The required simplication of rational expression is -(4 + x) / (x - 5).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Simplifying the rational expression, 12 - x - x² / x² - 8x + 15
Given a rational expression,
12 - x - x² / x² - 8x + 15
On simplifying, we get,
For numerator, 12 - x - x²: (3 - x)(4 + x)
For denominator, x² - 8x + 15: (x - 5)(x - 3)
Now, 12 - x - x² / x² - 8x + 15 = (3 - x)(4 + x) / (x - 5)(x - 3)
= -(4 + x) / (x - 5)
Restriction is that the denominator, x - 5 should not be 0.
Hence, the required simplication of rational expression is -(4 + x) / (x - 5)
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A sketch of y = x² + 6x + 15 has been drawn.
Complete the sketch by entering the
corresponding values on the axes.
Answer:
Vertex=(-3,6) and Y intercept is 15/(0,15)
There are 24 classrooms and 600 students. What is the ratio of classrooms to students written in fraction simplest form?
Answer:
1 : 25.
Step-by-step explanation:
24 : 600
= 24/24 : 600/24
= 1 : 25.
(20 POINTS)
If a polynomial f(x) has a remainder of -4 when divided by x-8, what is f(8)?
Based on the given parameters, the value of the polynomial function f(8) is -4
What are polynomials?Polynomials are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the polynomial function?The polynomial function is given as
Polynomial = f(x)
Also, we have the following statement
a remainder of -4 when divided by x-8
To start with, we set the divisor to 0
So, we have
x - 8 = 0
Add 8 to both sides of the equation
So, we have
x = 8
Express as a function
f(x) = f(8)
Set the equation to the remainder
So, we have
f(x) = f(8) = -4
Hence, the value of the polynomial function f(8) is -4
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12(?-21)=144 what is the answer
.What is the slope between
(-8,4) and (3,-1)?
What is the slope of
4x-3y=13?
How do you know a graph represents direct variation?
What is true about the slopes of parallel lines? What is true about the slopes of perpendicular lines?
The slope between (-8,4) and (3,-1) is -5/11 and the slope of 4x - 3y = 13 is 4/3
What is the slope between (-8,4) and (3,-1)?The points are given as
(-8,4) and (3,-1)
The slope between the points is calculated using
Slope = (y2 - y1)/(x2 - x1)
So, we have
Slope = (-1 - 4)/(3 + 8)
Evaluate
Slope = -5/11
Hence, the slope between (-8,4) and (3,-1) is -5/11
What is the slope of 4x - 3y = 13?The equation of the line is given as
4x - 3y = 13
Make 3y the subject of the formula
So, we have
3y = 4x - 13
Make y the subject of the formula
So, we have
y = 4/3x - 13/3
A linear equation is represented as
y= mx + c
Where
Slope = m
By comparison, we have
m = 4/3
Hence, the slope of 4x - 3y = 13 is 4/3
How do you know a graph represents direct variation?A graph that represents direct variation is a linear graph that passes through the origin
What is true about the slopes of parallel lines?The slopes of parallel lines are equal
i.e. m1 = m2
What is true about the slopes of perpendicular lines?The slopes of perpendicular lines are opposite reciprocals
i.e. m1 = -1/m2
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An equilateral triangle has a length of 10 inches.What is the area of the triangle in simplest radical form?
Answer: The area of Triangle is A = 43.25
Step-by-step explanation:
In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3 [tex]s^{2}[/tex]* s = √3/4([tex]s^{2}[/tex])
Define Area of Triangle:
In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4([tex]s^{2}[/tex]) . The perimeter of an equilateral triangle is 3s.
So, we can write,
A = √3/4([tex]s^{2}[/tex])
It means, A = Area of the Triangle
S = length of Triangle = 10inches.
A = √3/4([tex]s^{2}[/tex])
A = √3/4([tex]10^{2}[/tex])
A= √3/4*100
A = 1.73/4*100
A = 0.4325*100
A = 43.25
The area of Triangle is A = 43.25
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49
#
2. The equation x = 3 is graphed on the coordinate plane shown.
a. Graph the line perpendicular to x = 3 that passes
through (-2, 4).
The linear function y = 4, perpendicular to x = 3, is graphed at the end of the answer.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.When two linear functions are perpendicular, they intersect forming an angle of 90º between them.
For this problem, we want a line perpendicular to x = 3.
x = 3 is a vertical line.The line perpendicular to a vertical line is an horizontal line, in the format y = 4.The line passes through (-2,4), with y-coordinate of 4, hence the line is given by:
y = 4.
On the graph given at the end of the answer, it is shown that the two lines are perpendicular, forming an straight angle. The line y = 4 is graphed in blue.
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Can a quadratic equation with real coefficients have exactly one imaginary root? Explain your answer.
A real coefficient quadratic equation cannot have one real root and one imaginary root.
What is a quadratic equation?A quadratic problem is a type of problem in mathematics that deals with a variable multiplied by itself — an operation known as squares. The area of a square is defined as its side length multiplied by itself in this language. The term "quadratic" is derived from the Latin word quadratum, which means "square." Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. Where x is an unknown variable and the numerical coefficients a, b, and c.A rational coefficient quadratic equation cannot have one real root and one imaginary root.Therefore, a real coefficient quadratic equation cannot have one real root and one imaginary root.
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Write an expression for “3 times the sum of a number and 2”
Answer:
3*2
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints (2,-9) (-4,-4)
Answer:
the answer will be (-1, -6.5)
Step-by-step explanation:
The midpoint formula is [tex](\frac{x^1 + x^2}{2} , \frac{y^1 + y^2}{2} )[/tex]
so you would do [tex](\frac{2 - 4)}{2} , \frac{-9-4}{2} )[/tex] , the only reason it is subtracting is that a positive and a negative make a negative so you might as well subtract, either way, if you insert the equation by doing 2 + (-4) you will get the same thing
then you would just do the math and get your answer
Hope this helps :)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -4 +2}{2}~~~ ,~~~ \cfrac{ -4 -9}{2} \right) \implies \left(\cfrac{ -2 }{2}~~~ ,~~~ \cfrac{ -13 }{2} \right)\implies \left(-1~~,~~-6\frac{1}{2} \right)[/tex]
What is the solution of √4 x+1 -5=0 ?
The solution is 6
Rewriting the given equation
√(4x + 1) - 5 = 0
Now, taking square of the equation to find the solution of equation -
(√(4x + 1))² = 5²
On squaring both sides we get the equation -
4x + 1 = 25
Shifting 1 to the Right Hand Side of the equation
4x = 25 - 1
Performing subtraction on Right Hand Side of the equation
4x = 24
Shifting 4 to the Right Hand Side of the equation as denominator
x = 24 ÷ 4
Performing division on Right Hand Side of the equation
x = 6
Thus, the solution is 6
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The correct question is - sqrt(4x+1)-5=0
The time t in seconds for a swinging pendulum to complete one full cycle is given by the function t=0.2√I, where l is the length of the pendulum in centimeters. To the nearest tenth, how long is a full cycle if the pendulum is 10 cm long? 20cm long? How long, in centimeters, is a pendulum that takes 2 seconds for one full cycle?
A full cycle, if the pendulum is 10 cm, is 0.6 seconds long. A full cycle, if the pendulum is 20 cm, is 0.9 seconds long. A pendulum that takes 2 seconds for one full cycle is 100 cm long.
Given,
The time t in seconds for a swinging pendulum to complete one full cycle is given by the function t as,
t = 0.2 √I
Here, l is the length of the pendulum in centimeters.
For the first part, two lengths are given for the pendulum is given
We can obtain the value of t by substituting the value of l
This implies,
For l = 10 cm
t = 0.2 √10 = 0.632 = 0.6 seconds
For l = 20 cm
t = 0.2 √20 = 0.894 = 0.9 seconds
For the second part, time is given
We can obtain the value of l by substituting the value of t
This implies,
For t = 2 seconds
l = t² / (0.2)² = t² / 0.04 = 2² / 0.04 = 4 / 0.04 = 100 cm
Therefore, A full cycle is 0.6 seconds long if the pendulum is 10 cm long, 0.9 seconds long if the pendulum is 20 cm long, and 100 cm long if the pendulum takes 2 seconds to complete one full cycle.
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Determine if each statement is true or false. Justify your answer.
log₄7- log ₄3= log₄4
The given logarithmic expression statement is false. Because log₄7- log ₄3 = log₄(7/3).
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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Can someone please help me with this one? I need it for my homework that I have to hand in tomorrow. Thank you!
The steps for constructing the bisector of an angle by using a ruler and compasses are as follows:
Step 1:
Take a compass and place its point on the angle's vertex Q.
Step 2:
Adjust the compass to the medium wide setting. The exact width is not important.
Step 3:
Without changing the compasses' width, draw an arc across each leg of the angle.
Step 4:
Now, place the compass on the point where one arc crosses a leg and draw the arc in the interior of the angle.
Step 5:
Without changing the compass setting repeat for the other leg so that the two arcs cross.
Step 6:
Now by using a ruler draw a line from the vertex to the point where the arcs cross.
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Use the Change of Base Formula to evaluate each expression.
log₇30
The evaluated value of [tex]log_{7}30[/tex] is 1.748
Change of base formula is used to change the base of the logarithm. It is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.
According to the change of base formula:
[tex]log_{a}b = \frac{log_{x}b }{log_{x} a}[/tex]
where base x is considered base 10
According to the question, we have to find the value of [tex]log_{7} 30[/tex]
Thus applying change of base formula we get
[tex]log_{7} 30 = \frac{log_{10} 30}{log_{10} 7}[/tex]
calculating the value of log from the calculator we get,
[tex]log_{7} 30 = \frac{1.477}{0.845}[/tex]
[tex]log_{7} 30 = 1.748[/tex]
Thus evaluated value of [tex]log_{7}30[/tex] is 1.748
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Solve each equation. Check your answers.
log (5-2 x)=0
The value of x for log (5-2 x)=0 is 2.
What is the logarithmic function?
It is established that the exponential equation x = ay and the logarithmic function y = logax are equal. Only when x = ay, a > 0, and a 1 do y and logax coincide. The base-a logarithmic function is what it is known as. Think about what it means for the exponential function to be inversed: x = ay.
Given,
log (5-2 x)=0
It can be expressed as -
5 - 2x = 10⁰
= 5 - 2x = 1
= x = 2
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The lengths of the four sides of a quadrilateral (in inches) are consecutive odd integers. if the perimeter is 120 inches, find the value of the longest of the four side lengths.
In a quadrilateral with a perimeter of 120 inches, the longest of the four sides has length equal to 33 inches.
A quadrilateral is a two-dimensional figure that has 4 sides and 4 vertices. The perimeter of any two-dimensional figure is the sum of all its sides.
If the lengths of the four sides of a quadrilateral (in inches) are consecutive odd integers, we can express each side as:
x = length of side 1(odd integer)
x + 2 = length of side 2
x + 4 = length of side 3
x + 6 = length of side 4
If the perimeter of the quadrilateral is 120 inches, then the sum of the four sides is equal to 120 inches.
x + (x + 2) + (x + 4) + (x + 6) = 120
Simplifying and solving for x.
4x + 12 = 120
4x = 108
x = 27
Substitute the value of x on the expression for the length of the 4th side(longest side).
longest side = x + 6 = 27 + 6
longest side = 33 inches
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Each term of a sequence is 2 more than the previous term. if the third term is 8, find the first five terms of the sequence.
The first five terms of the sequence area s follows:
4, 6 , 8 , 10, 12
How to find the terms of a sequence?Each term of the sequence is 2 more than the previous term.
The third term is 8.
The sequence is an arithmetic sequence base on the difference.
Using arithmetic sequence formula,
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore, let's used the third term to find the first term.
8 = a + 2d
8 = a + 2(2)
8 = a + 4
a = 8 - 4
a = 4
Therefore, the first term of the sequence is 4.
Hence, the first five terms of the sequence area s follows:
4, 6 , 8 , 10, 12
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Step 1: Think of any number
Step 2: Double the number.
Step 3: Add-5
Step 4: Double your new number.
Step 5: Subtract 6
Step 6: Divide by 4/
Step 7: Subtract your original number
Did you get 1 ? use algebra to show why this works.
Answer:
Step 1: 20
Step 2: 40
Step 3: 45
Step 4: 90
Step 5: 84
Step 6: 21
Step 7: 1
I did get 1 by following the steps.
please help me !!!!!
Solve the system of equations-2x+2y=-8 and -3x+y=8 by combining the equations
The required solution of the system of equations are x=-6 and y=-10.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The system of equations are
-2x+2y=-8 and -3x+y=8
According to given question we have
Consider the first equation.
-2x+2y=-8
Taking minus sign common from both sides we get
-(2x-2y)=-8
2x-2y=8
Taking 2 common from left sides, we get
2(x-y)=8
Divide by 2 on both sides we get,
x-y= 4....(i)
-3x+y=8...(ii)
By adding 2 equation we get
-2x=12
x=-6
Put the value of x in Equation (i) we get
x-y= 4
-6-y=4
-y=4+6
y=-10
Therefore, the required solution of the system of equations are x=-6 and y=-10.
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Evaluate the expression 7+(-2)•3^2
Answer:first do the exponents thats equal to 9 then times -2 is -16+7 is -11
hope that helps
Step-by-step explanation:
Answer:
-11.
Step-by-step explanation:
7+(-2)•3^2
= 7 - 2*9
= 7 - 18
= -11.
In a random sample of people, the mean commute time to work was minutes and the standard deviation was minutes. Assume the population is normally distributed and use a t-distribution to construct a % confidence interval for the population mean. What is the margin of error of ? interpret the results.
The margin of error is 3.083 min
Margin of Error: The margin of error is the range of error permitted around the sample statistic in order to estimate the population parameter. The margin of error indicates the size of the confidence interval. The breadth of the confidence interval increases with the margin of error.
Sample size, n=24
Sample mean, ¯x=31.5 min
Sample standard deviation, s=7.3 min
Confidence level, c=95%
=0.95
From the given information we can calculate the below-required quantities,
Significance level, α=1−c=1−0.95=0.05
Degrees of freedom, DOF=n−1
=24−1
=23
Now from the t-distribution table,
The value of t (α2, DOF) is,
t (0.025,23) = 2.069
Hence the margin of error will be,
MOE= t (α2, DOF) × s/√ n
=2.069×7.3/√24
=3.083 min
i. The upper limit of the confidence interval will be,
UL=¯x + MOE=31.5+3.083=34.583
The lower limit of the confidence interval will be,
LL=¯x−MOE
=31.5−3.083
=28.417
Hence, the 95% confidence interval is (28.417,34.583)
(28.417,34.583)
The answer is 28.417,34.583
ii. The required answer is MOE=3.083 min
ii. We have found the 95% confidence interval for the population mean to be (28.417,34.583). This means with 95 % confidence; it can be said that the population mean commute time is between the bounds of the confidence interval.
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Help me please asap please
Answer:
the first one is D. {3/2}
second one is C. {-10}
Step-by-step explanation:
hope this helps
Which equation has an extraneous solution?
Answer:
[tex] \sqrt[5]{x } = - 2 = - 35[/tex]
Find the difference.
3/4(3x+6)−1/4(5x−24)
Answer:
x+21/2.
Step-by-step explanation:
3/4(3x+6)-1/4(5x-24).
=9x/4-5x/4+9/2+6.
=x+21/2
Maryama bought 45 plain cookies for $2.20 each. She decorated them with icing and sold them for $3.75 each. How much profit did she make selling her decorated cookies?
45x2.20=99
meaning she spent $99
45x3.75=168.75
shows how much she made
168.75-99=69.75
shows what she profited
your answer is $69.75
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If the relationship is proportional, what is the missing value from the table?
x
y
8
6
16
?
24
18
Answer:
12.
Step-by-step explanation:
y /x = 6/8 = 3/4
y/x = 18/24 = 3/4
The relation is y = 3/4 x.
So, the missing value is 16 * 3/4
= 12.
Parallelogram has a base of 3.5 units and a corresponding height of 2 units what is it’s area
Answer:
The answer is 7
Step-by-step explanation:
The formula you would use is A=bxh
So you would just plug it in
3.5 x 2 which gives you 7
Hope this helps:)
Find the values of the variables.