The sum of an irrational number and a rational number can either be rational or irrational.
Depending on the specific numbers involved. There is no general expression for the sum of an irrational number and a rational number being irrational. If the sum of two numbers is irrational, it means that the result cannot be expressed as a simple fraction, and its decimal representation either goes on forever without repeating or repeats after a certain number of digits.
One example of the sum of an irrational number and a rational number being irrational is:
√2 + 1/2 = 1.732 + 0.5 = 2.232 (irrational)
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How do you find the Circumcentre of a triangle?.
The circumcenter of a triangle is the point where the perpendicular bisectors of all three sides of the triangle intersect.
To find the circumcenter of a triangle, you can:
Draw the perpendicular bisectors of all three sides of the triangle.
Locate the point where the three bisectors intersect. This is the circumcenter of the triangle.
To find the circumcenter of a triangle with the coordinates of its three vertices, use the circumcenter formula which is (x₁ + x₂ + x₃)/3 and (y₁ + y₂ + y₃)/3 for x and y coordinates respectively.
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the graph of a sinusoidal function has a maximum point at (0,5) and then has a minimum point at (2pi,-5). write the formula of the function, where x is entered in radians
The equation of the function is y = 10 * sin(x/2pi) + 5.
What is the sinusoidal function?
The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.
The graph of a sinusoidal function can be represented by the equation:
y = A * sin(B(x - C)) + D
where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.
From the information given, we know that the maximum point is at (0,5) and the minimum point is at (2pi,-5). We can use this information to find the values of A, B, C, and D.
The amplitude is the distance between the maximum and minimum points. In this case, it is 5 - (-5) = 10. So A = 10.
The period of the function is the distance between two consecutive maximum or minimum points. In this case, it is 2π.
So the frequency is 1/2π.
The horizontal shift is the amount by which the function is shifted along the x-axis. In this case, the maximum point is at x = 0, so the function is not shifted horizontally. So C = 0.
The vertical shift is the amount by which the function is shifted along the y-axis. In this case, the maximum point is at y = 5, so the function is shifted upward by 5. So D = 5.
So the equation of the function is:
y = 10 * sin(1/2pi (x - 0)) + 5
y = 10 * sin(x/2pi) + 5
where x is entered in radians.
Hence, the equation of the function is y = 10 * sin(x/2pi) + 5.
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1) Evaluate.
8²=?
2) Evaluate.
5²=?
3) Evaluate.
13²=?
8² = 64 , 5² = 25 and 13² = 169 . A number that has been multiplied by itself produces a square number.
What is the squares of the given numbers ?8² = 8 × 8 = 64 , 5² = 5 × 5 = 25 and 13² = 13 × 13 = 169 . Informally: A square number, perfect square, or simply "a square" is what is produced when you multiply an integer (a "whole" number), positive, negative, or zero, times itself. So all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so forth.
Similar to numbers like 2, 3, 5, 6, 24, 13, 125, etc., 12, however, is not a square. Consequently, its simplicity is somewhat usual. nevertheless, are 4, 16, 25, 81, 121, and other numbers. It is incorrect to say that the number 14 is a perfect square because it cannot be written as the product of two equal numbers. If n is a number, then n2 stands in for n.
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What is the sum of the polynomials x2 9 +- 3x2 11x 4?.
The sum of the polynomials (-x² + 9) and (-3x² - 11x + 4) is -4x² - 11x - 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 sum of the polynomials (-x² + 9) and (-3x² - 11x + 4)?
Which values are solutions to the inequality?
PLEASE AWNSER QUICKLY!!!
3r≤4r−6
Select each correct answer.
r = 4
r = 5
r = 6
r = 7
Answer:r=6,7
Step-by-step explanation:3(6)<4(6)-6= 18<24-6= 18<18
3(7)<4(7)-6= 21<28-6= 21<22
Hi,please help !
(see image!)
The perimeter of each shape are as follows:
a. 4x + 18 units
b. 6y + 4x units
c. 5x units
d. 16x + 12 units
The area of the square is 9x² units²
How to find the area and perimeter of a figure?The perimeter of a shape is defined as the total length of its boundary. In other words, the perimeter of a shape is the sum of the whole sides of the figure.
Therefore, let's find the perimeter of the shapes as follows:
a.
perimeter = x + 9 + x + 9 + x + x
perimeter = 4x + 18
b.
perimeter = 3y + 3y + 2x + 2x
perimeter = 6y + 4x
c.
perimeter = 2x + 2x + x
perimeter = 5x
d.
perimeter = 4x + 1 + 2x + 3x + 5 + 2x + 1 + 3x + 5 - 2x + 4x + 1 - (2x + 1)
perimeter = 16x + 12
Area of the square = l²
where
l = side lengthTherefore,
Area of the square = (3x)²
Area of the square = 9x²
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Miriam spent $80 on a concert ticket and 2
snacks. A movie ticket costs $65. How
much was spent on each snack (they cost
the same amount)
The equation represents the cost of snacks. Then the cost of each snack will be $7.5.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Miriam spent $80 on a concert ticket and 2 snacks. A movie ticket costs $65.
Let 'x' be the cost of each snack. Then the equation is given as,
65 + 2x = 80
Simplify the equation, then we have
65 + 2x = 80
2x = 80 - 65
2x = 15
x = 15 / 2
x = $7.5
The equation represents the cost of snacks. Then the cost of each snack will be $7.5.
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What are the 4 acute angles?.
Four acute angles are given by : Angle with measure 12 degrees, angle with measure 45 degrees , angle with measure 89 degrees and angle with measure 1 degree.
As given in the question,
Four angles representing acute angles are as follow :
Acute angles : Acute angles are geometrical figure, angles which has measure greater than zero degree and less than 90 degree.
Examples of acute angles are given by :
a. 12 degree : 12 degree is less than 90 degree and greater than 0 degree.
b. 45 degree : 45 degree is more than 0 and smaller than 90 degree.
c. 89 degree : 1 degree less than 90 and 89 more than 0.
d. 1 degree : 0 < 1 < 90.
Therefore, four acute angles are of measure 12 degree, 45 degree, 89 degree and 1 degree.
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UGRENT!
find the x vaults in each supplementary angle pair
Answer:
x=210
Step-by-step explanation:
supplementary angles add up to 180 so to find x in this problem we have to keep in mind that it is gonna be divided by 2. So first subtract 75 from 180 which equals 105. Then because x is going to be divided by 2 we are going to multiply 105 by 2 so when it’s eventually divided the 2 angles equal 180. So x= 210 and 210/2 = 105 and 105+75=180.
A sculptor begins work on a block of granite that has a mass of 400 kg. What is the density of the granite?
The method for density is d = M/V, where d is density, M is mass, and V is extent. Density is usually expressed in devices of grams in keeping with cubic centi meter.
what's the density of the granite?The common density of granite is between 2.65 and 2.75 g/cm3 (one hundred sixty five and 172 lb/cu feet), its compressive energy usually lies above hundred MPa (29,000 psi), and its viscosity close to STP is 3–6·1020 Pa·s.
GRN = GL * GW * GT/12 * a hundred seventy five
GRN is the Granite Weight (lb)
GL is the granite period (ft)
GW is the granite width (feet)
GT is the granite thickness (in)
The density of granite is high and tiers from 2.sixty three to two.75 g according to cm3. Its resistance to strain is between 1.000 and 1.4 hundred good enough in step with cm2.
Rock density can be very sensitive to the minerals that compose a particular rock kind. Sedimentary rocks (and granite), which can be rich in quartz and feldspar, have a tendency to be less dense than volcanic rocks.
Therefore, The method for density is d = M/V, where d is density, M is mass, and V is extent.
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A girl borrowed R128000 from a bank to buy a piece of land. If the land charge 15% p. A, compounded half yearly, what will he have to pay after 1½ year? Alo find fhe compound interet
Girl have to pay total R159014 to bank and compound interest is R31014.
A girl borrow R128000 from a bank to buy a piece of land.
Land charge is 15% Per Annum and time is 1 [tex]\frac{1}{2}[/tex] year.
Compounding with half yearly.
So land charge will be (15/2) % per half yearly and time will be 2 x 1 [tex]\frac{1}{2}[/tex] = 3 half years.
Total amount ( A ) =P (1+R/100)^T
P = initial principal = 128000
R = (15/2) %
T = 3 half yearly
A =P[tex](1+\frac{R}{100} )^{T}[/tex]
A=128000[tex](1+\frac{15}{2*100} )^{3}[/tex]
A=128000[tex](\frac{43}{40} )^{3}[/tex]
A=159014
Total interest amount = 159014 – 128000 = 31014
Therefore , total payable amount is R159014 and interest amount is R31014.
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Elena is 59 inches. Some people are taller than Elena
The height of Andre, given the height of Elena is 63 inches tall.
The height of Lin is 65 .5 inches tall.
The height of Noah is 59 + d inchs tall.
How tall are the people?The height of the other people given which include Andre, Lin, and Noah, are all dependent on the height of Elena.
Andre is 4 inches taller than Elena so the height is:
= 59 + 4
= 63 inches
The height of Lin is:
= 59 + 6 .5
= 65 .5 inches
The height of Noah is:
= 59 + d inches
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Answer the question below. Be sure to show all of your work.
Naomi earned $45 after babysitting for 5 hours one afternoon. Another day, she babysat for
8 hours and earned $72. Write two equations (one in point-slope and one in slope-intercept)
that represents the number of hours she babysits, x, and the amount of money she earns, y.
Leticia babysat 5 hours on Saturday.
How to calculate?First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. Leticia watched the children for four hours on Friday and for an undetermined period of time on Saturday.
earned $72, Therefore:
8 ( 4 + x ) = 72
( 4 + x ) = 72 / 8
4 + x = 9
x = 9 - 4
x = 5
Leticia babysat 5 hours on Saturday
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A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
Answer:
the answer is 56.58%
Step-by-step explanation:
The first step is to divide 43 by 76 to get the answer in decimal form:
43 ÷ 76 ≈ 0.5658
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.5658 × 100 = 56.58%
what is 1 and 2/5 as an improper fraction
Answer:
[tex]\displaystyle 1\frac{2}{5}=\frac{7}{5}[/tex]
Step-by-step explanation:
[tex]\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}[/tex]
Jackie’s pizzeria made 50 pizzas. 3 of the pizzas had thin crust and the rest had thick crust. What is the ratio of the number of thick-crust pizzas to the number of thin-crust pizza?
Answer:
47:3
Step-by-step explanation:
47 pizzas had thick crust and 3 had thin crust
what is 16 over 16 as a whole number
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
16/16
16 ÷ 16 = 1
So your answer is 1
HAVE A GREAT DAY!
What is the value of k for which the system of equations KX 2y 5 and 3x Y 1 has no solution?.
So, the system of equations kx + 2y = 5 and 3x + y = 1 has no solution when k - 6 ≠ k, which means k ≠ 6.
A system of equations has no solution when there are no values that can be assigned to the variables that make all equations true. This means that the equations are inconsistent.
In this case, the system of equations is kx + 2y = 5 and 3x + y = 1. To check whether the system has a solution or not, we can use different methods such as substitution, elimination, or graphing.
One of the methods that can be used to check for consistency is by finding the determinant of the system and comparing it with the determinant of the coefficient matrix. The determinant of the system is the determinant of the matrix formed by the coefficients of the variables and the constant terms.
The determinant of the system is |k 2| |3 1| = k1 - 23 = k - 6
The determinant of the coefficient matrix is |k 2| = k*1 = k
To have no solution, the determinant of the system must be non-zero but different from the determinant of the coefficient matrix.
Therefore, the system of equations kx + 2y = 5 and 3x + y = 1 has no solution when k - 6 ≠ k, which means k ≠ 6.
In other words, the system of equations kx + 2y = 5 and 3x + y = 1 has no solution when k is different from 6.
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the domain of y= csc is given by
The domain of the trigonometric equation y = cosec ( x ) is given by the relation domain of y = cosec ( x ) is x∈R , x≠π⋅n , n∈Z
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
y = cosec ( x ) be equation (1)
On simplifying the equation , we get
y = 1 / sin ( x )
Now , the domain and range of the function will be related to the sine function and range of the sine function -1 ≤ y ≤ 1
The domain of y = cosec ( x ) is every value in the domain of sine with the exception of where sin ( x ) = 0. Since the reciprocal of 0 is undefined. So we solve sin ( x ) = 0 and get x = 0 + π⋅n where n∈Z.
Therefore , the domain of y = cosec ( x ) is x∈R , x≠π⋅n , n∈Z
Hence , the domain is x∈R , x≠π⋅n , n∈Z
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Conider triangle PQR. What i the length of ide QR?
8 unit
8 StartRoot 3 EndRoot unit
16 unit
16 StartRoot 3 EndRoot unit
The length of side QR of triangle PQR can be calculated by using the Pythagorean Theorem. The length of QR is equal to the square root of the sum of the squares of the length of the other two sides. Therefore, if the length of sides PQ and PR are 3 units each, then the length of side QR is 8 Start Root 3 End Root units.
The length of side QR of triangle PQR can be determined by using the Pythagorean Theorem. This theorem states that in a right triangle, the sum of the squares of the lengths of the two sides is equal to the square of the length of the hypotenuse. Therefore, for triangle PQR, if the lengths of sides PQ and PR are 3 units each, then the length of side QR can be calculated by taking the square root of the sum of the squares of the lengths of the other two sides. This means that the length of side QR is 8 Start Root 3 End Root units. To calculate this, first, calculate the squares of the lengths of the other two sides by multiplying them by themselves, i.e. 3 x 3 = 9 and 3 x 3 = 9. Then, sum the squares of the lengths of the other two sides, i.e. 9 + 9 = 18. Finally, take the square root of the sum of the squares of the lengths of the other two sides, i.e. Start Root 18 End Root = 8. Thus, the length of side QR is 8 Start Root 3 End Root units.
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Sebatian i having a tea party at home for which he ha invited ome of hi friend. If 8 bottle
of mango juice cot AED 16 , then how much hould he pend for 15 uch bottle?
15 bottles of Mango juice cost AED 30
Will this solve this question by the unitary method
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What would he pay for 15 bottles of mango juice if 8 bottles cost AED 16?
so,
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
8 bottle=AED16 So I bottle of mango juice costs AED 2.
2x15=30
So,15 bottles of Mango juice cost AED 30
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4x-8=3x+72
please answer in linear equations
By calculating, The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and the sum of three angles is always 180 degrees
Given expression ,
4x-8 = 3x+2
4x-3x = 2 + 8
x = 10
So the sides given in the triangle are 5x+1 , 2x+3 and 5x+2
So put x=10 in the give sides
we get,
5x+1 = 5*10 + 1 = 51
2x+3 = 2*10 + 3 = 20 + 3 =23
5x+2 = 5*10 + 2 = 50 + 2 = 52
The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.
Hence, By calculating, The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.
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What is the product of X+ a and x b )?.
The product of expressions ( x + a ) and (x + b ) is equals to the x² + (a - b)x - ab.
Product is an important arithmetic operation. The multiplication or product of algebraic expressions is a method of multiplying two expressions consisting of variables and constants. The product of two factors with the same signs will be positive, and the outcome of multiplying two terms with two, unlike signs, will be negative. We have two algebraic expressions as ( x + a) and ( x - b) and we have to calculate their product.
=> (x + a) ( x - b) = x( x- b) + a(x - b)
=> (x + a) ( x - b) = x² - xb + ax - ab
=> (x + a) ( x - b) = x² + (a - b)x - ab
Hence, required product is x² + (a - b)x - ab .
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Complete question:
What is the product of (x + a )and (x - b )?.
What is the trigonometric ratio of sin θ?.
The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
In arithmetic, the trigonometric functions (also known as circular features, perspective features, or goniometric functions) are actual features that relate an angle of a proper-angled triangle to ratios of side lengths. they may be extensively utilized in all sciences which might be associated with geometry, such as navigation, strong mechanics, celestial mechanics, geodesy, and lots of others. they are a few of the handiest periodic features, and as such are also extensively used for analyzing periodic phenomena through Fourier analysis.
The trigonometric functions most extensively used in cutting-edge mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. each of these six trigonometric capabilities has a corresponding inverse function and an analog most of the hyperbolic features.
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What is the distance between points − 6 − 7 and − 1 5 on the coordinate plane?.
The distance between points A(-6,7) and B(-1,-5) is 13 units.
We know that the distance formula.
According to distance formula distance between points (x₁, y₁) and (x₂, y₂) is given by,
[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]
Here we have been given points A(-6,7) and B(-1,-5)
Let us assume that (x₁, y₁) = (-6, 7)
and (x₂, y₂) = (-1, -5)
Also, d represents the distance between points A(-6,7) and B(-1,-5)
Using above distance formula,
[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-1 - (-6))^2 + (-5 - 7)^2]}\\\\\Rightarrow d = \sqrt{[(-1+6)^2 + (-12)^2]}\\\\\Rightarrow d = \sqrt{[(-5)^2 + (-12)^2]}\\\\\Rightarrow d = \sqrt{25+144}\\\\\Rightarrow d = \sqrt{169}\\\\\Rightarrow d = 13~units[/tex]
Therefore, the distance between points A and B is 13 units.
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The complete question is:
What is the distance between points A(-6,7) and B(-1,-5) on the coordinate plane?
3. Last week Thema ran 2 fewer than 4m miles.
This week she ran 0.5 miles more than last
week. Write an expression for the total number
of miles Thema ran in the two weeks. Then
combine like terms.
The expression for the total miles Thema ran in two weeks will be 8m-3.5 miles.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
As given last week Thema ran=4m-2 miles
this week thema ran=4m-2+0.5 miles
Hence,
expression for the total number of miles Thema ran in the two weeks will be 4m-2+4m-1.5
=8m-3.5 miles
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What is the inverse of an exponential function?.
The inverse of an exponential function is the natural logarithm function. More specifically, if f(x) = a^x, where a is a positive constant and x is a real number, then the inverse function, denoted as f^-1(x), is given by f^-1(x) = log_a(x).
An inverse function is a function that "undoes" the effect of another function. In other words, if we have two functions, f and g, such that g(f(x)) = x for all x in the domain of f, and f(g(x)) = x for all x in the domain of g, then f and g are inverses of each other.
In the case of exponential functions, f(x) = a^x where a is a positive constant and x is a real number, the inverse function is the natural logarithm function, g(x) = log_a(x).
The natural logarithm function "undoes" the effect of the exponential function by taking the logarithm of the output of the exponential function with base 'a' and returns the input value.
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The base of a right triangle is 48cm and its hypotenuse is 50cm. What will be the areas of the triangle? class 9
The area of a triangle can be found using the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 48cm and the hypotenuse is 50cm. Since this is a right triangle, we can use the Pythagorean theorem to find the length of the height. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So,
c^2 = a^2 + b^2
50^2 = 48^2 + b^2
2500 = 2304 + b^2
b^2 = 2500 - 2304
b = √(2500 - 2304)
b = √(196)
b = 14
So, the height of the triangle is 14cm.
Area = (1/2) * 48 * 14 = 336cm^2
Is 2x 3y =- 6 in standard form?.
Yes, 2x + 3y = -6 is in standard form.
The standard form of a linear equation is an equation where the variables are written with a coefficient of 1 or -1, and the constant term (the term with no variables) is written on the right side of the equation. The equation is also written in the form of Ax + By = C, where
x and y are variablesA, B, and C are constants.In equation 2x + 3y = -6, the variables x and y are written with coefficients of 2 and 3 respectively, and the constant term -6 is on the right side of the equation. This satisfies the criteria for standard form as described above.
Key points:
In summary, 2x + 3y = -6 is in standard form because it satisfies the following key points:
The variables are written with a coefficient of 1 or -1.The constant term is written on the right side of the equation.The equation is written in the form of Ax + By = CThe coefficients of the variables are positive or negative but not zero.Learn more about linear equations here:
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The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.
The expression [tex]x^{3} +3x^{2}[/tex] represents the volume of the prism, in cubic units.
We have given that the,
The height of a right rectangular prism is 3 units greater than the length of the base.
The edge length of the square base is x units.
The volume of a rectangular prism = width*length*height
V=w*l*h ......(1)
We have given that the
h=3 greater than the length of the base
and the length of the base is x
Hence, h=x+3
length of base = x
width = x
Substituting values l h and w into the formula (1) we get,
V=w*l*h
= [tex](x)*(x)*(x+3)[/tex]
= [tex]x^{2}*(x+3)[/tex]
=[tex]x^{3}+3x^{2}[/tex]
Therefore the expression
[tex]x^{3}+3x^{2}[/tex] represents the volume of the prism, in cubic units.
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