We can demonstrate the solution set in a number of different ways. Number line, interval notation, and set notation are all options for accomplishing this.
Depending on the question, these methods may or may not be used.
There are two ways to write the interval notation solution set.
The closed interval is the first. The solution is enclosed by square brackets and includes the endpoints in a closed interval.
The form [a, b] is used to indicate this. The set notation, on the other hand, is x a x b. This indicates that the solution set runs from a to b, with the second interval being open. The endpoints are not included in the solution when an open interval is enclosed by round brackets ().
The format used for this is (a, b). The set notation, on the other hand, is x a x b. The solution set is therefore situated between a and b.
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How many solutions does the system of equation posses 2x 4y 10 3x 6y 12?.
So, the given system of equations has no solutions.
The system of equations 2x + 4y = 10 and 3x + 6y = 12 can be written in matrix form as:
| 2 4 | | x | | 10 |
| 3 6 | | y | = | 12 |
To find the number of solutions, we can use the concept of the determinant of a matrix. The determinant of a matrix is a scalar value that can be calculated from the elements of a square matrix. If the determinant of the matrix is non-zero, the system of equations has a unique solution. If the determinant is zero, the system may have either no solutions or infinitely many solutions.
To find the determinant of the matrix, we can use the formula:
| 2 4 |
| 3 6 | = (26) - (43) = 12 - 12 = 0
Since the determinant of the matrix is zero, the system of equations has either no solutions or infinitely many solutions.
To determine which case applies, we can use the concept of the rank of a matrix. The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of the matrix is less than the number of variables, then the system has no solutions. If the rank of the matrix is equal to the number of variables, then the system has a unique solution.
The rank of the matrix can be found by converting it into the row echelon form or reduced row echelon form.
| 2 4 | | 2 4 |
| 3 6 | = | 0 0 |
The rank is 1, which is less than 2, the number of variables. Therefore, the system of equations has no solutions.
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For what value of k pair of linear equations has infinitely many solutions KX 4y K 8 0 4x KY 4 0?.
The pair of the linear equations Kx + 4y + (μ+8) = 0 and 4x + ky + 4 = 0 has infinitely many solutions for k = ± 4.
Given lines are
kx + 4y + (μ+8) = 0
4x + ky + 4= 0
for lines to have infinite solutions
a₁/a₂ = b₁/b₂ = c₁/c₂ [a₁x + b₁y + c₁ = 0, a₂x + b₂y + c₂ = 0]
∴k/4 = 4/k = (μ+8)/4
∴k/4 = 4/k
⇒k² = 16
⇒k = ±4
We have, 4/k = (μ+8)/4
For, k = +4
⇒4/4 = (μ+8)/4
⇒μ = −4
For, k=−4
⇒4/-4 = (μ+8)/4
⇒μ = −12
∴ for k = ±4, the line has infinite solutions.
--The given question is incomplete; the complete question is
"For what value of K, the following pair of the linear equation has infinitely many solutions
Kx + 4y = (μ+8) = 0
4x + ky + 4 = 0"--
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4 less than the product of 1 and x
4 less than the product of 1 and x is x - 4.
How to represent word expression in algebraic expression?An algebraic expression is a variable expression described using its terms, and operations on the terms.
In other words, algebraic expression are mathematical expressions where variables and constant are combined using operations such as subtraction, addition, multiplication etc.
Therefore, let's express the word expression in algebraic expression,
Hence, 4 less than the product of 1 and x is represented as follows:
(1 × x) - 4
x - 4
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Pleaseeee helppp need this by tonight
Answer:
the domain is x ≥ -4
Step-by-step explanation:
on the x-axis, the graph does not extend below -4. the point on the graph is filled in, which makes the domain greater than or equal to -4.
hope this helped, good luck!
What is the value of the expression below when
�
=
3
x=3?
7
�
2
+
9
�
−
3
7x
2
+9x−3
Answer:
The value of the expression when x=3 is:
7^(3/2) + 9x - 3
We can simplify it as:
49 + 9*3 - 3
= 49 + 27 -3
= 73
So the final value of the expression is 73.
Given expression y=7x²+9x-3
Given value of x=3
We want to find the value of y.
Substitute the value of x=3 in y expression
y=7(3²)+9(3)-3
y=7*9+9*3-3
y=63+27-3
y=87
Therefore, the value of given expression is 87
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Complete question
What is the value of the expression below when x=3,
y=7x²+9x-3
A peron in a wheelchair exert a force of 25 n to go up a ramp that i 10 m long. The weight of the peron and wheelchair i 60 n and the height of the ramp i 3 m
To determine the amount of work done by the person in the wheelchair going up the ramp, you can use the formula for work:
work = force x distance x cos(theta)
where force is the force exerted by the person (25 N), distance is the distance traveled (10 m), and theta is the angle between the force and the displacement.
The angle between the force and the displacement is 90 degrees because the force is perpendicular to the displacement.
The force exerted by the person is to overcome the force of gravity on the person and wheelchair weight (60 N).
work = force x distance x cos(90)
work = (25 N + 60 N) x 10 m x cos(90)
work = 85 N x 10 m x 0
work = 0 J
It's impossible to do work when the angle between the force and the displacement is 90 degrees because the force and the displacement are perpendicular to each other.
The height of the ramp (3 m) is not used in this calculation, as it is not related to the force or distance.
The work done by the person in the wheelchair is 0 J because the force exerted by the person is perpendicular to the displacement. However, the person will be expending energy to overcome the force of gravity and move the wheelchair up the ramp.
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What ordered pairs are the solutions of the system of equations shown in the graph below?
NEED HELP ASAP
it is 21
Step-by-step explanation:
hi please help thanks
The letter on the number line that represents the given number is B.
What is a number line?A number line is a straight line which extends from -∞ to -∞, on which the position or location of all directed numbers can be identified.
Directed numbers are numbers which have either a negative or positive sign. Examples include; -4, -1 2/3. 9 etc. Therefore all numbers can be located on a number line.
Considering the given question, to locate the position of 1 85/100. The whole number make us to understand that its position falls between 1 and 2. And the fraction part shows that the number is closer to 2 more than 1.
Therefore, the letter on the number line that represents 1 85/100 is B.
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Brexton wants to lay some brown and yellow square tiles to cover the
floor. Each tile is one square meter. The number of brown tiles is 3
times the number of yellow tiles. He uses 60 brown tiles. How many
yellow tiles will he need? Explain your answer and show your work.
Select the correct answer from each drop-down menu.
The
of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the
pyramids are the same.
The volume of pyramid A
Is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B
Is the volume of pyramid A.
Pyramid A's base is a 20-meter-wide by 10-meter-long rectangle.
Base of Pyramid B has a square shape with 10-meter sides.
The heights are equal.
(L × W × H) / 3 equals the volume of a rectangular pyramid.
Square pyramid volume = a² × h/3
Assume that there are 10 meters above ground.
The rectangular pyramid's V is equal to (10m × 20m × 10m)/3, or 2000/3, or 666.67 m3.
V of Square pyramid: = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³
Pyramid A's volume is TWICE that of pyramid B's.
In the event when Pyramid B's height doubles that of Pyramid A (from 10m to 20m),
The square pyramid's V is equal to (10m)2 × (10 × 2)/3, 100m² × (20m/3), and 100m2 × 6.67m, or 666.67 m³
The volume of pyramid B has increased to the same level as pyramid A.
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How will you describe the nature of roots of 2x² 4x 7?.
Therefore, the real and unequal roots of the quadratic equation. The roots are uneven and real when the discriminant is bigger than zero. The roots are equal and real when discriminant is equal to zero.
When are the real and unequal quadratic equation roots?When a, b, and c are real integers and the discriminant is bigger than zero (b2 - 4ac > 0), the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal.
Which quadratic equation's roots are rational and unequal?In this situation, we say that the roots are hypothetical. Ax2 + bx + c = 0 has real, rational, and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive and perfect square.
D=b \s2 \s −4ac=42 \s −4×2×(−7)=16+56=72>0.
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Full Question = What will be the nature of roots of quadratic equation 2x 2 +4x−7=0?
THIS IS URGENT!!!!!!!!!!!!!!
what is the sum of 11 of the interior angles of a regular dodecagon?
The sum of 11 of the interior angles of a regular dodecagon is 1650°.
The formula (180n-360)/n is used to determine the interior angle of a regular polygon. n=11 for an undecagon.
The interior angle of a regular dodecagon is 150°.The sum of 11 of the interior angles of a regular dodecagon is 150* 11 = 1650°.
The interior angles of a dodecagon are a bit harder. You can use this generic formula to find the sum of the interior angles for an n-sided polygon (regular or irregular).Sum of interior angles = (n-2)\times 180°(n−2)×180°
Sum of interior angles = 10\times 180°=1800°10×180°=1800°
Therefore, the sum of 11 of the interior angles of a regular dodecagon is 150* 11 = 1650°.
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5
r
−
8.35
s
when
r
=
12
and
s
=
4
?
Answer:
26.40
Step-by-step explanation:
r=12
s=4
5r − 8.35s =
5(12) - 8.35(4) = ==> plug in 12 for r and 4 for s
60 - 33.40 = ==> simplify
60.00 - 33.40 =
60 - 33 + 0.00 - 0.40 =
27 - 0.40 = 26.40
Jayden owns 32 rabbits. If 12 of his rabbits are male, what percentage of Jayden's rabbits are male
Answer:
37.5%
Step-by-step explanation:
We take
12 divided by 32, then times 100% = 37.5%
So, 37.5% of Jayden's rabbits are male
9. - Laura, Raúl y Miguel compraron un terreno de 900 metros cuadrados con valor de 540,000 pesos.
Laura puso 300,000 mil pesos, Raúl puso 200,000 mil pesos y Miguel 40,000 mil pesos. ¿Qué cantidad
de terreno le debe tocar a Laura?
a) 600 m2
b) 24 m2 c) 500 m2 d) 30 m2
The amount of yard that has to be given to Laura is c) 500 m2
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information:
Total of money = 540 000
Laura's money = 300 000
Lets represent the amount of money Laura gave:
Laura's % = (300 000 / 540 000) * 100
Laura's % = 30/54 * 100
Laura's % = 5/9 * 100
Laura's % = 55.56%
The amount of yard should be for Laura is:
Laura's yard = Total yards area * Laura's %
Laura's yard = 900 m^2 * 55.56%
Laura's yard = 500 m^2
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20 POINTS PLEASE SOLVE I NEED TO HAVE THIS SUBMITTED!
Interpret the notation that defines the reflection. Show your work and explain the steps
you used to solve.
Therefore , we can conclude from the answer to the above problem that the equation for a reflection from across y-axis is - (x,y) -> (x,y).
Describe the y-axis.The x-axis and y-axis are the coordinate plane two crucial axes. In contrast to the x-axis, which is a horizontally number line, the y-axis is vertical. Its two orthogonal axes make up a coordinate plane. The ordinate refers to the y-axis, whereas the abscissa refers to the x-axis.
Here,
The Y-axis is the line that runs vertically along the graph from bottom to top. The measurement coordinates are parallel to the this axis.
The numbers on the y-axis are known as y-coordinates.
When expressing following result, the x-coordinate and y-coordinate go in parentheses in that order.
(x, y).
A' ( -1, 1 ) => A"(-1, -1) (-1, -1)
B' (-2, 2) => B"(-2, -2) (-2, -2)
C' (-2, 3) => C"(-2, -3) (-2, -3)
and D' (-1, 4) => D " (-1, -4)
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What is the degree of the polynomial 2x² 5x³ 7 3?.
The degree of the polynomial 2x² 5x³ 7 is 5.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
What is the degree of the polynomial 2x² 5x³ 7?
Are all right triangles 30 60 90 triangles?.
No, All 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles.
No, not all right triangles are 30-60-90 triangles. A right triangle is a type of triangle that has one right angle (90 degrees) and two acute angles. The other two angles in a right triangle can have any measurement, they don't have to be 30-60-90 degrees.
A 30-60-90 triangle is a special type of right triangle that has specific angle measurements: one angle is 90 degrees (the right angle), one angle is 30 degrees, and one angle is 60 degrees. The ratio of the sides in a 30-60-90 triangle is also fixed, the longest side is opposite the 90-degree angle and it is always twice the length of the shortest side and the medium side is opposite the angle of 60 degrees and it's always the square root of 3 times the length of the shortest side.
For example, if a right triangle has angles of 45 degrees, 45 degrees, and 90 degrees, it is not a 30-60-90 triangle. The angles do not fit the pattern of 30-60-90 degrees.
Therefore, In short, all 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles. A 30-60-90 triangle is a special type of right triangle with specific angle measurements and side ratios.
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An artist is going to cut four similar right triangles from a rectangular piece of paper like the one shown to the right. What is BE to the nearest tenth when AC=13
The measurement of altitude BE is 4 unit.
What is an altitude?As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.
As ABCD is rectangle
AD = BC = 12
ΔABC = ΔBCD
BE = FD
5² = 3²+BE²
AE = 3
BE = √(5²-3²)
BE = 4
Thus, The measurement of altitude BE is 4 unit.
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How do you draw a line Y X?.
By plotting the points (1, 1) and (4, 4) on the graph and joining the points we get a straight line which is the graph of y = x
Given, the linear equations are y = x and y = -x
We have to draw the graphs of the equations on the same cartesian plane.
Considering the equation y = x
We need a few points to plot on the graph.
For x = 1, y = 1
For x = 4, y = 4
Therefore, the points of the equation are (1, 1) and (4, 4)
By plotting the points (1, 1) and (4, 4) on the graph and joining the points we get a straight line which is the graph of y = x
Considering the equation y = -x
We need a few points to plot on the graph.
For x = 3, y = -3
For x = -4, y = 4
Therefore, the points of the equation are (3, -3) and (-4, 4)
By plotting the points (3, -3) and (-4, 4) on the graph and joining the points we get a straight line which is the graph of y = -x.
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i need answer by today
Answer:
5.196152421cm
Step-by-step explanation:
tan= opposite(perpendicular)/adjacent(base)
tan60=9/x
1.732050808=9/x
1.732050808x=9
x=9/1.732050808
x=5.196152421
your investment of 18500 at 17.6% compounded quarterly for 7.5 years will be worth how much ?
The investment of $18,500 at 17.6% compounded quarterly for 7.5 years will be worth (a future value of) $67,326.60.
What is the future value?The future value is the present value compounded periodically at an interest rate.
Compounding involves computing interest on interest.
The future value of the investment after the stated period can be determined using an online finance calculator as follows:
N (# of periods) = 30 years
I/Y (Interest per year) = 17.6%
PV (Present Value) = $18,500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $67,326.60
Total Interest = $48,826.60
Thus, in 7.5 years' time, the investment will be worth $67,326.60.
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A group of friends went to lunch. The bill, before sales tax and tip, was 37.50. A sales tax of 8% was added..The group then tipped 18% on the amount after the sales tax was added.What was the amount in dollars of the sales tax?
what was the total amount the group paid,including tax and tip?
The amount of sales tax is $3,
The total amount the group paid, including tax and tip is $47.79.
What is the percentage?A percentage is a figure or ratio that can be stated as a fraction of 100.
If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given The bill, before sales tax and tip,
amount of the bill before sales tax and tip = $37.50
sales tax is 8% on bill
sales tax = 8% of 37.50
sales tax = 37.50*8/100
sales tax = 37.50*0.08
sales tax = $3
amount after sales tax = $37.50 + $3
amount after sales tax = $40.5
the tip is 18% of the amount after the sales tax
tip = 18% of 40.5
tip = 40.5*18/100
tip = 40.5*0.18
tip = $7.29
total bill amount = $37.50 + $3 + $7.29
total bill amount = $47.79
Hence the sales tax is of $3 and the total amount is $47.79.
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How do you solve log2 equations?.
There is a formula to calculate logarithms to base 2 or log base 2 equations. The formula is stated by log₂x = log₁₀x/log₁₀2.
A logarithm is an exponent to which a base must be raised to generate a given number. Expressed mathematically, x is the logarithm of n to the base a if ax = n, in which case one writes x = logₐn.
A logarithm is defined using an exponent.
aˣ = b ⇔ logₐb = x
Here, "log" stands for logarithm. The arrow's right part is read as "Logarithm of b to the base a is equal to x".
Let us take an example of log base 2 equations,
log₂49
Using the change of base formula,
= log₂x = log₁₀x/log₁₀2
= log₂49 = log₁₀49/log₁₀2
= 1.69019608/0.301030
= 5.6147
Therefore, the value of log₂49 is 5.6147.
--The given question is incomplete; the complete question is
"How do you solve log base 2 equations?"--
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please help!!!! asap!!!! piecewise functions
Answer:
undefined
Step-by-step explanation:
You want the value of f(-1), given the piecewise defined function f(x).
DomainThe function is defined for values of x greater than 1. The value x=-1 is not part of the domain of the function:
f(-1) = "undefined"
How do you solve 2x 3y =- 6?.
The value of y in equation 2x-3y=-6 is y = (2x+6)/3
Let us proceed to solve the equation 2x - 3y = -6
We take the term 3y to the right-hand side of the equation which gives 2x = -6 + 3y
Now we bring 6 to the left side of the equation 2x + 6 = 3y
And lastly, we bring the 3 also to the other side of the equation thus dividing the term (2x-+6) by 3 which ultimately gives us the value of y.
(2x + 6) /3 = y
Thus, The value of y in equation 2x-3y=-6 is y = (2x+6)/3
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Wbić is the od one out
The odd one out is the furthest to the right. the Nickels.
The first square is 25 cents. The second square is 25 cents. The third square is 15 cents.
I hope this helps you :D
What is the formula of linear equation in two variables Class 9?.
An equation that has two variables which the formula Ax + By = C.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1.
So, an equation that has two variables which the formula Ax + By = C.
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Classify the system and give the number of solutions.
Please explain too
The system formed by linear equations - 8 · x + 8 · y = 1 and - 32 · x + 32 · y = - 5 has no solution.
How to classify a system of linear equations
In this problem we find a system formed by two linear equations with two variables. There are three kinds of systems of linear equations:
One solutionInfinite solutions - When a equation is a multiple of the other one.No solution - When an absurdity exists between independent coefficients.First, write the system of linear equations:
- 8 · x + 8 · y = 1
- 32 · x + 32 · y = - 5
Second, multiply the first equation by 4:
- 32 · x + 32 · y = 4
Third, use transitive property:
4 = - 5 (CRASH!)
The system of linear equations has no solution.
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