0 on the x axis. Then you move up 6 spaces from 4 on the y-axis. If you didn't move up, you'd be stuck at (4,0). It's important to keep in mind that (x,y).
Find the value of x.
To mail a letter to Vienna, Austria the post office charges a flat rate of $5.50 and an additional $0.25 for every ounce the letter weighs. The cost of mailing a letter is
determined by the equation y = 0.25x + 5.50, where y is the cost of the postage and x is the weight of the letter in ounces.
Step 1 of 2: Graph the equation by finding two points that satisfy the equation and plotting them on the graph. To plot a point, click on the appropriate position on
the graph. You may move a point by clicking and dragging.
Answer:
Step-by-step explanation:
See attached graph
Two pints selected are:
2 packages = $6
5 packages = $6.80
Find the value of a. Enter a numeric answer only.
Solution
For this case we have the following, the sum of the angles needs to be 360 since we have a circumference:
10a-4 +6a-2 +8a+6=360
Regrouping we have:
10a +6a +8a -4 -2 +6= 360
24a= 360
a= 360/24= 15
Parallel and transversals
I was in a rush so I couldn't write fown the steps. If you need the explanations for how they were gotten, please say.
