Answers
Given expression [tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] is equivalent to [tex]2x+5 -\frac{36}{x+3}[/tex].
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
Given expression:
[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] for [tex]x[/tex] ≠ -3 or 0.
Using long division method and euclid lemma
On dividing [tex]2x^3+11x^2-21x[/tex] by [tex]x^2+3x[/tex] we get, (given in the snip)
As we know division can be written as
dividend = divisor × quotient + remainder
[tex]2x^3+11x^2-21x = (2x+5)(x^2+3x)-36x[/tex]
⇒ [tex]2x^3+11x^2-21x = 2x+5 -\frac{36x}{x^2+3x}[/tex]
⇒ [tex]2x^3+11x^2-21x = 2x+5 -\frac{36}{x+3}[/tex]
Therefore, given expression [tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] is equivalent to [tex]2x+5 -\frac{36}{x+3}[/tex].
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Related Questions
James’ dealership uses a one-price, “no haggle” selling policy. The dealership averages 13% profit on new car sales. If the dealership pays $15,600 for a Rancho Turbo, find the selling price after adding the profit to the dealer’s cost.
Help me and I will give you 5 stars!!!:):):)
Answers
The selling price after adding the profit to the dealer’s cost is $17628
The dealership averages 13% profit on new car sales
If the dealership pays $15,600 for a Rancho Turbo,
The profit is 13% of the dealership
profit =(13/100) 15600
profit = 2028
Selling proce = cost price + profit
= 15600 + 2028
= 17628
Therefore, the selling price after adding the profit to the dealer’s cost is $17628
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⁰which of the following is the volume of a hemisphere with a radius of 8 inches?
Answers
The general expression for the volume of hemisphere is :
[tex]\text{ Volume = }\frac{2}{3}\Pi\text{ }\times radius^3\text{ }^{}^{}[/tex]In the given question we have radius = 8 inches
Substitute the value of r = 8 in the expression for the volume of hemisphere :
[tex]\begin{gathered} \text{ Volume = }\frac{2}{3}\Pi\text{ }\times radius^3\text{ }^{} \\ \text{Volume}=\frac{2}{3}\times3.14\times8^3 \\ \text{Volume =}1071.78666 \\ Volume\text{ = 1071.70 inches cubed} \end{gathered}[/tex]B) 1071.79 inches cube
Answer
The tin can shown below has the indicated dimensions.1.5in.3.25in.A cylinder is shown. The radius of the top circular base is labeled (1 .5) inches and the altitude is labeled (3.25) inches.Estimate the number of square inches of tin required for its construction. (Hint: Include the lid and the base in the result. Use your calculator value of . Round your answer to two decimal places.)in2
Answers
Given:
A cylinder having radius 1.5 inches and a height of 3.25 inches
Required:
Estimate the number of square inches of tin required for its construction.
Explanation:
To calculate the number of square inches of tin required for its construction we have to calculate the area of the lid and base and the curved surface then add them all.
[tex]\begin{gathered} \pi r^2+\pi r^2+2\pi rh \\ \Rightarrow\frac{22}{7}\times1.5^2+\frac{22}{7}\times1.5^2+2\times\frac{22}{7}\times1.5\times3.25 \\ =44.76769531\text{ in}^2 \\ =44.77\text{ in}^2 \end{gathered}[/tex]Final Answer:
44.77 inches square
what two intergers does the square root of 15 fall between
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
2 integers ===> √15
Step 02:
[tex]\sqrt[]{15}=\text{ }3.87[/tex]integer 1 = 3
integer 2 = 4
That is the solution.
identify the percentage of change and increase or decrease 75 people to 25 people increase or decrease find the percent of change round to the nearest tenth of a percent
Answers
dentify the percentage of change and increase or decrease 75 people to 25 people increase or decrease find the percent of change round to the nearest tenth of a percent
we have that
75 people represent the 100 % so
Applying proportion, find out how much percentage represent the difference (75-25=50)
so
100/75=x/50
solve for x
x=(100/75)*50
x=66.7 %
therefore
Its a decrease and the percentage of change is 66.7%Find the measure of ZGHJ and ZGI.68°H31°.K115°angle GHJ =degreesangle GIJ =degrees
Answers
We are asked to determine angles GHJ and GIJ. To do that we need to have into account that these two angles are half the measure of their respective intercepted arc. Since both intercepted arcs are the same then the angles are equal. The intercepted arc is given by:
[tex]\begin{gathered} \theta=360-68-31-115 \\ \theta=146 \end{gathered}[/tex]Therefore, the angles are:
[tex]\angle GHJ=\angle GIJ=\frac{\theta}{2}=\frac{146}{2}=73[/tex]A company wants to decrease their energy use by 15%. If their electric bill is currently $1,700 a month, what will their bill be if they are successful? Give your answer accurate to at least the nearest dollar.$
Answers
We will determine it as follows:
[tex]x=1700-1700(0.15)\Rightarrow x=1445[/tex]So, they will pay $1445 if they manage to decrease the consumption by 15%.
Determine the remainder when 6x^3+ 23x^2 - 6x -8 is divided by 3x-2. What information does the remainder provide about 3x-2? Explain.
Answers
we have
6x^3+ 23x^2 - 6x -8 : (3x-2)
step 1
Verify if (3x-2) represents a factor
If (3x-2) is a factor
then
3x-2=0 ------> x=2/3
Substitute the value of x=2/3 in the given expression
6(2/3)^3+23(2/3)^2-6(2/3)-8
6(8/27)+23(4/9)-4-8
(16/9)+(92/9)-12
12-12=0
that means
(3x-2) is a zero of the given function
therefore
when divide (6x^3+ 23x^2 - 6x -8 ) by (3x-2), the remainder is zeroThe permeter of then figure below is 110cm.Find the length of the missing side.
Answers
Perimeter of a plane shape is the sum of all lenth of side of outer boundary.
Perimeter = 110cm
perimeter = 8.6 + 34.6 + 8.6 + 17.3 + 11.6 + 11.6 + 11.6 + x
110 = 103.9 + x
x = 110 - 103.9
x = 6.1cm
which inequality is shown in the graph below? A x<2 B x>2 C y>2 S y<2
Answers
In the picture, we can see that the solution to the inequality are those x-values greater than 2 (2 is not included) no matter which value the y-variable has. This corresponds to: x > 2.
Find the magnitude of the vector (-4,-4).Write your answer in simplified radical form.030/0 (0,0)ХX6?
Answers
Given the vector < -4, 4 >
The magnitude of the vector =
[tex]\sqrt[]{(-4)^2+(4)^2}=\sqrt[]{2\cdot4^2}=4\sqrt[]{2}[/tex]so, the answer will be:
[tex]4\sqrt[]{2}[/tex]Benjamin invested an amount of $12,000.00 in a mutual fund. After 4 years and 6 months the accumulated value of his investment was $13,407.58. What is the nominal interest rate of the investment if interest is compounded semi-annually?__________%
Answers
Given the following parameters
[tex]\begin{gathered} PV\Rightarrow\text{Present value}\Rightarrow12000.00 \\ T\Rightarrow\text{time}\Rightarrow4\text{years and 6 month} \\ FV\Rightarrow\text{Future Value}\Rightarrow13407.58 \\ n=2 \end{gathered}[/tex]To calculate the nominal rate, we will have to calculate the interest rate and the compounded period, the following formula will be used to find the interest rate and the compounded period.
[tex]\begin{gathered} i=(\frac{FV}{PV})^{\frac{1}{n}}-1 \\ m=\frac{n}{t} \end{gathered}[/tex]To find the value of the interest, we have
[tex]\begin{gathered} i=(\frac{13407.58}{12000.00})^{\frac{1}{2}}-1 \\ i=(1.117298333)^{\frac{1}{2}}-1 \\ i=1.057023336-1=0.05702336 \end{gathered}[/tex]To find the compounded period we will have that
[tex]\begin{gathered} m=\frac{n}{t} \\ n=2 \\ t=4.5 \\ m=\frac{2}{4.5} \\ m=0.4444444444 \end{gathered}[/tex]Thus, the nominal rate formula is given as;
[tex]\begin{gathered} j=m\times i \\ \end{gathered}[/tex]Substitute for m and i to find the nominal rate
[tex]\begin{gathered} i=0.05702336 \\ m=0.4444444444 \\ j=0.05702336\times0.4444444444 \\ j=0.02534371556\approx0.0253 \end{gathered}[/tex]The nominal rate in percentage is
[tex]\begin{gathered} j=0.0253\times100\text{ \%} \\ j=2.53\text{ \%} \end{gathered}[/tex]Hence, the nominal rate of the investment if interest is compounded semi-annually is 2.53%
Mr. Fawcett is building a ramp for loading motorcycles onto atrailer. The trailer is 2.8 feet off the ground. To avoid makingit too difficult to push a motorcycle off the ramp, Mr. Fawcettdecides to make the angle between the ramp and the ground15°. To the nearest hundredth of a foot, find the length ofathe ramp.
Answers
Solution
- The illustration described can be sketched as follows:
- From the above diagram, we can observe that the ramp forms a right-angled triangle with the ground.
- The Opposite of the triangle is 2.8 feet, the angle made by the ramp with the ground is 5 degrees., whilethe length of the ramp is labeled as x.
- Thus, we can apply SOHCAHTOA to find the value of x as follows:
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \\ \theta=15\degree,Opposite=2.8,Hypotenuse=x \\ \text{ Thus, we have:} \\ \sin15\degree=\frac{2.8}{x} \\ \\ \therefore x=\frac{2.8}{\sin15\degree} \\ \\ x=10.8183692544...\approx10.82ft \end{gathered}[/tex]Final Answer
The length of the ramp is 10.82 feet
Solve the system of two linear inequalities graphically.ſr<62-3Step 2 of 3 : Graph the solution set of the second linear inequality.AnswerKeyboThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (-)Enter two points on the boundary line:510-35Select the region you wish to be shaded:
Answers
Answer and Explanation:
Given the system of two linear inequalities;
[tex]\begin{gathered} x<6 \\ x\ge-3 \end{gathered}[/tex]To solve the above system of inequalities graphically, we follow the below steps;
Step 1: Graph the first inequality;
Since the first inequality has a less than sign, we'll shade the region to the left of the line.
Also, the first inequality does not have an equality sign, so the line will be a dashed line.
See below the graph of the first inequality;
Step 2: Graph the second inequality on the same grid;
Since the inequality has an equality sign, the line will be a solid line.
Also, the inequality has the greater than sign, so we'll shade the region to the right of the line
See below the image of the graph;
Step 3: The solution set of the two systems of inequalities is the region where the shading overlaps.
As can be seen in the above graph, the shaded region between the dashed line and the solid line is the solution of the system of inequalities.
The graph of the solution set of the second inequality is as shown below;
On the boundary line we can select the below points;
[tex]\begin{gathered} \lparen-3,5) \\ \lparen-3,-5) \end{gathered}[/tex]Difference of Squares gives which complex factors for the expression x2 +11?A. (x + W11)(x - 111)B. (x+in/11)(x +111)C. (x + 111)2(x - in 11)D. (x - iw/11)(x-in 11)SUBMIT
Answers
we have that
[tex](x+i\sqrt[\square]{11})\cdot(x-i\sqrt[\square]{11})=x^2-(i^2)(11)=x^2+11[/tex]answer is the first option
option A
Express the given equation in standard form by solving for x. Simplify your answer
Answers
SOLUTION
Recall that a linear equation in one variable is in standard form if it is in the form:
[tex]ax+b=0[/tex]Hence the equation:
[tex]x+1=0[/tex]Is in tandrd form
Solving for x gives
'
[tex]x=-1[/tex]Solve the problem below, inputting your answer in decimal form.32 3/4 + 12 1/2
Answers
Answer:
45.25
Explanation:
To find the value of the expression given, we first convert the mixed numbers into fractions .
[tex]32\frac{3}{4}=32+\frac{3}{4}[/tex]multiplying 32 by 4/4 gives
[tex]undefined[/tex]Given Point A, what is the coordinate for A' after the following transformation has occurred?A (5,7)AC
Answers
Using the following given,
[tex]\begin{gathered} (x,y)\Rightarrow(x-5,-y+2) \\ (5,7) \end{gathered}[/tex]substitute the given coordinates to the new coordinates.
[tex](5,7)\Rightarrow(5-5,-7+2)[/tex]Simplify the coordinates.
[tex](5,7)\Rightarrow(0,-5)[/tex]Thus, the coordinates of A' is (0, -5).
For the polynomial function ƒ(x) = .5x3 + .25x2 + .125x + .0625, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.x = .5, touchx = −.5, touchx = .5, crossx = −.5, cross
Answers
Given:
The polynomial is
[tex]f(x)=.5x^3+.25x^2+.125x+0.0625[/tex]Required:
Find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.
Explanation:
The zeros of polynomial are
[tex]\begin{gathered} x\approx0.5 \\ x=\pm0.5i \end{gathered}[/tex]Now,
So, graph is crossing at -0.5
Answer:
Hence, fourth option is correct.
What percent of the data is greater than the median?A box-and-whisker plot. The number line goes from 0 to 20. The whiskers range from 2 to 19 and the box ranges from 6.5 to 18. A line divides the box at 17.a.20%c.50%b.25%d.80%
Answers
1) Consider that the 1st Quartile corresponds to 25%, the Median is equivalent to 50% of the data, the Third Quartile to 75% of the data as the sketch below:
Notice that the Median is that bar inside the box, also known as the 2nd Quartile.
2) So the percentage of the data greater than the median is:
[tex]75\%-50\%=25\%[/tex]Sonic runs down a ladder of 19 ft against a wall and the base of the ladder is 30 degrees to the ground. What is the distance from the base of the ladder to the wall?
Answers
The distance from the base of the ladder to the wall is 16.45 ft.
Given,Sonic runs down a ladder of 19 ft against a wall and the base of the ladder is 30 degrees to the ground.
we are asked to determine the distance from the base of the ladder to the wall=?
Since we have given that
Angle of elevation with the ground = 30°
Here, AC is the ladder .
Distance between the foot ladder from the wall = ?
length of the ladder = 19 ft.
So, we will use "Cosine Rule":
cos 30° = BC/AC
√3/2 = BC/19
2BC = √3×19
2BC = 32.9
BC = 32.9/2
BC = 16.45 ft
Hence the distance from the base of the ladder to the wall is 16.45 ft.
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4. Enter the total area of the figure ABCD in square centimeters 8 cm А 6 cm F C 15 cm 8 cm D O 268 O 336 168 O 37
Answers
The figure ABCD has the shape of a Rhombus with diagonals AC and BD.
To determine the area of a Rhombus you have to multiply the length of both diagonals and divide the result by 2, following the formula:
[tex]A=\frac{pq}{2}[/tex]Where
p represents the horizontal diagonal
q represents the vertical diagonal
For the quadrilateral ABCD, the lengths of the diagonals are:
AC=6cm + 15cm =21cm
BD= 8cm + 8cm=16cm
[tex]\begin{gathered} A=\frac{AC\cdot BD}{2} \\ A=\frac{21\cdot16}{2} \\ A=\frac{336}{2} \\ A=168\operatorname{cm}^2 \end{gathered}[/tex]The area of the figure is 168cm²
One of the roofers claims that the roof area of each pillar is the same as the area of a square with edges of 21.5 feet.The roofer is correct or incorrect?
Answers
SOLUTION
We have been given the height of each lateral triangular face of the roof h as 13.4 ft and the length of the square base of the pyramid as 21.5 feet
We want to know if the area of the square base is the same as the area of each triangular lateral face
Area of the square base is
[tex]21.5\times21.5=462.25\text{ ft}^2[/tex]Area of the four triangular lateral face becomes
[tex]\begin{gathered} 4(\frac{1}{2}\times b\times h) \\ =4\times\frac{1}{2}\times21.5\times13.4 \\ =2\times21.5\times13.4 \\ =576.2\text{ ft}^2 \end{gathered}[/tex]From our calculations, the area of the square base is 462.25 square-feet,
While the area of the four lateral face triangle of the roof is 576.2 square-feet
Hence the roofer is incorrect
Suppose that $4000 is placed in a savings account at an annual rate of 9%, compounded monthly. Assuming that no
withdrawals are made, how long will it take for the account to grow to $6216?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
_ years
Answers
Answer:
below
Step-by-step explanation:
The equation to use
FV = PV ( 1 + i)^n FV = 6216 PV = 4000
i = decimal interest per period = .09/12
n = how many months?
6216 = 4000 ( 1 + .09/12)^n
6216/4000 = (1 + .09/12)^n
1.554 = 1.0075 ^n
log 1.554 / log(1.0075) = n = 59 months (approx 5 years )
Correctnomial function with the stated properties. Reduce all fractions to lowest terms.Third-degree, with zeros of - 3, - 1, and 2, and passes through the point (3, 5).
Answers
We must construct a polynomial with the following characteristics:
0. degree: 3,
,1. zeros: x₁ = -3, x₂ = -1 and x₃ = 2,
,2. passes through the point (3, 5).
The general form for this polynomial is:
[tex]p(x)=a*(x-x_1)(x-x_2)(x_{}_{}-x_3).[/tex]Where a is a constant factor and x₁, x₂ and x₃ are the zeros of the polynomial.
Replacing the values of the zeros, we have:
[tex]p(x)=a*(x+3)(x+1)(x-2).[/tex]Using the condition that the polynomial passes through (3, 5), we have:
[tex]y=a*(3+3)(3+1)(3-2)=a*24=5.[/tex]Solving for a, we get a = 5/24. Replacing this value in the equation above, we get:
[tex]p(x)=\frac{5}{24}(x+3)(x+1)(x-2).[/tex]Answer[tex]p(x)=\frac{5}{24}(x+3)(x+1)(x-2)[/tex]How many solutions does the system of equations below have?4x − 8y = –17x − 14y = 4No solutionOne solutionInfinitely solutions
Answers
start clearing the x in the first equation
[tex]\begin{gathered} 4x=-1+8y \\ x=-\frac{1}{4}+2y \end{gathered}[/tex]insert this equation into the second one
[tex]\begin{gathered} 7\cdot(-\frac{1}{4}+2y)-14y=4 \\ -\frac{7}{4}+14y-14y=4 \\ -\frac{7}{4}\ne4 \end{gathered}[/tex]the system has no solution
Danny deposits $12,500 into a pension fund that invests in stocks. After a successful two years in investing on the stock market, the fund agrees to pay a simple interest rate of 12% per year. What will the balance on the account be after two years? Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer. For example if your answer is $1,234.56 enter 1235.
Answers
To obtain the final amount after 2 years of simple interest, subtitute the values in the following formula:
[tex]A=P(1+rt)[/tex]where A is the final amount of the investment, P is the principal or the starting amount, r is the rate in decimals, and t is the time in years.
From the problem, we have the following given:
[tex]\begin{gathered} P=12500 \\ r=12\%=0.12 \\ t=2 \end{gathered}[/tex]Substitute the values into the formula.
[tex]\begin{gathered} A=P(1+rt) \\ A=12500\lbrack1+(0.12)(2)\rbrack \end{gathered}[/tex]Simplify the right side of the equation.
[tex]\begin{gathered} A=12500(1+0.24) \\ =12500(1.24) \\ =15500 \end{gathered}[/tex]Therefore, after 2 years, the value of the investment will be $15500.
people leaving a football match with acid be supported in Manchester United or Newcastle
Answers
How many people were asked the questions in total?
40 + 2 + 8 + 20 = 70.
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers. If the perimeter is 110 inches, find the value of the longest of the four side lengths.
Answers
The value of the longest side of the quadrilateral is 29 inch when its perimeter is 110 inches.
Perimeter of quadrilateral
The sum of all length of sides of a quadrilateral is known as the Perimeter of quadrilateral.
For example, if ABCD is the quadrilateral, then its perimeter is calculated as,
P = AB + BC + CD + AD
Where
AB, Bc, CD, and Ad are the values of the sides of ABCD.
Given,
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
Here we need to find the longest side value when the perimeter is 110 inches.
We know that, the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
So, let us consider the length of quadrilateral are x, x + 1, x + 2 and x + 3
Through this we have identified that the longest length = x + 3
We know that the perimeter is 110 inches.
So, it can be written as,
=> x + (x + 1) + (x + 2) + (x + 3) = 110
=> x + x + 1 + x + 2 + x + 3 = 110
=> 4x + 6 = 110
=> 4x = 110 - 6
=> 4x = 104
Therefore, the vale of x is 26 inch
Hence, longest length is calculated as,
=> x + 3
=> 26 + 3
=> 29 inch
Therefore, the value of the longest side of the quadrilateral (in inches) is 29 inch.
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2. What type of quadrilateral do the following points represent? A (2,1) B (4,3) C (8,3) D (6, 1)
Answers
The quadrilateral is a parallelogram (the opposite sides are parallel and equal)