The domain of the relation as given in the task content; (x,y): y = x(x-3) / (x+4)(x-7) is the set of all real number values except; -4 and 7 and hence is represented as; { x : x R, x ≠ -4, x ≠ 7}.
What is the domain of the relation given; { x : x R, x -4, x 7}?It follows from the task content that the domain of the relation given in the task content be determined.
On this note, since the domain of a relation or function simply refers to the set of all possible input values of such function.
Since the relation in this scenario is a rational function, it follows that the domain is the set of all real number values except that which renders the relation undefined.
Therefore, since the values which render the relation undefined, render the denominator equal to 0; we have;
(x+4)(x-7) = 0.
x = -4 OR x = 7.
Ultimately, the domain of the relation is the set of all real numbers except; x = -4 and x = 7.
Therefore, when represented by set builder notation; we have; { x : x R, x ≠ -4, x ≠ 7}.
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Please Help me, I will mark brainiest. What are the vertex and range of y = |x + 2| − 3?
(−2, −3); −∞ < y < ∞
(−2, −3); −3 ≤ y < ∞
(0, −1); −∞ < y < ∞
(0, −1); −3 ≤ y < ∞
The vertex and the range of the absolute value function are given as follows:
(−2, −3); −3 ≤ y < ∞.
How to find the vertex and the range of the absolute value function?The absolute value function in the context of this problem is defined according to the following rule:
y = |x + 2| − 3.
For the general equation, with vertex (h,k), the definition is given as follows:
y = |x - h| + k.
Hence, in the context of this problem, the coefficients of the vertex are given as follows:
h = -2, k = -3.
Hence the vertex is:
(-2,-3).
The range of a function is the set containing all the output values assumed by the function. For the absolute value function, it is given by the following interval:
k ≤ y < ∞
Hence, for the function defined in this problem, the interval is given by:
-3. ≤ y < ∞
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2. Write an equation in slope-intercept form of the line that passes through the point (-5, 7) and is perpendicular to the line y = 5x-1.
The general slope intercept form equation of a line is as stated below;
[tex]y=mx+b[/tex]where m is the slope and b is the intercept.
If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.
The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;
So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);
Remember, the point slope form equation of a line is given as;
[tex]y-y_1=m(x-x_{1)}[/tex]Substituting the above values, we'll have
[tex]y-7=-\frac{1}{5}(x+5)[/tex]Let's open up the parenthesis first, we'll have;
[tex]\begin{gathered} y-7=-\frac{1}{5}x-\frac{5}{5} \\ y-7=-\frac{1}{5}x-1 \end{gathered}[/tex]Let's isolate y by adding 7 to both sides of the equation;
[tex]y=-\frac{1}{5}x+6[/tex]The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).
I really need help on this, tyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:3
Step-by-step explanation: 105 divided by 3 is 35 there are 3 groups so 1 ten would go in each group.
Exercice n'11: Calcule:
A = 19+ (8-25);
B=(-15+6)-(23-18)
C = (154-6) +3-(-9+7):
D=-13+ (5+8)-(-4+8)
E = (-5)-(17+ (-13))-((-8) - (+2)):
F = (12-(-3)) - (12-(-3))
G=15-(-3-((+12)-16)):
H=-12-(-15 +30) -(65-20) - 20
Answer:
Step-by-step explanation:
Here in all these questions we need to follow the rules of BODMAS which tells us the steps to solve and mathematical operation.
B-Bracket
O-Of
D- Division
M-Multiplication
A-Addition
S-Subtraction
now,
A. 19+(8-25)
we need to solve what's inside the bracket first
so, 8-25= -17
=19+(-17)
=2
B. (-15+6)-(23-18)
=(-9)-5
= -14
C. (154-6)+3-(-9+7)
= 148+3-(-2)
=148+3+2
= 153
D. -13+(5+8)- (-4+8)
= -13+13-4
= -4
E. (-5)-(17+(-13))-((-8) -(+2))
= -5 -(4)-(-10)
= -5-4+10
= 1
F. (12-(-3))-(12-(-3))
= 15-15
=0
G. 15 -(-3-((+12)-16))
= 15-(-3-(-4))
= 15- 1
= 14
That's how we do it try the last one by your self!
v=u+ at
u= 2 a=-5
Work out the value of v.
Substitution
Tynel
4
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Revision for 10Y1 October
Answer:
v=-0.5
Step-by-step explanation:
v=2+(-5×0.5)
v=2-2.5
v=-0.5
The value of [tex]\tan 1^{\circ}\tan 2^{\circ}+\tan 2^{\circ}\tan 3^{\circ}+\tan 3^{\circ}\tan 4^{\circ}+\cdots+\tan 88^{\circ}\tan 89^{\circ}[/tex] can be expressed in the form [tex]\cot^2 1^{\circ}-n[/tex]. What is the value of [tex]n[/tex]?
Answer:
n = 89Step-by-step explanation:
Use of identitiestan (x - y) = (tan x - tan y)/(tan x tan y + 1) 1/tan x = cot xtan (90 - x) = cot xtan (- x) = - tan xConvert the first one above:
tan x tan y = (tan x - tan y) / tan (x - y) - 1Apply this to each term of the given expression to get:
tan1°tan2° + tan2°tan3° + ... + tan88°tan89° = (tan1° - tan2°)/(tan-1°) - 1 + (tan2° - tan3°)/(tan-1°) - 1 + ... + (tan88° - tan89°)/(tan-1°) - 1 = (tan1° - tan2° + tan2° - tan3° + ... + tan88° - tan89°)/(tan-1°) - 88 = (tan1° - tan89°)/(tan-1°) - 88 = tan1°/ (tan-1°) - tan89°/tan-1° - 88 = - 1 - cot1*(- cot1°) - 88 = cot² 1° - 89The value of n is 89.
Answer:
n = 89
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan double angle identity}\\\\$\tan (A - B)=\dfrac{\tan A - \tan B}{1 + \tan A \tan B}$\\\end{minipage}}[/tex]
Rewrite the tan double angle identity to isolate tanAtanB:
[tex]\implies 1 +\tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}[/tex]
[tex]\implies \tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}-1[/tex]
Therefore:
[tex]\implies \tan 1^{\circ} \tan 2^{\circ}+\tan2^{\circ}\tan3^{\circ}+...+\tan88^{\circ}\tan89^{\circ}[/tex]
[tex]\implies \left(\dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (1 - 2)^{\circ}}-1\right)+\left(\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (2 - 3)^{\circ}}-1\right)+...+\left(\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (88 - 89)^{\circ}}-1\right)[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}-1+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}-1+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-1[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}+\tan 2^{\circ}- \tan 3^{\circ}+...+\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{\tan (-1)^{\circ}}-\dfrac{ \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{ \tan(-x)=-\tan(x)}:[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{-\tan 1^{\circ}}+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies -1+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies \dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\tan(90-x)=\cot(x)}:[/tex]
[tex]\implies \dfrac{\cot1^{\circ}}{\tan1^{\circ}}-89[/tex]
[tex]\implies \cot 1^{\circ} \cdot \dfrac{1}{\tan1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\dfrac{1}{\tan(x)}=\cot(x)}:[/tex]
[tex]\implies \cot 1^{\circ} \cdot \cot 1^{\circ}-89[/tex]
[tex]\implies \cot^21^{\circ}-89[/tex]
Therefore, n = 89.
simplify (2a)^-1 ×3a^2 URGENT
Answer:
Hope the picture will help you.......
Solve this inequality
-3 < x + 5 < 10
Answer:
-8 < x < 5
Step-by-step explanation:
-3 < x + 5 < 10
=> Minus 5 in all sides
=> -8 < x < 5
A building company employs 3 labourers 12 joiners 8 electrician 4 plumbers. For a job, the company needs one of each type of worker in how may ways can the company choose four workers
The number of ways that the company can choose four workers is 40920 ways.
How to calculate the number?From the information, the building company employs 3 laborers 12 joiners 8 electrician 4 plumbers. The total number of workers will be:
= 3 + 12 + 8 + 4
= 27 workers
It should be noted that combination will be used to choose the 4 workers. This is illustrated as
Combination formula
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
where n = 33
r = 4
ⁿCr = n! / ((n – r)! r!)
³³C₄ = 33! / (33 - 4)! 4!
= 33! / 29! 4!
= 33 × 32 × 31 × 30 / 4 × 3 × 2
= 40920 ways
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if l //m and m<4=5x-42 and m<5=-x+82, what is the m<5
The measure of <5 is 47
what is parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance away from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
m<4=5x-42
and m<5=-x+82
as, <4 and <5 are in co- interior angle
<4 + <5 = 180
5x - 42 + (-x + 82) = 180
5x -42 - x + 82= 180
4x +40 = 180
4x = 140
x= 140/4
x= 35
Hence, the measure of <5 = -x+ 82 = -35 + 82 = 47
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7+4x= -5 helppppppppppppp
Jett is 6 feet 2 inches tall.
How tall is he in inches?
Answer:
74 inches
Step-by-step explanation:
6 feet= 72 inches plus 2 inches equals this amazing height
4(a-c)+2(a-b)
x(x-y)+y(y-x)
Answer:
hi how are you . i cant find the answer youre looking for
Answer:
1) 6 ( a - b )
2) x² - 2xy + y²
Step-by-step explanation:
1) 4 ( a - c ) + 2 ( a - b )
First, solve the brackets.
4a - 4c + 2a - 2b
Combine like terms.
6a - 6b
Take the common factor out.
6 ( a - b )
2) x ( x - y ) + y ( y - x )
First, solve the brackets
x² - xy + y² - xy
Combine like terms.
x² - 2xy + y²
Find the value of x to the nearest tenth.
Given: <1 and <2 are complementary; <1=<4 prove: <3 and <4 are complementary
Statements:
1. <1 and <2 are complementary
2. m<1 + m<2= 90°
3. <1=~<4
4. m<1 = m<4
5. <2 =~<3
6. m<2 = m<3
7. m<4 + m<3 = 90°
8. <3 and <4 are complementary
Please list reasons (geometry)
Answer:
<3 and <4 are complementary
C(0)=0
Let c(t) be the number of customers in a restaurant t hours after 8am Explain the meaning of each statement please help
The meaning of each statement is shown below.
Step-by-step explanation:
Assume that the given statements are
(a) c(0)=0
(b) c(3)=c(8)
(c) c(n)=29
(d) c(13)<c(12)
Let c(t) be the number of customers in a restaurant t hours after 8 A.M.
We need to find the meaning of each given statement.
(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.
(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).
(c) c(n)=29 means the number of customers n hours after 8 A.M is 29.
(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.)
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À La Mode Ice Cream Parlor uses the function f(x) to calculate its profits. When the parlor sells x cones, it makes f(x) dollars in profit. What does f(50)=85 tell you?
f is the given profit function whose input is number of cones and output is profit, f(50)=80 tells that $80 profit is made by selling 50 cones of ice cream.
What is function?A function is a relation that assigns each element of a set a unique element of another set.
f(x) denotes that function f works on the input values x and give output f(x).
If f is a function and f(x) = x+2, then if we have to check x= 1 , then
f(1) = 1+2 = 3 is the value of the function f at x=1
A La Mode Ice Cream Parlor uses a function f as profit function
The input x is the number of cones it sells and output is profit
f(50) = 85
⇒x = 50 and f(50) = 85
It means that when the parlor sells x = 50 cones , it makes profit $ f(50) = 85
or On selling 50 cones the profit made is $80
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If * = 8 units, y= 13 units, and h= 11 units, then what is the area of the parallelogram shown above?
The figure below has an area equivalent to 88 square units.
The parallelogram's characteristicsIn Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides.
The opposing or confronting sides and the opposing angles in a parallelogram are of equal length.
Area = length * breadth is the formula for computing the area of a parallelogram.
Substituting the given values
Area = x * h
Area of the parallelogram = 8 * 11
Area of the parallelogram = 88 square units.
Consequently, the parallelogram above has an area of 88 square units.
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Solve for x: 3x/6 + 1 = 7
Answer:
X = 12
Explanation:
3x/6 + 1= 7
/2 + 1 = 7
x/2 + 1 = 7
x/2 + 2/2 = 7
X+2/2 = 7
X = 12
hope this helps you :)
On a piece of paper, Graph y = 2x-3. Then determine which answer matches the graph you drew.
A graph of the linear function (y = 2x - 3) which matches the answer is shown in the image attached below.
What is a graph?A graph refers a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
Generally speaking, the graph of any proportional relationship such as a linear function is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis decreases or increases, the values on the y-axis decreases or increases simultaneously as shown in the image attached below.
In conclusion, a graph representing the given linear function shows a proportional relationship between the value of x and y.
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what is the answer to the absolute value equation? |5x-3|=-2
Answer:
No answer
Step-by-step explanation:
An absolute cannot equal a negative number
if apples cost $3 per pound and bananas cost $5 per pound, how many whole pounds of apples should bill buy if he wants to maximize his utility and he has $31 to spend?
I f Bill wants to maximize his utility while spending $31 on apple. Bill van buy 10 whole pounds of Apples
How to find the number of whole pounds of apples bill can buy if he has $31 to spendgiven data
Apples cost $3 per pound
Bananas cost $5 per pound
amount Bill has to spend $31
The number of whole apple Bill can buy
Using $31 the number of whole apples this can buy is gotten dividing the the total amount by the price of apple per pound.
= amount Bill has to spend $31 / Apples cost $3 per pound
= 31 / 3
= 10.33
Since we are solving for whole pounds of apple Bill can buy 10 whole pounds of apples
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Need help with this, if you can edit it and send back,, that’ll help, thank you<3
The quotient of the triangle side lengths are same as below for different triangle ( please refer attached image for better understanding)-
For ABC - 9/4 or 2.25, 9/6 or 1.5, 6/4 or 1.5
For DEF - 18/8 or 2.25, 18/12 or 1.5, 12/8 or 1.5
For GHI - 27/12 or 2.25, 27/18 or 1.5, 18/12 or 1.5
For JKL - 4.5/2 or 2.25, 4.5/3 or 1.5, 3/2 or 1.5
Quotient in mathematics, can be defined as the result of the division of a number by any divisor.
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Which of the following acids contain equal numbers of atoms?
A Sulfuric Acid H2SO4
B Phosphoric Acid H3PO4
C Vinegar C2H3O2
D Boric Acid H3BO3
Which of the following acids contain equal numbers of atoms?
A Sulfuric Acid H2SO4
B Phosphoric Acid H3PO4
C Vinegar C2H3O2
D Boric Acid H3BO3
A, C and D
A, B and C
A and B
B and D
Sulfhuric acid, boric acid and vinegar have 7 atoms present in them
Equivalent Number of Atoms
To find the compounds with equal number of atoms, we must take each individual atoms and find how many atoms are present in them.
In the first compound, we have sulfuric acid.
[tex]H_2SO_4 = 7 atoms\\[/tex]
Second compound, we have phosphoric acid
[tex]H_3PO_4 = 8 atoms[/tex]
Third compound, we have vinegar
[tex]C_2H_3O_2 = 7 atoms[/tex]
Fourth compound, we have boric acid
[tex]H_3BO_3 = 7 atoms[/tex]
From the above, only sulfuric acid, vinegar and boric acid have equal number of atoms present in them.
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An angle measures 4pi/5 radians. What is this angle's measure in degrees?
4π/ 5 radians = ?
Then if
π radians= 180°
(4/5)•π radians = 180• 4/5
. = 144
Answer is
4pi/5 radians = 144 degrees
Cynthia was offered two different jobs for the summer. Working as a camp counselor, she will earn $20 per hour plus an additional $25 bonus. Her earnings after x hours can be represented by the function f(x) = 20x + 25. Working as a lifeguard, Cynthia will earn $15 per hour and an additional $50 bonus. Her earnings after x hours can be represented by the function g(x) = 15x + 50. The arithmetic operation (f − g)x can be used to determine the difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours. What is the function (f − g)x?
The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours (f − g)x = 5x - 25.
What is a function?A function can be defined as the set of inputs that results in output.
Given, Cynthia earns 20 dollars per hour working as a camp counselor plus an additional 25 dollars as a bonus which is f(x) = 20x + 25, and as a lifeguard 15dollars per hour and an additional 50 dollars bonus which is g(x) = 15x = 50.
We know (f - g)x = f(x) - g(x).
∴ The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours is f(x) - g(x).
= (20x + 25) - (15x + 50).
= 20x - 15x + 25 - 50.
= 5x - 25.
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solve for p 3w+4pw=a
The average U.S. home uses about 11,000 kilowatt-hours (kWh) of electricity per year. Appliances and refrigeration account for about 17% of this total. If electricity costs $0.16 per kWh in a particular area, how much would the average U.S. homeowner pay annually to run appliances and refrigeration?
First we need to find the 17% of 11,000
ad and solve the problems.
Dan builds identical model cars and sells them
online. He records the number of models he
completes every couple of hours. The graph shows
Dan's data. Choose two pairs of points on the line
and calculate the slopes between them. Is Dan's
productivity constant? Explain.
The slope between the two pair of points is 3/2. Yes, Dan's productivity is constant.
Number of model are represented on y axis and the hours are represent on x axis.
As we can observe,
One pair of points on the graph is (4,6) and (2,3) and the other pair of points is (6,9) and (0,0)
The slope m between any two points (a,b) and (c,d) can be calculated as,
m = (d-b)/(c-a)
The two points we have are (4,6) and (2,3), so the slope M between them is,
M = (3-6)/(2-4)
M = -3/-2
M = 3/2.
And the slope M' between other two point (6,9) and (0,0) is,
M' = (9-0)/(6-0)
M' = 9/6
M' = 3/2.
As we can see, the slope is same. The slope represents the ratio of number of models and hours. We can conclude that Dan's productivity is constant.
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The diagram shows a rhombus inside a regular pentagon.
Work out the size of angle x.
The size of the angle x in the pentagon is 36 degrees.
How to find the angles in a pentagon?A regular pentagon is a polygon with five sides. The angles of a regular polygon is equal to each other.
Therefore,
the sum of angles in a regular pentagon = 540 degrees.
Each angle in a regular pentagon is 540 / 5 = 108 degrees.
The rhombus is inside the pentagon. Opposite angles in a rhombus are equal.
Therefore, the sum of interior angles of a rhombus adds up to 360 degrees
Hence,
108 + 108 + 2y = 360
where
y is the angle of the rhombus on the x variable.
Therefore,
2y = 360 - 216
2y = 144
y = 144 / 2
y = 72°
Therefore,
x = 108 - 72
x = 36 degrees
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