The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient.
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
here, we have,
In this case, the system of equations is given as
6x - 5y = -8
6x - 5y = -8
Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8
6x - 5y = -8
(-) 6x - 5y = -8
----------------------
0 = 0
This in other words means that the difference between both equations is 0.
When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions.
Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.
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volume of a cone = r²h,
where r is the radius and h is the height.
A frustum is formed by removing a small cone from a similar, larger cone, as
shown below.
a) Calculate the radius of the original large cone.
b) Calculate the volume of the frustum to the nearest integer.
50 m height
10 m height of frustum
6m radius of frustum
Answer:
7.5 m 457.5[tex]\pi[/tex] [tex]m^{2}[/tex]
Step-by-step explanation:
First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.
The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = [tex]\frac{1}{3} \pi r^{2}h[/tex].
Original Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *7.5^{2}*50[/tex] = 937.5[tex]\pi[/tex]
Smaller Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *6^{2}*40[/tex] = 480[tex]\pi[/tex]
Frustum = 937.5[tex]\pi[/tex] - 480[tex]\pi[/tex] = 457.5[tex]\pi[/tex]
[tex]\mathbb Question[/tex]
Attached above!!
Answer:
see explanation
Step-by-step explanation:
(a)
play ends at 9 : 55 pm
15 minutes to get to bus stop , then time is
9 : 55 + 15 min = 10 : 10 pm = 22 : 10
the earliest bus she can catch is 22 : 25
(b)
time to wait 22 : 10 → 22 : 25 = 15 minutes
Finding a sunken submarine in the middle of the ocean using Bayes' theorem: the search for the Scorpion.
Finding a sunken submarine in the middle of the ocean using Bayes' theorem to the search for USS Scorpion.
In the event of a missing vessel or aircraft at sea, in this case a submarine, Bayes search theorem can be applied.
The ocean using Bayes' theorem: the search for the Scorpion.
In May 1968, the U.S. Navy's nuclear submarine USS Scorpion (SSN-589) failed to arrive as expected at her home port of Norfolk. The command officers of the U.S. Navy were nearly certain that the vessel had been lost off the Eastern Seaboard, but an extensive search there failed to discover the remains of Scorpion.Then John P. Craven, a Navy deep-water expert, proposed that Scorpion had sunk somewhere else. Based on a contentious approximation of hydrophone triangulation, Craven organized a search southwest of the Azores. He was only given one ship, Mizar, and to make the most of his resources, he sought help from a team of consulting mathematicians. A Bayesian search approach was used. To develop theories regarding what might have led to Scorpion's loss, veteran submarine commanders were questioned.What is Bayes' theorem?
Bayes' theorem is a theorem in probability theory. It is a trivial consequence of the definition of conditional probability.Bayesian search theory is the application of Bayesian statistics to the search for lost objects.Learn more about Bayes' theorem
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A population of a certain city increases exponentially at a rate of 6.5%. Initially, it is 1.50 million. After how many years will the population reach 2.31 million?
6.546
6.643
6.123
6.142
Answer:
Below in bold.
Step-by-step explanation:
P = 1.50(1.065)^t where P = population in millions and t = no. of years.
So we have
2.31 = 1.50(1.065)^t
(1.065)^t = 2.31/1.50
Taking logs:
t log 1.065 = log (2.31/1/50)
t = log (2.31/1/50) / log 1.065
= 6.856 years.
Solve the equation 3x^2-2x-10=0
Show all your working and give your answers correct to 2 decimal place
Answer:
Step-by-step explanation:
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -2
C = -10
B2 - 4AC =
4 - (-120) =
= 124
Applying the quadratic formula :
2 ± √ 124
x = —————
6
√ 124 simplified
The prime factorization of 124 is
2•2•31
To be able to remove something from under the radical, there have to be 2 instances of it
√ 124 = √ 2•2•31 =
± 2 • √ 31
√ 31, rounded to 4 decimal digits, is 5.5678
So now we are looking at:
x = ( 2 ± 2 • 5.568 ) / 6
Two real solutions:
x =(2+√124)/6=(1+√ 31 )/3= 2.189
or:
x =(2-√124)/6=(1-√ 31 )/3= -1.523
Answer:
Step-by-step explanation:
3x^2-2x-10=0
This is a quadratic equation that can be solved using the quadratic formula where
a = 3, b = -2, and c = -10
x=−b±(b^2−4ac)^(1/2)/2a
x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))
x=2±(124)^(1/2)/6
Simplify the Radical:
x=((2/6) ±2(31)^(1/2))/6
x=26±231−−√6
Simplify fractions and/or signs:
x=1/3±√31/3
which becomes
x=2.18925
See the attached image for a more clear display of solving using the quadratic equation.
x=−1.52259
She spent 18.62 in grosherys she has 43.55 left how much did she have before she bought grashery
Answer:
Step-by-step explanation:
43.55 + 18.62 = 62.17
PLEASE HELP ASAP
I think it’s supposed to be an arithmetic series or sequence.
Kaydence is saving for an RRSP. She saved $100 the first year, $200 the second year, $300 the third year, and so on. If she put $100 away on January 1, 2014, $200 away on January 1, 2015, and continued to put money away on the first of each year, how much money would Kaydence have saved by the end of the day on January 1, 2050?
Answer:
$70,300
Step-by-step explanation:
The amount Kaydence saved is the value of an arithmetic series with first term 100 and common difference 100. The number of terms in the sum is 37. The formula for the sum can be used.
Sum of an arithmetic seriesThe formula for the sum of n terms of an arithmetic series is ...
Sn = (2a1 +d(n -1))(n/2) . . . . . . first term a1, common difference d
ApplicationThe number of terms being added is ...
2050 -2014 +1 = 37 . . . . . . years Kaydence made deposits
The formula with a1=100, d=100, and n=37 is ...
[tex]S_{37}=(2\cdot100+100(37-1))\dfrac{37}{2}=\dfrac{(200+3600)\cdot37}{2}\\\\S_{37}=70,\!300[/tex]
Kaydence would have saved $70,300 by the end of Jan 1, 2050.
The range of a list of integers is 20, and the median is 17. What is the smallest possible number of integers in the list?
Answer:
4 is the smallest possible number of integers in the list.
A certificate of deposit offers a nominal interest rate of 5.5 percent annually.If inflation is 2.5 percent, what is the real rate of return?
The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The real rate of return exists at 2.926%.
How to estimate the real rate of return?The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The formula for the real rate of return:
R = (1+N)/(1+i) - 1
Where, N exists the nominal rate and i exists the inflation rate, as decimals.
A certificate of deposit offers a nominal interest rate of 5.5 percent annually.
This means that N = 0.055
Inflation exists 2.5 percent
i = 0.025
Substitute the values in the above equation, we get
[tex]$R = [(1+0.055)/(1+0.025)] -1[/tex]
= [1.055/1.025] - 1
= 1.02926 - 1
= 0.02926
0.02926 [tex]*[/tex] 100% = 2.926% ~ 3%
The real rate of return exists at 2.926%.
Therefore, the correct answer is option D. 3%.
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ASAP GUYS PLEASE I NEED UR HELP THIS IS SO HARD
Solve: 5 − 7 ( z + 1 ) = 7 ( − 9 − 3 z )
Answer:
[tex]-\frac{61}{14}[/tex]
Step-by-step explanation:
Question: 5 - 7(z+1) = 7(-9-3z)
We multiply the number in front of the bracket first, since that is multiplication.
--> 5 -7z -7 = -63 - 21z
--> -7z -2 = -63 - 21z
Now, we move all the z and all the numbers to each side.
--> -7z +21z = -63 +2
--> 14z = -61
--> z = -61/14
This cannot be simplified further, so z is -61/14.
PLEASE HELP 50 POINTS
I think for the first part 505 m and 53.1 degrees (Like they wrote, you need to repeat it) and same goes for the drcond part. In the last part, I think you need to add the directions. HOPE IT HELPS
*TIP: you can delete the answer the second person gave you to be able to recive more answers :)
Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?
On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3. It comes up from quadrant 4 and increases and curves into quadrant 3. It goes through (2, negative 6), (0, negative 1).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It increases into quadrant 2 and goes through (negative 1, 2) and (negative 2, 6).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2. It increases into quadrant 1 and goes through (1, 2) and (2, 6).
Using translation concepts, the graph that represents a reflection across the x-axis of [tex]g(x) = \frac{3}{4}(3)^x[/tex] is:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A reflection across the x-axis of g(x) means that:
f(x) = -g(x).
g(x) increases from the second quadrant into the first, hence for f(x) it will be from quadrant 3 into quadrant 4.
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Answer:
Option B
Step-by-step explanation:
Edge 2022
Jonathan bought a new computer for $1,716 using the electronic store's finance plan. he will pay $143 a month for 12 months. which equation can jonathan use to find out how much money he still owes after each month of the plan?
By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.
According to the statement
Jonathan bought a new computer for $1,716
He will pay $143 a month for 12 months.
Total amount he will for 12 months is 143(`12)
Now,
y = the money he still owes
x = the number of months (from x = 0 to x = 12)
y = 1,716 - 112x
So, By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.
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You can approximate e by substituting large values for ninto the expression
You can approximate e by substituting large values for (1 + 1/n)^n into the expression.
How to illustrate the expression?It should be noted that an expression can simply be used to illustrate the information given in a data.
In this case, you can approximate e by substituting large values for (1 + 1/n)^n into the expression.
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ucscout word problem define the variables. (see screenshot) please help
Integrated math 3
The exponential equation for the number of Bacterian Camels in Mongolia is:
[tex]P(t) = 600(0.982)^t[/tex]
The parameters can be described as follows:
P is the population after t years.A is the initial population.r is the decay rate, as a decimal.t is the time in years.What is an exponential function?A decaying exponential function is modeled by:
[tex]P(t) = A(1 - r)^t[/tex]
In which:
P is the population after t years.A is the initial population.r is the decay rate, as a decimal.t is the time in years.For this problem, the values of the parameters are given as follows:
A = 600, r = 0.018.
Then the equation is:
[tex]P(t) = A(1 - r)^t[/tex]
[tex]P(t) = 600(0.982)^t[/tex]
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
I think it is 6. It may be because we can see the intersect of line is in (1,6) and (-1,-6). So I think that it is 6.
Ummm can y’all solve these problems I’ll give extra points for this
Pls solve step by step and label which is which
What's the slope and y-intercept?
Answer:
Slope: 2; Y-Intercept: (0,3)
Step-by-step explanation:
As you can see from the graph, it rises 4 and runs 2. So, the slope is 2. It intersects the y axis at (0,3)
Answer:
Slope: 3/2
Y-intercept: 3
Step-by-step explanation:
The line passes the y-axis at 3, and to find the slope you use rise over run. Our rise (which is going up) is 3, and our run (which is going across) is 2 (and since it moves from left to right, it is positive). The slope would be 3/2.
I hope it helps! Have a great day!
bren~
what is the distance between the points (23,-33) and (4,9) if necessary round your answer to two decimal places
The distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
What is the distance between the points (23,-33) and (4,9)?The distance between two points on a graph can be determined using the equation;
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
Given that;
x₁ = 23x₂ = 4y₁ = -33y₂ = 9We substitute our values into the equation above.
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
D = √[ ( 4 - 23 )² + ( 9 - (-33) )² ]
D = √[ ( -19 )² + ( 42 )² ]
D = √[ 361 + 1764 ]
D = √[ 2125 ]
D = 46.10
Therefore, the distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
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Escribe una ecuación de la recta que pasa por el punto (5, –8) con pendiente 5.
Considerando la expresión de una ecuación lineal, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.
Ecuación linealUna ecuación lineal o línea se puede expresar en la forma y = mx + b
donde
x y son coordenadas de un punto.m es la pendiente.b es la ordenada al origen y representa la coordenada del punto donde la línea cruza el eje y.La ecuación lineal se puede expresar también mediante la ecuación punto-pendiente de la recta, que se plantea si se conoce la pendiente de la recta y cualquiera de sus puntos. Con ello queda determinada la recta, conociendo la pendiente “m” y un punto (x1, y1) dado:
y - y1= m(x -x1)
Ecuación de la recta en este casoEn este caso, la recta que pasa por el punto (5, –8) con pendiente 5.
Reemplazando en la ecuación punto-pendiente de la recta:
y - (-8)= 5(x -5)
Resolviendo:
y + 8= 5(x -5)
Aplicando propiedad distributiva:
y + 8= 5x - 5×5
y + 8= 5x - 25
Aislando la variable "y":
y= 5x - 25 - 8
y= 5x - 33
Finalmente, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.
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Visual Description for Figure 1
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
The slope in question seven is 1. Below are the solutions to the remaining questions
In what means can Transformation occur ?Transformation of an object can occur in different ways. Such as translation, rotation, enlargement of different scale factors, reflection and dilation.
Given that Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. The transformations to use on the blue segment CD to get it to match with the red segment C2D2 is ROTATION of 180° Clockwise
2.The transformations to use on the blue triangle to get it to match with the red triangle is ROTATION of 360° Clockwise Explain your movement using the coordinates of the vertices.
3.The line segments on the boat that is parallel is line B2 to A2 because it is parallel to line D2 to C2
4.The line segments on the boat is perpendicular is line BCA because they are perpendicular to line CFD and AB.
5.The line segments on the boat have a slope of 0 is line BCA because change in y axis is 0
6.The line segments on the boat have an undefined slope is line DFC because change in x axis is 0. When denominator is zero, the fraction is undefined.
7.Given that E is at (−11,4) and D is at (−10,5), the slope of ED will be
Slope = Δy ÷ Δx
Slope = (5 - 4) ÷ (-10 + 11)
Slope = 1 ÷ 1
Slope = 1
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You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
Answer:
Step-by-step explanation:
You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
what is the solution to the equation 35-2x=23
Answer:
x = 6
Step-by-step explanation:
35 - 2x = 23
35 - 23 - 2x = 0
35 - 23 = 2x
12 = 2x
x = 6
35- 2x = 23
Subtract 35 from both sides.
-2x = 23 - 35Subtract 35 from 23 to get −12.
-2x = -12Divide both sides by −2.
x = -12 / - 2Divide −12 by −2 to get 6.
x = 6 ===> AnswerDetermine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer:
A. f(-x) = f(x)
Step-by-step explanation:
When plugged into a graph, we can see that the y value of -x is equal to x.
This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.
The segments shown below could form a triangle.
A
5
с
B
8
B
6
Based on the triangle inequality theorem, the statement that the given segments will form a triangle is TRUE.
What is the Triangle Inequality Theorem?If a, b, and c are lengths of a triangle, then,
a + b > c
a + c > b
b + c > a
Given the segments:
AC = 6
CB = 5
BA = 8
6 + 5 > 8 [true]
6 + 8 > 5 [true]
5 + 8 > 6 [true]
Therefore, it is true that the segments given could form a triangle.
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Find the surface area of the composite figure.
5 cm
10 cm
4 cm
5 cm
SA =
10 cm
-8 cm
4 cm
12 cm
[?] cm²
If you'd like,
you can use a
calculator.
Enter
Answer:
Step-by-step explanation:
5*10*2=100
8*10/2=40
12*4*2=96
12*5=60
4*5*2=40
100+40+40+96+60=336cm²
The surface area for the given composite figure is 442 cm²
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given is a composite figure, composed of a triangular prism and rectangular prism, attached to each other.
We will find the surface area of the composite figure by adding surface areas of both the solids and subtracting the common base area from it.
We know that, surface area of a triangular prism and rectangular prism, are S = bh+(b1+b2+b3)l and 2(lh+wh+lw) respectively.
Therefore, SA = 12(8)+(12+10+8)5 +2(12×5+4×5+12×4) - lw
= 96+150+2(60+20+48) - 12×5
= 246+256-60
= 442
Hence, The surface area for the given composite figure is 442 cm²
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The cost of attending an amusement park is $10 for children and $20 for adults. On a particular day, the attendance at the amusement park is 30,000 attendees, and the total money earned by the park is $500,000. Use the matrix equation to determine how many children attended the park that day. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
Using a system of equations, it is found that 10,000 children attended the park that day.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable c: Number of children in the park.Variable a: Number of adults in the park.The attendance at the amusement park is 30,000 attendees, hence:
c + a = 30,000, which is the first equation in matrix form.
Then:
a = 30,000 - c
The cost of attending an amusement park is $10 for children and $20 for adults. The total money earned by the park is $500,000, hence:
10c + 20a = 500,000, which is the second equation in matrix form.
Since a = 30,000 - c, we replace:
10c + 20a = 500,000
10c + 20(30000 - c) = 500,000
10c = 100,000
c = 10,000.
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which is most likely to be the first step in solving a system of nonlinear equations by substitution
The correct option is C. Isolating a variable in one of the equations.
The first step in solving a system of nonlinear equations by substitution is to isolate a variable in one of the equations.
What is system of nonlinear equations?A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations.
The method to solve a system of nonlinear equations by substitution is-
Figure out each equation's graph.One of the equations should be solved for either variable.Fill in the other equation using the expression from step 2.Put the resultant equation to use.The importance of systems of nonlinear equations are-
They aid in a lot of our everyday predictions. In addition, nonlinear equations need not involve numbers. Sometimes you have to deal with the numbers, but more often than not you are only dealing with the graph's shape, and in such case it pays to be aware of the characteristics of certain shapes.To know more about the system of equations, here
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The complete question is-
Which is most likely the first step in solving a system of nonlinear equations by substitution?
A. Substituting a number for one of the variables
B. Substituting one equation into the other equation
C. Isolating a variable in one of the equations
D. Taking the square root of both sides of one of the equations
Answer:
Isolating a variable in one of the equations.
Step-by-step explanation:
In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5, and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. 1:4
B. 1:5
C. 1:25
D. 3:10
The odds in favor of winning $5 or more is 3 : 13
What are the odds in favor of winning $5 or more?The odds of winning $5 or more can be determined by finding the ratio of the total value of tickets that have a value of $5 or greater to the total value of tickets.
Total number of the tickets that have a value of $5 or more = 25 + 5 = 30
Total number of ticket = 25 + 5 + 100 = 130
Ratio : 30 : 130
3 ; 13
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For the function F defined by F(x)=x2−2x+4, find F(|−4|)
By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
How to evaluate a quadratic equation with an absolute value
Herein we must apply the definition of absolute value prior to evaluating the quadratic equation defined in the statement. From algebra we know that absolute values are defined as:
|x| = x, when x ≥ 0 or - x, when x < 0. (1)
Then, we apply (1) on the quadratic equation:
F(|x|) = |x|² - 2 · |x| + 4
As x < 0, by absolute value properties:
F(|x|) = x² + 2 · x + 4
F(|- 4|) = (- 4)² + 2 · (- 4) + 4
F(|- 4|) = 16 - 8 + 4
F(|- 4|) = 12
By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
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