Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.
Solution:
To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X
So,
X+1 = 0
X = -1
X-4 = 0
X = 4
When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables
= (x2+4x+3)/(x2-3x-4)
= (x+1) (x+3)/(x+1) (x-4)
Now cancel the common factor (x+1)
= x+3x-4
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a power a *a power 3/a power b
Answer:
power b=3
Step-by-step explanation:
because of the ques statement 3/a of course b=3then only b/a
Write the equation of the line through each point. Use slope-intercept form.
(-7,10) ; parallel to 2x - 3y = -3 .
The equation of the line in slope-intercept form passing through the point (-7 , 10) and parallel to 2x - 3y = -3 is y = (2/3)x + 44/3.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
If the line is parallel to 2x - 3y = -3, then their slopes are equal. First, express the equation in slope-intercept form y = mx + b to get the slope, m.
2x - 3y = -3
-3y = -2x - 3
y = -2/-3 x - 3/-3
y = 2/3 x + 1
m = 2/3
Substitute the values of the slope and the point to solve for the y-intercept, b.
y = mx + b
10 = 2/3(-7) + b
b = 44/3
Write the equation of the line by plugging in the value of the slope and y-intercept.
y = mx + b
y = (2/3)x + 44/3
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what are composite numbers
A welder gets paid $12 per hour for the first 40 hours worked, and then $20 for each overtime
hour. The welder wants to make at least $600 a week. Which inequality can be used to find
the number of overtime hours, x, that the welder needs to work each week?
To find the number of overtime hours, x, that the welder needs to work each week can be found by the inequality 20x if x>40.
What is an inequality?
Inequality, A mathematical declaration expressing an order connection between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Let x be the number of overtime hours.
A welder gets paid $12 per hour for the first 40 hours worked
⇒ 12x if x≤40
A welder gets paid $20 per hour for each overtime.
⇒ 20x if x>40
Now the welder wants to make $600 per hour,
So, the inequality used for finding the value of x is -
⇒ 20x if x>40
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surface area of a shape with the measurements 4 mm, 8 mm, 2 mm
Answer:
112 mm^2.
Step-by-step explanation:
Total surface area
2(4*8 + 4*2 + 2*8)
= 2 * 56
= 112 mm^2.
If angle A is 4x+2 and angle B is 11x, what is the value of x? (round to the nearest tenth)
The value of the x in the vertical angles are the 7/2.
According to the statement
We have to find that the value of the x in the given angles.
So, For this purpose, we know that the
An angle is formed when two straight lines or rays meet at a common endpoint.
From the given information:
If angle A is 4x+2 and angle B is 11x.
Then from the given figure, The given angles are the verticals.
We know that the Verticals angles are equal.
Then
4x+2 = 11x
7x = 2
x = 2/7.
Here the values of the x in the given vertical angles are 7/2.
So, The value of the x in the vertical angles are the 7/2.
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The Smith family has three vehicles. Jeff fills up his vehicle for x dollars a gallon. Valerie also fills up her vehicle for x dollars a
gallon. Megan fills up her vehicle for y dollars a gallon. The expression below represents the total cost of the Smith family
filling up all of their vehicles with gasoline.
ay + bx
What is the best interpretation of bx in the above expression?
OA. The total amount it costs Valerie to fill up her vehicle.
OB. The total amount it costs Jeff and Megan to fill up their vehicles.
OC. The total amount it costs Megan to fill up her vehicle.
OD. The total amount it costs Jeff and Valerie to fill up their vehicles.
The total amount it costs Jeff and Valerie to fill up their vehicles.
The correct option is D.
Briefing:bx is most likely the amount it costs Jeff and Valerie to fill up their cars because they both pay x dollars per gallon.
Ay = Megan Bx
= Valerie and Jeff
Ay + Bx = Megan + Valerie and Jeff
Algebra described as:Algebra is a field of mathematics that assists in the depiction of problems or situations using mathematical expressions. To produce a meaningful mathematical expression, variables like as x, y, and z are used, as well as mathematical operations such as addition, subtraction, multiplication, and division.
What is algebra's first rule?Working from left to right, first complete multiplication and division, then addition and subtraction.
What are algebra fundamentals?The principles of algebra include numbers, variables, constants, expressions, equations, linear equations, as well as quadratic equations.. It also includes basic mathematical operations such as addition, subtraction, multiplication, and division within algebraic equations.
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Use this activity to explain how the SAS criterion for triangle congruence follows frum the definition of congruence in terms of rigid motions. (Hint: Extend lines, on the tracing paper.)
Any method of repositioning a figure in which the relative positions of the figure's points and vertices remain unchanged and the relative distance between them stays the same.
What does the mathematical meaning of congruence mean?
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.
Rigid motion satisfies these requirements because it is rigid, which means that everything that moves remains unchanged except from the location of the overall figure.
Translation, reflection, and rotation are the three basic types of rigid motion.
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20x+25x=180 finding the number for X WITH STEPS pls
Answer:
x=4
Step-by-step explanation:
20x+25x=180
45x = 180
x = 4
plot 1/5 and -0.6 and their opposites on a number line
Answer:
here ya go ! also , 0.6 = 3/5 and 1/5 = .2
Step-by-step explanation:
Write an equation in slope-intercept form of the line having the given slope and y intercept.
m: 1/2, y- intercept: 4
The equation in slope intercept form of the line having the slope m= 1/2 and y intercept 4 is [tex]y=\frac{1}{2}x+4[/tex]
Given,
The slope of the line = [tex]\frac{1}{2}[/tex]
The y-intercept = 4
We know,
The slope intercept form of the line y = mx + b
Substitute the values in the equation
y= [tex]\frac{1}{2}x+4[/tex]
Hence, the equation in slope intercept form of the line having the slope m= 1/2 and y intercept 4 is [tex]y=\frac{1}{2}x+4[/tex]
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Please help me with this
The complete table for the electrician charges is shown below:
x y
1 125
2 175
3 225
4 275
How to complete a table with two variables
According to the statement, there are two variables. First, the number of hours of work (x) and, second, the total fee. The total fee changes linearly with the number of hours and the expression is defined below:
y = x' + (Δy / Δx) · x (1)
Where:
x' - Base fee, in dollars.Δx - Change in time, in hoursΔy - Change in total fee, in dollars.x - Time, in hours.If we know that x' = 75, Δx = 1 h and Δy = 50, then the values of the table are shown below:
x = 1
y = 75 + 50 · 1
y = 125
x = 2
y = 75 + 50 · 2
y = 175
x = 3
y = 75 + 50 · 3
y = 225
x = 4
y = 75 + 50 · 4
y = 275
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The population of China is about 1.4 x 109
people, while the population of South Korea is
approximately 50,000,000 people. How many
times greater is the population of China than
the population of South Korea?
The population of China is 28 times greater than that of South Korea, calculated using solving of basic linear equation.
As per the question statement, the population of China is about (1.4 × 10⁹) people, while that of South Korea is approximately 50,000,000 people.
We are required to calculate that, by how many times is the is the population of China greater than that of South Korea.
To solve this question, let us assume that, the population of China is "x" times greater than that of South Korea. Hence, we will form a linear equation of single variable (x) and solving for "x", we will obtain our desired answer.
Since the population of China is assumed to be "x" times greater than that of South Korea,
[tex](50000000*x)=1.4*10^{9}\\ or,5*10^{7}*x=1.4*10^{9}\\or,5x=\frac{1.4*10^{9}}{10^{7}} \\or, 5x=1.4*10^{2}\\ or,5x=1.4*100\\or,5x=140\\or,x=\frac{140}{5}\\ or,x=28[/tex]
That is, The population of China is 28 times greater than that of South Korea.
Linear Equation: As the name itself suggests, a linear equation is an equation between variables, (typically Two) that gives a straight line when plotted on a graph, and also has a degree of 1.To learn more about Linear Equations, click on the link below.
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is it possible for a system of lineaf equations to have no solutions
yes
when equations are parallel
&
when you solve the equations you have
DIFFERENT NUMBERS on either side of the equal sign
for example when you do the math you would end up with something like :
7 = 0
mrviolamath
khan academy
Translate the phrase into an algebraic expression.
The sum of c and 2
Years ago, a cell phone plan cost $70 per month for unlimited calling plus $0.10 per text message.
Answer:
so the cell phone plan is $70 per month
Step-by-step explanation:
solution in question
An airplane flying at an altitude of 30,000 feet flies up to avoid a storm. Immediately after passing the storm, the airplane returns to its original altitude.
A. What interger represents the airplane's change in altitude to avoid the storm.?
B. What integer represents the airplanes change in altitude immediately after passing the storm?
C. Use appropriate tools, draw a number line to represent the airplanes changed altitude.
Answer: The number 8,000 represents the change in height necessary to dodge the storm.
The integer representing the altitude after passing the storm is 30,000
Use appropriate tools, draw a number line to represent the airplanes changed altitude = 34000
Step-by-step explanation:
In the picture that is attached, the diagram for this query is displayed.
We are informed that the aircraft's starting height was 30,000 feet.
A. What integer represents the airplane's change in altitude to avoid the storm.?
During the storm:
The plane flew at at altitude of 38,000 feet
We will deduct the end altitude from the starting altitude to obtain the change in altitude.
change of altitude = final altitude - initial altitude
change of altitude = 38,000 - 30,000
= 8,000 ft
Therefore, the integer representing the change of altitude to avoid the storm is 8,000
B. What integer represents the airplanes change in altitude immediately after passing the storm?
After the storm:
We are aware that the aircraft returned to its original height following the storm.
The number reflecting the altitude after passing the storm would be 30,000 ft given that the starting altitude is 30,000 ft.
C. Use appropriate tools, draw a number line to represent the airplanes changed altitude.
See a picture.
Use appropriate tools, draw a number line to represent the airplanes changed altitude = 34000
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Write a function for the height, T of the taller candle in terms of the number of hours it has burned, h.
The linear function for the height of the taller candle after t hours is given by:
h(t) = 18 - 3.1t.
What is the missing information?The missing information is that a 18 inch candle is burning at a rate of 3.1 inches an hour.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The initial height of 18 inches is the intercept.The burning rate is the slope, as a negative, as burning means that the height of the candle is decreasing.Hence the linear function for the height of the taller candle after t hours is given by:
h(t) = 18 - 3.1t.
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[tex] \frac{x + 7}{3 } = \frac{10}{6} [/tex]
help me with this problem please
x = -2
Step-by-step explanation:
x + 7/3 = 10/6
Multiply both sides by 3 so we can divide without getting decimals.
3x + 21/3 = 30/6
Then divide 3x + 21 by the denominator and 30 by 6
x + 7 = 5
Subtract 7 from each side to get x by itself
x = -2
i need help solving this
Answer:
x = 9.
Step-by-step explanation:
12x + 7 = 115
12x + 7 - 7 = 115 - 7
12x = 108
x = 9.
Which equation is neither perpendicular nor parallel to line k?
According to the question, the two equations are neither parallel nor perpendicular is 4x + 2y = 10 and x+2y =6.
When the slope of the two lines are same, then the lines are parallel to each other. And when the multiplication of the two slope is negative one, then the lines are perpendicular with each other.
Now, the slope of the first equation that is 4x + 2y = 10
slope([tex]m_{1}[/tex]) = (10 - 4x)/2 = 5
Comparing the above equation with y = mx + c
Similarly,
slope([tex]m_{2}[/tex]) = (6 - x)/2 = 3
Therefore, the calculated slopes are neither parallel nor perpendicular.
What is slope?
The slope of the line is the ratio of the horizontal axis and the vertical axis. And to calculate the slope of the lines which are parallel or perpendicular by comparing it with the standard equation. When the slopes of two or more equations are same then the lines are parallel. When the multiplication of the slope between the lines is negative one, then it is perpendicular.
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Look at the picture uploaded.
The lengths of each line segment are listed below:
AB ≈ 5.385 CD ≈ 5.099 EF ≈ 6.083How long is each line segment?
In this problem we find three line segments, of which the coordinates of all ends are known, and we must determine the lengths of each segment, task to be done by applying Pythagorean theorem.
If we know that A(x, y) = (0, 2), B(x, y) = (5, 4), C(x, y) = (- 6, 0), D(x, y) = (- 7, 5), E(x, y) = (- 5, - 8), F(x, y) = (- 6, - 2), then the length of each segment is:
AB = √[(5 - 0)² + (4 - 2)²]
AB = √(5² + 2²)
AB = √(25 + 4)
AB = √29
AB ≈ 5.385
CD = √[[- 7 - (- 6)]² + (5 - 0)²]
CD = √[(- 1)² + 5²]
CD = √(1 + 25)
CD = √26
CD ≈ 5.099
EF = √[[- 6 - (- 5)]² + [- 2 - (- 8)]²]
EF = √[(- 1)² + 6²]
EF = √(1 + 36)
EF = √37
EF ≈ 6.083
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f(x)=(-19/12)x-(17/3)f(-8)=
Traveling carnivals usually shut down for the winter months. Suppose a traveling carnival decided to instead remain open for business indefinitely in its last stop of the season. Assume its usual revenue projections hold($15,000 on the first nigh, and each night's revenue after the first night will be about 75% of the previous night revenue). To the nearest dollar, what is the maximum amount of revenue the carnival can expect in the town?
The maximum amount of revenue the carnival can expect in the town in the 5th night is; $4746.093.
How to solve Geometric Progression?A geometric progression is defined as a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
We are told that Revenue in the first night = $15000
Now revenue of new night is 75% of the previous night. Thus;
2nd night = 15000 × 75/100 = $11250
3rd night = $11250 × 75/100 = 8437.5
Therefore, the given geometric sequence is ;
15000, 11250, 8437.5 ...
First term; a = $15000
Common ratio (r) = 11250/15000 = 0.75
The formula for the nth term of a GP is given by ;
aₙ = arⁿ ⁻ ¹
Thus, revenue for the 5th night is;
a₅ = ar⁵⁻¹
a₅ = 15000(0.75)⁴
a₅ = 4746.093
We conclude that the revenue in the 5th night in two will be $4746.093.
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20. The difference between the compound interest and the simple interest on a certain
Sum at 9% per annum for 2 years is 324. Find the sum.
The sum is 40,000.
The difference between compound interest and simple interest is 324 on a certain sum at 9% for 2 years.
So,
Compound interest - Simple interest = 324
C.I - SI = 324
The formula for compound interest is given as:
C.I = P( 1 + r/100 )ⁿ - P
Where P is the principal amount, r is the rate and n is the time in years.
Therefore,
C.I = P( 1 + 9/100)² - P
C.I = P( 1 + 0.09)² - P
C.I = P(1.09)² - P
C.I = 1.1881P - P
C.I = 0.1881P
Now, the formula for simple interest is given as:
S.I = ( P × R × T / 100 )
Where P is the principal amount, R is the rate and T is time in years.
Therefore,
S.I = ( P × 9 × 2 / 100 )
S.I = 18P / 100
S.I = 0.18P
Now,
C.I - S.I = 324
0.1881P - 0.18P 324
0.0081P = 324
P = 324 / 0.0081
P = 324 × 10000 / 81
P = 4 × 10000
P = 40000
Hence, the principal amount is 40,000.
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Find the measure of each numbered angle. (Lesson 4-2)
m ∠ 4
The measurement of angle ∠1 is 45°.
What do we mean by an angle?An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles formed by two rays are located in the plane containing the rays. Angles are also formed when two planes intersect. These are known as dihedral angles.So,
An octagon has 8 sides. Sum of interior angles = 180° x (n-2) = 180° x (8-2) = 180° x 6 = 1,080°1,080° ÷ 8 sides = 135° interior angle.Angle 2 = 135° / 2 = 67.50°Angle 1 = 180° - 135° = 45°Therefore, ∠1 is 45°.
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The correct question is given below:
Given the regular polygon, find the measure of each numbered angle.
m ∠ 1
Find x. 30² + 35² = x²
The unknown variable's result of the equation 30² + 35² = x² is 46.10
To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:
What is adding goes to the other side of the equality by subtracting.What is multiplying goes to the other side of the equality by dividing.30² + 35² = x²
900 + 1225 = x²
x² = 2125
x = [tex]\sqrt{}[/tex]2125
x = 46.10
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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can someone please help me solve, it's on factor theorem, I got most of the answer it's just for the remainder what is it? is what I'm doing correct?
Answer:
remainder: 3/4
Step-by-step explanation:
You want to divide the polynomial (2x^4-9x^3-x^2+2) by (2x-1).
Polynomial long divisionThe attachment shows the division worked out.
Your work has a sign error in the second product: (-4x²)(2x-1) should be (-8x³+4x²).
Factor theoremThe factor theorem tells you that if division by (2x-1) gives a remainder of 0, then (2x-1) is a factor of the dividend polynomial. Alas, here, the remainder is not zero, so 2x-1 is not a factor.
Remainder theoremThe remainder theorem tells you that the remainder of p(x) divided by (x-a) is p(a). We can evaluate the polynomial for x=1/2, the value that makes the divisor zero:
f(1/2) = ((2(1/2) -9)(1/2) -1)(1/2)^2+2 = ((-8)(1/2) -1)(1/4) +2 =(-5)(1/4) +2 = 3/4
The remainder from division by (2x -1) is 3/4.
__
Additional comment
We did the polynomial evaluation by writing it in Horner form. This minimizes the number of arithmetic operations required, and generally makes them simpler.
Find the distance between the pair of points. Round to the nearest tenth.
J(7,11) and K(-1,5)
The distance between the pair of points J( 7, 11) and K (-1, 5) is equal to 10.
As given in the question,
Given pair of points are J( 7, 11) and K (-1, 5)
Let J( x₁ ,y₁) = J( 7, 11) and K (x₂, y₂) = K (-1, 5)
Distance between pair of points ( x₁ ,y₁) , (x₂, y₂) is equal to
[tex]= \sqrt{(y_{2}-y_{1})^{2}+ (x_{2}-x_{1})^{2} } \\\\=\sqrt{(5-11)^{2}+ (-1-7)^{2} }\\\\= \sqrt{36 +64}\\ \\=\sqrt{100}[/tex]
= 10 units
Therefore, the distance between the pair of points J( 7, 11) and K (-1, 5) is equal to 10.
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A stop sign in the shape of a regular octagon is inscribed in a circle. Find following measure.
m < LSR
The shape of a stop sign is the shape of a regular octagon. Each interior angle of the regular octagonal, m < LSR = 135.
What is the area of a regular octagon inscribed in a circle?
A regular octagon's area is inscribed in a circle with a radius of one unit. Divide the octagon into eight congruent triangles. The area of one triangle and multiply it by 8 to get the area of the entire octagon.
Because of its eight connected vertices, an octagon has eight sides. As a result, when we assign circle = 1, it has only one side, which is a curve, whereas when we assign octagon = 8, it has eight sides, so we assign it the value 8.
The shape of a stop sign is the shape of a regular octagon.
Each exterior angle of the regular octagonal sign is 360/8 = 45.
So, each interior = 180 – 45 = 135.
m < LSR = 135.
Therefore, the interior angle of the regular octagonal, m < LSR = 135.
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