Justification for equation 23x−13=2(x+2) with Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality. We also combined and isolated variable. The final solution is x = -1.1905.
Here is a step-by-step justification for each step in the solution of the equation 23x−13=2(x+2):
Step 1: Given
The equation 23x−13=2(x+2) is given as part of the problem statement.
Step 2: Distributive Property
We distribute the 2 on the right side of the equation by multiplying it by both terms inside the parentheses to get 2x + 4. This results in the equation 23x − 13 = 2x + 4.
Step 3: Combine like terms
We combine the like terms on the right side of the equation to get 6x + 12. This results in the equation 23x − 13 = 6x + 12.
Step 4: Distributive Property
We subtract 2x from both sides of the equation to isolate the variable on one side. This results in the equation 21x - 13 = 12.
Step 5: Addition or Subtraction Property of Equality
We add 13 to both sides of the equation to isolate the variable. This results in the equation 21x = 25.
Step 6: Division Property of Equality
We divide both sides of the equation by 21 to solve for x. This results in the solution x = 25/21 or x = -1.1905.
In conclusion, the Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality were used to support each step in the solution of the problem 23x13=2(x+2). In order to make the equation simpler and isolate the variable on one side, we additionally combined like terms. x = -1.1905 is the solution's final form.
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The equation of the piecewise defined function f(x) is below. What is the value of f(1)?
[x²+1, -4
f(x) = -x², 1
3x, x22
f(1) = -2
f(1) = -1
f(1) = 2
f(1) = 3
The second piece of the function applies to x = 1, which is f(x) = -x².
Thus, f(1) = -(1)² = -1. The correct answer is f(1) = -1.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.
To find the value of f(1), we need to determine which piece of the function applies to x = 1.
Since 1 is greater than 0 and less than 2, the second piece of the function applies to x = 1, which is f(x) = -x².
Thus, f(1) = -(1)² = -1.
Therefore, the correct answer is f(1) = -1.
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Drag the similar figure into the table. Angle measures are rounded to the nearest integer.
Triangle (B) is a comparable number that you must drag into the table.
What are angles?
An angle is formed when two straight lines or beams meet at a singular endpoint.
The intersection of two locations is known as the vertex of an arc.
The word "angle" is derived from the Latin word "angulus," which means "corner."
But there are some basic viewpoints.
Combining different shots greatly expands your camera options.
The most confusing of the five angles involves taking a scene from straight overhead.
So, the following:
Using the provided figure, we obtain:
A 60-degree equilateral triangle is depicted in the image.
And as can be seen in figure B, we obtain an equilateral triangle with a 60-degree inclination on each side.
Therefore, triangle (B) is a comparable number that you must drag into the table.
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A box with a square base and open top must have a volume of 13,500 cm^3. Find the dimensions of the box (in cm) that minimize the amount of material used.
There are 2 answer, the height and the sides of the base.
Let the side length of the square base be x cm and the height of the box be h cm. Then the volume of the box is given by:
V = x^2 * h = 13,500 cm^3
We want to minimize the amount of material used, which is the surface area of the box. The surface area A is given by:
A = x^2 + 4xh
We can use the volume equation to solve for h in terms of x:
h = 13,500 / x^2
Substituting this into the surface area equation gives:
A = x^2 + 4x(13,500 / x^2) = x^2 + 54,000 / x
To minimize A, we take the derivative with respect to x and set it equal to zero:
dA/dx = 2x - 54,000 / x^2 = 0
Solving for x, we get:
x^3 = 27,000
x = 30
Substituting this back into the volume equation gives:
h = 13,500 / (30^2) = 15
Therefore, the dimensions of the box that minimize the amount of material used are 30 cm by 30 cm by 15 cm.
What is a rectangular prism?
A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.
The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.
How do I find the volume of a rectangular prism?
The rectangular prism volume formula is:
volume = h × w × l,
where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:
Find the box length. For example, it can be equal to 18 in.
Determine its width. Let's say you measured 12 in.
Find out the rectangular prism height. Assume it's 15 in.
Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.
How do I find the area of a rectangular prism?
The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:
surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),
where h is prism height, w is its width, and l is its length.
Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:
Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².
Or save yourself some time and use our rectangular prism calculator.
Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.
How do I calculate the diagonal of a rectangular prism?
To determine the diagonal of a rectangular prism, apply the formula:
diagonal = √(l² + h² + w²)
where h is prism height, w is its width, and l is its length.
Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.
How to calculate volumes of the other solids?
That rectangular prism was a piece of cake! If you are amazed at how easily you can calculate the volume with our tool, try out the other volume calculators:
triangular prism calculator
cylinder volume calculator
sphere volume calculator
cone volume calculator
pyramid volume calculator
Suppose a pendulum is L meters long. The time, f, in seconds that it takes to swing back and forth once is given by t=2.01 √L. If a pendulum is 13.69
meters long, how long does it take to swing back and forth once?
Round your answer to the nearest tenth.
Rounded to the nearest tenth, the approximate duration for one swing of a pendulum with a length of 13.69 meters is 7.7 seconds.
We are given that the time, t, in seconds it takes for a pendulum to swing back and forth once is given by:
t = 2.01√L
where L is the length of the pendulum in meters.
We are asked to find the time it takes for a pendulum of length 13.69 meters to swing back and forth once. So we can substitute L = 13.69 into the equation above to get:
t = 2.01√(13.69) ≈ 2.01 × 3.7 ≈ 7.7
Therefore, the time it takes for a pendulum of length 13.69 meters to swing back and forth once is approximately 7.7 seconds (rounded to the nearest tenth).
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Need help with HW question 5
The characteristic polynomial of A is λ³ - 4λ² - 3λ + 14. The eigenvalues of A are 2, 1, and 7.
What is rational root theorem?According to the rational root theorem, p is a factor of the constant term and q is a factor of the leading coefficient if a polynomial with integer coefficients has a rational root of p/q, where p and q are integers without any shared factors. As the leading coefficient is 1 and the constant term is 14, the only potential rational roots in this situation are 1, 2, 7, and 14.
The characteristic polynomial of a matrix is given as
det(A - λI)
Here, λ is the eigen value.
det (A - λI)
[tex]\left[\begin{array}{ccc}1 - \lambda&0&1\\2&3 -\lambda&-1\\0&6& \lambda\end{array}\right][/tex]
Taking the determinant we have:
det(A - λI) = (1-λ)[(3-λ)(-λ) - (-1)(6)] - 0[2(-λ) - (-1)(0)] + (-1)[2(6) - (3-λ)(0)]
det(A - λI) = (1-λ)(λ² - 3λ - 6) - (-1)(12) = λ³ - 4λ² - 3λ + 14
Hence, the characteristic polynomial of A is λ³ - 4λ² - 3λ + 14.
The eigen values is the solution of the polynomial.
Using the rational roots of polynomial we have:
λ³ - 4λ² - 3λ + 14. factors as (λ-2)(λ-1)(λ-7)
Hence, the eigenvalues of A are 2, 1, and 7.
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Naomi wants to wrap a gift for her sister. The gift is in a box with a length of 10 inches, a height of 2 inches, and a depth of 3 inches. If Naomi is calculating the minimum amount of wrapping paper to wrap the gift, would she be finding the Volume or Surface Area?
To calculate the minimum amount of wrapping paper needed to wrap the gift, Naomi would be finding the Surface Area.
The Surface Area of a three-dimensional object is the sum of the areas of all its faces. In this case, the gift is a rectangular prism with dimensions of length 10 inches, height 2 inches, and depth 3 inches.
To wrap the gift, Naomi would need to cover all six faces of the rectangular prism with wrapping paper. The formula for the Surface Area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, h, and w are the length, height, and width of the rectangular prism, respectively.
Substituting the values for the length, height, and depth of the gift, we get:
Surface Area = 2(10 x 2) + 2(10 x 3) + 2(2 x 3)
Surface Area = 20 + 60 + 12
Surface Area = 92 square inches
Therefore, Naomi would need at least 92 square inches of wrapping paper to cover the gift, which is the Surface Area of the rectangular prism.
The diameter of a cylindrical construction pipe is 3ft . If the pipe is 16ft long, what is its volume?
(I THINK I USED THE RIGHT CALCULATOR)
Answer: V≈113.1
Step-by-step explanation:
V=πr2h=π·1.52·16≈113.09734
15. a = 3, b = 4, C = 40°
18. a = 6, b = 4, C = 60°
26. a=4, b=3, c=6
39. Dimensions of Home Plate The dimensions of home plate at any major league baseball stadium are shown. Find the area of home plate.
The area of this home plate is equal to 216.5 in².
How to determine the area of home plate?In order to determine the area of home plate, we would have to apply the law of cosine:
C² = A² + B² - 2(A)(B)cosθ
Where:
A, B, and C represent the length of side or side length of a given triangle.
By substituting the given side lengths and angle into the law of cosine formula, we have the following;
C² = A² + B² - 2(A)(B)cosθ
17² = 12² + 12² - 2(12)(12)cosθ
284 = 144 + 144 - 288cosθ
1 = -288cosθ
cosθ = (-1/288)
θ = 90.199
For the area of home plate, we have:
Area of home plate = Area of rectangle + Area of triangle
Area of home plate = 17(8.5) + 1/2(12)(12)sin90.199
Area of home plate = 144.5 + 72(0.9999940)
Area of home plate = 216.5 in².
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WILL MARK BRAINLIEST
a quadratic function is represented by the graph
what is the equation of the axis of symmetry of the function?
what are the coordinates of the vertex of the function
what are the coordinates of the x-intercepts of the function
what are the coordinates of the y intercept of the function
The equation of the axis of symmetry of the quadratic function is given by y = -2x² + 8x - 5.
x = 4 is the x-coordinate of the vertex.
x = 0 and x = 4 are the x-coordinates of the x-intercepts.
y = -5 is the y-coordinate of the y-intercept.
What is quadratic function?A quadratic function has two variables that can be used to model real-world problems. It has a distinct shape of a parabola, which is a symmetrical U-shaped curve.
The coordinates of the vertex of the function can be calculated by taking the derivative of the given equation and setting it equal to 0.
This yields x = 4 as the x-coordinate of the vertex.
Substituting this value in the given equation gives us the y-coordinate of the vertex, which is y = 11.
The coordinates of the x-intercepts of the function can be found by setting y = 0 in the given equation.
This yields x = 0 and x = 4 as the x-coordinates of the x-intercepts. Substituting these values in the given equation gives us the corresponding y-intercepts, which are
y = -5 and y = 0 respectively.
The coordinates of the y-intercept of the function can be found by setting x = 0 in the given equation.
This yields y = -5 as the y-coordinate of the y-intercept.
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Solve the systems by substitution.
y=4x+6
y = 7x
Answer:
x = 2
y = 14
Step-by-step explanation:
{y = 4x + 6;
{y = 7x;
.
Let's replace y in the second equation with the value given in the 1st equation:
4x + 6 = 7x
4x - 7x = -6
-3x = -6 / : (-3)
x = 2
x = 2y = 4 × 2 + 6 = 8 + 6 = 14
2477 how to make persantage please if you dont answer you are from ohio
Answer:
247700% I'm not sure
I'm not good I'm maths
Shirley uses pattern blocks to measure the straight angle. Select all the combinations of pattern block angles that Shirley could use to measure the angle
To measure a straight angle, Shirley could use any combination of pattern blocks that adds up to 180 degrees.
What are the pattern block angle combinations Shirley could use to measure the angle?
One hexagon (120 degrees) and three triangles (60 degrees each): 120 + 60 + 60 + 60 = 300 degrees (not a straight angle)Two triangles (60 degrees each) and two hexagons (120 degrees each): 60 + 60 + 120 + 120 = 360 degrees (a full circle, which includes a straight angle)One trapezoid (270 degrees) and one triangle (60 degrees): 270 + 60 = 330 degrees (not a straight angle)One rhombus (120 degrees) and two trapezoids (270 degrees each): 120 + 270 + 270 = 660 degrees (not a straight angle)Three rhombuses (120 degrees each) and one triangle (60 degrees): 120 + 120 + 120 + 60 = 420 degrees (not a straight angle)Six triangles (60 degrees each): 60 + 60 + 60 + 60 + 60 + 60 = 360 degrees (a full circle, which includes a straight angle)As a result, the pattern block angle combinations that Shirley could use to measure the angle are:
Two triangles (60 degrees each) and two hexagons (120 degrees each)Six triangles (60 degrees each)
Incomplete question provided, below is the complete question -
Shirley measures the straight angle using pattern blocks. Choose every possible combination of angle possibilities for pattern blocks Shirley could use to calculate the angle.
# The tan pattern block has six minor angles.
# On the red pattern block, there are two angles: one large and one small.
# On the red pattern block, there is one large angle and three small angles.
# The tan pattern block has four tiny angles, and the red pattern block has one tiny angle.
# The red pattern block has two sharp angles.
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An inverse variation includes the points (5, 3) and (1, n). Find n.
Write and solve an inverse variation equation to find the answer.
n=
Submit
Answer:
n = 15
Step-by-step explanation:
the equation for inverse variation is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the point (5, 3 ) , that is y = 3 when x = 5 , then
3 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )
15 = k
y = [tex]\frac{15}{x}[/tex] ← equation of variation
substitute (1, n ), that is x = 1, y = n into the equation
n = [tex]\frac{15}{1}[/tex] = 15
I need help on this one
Answer:
19 degrees
Step-by-step explanation:
hope this helps
Pls help i need to pass
The total surface area of the square pyramid is 39 ft².
What is the total surface area?The total surface area of a square pyramid can be determined by adding the area of the lateral surfaces and the base together. A square pyramid has four lateral sides and one base.
Total surface area= area of the base + area of the lateral sides
Area of the base = area of a square = length² = 3² = 9 ft²
Area of the lateral sides = 2 x base x height
2 x 3 x 5 = 30 ft²
Total surface area = 30 + 9 = 39 ft²
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will give brainiest if correct and quick
Answer: -2， 6
（-2）Because from 3a³ to (1)a³, it needs to subtract 2a³.
(6) Because from -5b³ to b³, it needs to add 6.
Valeria is tilling her kitchen wall with two types of traditional hand painted Mexicano tiles. If she uses 56 flower tiles how many sun tiles dose she need to maintain the pattern?
A=28
Therefore, Aditi's mother requires 342 yellow tiles and 57 red tiles for the floral design on the kitchen wall.
What is proportion?Proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities and is written in the form of a fraction. A proportion can be written in the form of a:b = c:d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. We can also write a proportion as a fraction, where the numerator is the product of the means (ad) and the denominator is the product of the extremes (bc). Proportions are commonly used in mathematics to solve problems involving ratios and rates.
Here,
Since the floral design is made up of yellow and red hexagonal tiles, we need to determine the proportion of yellow tiles and red tiles in the design. Let's assume that the design consists of x yellow tiles and y red tiles. Each flower in the design consists of 7 hexagonal tiles - 6 yellow tiles and 1 red tile. Therefore, the total number of tiles in the floral design is:
Total number of tiles = 57 flowers x 7 tiles per flower
Total number of tiles = 399 tiles
Since each flower consists of 6 yellow tiles and 1 red tile, the total number of yellow tiles in the design is:
Number of yellow tiles = 6 x Number of flowers
Number of yellow tiles = 6 x 57
Number of yellow tiles = 342
Similarly, the total number of red tiles in the design is:
Number of red tiles = 1 x Number of flowers
Number of red tiles = 1 x 57
Number of red tiles = 57
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Complete question:
Aditi's mother is renovating her kitchen. One of the walls of kitchen is entirely made up of tiles. She wants to have a row of floral designs made up of yellow and red hexagonal tiles in the middle of the wall as shown in the adjoining figure. If there are 57 flowers in a row, find out how many yellow-and red-coloured tiles she requires for that wall.
Q3: The standard form of (7.2 x 10)-(3.4 x 10") a) 2.14 x 10 b) 2.11 x 10 2.12 x 102 d) 2.12 x 10
The standard form of the expression (7.2 × 10⁵) ÷ (3.4 × 10³) include the following: C. 2.12 x 10².
What is an exponent?In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the law of indices for powers of the same base number and division, we have the following:
(7.2 × 10⁵) ÷ (3.4 × 10³
(7.2/3.4) × 10⁵⁻³
2.12 x 10².
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Complete Question:
The standard form of (7.2 × 10⁵) ÷ (3.4 × 10³)
a) 2.14 x 10
b) 2.11 x 10
c. 2.12 x 10²
d) 2.12 x 10
please help me i need to get these right
The value of x in the right angled triangle above is 7√3.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.
To calculate the value of x in the right angle triangle above, we use the formula below.
Formula:
tan∅ = opp./adj.Where:
∅ = Included angle = 30°opp. = Opposite = 7adj. = Adjacent = xtan30° = 1/√3Substitute these values into equation 1 and solve for x
tan30° = 7/xx = 7/tan30°x = 7/(1/√3)x = 7√3
Hence, the value of x is 7√3.
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Three different athletic teams were surveyed about the
number of glasses of water consumed each day. The
results are represented in the segmented bar graph.
Water Consumed by Athletes
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Track
Softball Baseball
<4 Glasses
4-8 Glasses
>8 Glasses
Which statement is true?
About 30% of track athletes consume 8 glasses of
water or less each day.
About 70% of track athletes consume 4 to 8 glasses
of water each day.
About 60% of baseball players consume 4 to 8
glasses of water each day.
About 12% of softball players consume more than 8
glasses of water each day.
After answering the presented question, we can conclude that Softball graphs players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a relationship between two or more things. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential growth. A triangle-shaped logarithmic graph.
70% of track athletes drink 4 to 8 glasses of water every day.
We can observe that the blue segment, which represents the number of track athletes who drink 4 to 8 glasses of water each day, accounts for almost 70% of the whole bar. The graph does not support any of the other statements. According to the graph, approximately 25% of track athletes take less than 4 glasses of water, while approximately 5% consume more than 8 glasses. Baseball players drink less than 4 glasses of water, 35% drink 4 to 8 glasses, and 25% drink more than 8 glasses. Softball players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.
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Jessie bought some pizzas and burgers. 3/4 of the food bought were burgers. Jessie bought 18 burgers. How many pizzas and burgers did Jessie buy altogether?
Answer:
24
Step-by-step explanation:
Total number of food = x
If ¾ of food = number of burgers bought
Then 3/4 times x = 3x/4
3x/4= 18
x = 24
At what rate of interest will a sum of 10,000 become 12,544 in 2 years if the interest is compounded annually
=
Divide.
O EXPONENTS AND POLYNOMIALS
Dividing a polynomial by a monomial: Multivariate
(12y'u²-32ysu+15y¹uº) ÷ (-4y²u³)
Simplify your answer as much as possible.
0
X
010
Ś
The simplified expression when a polynomial is divided by a monomial is [tex]y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).[/tex]
What is factoring?A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.
Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S
For the given expression [tex](12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)[/tex] factor the common term.
[tex](12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)[/tex]
Cancelling the -4:
[tex]= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)[/tex]
Hence, the simplified expression is [tex]y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).[/tex]
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3. Se tienen los puntos A. M. B, colineales y consecutivos, donde AB = 52 cm y M es punto medio de AB. ¿Cuanto mide el segmento AM?
Answer:
Por lo tanto, el segmento AM mide 26 cm.
Step-by-step explanation:
Como M es el punto medio de AB, entonces AM tiene la misma longitud que MB. Por lo tanto, la longitud de AM es:
AM = MB = AB / 2
Sustituyendo los valores dados, tenemos:
AM = MB = AB / 2 = 52 cm / 2 = 26 cm
Solve this system of linear equations. Separate
the x- and y-values with a comma.
9x - 19y = 74
3x + 3y = 6
Step-by-step explanation:
We can start by solving the second equation for one of the variables. Let's solve for y:
3x + 3y = 6
3y = 6 - 3x
y = 2 - x
Now we can substitute this expression for y into the first equation:
9x - 19y = 74
9x - 19(2 - x) = 74 (substituting y = 2 - x)
9x - 38 + 19x = 74
28x = 112
x = 4
Now we can use this value to find y:
y = 2 - x
y = 2 - 4
y = -2
Therefore, the solution to the system of equations is x = 4 and y = -2.
Hopes this helps
An area of a triangle and rectangle
12m
3m
6cm
Area=
Answer:
The dimensions of the t r including the path are 12+3+3 and 6+3+3 which is 18x12=216 m2
If we subtract the tr area 12x6=72m2
216m2–72m2=144m2
Step-by-step explanation:
The graph shown here is the graph of which of the following rational functions?
O A. F(x) = 1/X2
O B. F(x) = 1/(x-2)(x+1)
O C. F(x) = 1(x+2)(x-1)
The equation of the rational function is F(x) = 1/(x-2)(x+1). Thus, the answer is B. F(x) = 1/(x-2)(x+1).
What is a rational function?It is a type of function that can be expressed in the form f(x) = p(x) / q(x), where p(x) and q(x) are polynomials and q(x) is not equal to zero. Rational functions are used in various areas of mathematics, including calculus and algebra.
The graph of a rational function is the set of points which satisfy the equation of the rational function.
In this case, the equation of the rational function is F(x) = 1/(x-2)(x+1).
The graph of this function is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.
The graph of a rational function can be determined by finding the zeroes, vertical and horizontal asymptotes, and intercepts of the function.
The zeroes of F(x) = 1/(x-2)(x+1) are x = 2 and x = -1. The vertical asymptote is x = 0 and the horizontal asymptote is y = 0.
The intercepts are (2, 0) and (-1, 0).
The graph of F(x) = 1/(x-2)(x+1) is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.
This is different from the graph of F(x) = 1/X² which is a parabola and from the graph of F(x) = 1(x+2)(x-1) which is two lines intersecting at (2, 0) and (-1, 0).
Therefore, the correct answer is B. F(x) = 1/(x-2)(x+1).
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principle amount =750 interest rate =5% time = 4 years
how much interest is gained after 4 years ?
Answer:
Step-by-step explanation:
use formula I = prt
I=Interest P=principal R=rate T=time so Interest is = to 750 x 5% or 0.05 x 4 which is 150 so after 4 years 150 interest is gained
According to the graph, what is the value of the constant in the equation below?
According to the graph, the value of the constant in the equation below is 2. The correct option is B.
What is constant in a graph?A constant function in mathematics is one whose (output) value is constant regardless of the input value.
We are given the equation for the height.
On the graphic, height, and width are related. By choosing a point, we can find the value of the constant.
To find a constant in a graph, the width is multiplied by height.
(Height)(Width) = Constant.
Multiply any of the coordinate values shown, and you will see the constant is 2.
3 × 1.5 = 2 × 1 = 8 × 4 = 7 × 3.5 =
we will take only one variable which is 2 x 1 = 2, so the constant is 2
Therefore, the correct option is B, 2.
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