the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.
Option (C) is CORRECT.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, that the coordinates of the vertices of a quadrilateral composed in the first quadrant of the coordinate plane are (0,0) (a, b), (a + c, b), and (c, 0).
We are to select the most accurate classification of the quadrilateral.
Let the coordinates of the vertices of the quadrilateral be P(0,0), Q(a, b), R(a + c, b), and S(c, 0).
The lengths of the sides are calculated using the distance formula as follows :
PQ = √(a² + b²)
QR = √(a +c -a)² + (b-b)² = √c² = c
RS = √(a² + b²)
SP = c
So, the opposite sides are equal in length.
And, the slopes of the sides are calculated as follows :
The slope of PQ(m₁) = (b-0)/(a-0)
The slope of QR(m₂) = (b-b)/(c-a-c) = 0
The slope of RS(m₃) = 0-b/(c-a-c) = 0
The slope of SP(m₄) = (0-0)/(0-c) = 0
So, the slopes of the opposite sides are equal but:
m₁ *m₂ = 0 ≠ -1
m₃ *m₄ = 0 ≠ -1
Therefore, the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.
Option (C) is CORRECT.
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Find the product of the binomial factors using the appropriate special product (difference of two squares, square of a binomial sum, or square of a binomial difference).
(x+8)2
The product of the binomial factors is x² + 16x + 64
How to determine the product of the binomial factorsfrom the question, we have the following parameters that can be used in our computation:
(x+8)2
Express properly
So, we have
(x+8)²
Using the square of a binomial sum, we have
(x+8)² = x² + 2 * x * 8 + 8²
Evaluate
(x+8)² = x² + 16x + 64
Hence, the solution is x² + 16x + 64
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row reduce the matrices in exercises 3 and 4 to reduced echelon form. circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.
Reduced matrix to its reduced echelon form Original Matrix:
[tex]$$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]
Pivot Positions (Original): (1,1), (2,2), (3,4)
Pivot Columns (Original): 1, 2, 4
Reduced Echelon Form:
[tex]$$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]
Pivot Positions (Reduced): (1,1), (2,2), (3,4)
Pivot Columns (Reduced): 1, 2, 4
To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:
1. Divide row 1 by 1 to get the leading 1 in the first column
2. Subtract two times row 1 from row 2 to get the leading 1 in the second column
3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column
4. Divide row 2 by 3 to get the coefficient 2/3 in the third column
5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column
6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column
Exercise 4:
Original Matrix:
[tex]$$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$[/tex]
Pivot Positions (Original): (1,1), (2,2), (3,3)
Pivot Columns (Original): 1, 2, 3
Reduced Echelon Form:
[tex]$$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$[/tex]
Pivot Positions (Reduced): (1,1), (2,2), (3,3)
Pivot Columns (Reduced): 1, 2, 3
To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:
1. Divide row 1 by 1 to get the leading 1 in the first column
2. Subtract two times row 1 from row 2 to get the leading 1 in the second column
3. Subtract row 1 from row 3 to get the leading 1 in the third column
4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column
5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column
6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively
7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column
8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column
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Time to walk 3 1/3 miles on Saturday and 2 4/5 mile on Sunday how much farther does Tonya walk on Saturday then on Sunday
The distance that Tonya walk on Saturday more than on Sunday would be = 8/15 miles
What is distance?Distance is defined as the quantity that describes the space that exists between two locations in a field.
The number of miles Tonya covered on Saturday = 3 ⅓ miles
The number of miles that Tonya covered on Sunday = 2 ⅘
Therefore the distance that Tonya walk on Saturday more than on Sunday would be the difference between the distance covered in Saturday and Sunday.
That is; 3⅓ - 2⅘ ( change to single fraction form)
= 10/3 - 14/5
= 50-42/15
= 8/15
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A 20.00 g milk chocolate bar is found to contain 12.00 g of sugar.
A) How many milligrams of sugar does the milk chocolate bar contain?
B) What will be the amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g?
The amount of sugar present in the milk chocolate bar is, 12000 milligrams.
Given,
Amount of milk chocolate bar = 20.00 grams
Amount of sugar = 12.00 grams
The conversion used for grams to milligram is :
1 gram = 1000 milligram
As per question we are given that, 12 grams of sugar
As, 1 gram of sugar = 1000 milligram of sugar
So, 12.00 grams of sugar = (12/1) x 1000
= 12000 milligrams of sugar
Therefore, the amount of sugar present in the milk chocolate bar is, 12000 milligrams.
(b) THe reduced size is 3 g
3 g bar has 12x3/20 g of sugar
i.e 7.2 g
hence , he amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g is 7200mg.
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Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10* micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
IIn a case whereby Transistors are used to build computer chips and the size of the earliest transistors was about 1 x 10* micrometers and today, transistors can measure smaller than 1 × 10-2 micrometer the numbert of times the old is as great as the size of transistors today is 1 × 10^6.
How can the size of transistors be known?The concept that will be use here is division. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math.
We were told that the side of the earliest form of transistors for computer was 1 × 10⁴.
In another sentence, we were told that the size of the transistor today is expressed as 1 × 10^-2
We can then know the difference in size will which will be
= 1 × 10^4 / 1 × 10^-2
= 1 × 10^6
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complete question:
Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10^4 micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
Let f(x)= x^2 + 7 and g(x)= x^2+2. Find the following functions, and simplify each as much as possible: your final answer should be a polynomial with only one term in each power of x. (a) f(x) + g(x) = (b) f(x) - g(x) = (c) f(x).g(x)= (c) f(x)/g(x)= (For part (d), you need not simplify as you did in (a)-(c).)
For function f(x)= x² + 7 and g(x)= x² + 2,
a) f(x) + g(x) = 2x² + 9
b) f(x) - g(x) = 5
c) f(x) . g(x) = x⁴ + 9x² + 14
d) [tex]\frac{f(x)}{g(x)} =\frac{x^2 + 7 }{ x^2+2}[/tex]
Consider given functions f(x)= x² + 7 and g(x)= x² + 2
a) To find addition of functions: f(x) + g(x)
f(x) + g(x)
= (x² + 7) + (x² + 2)
= x² + x² + 7 + 2 .............(associative property of addition)
= 2x² + 9 ................(combine like terms)
b) to find subtraction of functions : f(x) - g(x)
f(x) - g(x)
= ( x² + 7 ) - (x² + 2)
= 7 - 2
= 5
c) To find multiplication of functions: f(x).g(x)
f(x) . g(x)
= ( x² + 7 ).(x² + 2)
= x² (x² + 2) + 7(x² + 2)
= x⁴ + 2x² + 7x² + 14
= x⁴ + 9x² + 14 ................(combine like terms)
d) To find division of functions: f(x)/g(x)
[tex]\frac{f(x)}{g(x)}\\\\ =\frac{x^2 + 7 }{ x^2+2}[/tex]
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Please help!! It’s due in 10 minutes!!! Also please explain how you got the answer!
Answer: 22 vaccines
Step-by-step explanation:
first, reduce the amount that doctors leave out from the total amount of a vial
6 - 0.5 = 5.5
next divide 5.5 by the amount that is given to each person, which will give you the number of vaccinations the doctor can give
5.5/ 0.25 = 22 vaccines
Merle tiene una oferta de un emisor de tarjeta de crédito para una APR del 0
% durante los primeros 60 días y una APR del 23,19 % después, con
capitalización diaria. ¿Qué tasa de interés efectiva se ofrece Merle?
UNA 26.00%
La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.
¿Cómo determinar la tasa de interés efectiva anual?
En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.
Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:
I = (1 + r / 36500)ⁿ
Donde:
r - Tasa de interés anual.n - Número de días.I - Ganancia por interés.La situación es descrita por la siguiente expresión matemática:
1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵
Donde R es la tasa efectiva de interés anual.
Finalmente, despejamos la variable correspondiente:
R = 21,375
La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.
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Use the graphs of f and g to evaluate g(f(2))
I have added the photo of the graphs.
When I answered it the first two times I put -2 and then for the second time I put 4 and I got both of them wrong
Answer:
1
Step-by-step explanation:
We have g(f(2))
Working from the inside out, we start with f(2)
So we go to the f(x) graph and find where X is 2. We get to the point (2, -2). f(2) is pretty much asking for the Y value at 2. On this graph the y value is -2
Now that we know f(2) is -2, we can plug that into g(f(2)), giving us g(-2)
Now we can go to the other graph, g(x) and find where X is -2.
That's where we find the point (-2,1)
Like last time, g(2) is asking for that Y value at that point of -2. On this graph, it's 1
Now we can conclude g(f(2)) = 1
Using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.
What is the graph?
A graph is a visual representation of data or information, often used in mathematics and science to depict relationships between variables. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts.
To evaluate g(f(2)), we need to first find the value of f(2) using the graph of f. From the graph, we can see that f(2) is approximately 4. So, g(f(2)) = g(4).
Then, using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.
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Which graph is defined by f(x) = x²-x-2|?
O A.
О в.
OC.
O D.
graph A
graph B
graph C
graph D
The vertices of triangle xyz are x=(-2,6), y=(4,10), and z=(14,6). Find the coordinates of the centroid of triangle xyz
The centroid of the given triangle is =(5.3 , 7.3)
What is Centroid of triangle?The centroid is the term for the object's geometric centre. We apply the centroid formula to find the triangle's centroid's coordinates. The intersection of a triangle's three medians yields the centroid, or centre, of the triangle. All of the medians are divided by the centroid of a triangle in a 2:1 ratio.
The centroid formula of a given triangle can be expressed as,
C = ((x1+x2+x3)/3 , (y1+y2+y3)3/3)
where,
C denotes the centroid of a triangle
x1,x2,x3 are the x-coordinates of the 3 vertices.
y1,y2,y3 are the y-coordinates of the 3 vertices
To find: Centroid of a triangle.
We are taking the Cordinates of the traiangle XYZ
as x1,y1,x1,y2,x3,andy3
so,Given parameters are,
(x1,y1)=(-2,6)
(x2,y2)=(4,10)
(x3,y3)=(14,6)
Using centroid formula,
The centroid of a triangle = ,
=-2+4+14/3 6+10+6/3
=5.3 7.3
The centroid of a triangle is ==(5.3 and 7.3)
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Determine the number of lines of symmetry for the figure.
The figure has ✓line(s) of symmetry.
Select the angles of rotation, if any, that map the figure onto itself.
O 30°
O 90°
☐ 180°
dh
O 45°
O 120°
Answer:
The figure has 4 lines of symmetry.Rotating through angles 90° or 180° will map the figure to itself.Step-by-step explanation:
You want the number of lines of symmetry of the 4-leaved rose shown in the figure.
Lines of symmetryThe figure is symmetrical about a line through opposite petals. It is also symmetrical about a line through the space between petals. The attachment shows the 4 lines of symmetry.
Rotational symmetryThe petals have the same geometry, but are rotated 90° from each other. That means any rotation that is a multiple of 90° will map the figure to itself. (180° is a multiple of 90°)
The figure maps to itself when rotated 90° or 180°.
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
0.325
0.625
0.750
0.875
Answer:
0.750
Step-by-step explanation:
Yellow sections: section 2 and section 3
Number of yellow sections: 2
Number of non yellow sections: 6
Total sections: 8
p(not yellow) = 6/8 = 0.75
Answer:
0.750
Step-by-step explanation:
you take a quarter and then you divide and think
Find the slope between the points:
(1,7) and (-5, -11)
Slope between the points (1,7) and (-5, -11) is m = 18/6 as a decimal m = 3
What is slope?The slope of a hill describes its steepness. The steepness of a line follows a similar pattern. The rise between two points, which is the vertical change, is divided by the run, which is the horizontal change between those same two points, to determine the slope.
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
step1:
calculate the slope m using the slope formula
slope m=y2-y1/x2-x1
with (x₁, y₁ )=(1,-5) and (x₂, y₂ ) =(-5,-11)
step2:
m=-11-7/-5-1=-18/-6=18/6
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is there a value of a that makes the statement |a| = - 2 true ? Explain your reasoning.
Answer:
No, there is no value of a that makes the statement |a| = -2 true.
Step-by-step explanation:
The absolute value of a number is the distance of that number from zero on the number line. It is always non-negative, so it can't be -2. The absolute value of a number is denoted by two vertical lines on either side of the number like this |a|.
For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. In both cases, the distance from zero is 5.
In the statement |a| = -2, the absolute value of a is -2, which is impossible as the absolute value can't be negative. Therefore, there is no value of a that makes the statement true.
Answer:
no
Step-by-step explanation:
You want to know if there's any value of the variable 'a' that would make its absolute value be -2.
Absolute valueThe absolute value of a number is always positive. There is no such thing as a number whose absolute value is negative, not -2 or any other negative number.
such a value of 'a' Does Not Exist (DNE)
Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building, what is the height of the building? Show your work.
The height of the building that cast the shadow 98 feet will be 61.25 feet.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.
Let 'h' be the height of the building. Then the equation is given as,
h / (90 + 8) = 5 / 8
h / 98 = 5 / 8
h = 98 x 5 / 8
h = 12.25 x 5
h = 61.25 feet
The height of the building that cast the shadow 98 feet will be 61.25 feet.
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pair of equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36
The slope of the given lines are representing that these lines are perpendicular.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36
Slope intercept form of both equations of a line
1) y = -7/8x - 1
it is already in a slope intercept form
2) 32x - 28y = -36
-28y = -32x -36
y = 8/7x + 9/7
Since their slope is inverse and had a negative constant.
The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.
Therefore, The slope of the given lines are representing that these lines are perpendicular.
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Find the unit vector perpendicular to the plane of given vectors.P =i−2j+ k^Q =2i+j−k^
The unit vector perpendicular to the plane of given vectors P =i−2j+ k and Q =2i + j − k is ( i + 3j + 5k )/√35
The vector that perpendicular to the plane is equal to the cross product of:
P ⨉ Q
Remember the properties of cross product of two vectors:
i ⨉ i = j ⨉ j = k⨉ k = 0
i ⨉ j = k
j ⨉ i = - k
j ⨉ k = i
k⨉ i = j
i⨉ k = -j
Hence,
P ⨉ Q = (i−2j+ k) ⨉ (2i+j−k)
= k + j +4k + 2i +2j - i
= i + 3j + 5k
The magnitude of P ⨉ Q is:
|| P ⨉ Q || = √(1² + 3² + 5²)
= √35
Therefore, the unit vector = ( i + 3j + 5k )/√35
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Two fractions with the same denominator that have numerators 5 and 7 what would the denominator be?
The denominator could be any real value
How to determine the possible denominatorFrom the question, we have the following parameters that can be used in our computation:
Fraction = same denominator
Such that the numerators are 5 and 7
This means that the fractions can be represented as
Fractions = 5/x and 7/x
There is no restriction on the possible value of x
hence, the denominator is any value
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E.
Carry out the following operations to the proper number of significant figures:
1. 212.45 +5.61-37.9
2. 89.001+2.50-91.50
3. 400+125= 500
4. 73.35-3.65-69.70
5. (81.7-23.456)+(78.44+2.72) =
By adding (81.7-23.456)+(78.44+2.72), we get 139.404
How does one determine the number of significant figures?Use the three rules below to calculate the number of significant figures in a number:
Non-zero digits are always meaningful.
Any zero between the first and second significant digits is significant.
Only the last zero or trailing zeros in the decimal section are important.
Numbers Have Rules INCLUDING a Decimal Point
START COUNTING FOR SIGNIFICANT FIGURES. On the very first non-zero digit.
STOP COUNTING FOR SIGNIFICANT FIGURES.
Non-zero numbers are ALWAYS meaningful.
After the first non-zero digit, any zero is still relevant. The zeroes preceding the first non-zero digit are unimportant.
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Figure out the polynomial being multiplied on top and then fill in the missing boxes
In order to factor your quadratic polynomials, the box method, as its name suggests, uses a box. You can divide your quadratic into its factors by using the box, which is essentially a square divided into four equal parts.
What is box method ?Be aware that not all quadratics can be factored. Some just lack relevant components. But if a quadratic polynomial does have components, you can utilize the box approach to simplify the operation.Drawing a square divided into four equal sections or a two-by-two grid is the first step. You then enter your first squared term into the upper left box and your final term into the lower right box. the product of your final term and first term.These new term's contributing components are found. You're seeking for a specific combination of elements that, when added together, give you your middle word. Write these elements in the two remaining empty boxes once you've identified this group of components. Your answer will remain the same no matter which empty box each term is entered into. Find the largest common factor for each row and column to determine the quadratic factors. The factors of your polynomial will then be determined by finding the biggest common factors from your columns and rows, respectively.Employing the Box Method
For our first quadratic, 6x2 - x - 12, let's utilize the box approach to solve it.
The first step is to create a two by two grid, as shown here:
using a box
Following that, we place the first term in the upper left box and the last term in the lower right box.
The Complete Question.
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how many four digit decimal number that has an estimated value of 10 when rounded off to the nearest tenths place
Answer:
There are 10,000 four-digit decimal numbers that have an estimated value of 10 when rounded off to the nearest tenths place. This is because each decimal number from 0.0001 to 0.9999 will have an estimated value of 10 when rounded off to the nearest tenths place.
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Allison can sew three scarves in 75 minutes. How many scarves can she sew in four hours?
The number of scarves in 4 hours is 9.6
How to determine the number of scarves in 4 hoursFrom the question, we have the following parameters that can be used in our computation:
Rate = 3 scarves in 75 minutes
Time = 4 hours
The number of scarves is then calculated as
Scarves = Rate * Time
substitute the known values in the above equation, so, we have the following representation
Scarves = (3/75 minutes) * 4 hours
Evaluate the product
Scarves = 9.6
Hence, the number of scarves is 9.6
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HELP!!!!!
Make a table for each equation
y=x-2
Chart:
x -2 -1 0 1 2
y ? ? ? ? ?
I basically just need he y row
Sasha ran at a constant speed of 3.8 meters per 1/2 hour.Then walked 1.3 meters per second for 1/2 hour. How far did she run and walk in 60 minutes.
Answer: 2343.8 meters
Step-by-step explanation: If 3.8 meters is walked in 1/2 hours then another 4680 meters per hour is ran for a half hour is 2340 meters add those 2 together
A group of meteorologists recorded the
temperature in some cities at noon on one
day.
They recorded the temperature in Leeds using
a thermometer that measures to the nearest
0.1 °C and found that the temperature was
16.8°C.
The temperature in Copenhagen was 12 °C
colder than in Leeds, to the nearest degree.
The temperature in Valletta was 23 °C warmer
than the temperature in Copenhagen, to the
nearest degree.
Work out the lower and upper bounds of the
temperature at noon in Valletta.
Give your answer in °C.
The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.
What is Temperature?A physical number known as temperature expresses the concepts of hotness and coolness in numerical form. With a thermometer, the temperature is measured.Thermometers are calibrated using a number of temperature scales that have defined distinct reference points and thermometric substances. The most widely used scales are the Kelvin scale (K), which is mostly used for scientific reasons, the Fahrenheit scale (°F), and the Celsius scale (°C), formerly known as centigrade, with the unit symbol °C. In the International System of Units, one of the seven base units is the kelvin.The upper bound of Valletta = Upper bound of Leeds - Copenhagen +23
upper bound of Valletta = 16.8 -12+23
upper bound of Valletta = 27.8 °C
Lower bound of Valletta = 0.1 -12+23
Lower bound of Valletta = 10.9 °C
Hence, The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.
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find the domain of each expression
1. y ^2+1)/(y^2-2y),
2. 25(y-9),
3. 32/y - (y+1)/Y+7)
The domain of each expression is given as follows:
1. All real values except y = 0 and y = 2.
2. All real values.
3. All real values except y = 0 and y = -7.
How to obtain the domain of the expressions?The domain of an expression is composed by the set of all the possible input values that the expression can assume.
For an expression that is a fraction, the denominator cannot be zero, hence:
Item 1: y² - 2y = 0 -> y(y - 2) = 0, hence the domain is all real values except y = 0 and y = 2.Item 3: y = 0 and y + 7 = 0 -> y = -7, hence the domain is all real values except y = 0 and y = -7.For item 2, the function is a multiplication, which has no restrictions on the domain, and thus the domain is composed by all real values.
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match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. enter the appropriate letter (a,b,c,d, or e) in each blank.
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials.
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. These functions are often used in applications such as navigation and surveying, as they allow us to calculate angles and distances in the real world. Examples of trigonometric functions include sine, cosine, tangent, cotangent, secant, and cosecant. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials. These functions are often used in engineering and scientific applications, as they allow for more precise calculations than trigonometric functions. Examples of non-trigonometric functions include polynomial functions, exponential functions, logarithmic functions, and hyperbolic functions. In each case, the function being used must be appropriate for the type of problem being solved. By understanding the differences between trigonometric and non-trigonometric functions, it is possible to choose the right function for the right problem.
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Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³
The values of (f + g) (x), (f - g) (x), (fg) (x) and (f /g) (x) for the functions are x/(x + 9) + x³, x/(x + 9) - x³, x³/(x³ + 9) and 1/ [x² (x + 9)] respectively
How to determine the values for the functions?
A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Since f(x) = x/(x + 9), g(x) = x³
(a) (f + g) (x) will be the addition of f(x) and g(x). That is:
(f + g) (x) = x/(x + 9) + x³ or x³ + x/(x + 9)
(b) (f - g) (x) will be the subtraction of f(x) and g(x). That is:
(f - g) (x) = x/(x + 9) - x³
(c) (fg)(x) substitute x = x³ into f(x). That is:
f(x)= x/(x + 9), g(x) = x³
(fg)(x) = x³/(x³ + 9)
(d) (f/g)(x) will be the division of f(x) by g(x). That is:
(f/g)(x) = [x/(x + 9)] / x³ = x/ [x³ (x + 9)] = 1/ [x² (x + 9)]
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What is 11 divided by 2.5 and can you show the work
If you divide 11 by 2.5 you will end up with 4.4. Answer = 4.4