[tex]{\huge{G = \frac{P-2M}{2} }}[/tex]
How many solutions does a system of 3 equations have?
A system of 3 equations can have 0, 1, 2, or infinitely many solutions.
It is possible for a system of 3 equations to have no solutions if the equations are incompatible, meaning that there is no combination of values for the variables that can satisfy all of the equations simultaneously. It is possible for a system of 3 equations to have exactly one solution if the equations are dependent, meaning that one of the equations can be derived from the other two. It is possible for a system of 3 equations to have exactly two solutions if the equations are independent, meaning that the equations are not related to each other and cannot be derived from each other. Finally, it is possible for a system of 3 equations to have infinitely many solutions if the equations are consistent and the variables are linearly dependent.
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Three sisters have were born in 3 consecutive years. The total of their ages is 30. What is the oldest sibling's age?
The oldest child is a 11-year-old boy.
What exactly is a sequential number?Three sisters have were born in 3 consecutive years. The total of their ages is 30.
Sequential numbers are those that follow one another continually, from lowest to biggest.
Here, assume that the youngest sibling is x years old.
Middle sibling's age will be (x+1) years old.
the oldest sibling's age is (x+2) years.
According to the inquiry,
x + (x+1) + (x+2) = 30
3x + 3 = 30
3x = 30-3
3x = 27
x = 27 / 3
x= 9
The oldest child is therefore (x + 2) years old, or 11 years old.
x+2 = 9+2 =11
The oldest child is a 11-year-old boy.
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please help a mate out aye? 80 points!! :D
Simplify the expression 3x(2x – 7).
(A)15x
(B)6x2 – 21
(C)6x2 – 21x
(D)6x – 21
Answer:
Hey no prob!
We take 3x(2x-7) and we distribute the 3x to both of the terms inside
3x times 2x is 6x^2
and
3x times -7 is -21x
the final answer would be C
6x^2-21x
Answer:
[tex] \sf \: c) \: 6 {x}^{2} - 21x[/tex]
Step-by-step explanation:
Given expression,
→ 3x(2x - 7)
Simplifying the expression,
→ 3x(2x - 7)
→ 3x(2x) + 3x(-7)
→ (3 × 2)x² + (3 × -7)x
→ (6)x² + (-21)x
→ 6x² - 21x
Hence, option (c) is correct.
What is the median of 4 2 7 3 10 9 13?
Answer: 3
Step-by-step explanation: The median is three (3) because its the middle number
Why can't you solve 3x 1?
We can't solve 3x + 1 because eventually reach 1 if you keep performing this operation, regardless of what odd number you started with.
Describe odd numbers.Even numbers are ones that can be divided into two equal parts, but odd numbers cannot be divided into two equal parts. The numbers 3, 5, 7, 9, 11, 13, and 15 are examples of odd numbers. Even numbers include 2, 4, 6, 8, 10, 12, and so on. Odd numbers are those that cannot be evenly divided by two. It cannot be evenly split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers.
Given
Three times, then add one.
Divide the largest power of 2 from the resultant even number to obtain the new odd number T. (x).
Do you eventually reach 1 if you keep performing this operation, regardless of what odd number you started with? This issue has not yet been resolved, to put it simply.
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a country's postal service will accept a package if its length plus its girth (the distance all the way around) does not exceed 96 inches. find the dimensions (in inches) and volume (in cubic inches) of the largest p
Dialyzer re-use efficiency is largely determined by the fiber bundle volume (FBV).
This estimation is performed after the dialyzer has been pressure cleaned and may underrate the level of coagulated strands a patient really experiences while on dialysis.
The package's dimensions:
length = 32 in
width = level = 16 in
Volume of bundle = 8192 in³
The square-shaped package is depicted in the attached image.
Expect that the length is y in and that width = level = x in (since the base is a square)
This implies that the circumference is 4*x = 4x in
We are given that the greatest amount of length and circumference is 96.
This indicates:
This can be rewritten as: y + 4x = 96
The volume of the package can be calculated as follows: y = 96 - 4x..............> I
Volume is equal to the following: length * width * height * y * x * x = x2y in3 Substitute equation I for the following volume equation:
Volume = x2 (96-4x) = 96x2 - 4x3 in3 to achieve maximum volume:
dV/dx = 0 indicates that:
2(96) x - 4(3) x2 = 0 192x - 12x2 = 0 x (192-12x) = 0
either x = 0.......> This is rejected because the side cannot be zero or 192 - 12x = 0...............> 192 = 12x...............> x = 16 in.......> accepted
In Part (b), y = 96 - 4x = 96 - 4(16) = 96 - 64 = 32: obtaining a volume:
The volume of the package is equal to 32 x 16 x 16 x 8192 in3.
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What is the median of 7 6 4 8 2 5 11?
To find the median of a set of numbers, you first need to put the numbers in order from smallest to largest. Then, if there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.
In this case, the set of numbers is already in order: [2, 4, 5, 6, 7, 8, 11]. There are 7 values, so the median is the middle value, which is 6.
So, the median of the set {7, 6, 4, 8, 2, 5, 11} is 6.
What in math is the median?the middle number, which is obtained by sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.
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What are the solutions of 3x² 6x 2 0?
x=3+√15/3 and x=3-√15/3 are the solutions of 3x²-6x-2=0.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given quadratic equation is 3x²-6x-2=0
Use the quadratic formula to find the solutions.
x=-b±√b²-4ac/2a
a=3, b=-6 and c=-2.
Now plug in these values in quadratic formula to find the solutions.
x=6±√-6²-4(3)(-2)/2(3)
x=6±√36+24/6
x=6±√60/6
x=3±√15/3
Hence, x=3+√15/3 and x=3-√15/3 are the solutions of 3x²-6x-2=0.
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please help its for finals
The numerical value of x and the length of side ST are 2 and 6 respectively.
What is the numerical value of x and the length of ST?An equilateral triangle is simply a triangle with all three sides having the same length.
Given that;
RS = 2x + 2ST = 3xTR = 5x - 4First, we determine the value of x.
Since all three sides are equal;
RS = TR
2x + 2 = 5x - 4
Solve for x
5x - 2x = 2 + 4
3x = 6
x = 6/3
x = 2
Now, for side ST.
ST = 3x
Plug in x=2
ST = 3( 2 )
ST = 6
Therefore, the value of x is 2 and side length of ST is 6.
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Is AAA congruence possible?
Angle-Angle-Angle (AAA) does not work because it can produce similar but not congruent triangles.
There are a few conditions for AAA:
The sides of the triangles may or may not be equal. For two triangles with the same respective angles, the congruence will hold true only if those triangles are similar."AAA" is when we know all three angles of a triangle, but no sides. AAA triangles are impossible to solve further since there is nothing to show us the size.
If two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.
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What are whole numbers explain with example?
Answer:
Whole numbers are positive numbers including zero that dont include fractions or intergers
Step-by-step explanation:
examples of this are 73, 68, 27
What type of function has an asymptote?
A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.
For example, a rational function is a function that can be written in the form of a ratio of two polynomials. These functions can have horizontal asymptotes if the degree of the denominator is greater than the degree of the numerator, and they can have vertical asymptotes if the denominator has a factor that is not present in the numerator.
Exponential functions can have horizontal asymptotes if the base of the exponent is less than 1, and they can have vertical asymptotes if the base of the exponent is greater than 1.
Logarithmic functions can have horizontal asymptotes if the base of the logarithm is less than 1, and they can have vertical asymptotes if the base of the logarithm is greater than 1.
It's also possible for a function to have both horizontal and vertical asymptotes, depending on its form.
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If the exponent's base is less than 1, an exponential function may have a horizontal asymptote; if it is greater, a vertical asymptote may occur.
If the base of the logarithm is less than 1, a logarithmic function may have a horizontal asymptote, and if the base is greater, a vertical asymptote.
What is the median of the distribution 34 22 13?
The median of the distribution 34 22 13 is 22.
To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.
In this case, the scores are 13, 22, and 34.
After arranging the scores in numerical order, we have 13, 22, and 34.
There are three scores in this set, so the median is the middle score, which is 22.
The median of the set is 22.
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∠1 and ∠2 are vertical angles. If m∠1 = (5x + 12)° and m∠2 = (6x - 11)°. Find m∠1.
Answer<2= 127°
Step-by-step explanation:
What is current i formula?
The formula of current I is I=V/R.
In the field of physics, current can be described as the rate that shows the intensity of electrons that are flowing from one place to another.
The current is the measure of the potential difference from which the current moves forward when resistance is also a factor that stops it. Electric current is directly proportional to the potential difference applied and is inversely proportional to the resistance in the object in which the electric current is flowing.
Based on this fact, the formula for current, which is represented by the letter I is I=V/R, here I is the current, V is the potential difference and R is the resistance.
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A box without a top is made from a rectangular piece of cardboard, with dimensions 25 inches by 20 inches, by cutting out square corners with side length x inches. which expression represents the volume of the box in terms of x?
Answer:
[tex]x(20-2x)(25-2x)[/tex]
Step-by-step explanation:
The length removed from each side is [tex]2x[/tex].
So, the length and width of the box are [tex]25-2x[/tex] and [tex]20-2x[/tex].
The height of the box is [tex]x[/tex], so the volume is [tex]x(20-2x)(25-2x)[/tex].
How do you find the vertical and horizontal asymptotes of a function using limits?
Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to locate the vertical asymptotes of a function using limits. Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction).Similary, To find the horizontal asymptotes of a function using limits, consider the behavior of the function as x becomes very large (in either the positive or negative direction). If the y-values of the function approach a fixed value as x becomes very large, then that value is the horizontal asymptote of the function.
what is an Asymptote?An asymtote is a line being approached by a curve but never touching the curve at any finite distance.It is a line that the graph approaches as either x or y in positive or negative infinity.
What is vertical asymptote?A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.
Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to identify the vertical asymptotes of a function using limits. The vertical asymptote is at that value of x if the function approaches positive infinity as x approaches the asymptote from the left and negative infinity as x approaches the asymptote from the right. Consider the function f(x) = 1/x as an illustration. We may take into account how the function behaves as x approaches 0 from the left and from the right in order to determine the vertical asymptotes of this function using limits.The y-values of the function become closer to negative infinity as x moves toward 0 from the left (negative x-values). The y-values of the function get closer to positive infinity as x gets closer to 0 from the right (positive x-values). As a result, we may infer that the function's vertical asymptote lies at x = 0.
Similary, Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction). The horizontal asymptote of the function is the point at which the y-values of the function begin to approach a fixed value when x increases significantly.
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evaluate f divided by 1/4 for f = 2/9
Answer:
8/9
Step-by-step explanation:
2/9 divided by 1/4 is 8/9
What are the 4 functions of a stem?
The 4 functions of a stem are fruits, flowers, leaves, and branches.
In plants, a stem's primary role is to aid in the transfer of water and minerals from the roots to the leaves and other sections of the plant. Additionally, it supports the buds, leaves, flowers, fruits, and branches of plants.
In a plant, a stem does the following tasks:
(i) It holds up the fruits, flowers, leaves, and branches.
(ii) It moves water and minerals from a plant's roots to its leaves and other areas.
(iii) It transports nourishment from the leaves to various plant sections.
(iv) The plant is kept upright by it.
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Is the mean of the following data is 14.7 find the values of P and Q?
The values of p and q are 11 and 3 respectively.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.
Given that,
∑f = 40
=> 26+p+q = 40
=>p+q=40-26
=> p+q = 14 .......................(i)
∵ x bar = ∑xf/∑f
=>14.7 = 408+9p+27p / 40 (since, x bar = 14.7)
=>588 = 408+9p+27p
=>588 - 408= 9(p+3p)
=>180= 9(p+3p)
=>p+3q=20......................(ii)
Solving equations (i) and (ii)
=>p+3q -(p+q)=20-14
=>p+3q-p-q=6
=>2q=6
=>q=3
Substituting this value in equation (ii)
∴p+3=14 => p = 11
Hence, the values of p and q are 11 and 3 respectively.
(Refer to the image attached for the missing data)
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Find the circumference of the circle (use 3. 14 for pi). Show your work. Round to the nearest tenth.
The circumference of the circle is C = 144.44 yd .
From the given figure :
we observe that the radius r = 23 yd
we know that ,
What is circumference of circle ?
Circumference is the distance around the perimeter of a circle. It is calculated by multiplying the distance across the center .
A circle's perimeter is known as its circumference.
Formula :
C = 2πr
= 2 * 3.14 * 23
= 46 * 3.14
= 46 * 314 / 100
= 14444 / 100
= 144.44 yd
Hence the circumference of the circle is 144.44 yd .
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Full question :
is in the image uploaded
2 balloons and 3 cakes = £16
4 balloons and 4 cakes = £24
Answer:
1 balloon is = £2 and 1 cake is = £4
Step-by-step explanation:
this is true because 2 balloons = £4
and 3 cakes = £12 so 4 + 12 = 16 and also
4 balloons = £8
and 4 cakes = £16 so 8 + 16 = £24
this is one of the possible answers
Answer:
A cake is £3.50
A Balloon is £2.75
Step-by-step explanation:
Let b be balloons and c be cake
2 balloons and 3 cakes = £16 = 2b + 3c = 16
4 balloons and 4 cakes = £24 = 4b + 4c = 25
First times -2 to the first equation
-4b - 6c = -32
4b + 4c = 25
Now let's find c first by adding the two equations together.
-2c = -7
c = £3.50
Now put 3.50 back in the c
4b + 4(3.50) = 25
4b + 14 = 25
4b = 11
b = £2.75
What do you say about Y 0 and y =- 5?
The pair of equations y=0 and y=−5 has no solution.
Since the provided variable y might take on a variety of values, the pair of equations y=0 and y=5 cannot have a solution.
A two-variable linear equation is one with the formula ax+by+c, where a, b, and c are all real numbers and a, b is not equal to zero. In a set of two linear equations in two variables, we deal with two such equations.Such equations have a point on their representational line as the solution. A two-sided statement with the same sign on both sides is called an equation.
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What will be the appearance of the graph when the degree is even and the leading coefficient is positive?
The graph of the equation will be a parabola that opens upwards, starting at the y-axis and increasing in value as x increases. The vertex of the parabola will be the lowest point on the graph, and the parabola will be symmetrical about the line of symmetry.
When the degree of an equation is even and the leading coefficient is positive, the graph of the equation will be a parabola. This parabola will open upwards, meaning that it will start at the y-axis and increase in value as x increases. The vertex of the parabola will be the lowest point on the graph, and this vertex will always be located to the right of the y-axis. Additionally, the parabola will be symmetrical about the line of symmetry, which is the vertical line that passes through the vertex. To further illustrate, consider the equation y = 4x^2 + 5x + 1. In this equation, the degree is even (2) and the leading coefficient is positive (4). Therefore, the graph of this equation will be a parabola that opens upwards and has its vertex to the right of the y-axis. Additionally, the parabola will be symmetrical about the line of symmetry, which is the vertical line that passes through the vertex. The vertex of the parabola will have coordinates (2.5, -2.625), and the parabola will increase in value as x increases from this point.
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The Santos family owns 30 acres of land. Of the 30 acres, only 20 acres can be farmed. What percent of the land is available for farming?(1 point)
Answer:66.67% to the nearest whole number is 67%
Step-by-step explanation:
The total number of acres available are 30
and only 20 acres of land can be farmed
20 acres out of 30 acres is available for farming
20/30 x 100%
To do with the calculator
20 ÷30 x 100=66.67% then add the percent sign
4000×20÷408-44
( what answer its it
The numeric value of the expression 4000×20÷408-44 is given as follows:
4000×20÷408-44 = 152.08.
How to obtain the numeric value of the expression?The expression for this problem is defined as follows:
4000×20÷408-44
We have a multiplication, a division and a subtraction operation, hence the precedence of the operations is given as follows:
Multiplication. (as multiplication and division have higher precedence over subtraction, and multiplication appears first).Division.Subtraction.Then the multiplication is given as follows:
4000×20 = 80,000.
The division is given as follows:
80000/408 = 196.08.
Finally, the subtraction is calculated as follows:
196.08 - 44 = 152.08.
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What is the perpendicular slope to the equation y = –34 + 3, through the point (1, -1)
Answer:
Step-by-step explanation:
I'm going to guess that the equation is really
y = -3x +3 not y = -34 + 3
we don't really need the point information to solve this, we know that a perpendicular line has an inverse slope with a sign change
so we know the slope of the perpendicular line is
[tex]\frac{1}{3}[/tex]
The um of two number i 4. The larger number i 12 more than three time the maller number. What are the number?
The larger number is 8 and the smaller number is -4.
Let us assume that the larger number is x and the smaller number is y.
Now according to the question:
The sum of two numbers is 4, so
x+y= 4....(1)
A two-variable linear equation has two variables and can be represented as: ax+by=c
Here x and y are the variables, a and b are the respective cofficients of the variables and c is a constant term.
And the larger number is 12 more than three times the smaller number.
So
x=y+12 ...(2)
By equation (1) and (2)
y+12+y=4
2y= 4-12=-8
y = -4
Now put the value of y in equation (2)
x= y+12=-4+12=8
So the larger number is 8 and the smaller number is -4.
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Polygon B is a scaled copy of Polygon A using
a scale
factor of 5.
How many
times as large is the area of Polygon B
compared to the area Polygon A?
Answer:
25 times larger
Step-by-step explanation:
given a scale factor of 5 from A → B
then the scale factor of the area is 5² = 25
area of B is 25 times larger than the area of A
ANSWER ASAP!! TY :)
Lyme disease is an infection caused by bacteria. A test for Lyme disease may be affected by other medications and medical conditions. The testing results are summarized in the table.
Tested positive Tested negative Row Totals
Has Lyme disease 53% 17% 70%
Does not have Lyme disease 12% 18% 30%
Column Totals 65% 35% 100%
What percentage of all patients who took the test had a false positive result?
12%
17%
18%
35%
The percentage of all patients who took the test and had a false positive result will be 35%. Then the correct option is D.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
Lyme illness is a disease brought about by microscopic organisms. A test for Lyme infection might be impacted by different prescriptions and ailments. The testing results are summed up in the table.
Tested positive Tested negative Row Totals
Has Lyme disease 53% 17% 70%
Doesnt have Lyme disease 12% 18% 30%
Column Totals 65% 35% 100%
The level of all patients who stepped through the examination and had a misleading positive outcome will be 35%. Then, at that point, the right choice is D.
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