Consider the equation below.x3 – 3x2 – 4 = 1/x-1+ 5The solutions to the equation are approximately x=and x=
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Question:
Solution:
Consider the following equation:
[tex]x^3-3x^2-4=\frac{1}{x-1}+5[/tex]this is equivalent to:
[tex]x^3-3x^2=\frac{1}{x-1}+5+4[/tex]that is:
[tex]x^3-3x^2=\frac{1}{x-1}+9[/tex]Multiplying both sides by (x-1), we obtain:
[tex](x-1)(x^3-3x^2)=1+9(x-1)[/tex]this is equivalent to:
[tex](x-1)x^3-3x^2(x-1)=1+9(x-1)[/tex]solving for x, we obtain that the correct solutions are:
[tex]x\text{ }\approx0.90672[/tex]and
[tex]x\approx\: 3.68875[/tex]
Related Questions
Find remaining zereos of f
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the function is:
degree: 4
and we know that some zeros are:
[tex]x=7i,3,-3[/tex]because the function is degree 4 we know that it should have 4 zeros. we also know that the function is symetric because of the real solutions, so the las solution will be the negative of the imaginari root so the remaining zeros are:
[tex]x=-7i[/tex]If the distance from South Bend to Grand Rapids has been rounded to the nearestten and is listed as 120 miles, the actual distance is between what two mile numbers?
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We need to have two numbers between 116 and 124. If we have these two numbers and average them, we can have:
[tex]\frac{116+124}{2}=120[/tex]If we rounded 116 to the nearest ten, it will be 120.
If we rounded 124 to the nearest ten, it will be also 120.
Then if we have these two numbers and average them, we finally have 120 miles.
The actual distance must be between 116 and 124.
In the X Y -plane, a line crosses the Y - axis at the point (0,3) and passes through the point ( 4,5). Which of the following is an equation of the line?A. y = x + 3 2B. y = 2x + 31 C. y = x – 4 2D. y = 2x – 4
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Given two points of a line (x1, y1) and (x2, y2), the equation of the line is:
[tex]\begin{equation*} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{equation*}[/tex]We are given the points (0, 3) and (4, 5). Plugging in these values:
[tex]y-3=\frac{5-3}{4-0}(x-0)[/tex]Operating and simplifying:
[tex]\begin{gathered} y-3=\frac{2}{4}x \\ \\ y=\frac{1}{2}x+3 \end{gathered}[/tex]Lola has 8 bear figurines. These bear figurines make up 40% of her collection of animal figurines. Find the total number
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Hence, the total number of bear figurines are 20
Two real numbers have coordinates w and t as shown on the number line below. Copy the number line into your Student Answer Booklet W + 2 3 -5 -4 3 2 1 0 1 4 5 a. What are the two real numbers represented by w and t on the number line? b. The coordinate of Point A on the number line is w + t. Plot and label Point A on the number line and explain how you decided upon its location. c. The coordinate of Point B on the number line is w — t. Plot and label Point B on the number line and explain how you decided upon its location, . d. The coordinate of Point C on the number line is wet. Plot and label Point C on the number line and explain how you decided upon its location.
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1.
The location of w and t on the number line arenot exact so you will need to approximate .
In the first point w, it is between -4 and - 3 but closer than -4 compared to -3.Additionally, the point w is located at a position greater than -3.5 .It will be okay to approximate point w at -3.6.
w= -3.6
In the second point t, it is located between 0 and 1 but closer to 0 than 1. Additionally, t is less than 0.5 because it is located at a position less than 0.5, hence it is approximately at : t = 0.4
w= -3.6 and t = 0.4 -------approximated actual values
The two real numbers for w and t will be :
w= - 4 and t = 0 ---------approximated real numbers.
NB;
w= -3.7 and t= 0.3 is also a correct approximate because the difference of +/- 0.1 can be allowed for this case.
Select all that apply. What value(s) for x make(s) the equation true?-8y - 2 = -8y - 2
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According to the given data we have the following equation:
-8y - 2 = -8y - 2
In order to calculate the value(s) for x make(s) the equation true we would have to calculate variable y as follows:
We would substitute the y with the values 0, -15, 37, 343
So, if we substitute for 0
-8(0)-2=-8(0)-2
0-2=0-2
-2=-2
value for x=0 applies.
if we substitute for -15
-8(-15)-2=-8(-15)-2
120-2=120-2
118=118
if we substitute for 37
-8(37)-2 +8(37)+2=0
-296-2 +296+2=0
if we substitute for 343
-8(343) -2 +8(343)-2=0
Graph the line 3x - 5y = 18
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Given:
3x - 5y = 18
To graph this line, rewrite the equation in slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Subtract 3x from both sides:
3x - 3x - 5y = -3x + 18
-5y = -3x + 18
Divide all terms by -5:
[tex]\begin{gathered} \frac{-5y}{-5}=\frac{-3x}{-5}+\frac{18}{-5} \\ \\ y=\frac{3}{5}x-\frac{18}{5} \end{gathered}[/tex]Thus, the slope intercept form of the equation is:
[tex]y=\frac{3}{5}x-\frac{18}{5}[/tex]Any line can be graphed using two or more points.
Let's determine two points on the line.
Input 6 for x and solve for y:
[tex]\begin{gathered} y=\frac{3}{5}\ast6-\frac{18}{5} \\ \\ y=\frac{18}{5}-\frac{18}{5} \\ \\ y=0 \end{gathered}[/tex]Also, the y-intercept is:
[tex](0,-\frac{18}{5})[/tex]convert the fraction to decimal:
[tex]-\frac{18}{5}=-3.6[/tex]Thus, we have the points:
[tex]\begin{gathered} (0,-3.6) \\ (6,\text{ 0)} \end{gathered}[/tex]x y
0 -3.6
6 0
Mark the points on a graph and make a straight line that passes through the points.
The graph is attached below:
Use to reflect over the x-axis. Identify the transformed vector.
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To reflect the given matrix over the x-axis, you have to multiply both matrices:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}[/tex]Multiply each term of the first row of the first matrix with the corresponding terms of the column of the second matrix and add the results:
Repeat the process for the second row of the first matrix
The resulting matrix is:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}=\begin{bmatrix}{(1\cdot7)+(0\cdot-12)} \\ {\square}(0\cdot7)+(-1\cdot-12)\end{bmatrix}=\begin{bmatrix}{7} \\ {12}\end{bmatrix}[/tex]The correct option is option D.
Estimate the mean of the data given in the following grouped frequency table.Value IntervalFrequency0−3124−7208−118Select the correct answer below:4.577.857.663.535.10
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The mean (or average) of observations is the sum of the values of all the observations divided by the total number of observations.
The mean for grouped data is given by:
[tex]Mean=∑(f_i.x_i)/∑f_i[/tex]• So; first we calculate each class mark xi, as:
(0 + 3)/2 = 1.5
(4 + 7)/2 = 5.5
(8 + 11)/2 = 9.5
• Now; we calculate fixi, as:
1.5 x 12 = 18
5.5 x 20 = 110
9.5 x 8 = 76
• Hence, the mean is given by:
[tex]Mean=\frac{18+110+76}{12+20+8}=5.10[/tex]ANSWER
5.10
Please help me!! This is really hard for me and I need a tutor to explain it to me
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SOLUTION
We want to find the solution of the equation
[tex]x^2=64[/tex]This becomes
[tex]\begin{gathered} x^2=64 \\ we\text{ move the square to the other side it becomes square root, we have} \\ x=\sqrt{64}\text{ the square root sign attracts }\pm,\text{ so we have } \\ x=\pm\sqrt{64} \\ x=\pm8 \end{gathered}[/tex]Hence the answer is
[tex]\pm8[/tex]Note that square root of 64 is 8
if p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<13 = ?
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Answer:
[tex]m\angle13=92^o[/tex]Explanation:
First, we match the angles
9 = 11
10 = 12
16 = 14
15 = 13
Therefore, if we find angle 15, we find an angle 13.
Angle 15 is supplementary to angle 16; therefore,
[tex]\angle16+\angle15=180^o[/tex]Since
[tex]\angle16=88^o[/tex]Therefore,
[tex]88^o+\angle15=180^o[/tex]subtracting 88 from both sides
[tex]\angle15=180^o-88^o[/tex][tex]\angle15=92^o[/tex]which is our answer!
pls help me here pls I need answers ty
Answers
2)
Answer: 87 liters
Explanation:
1 m^23 = 0.001 L
87000 cm^3 = 87000 * 0.001
= 87 liters
6. Use common denominators for these fractions. Arrange them from smallest to largest.
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Given the fractions:
[tex]\frac{9}{16},\frac{3}{8},\frac{1}{4},\frac{5}{8}[/tex]We will arrange them from the smallest to the greatest using the common denominators
So, the common denominator for the fractions will be = 16
[tex]\begin{gathered} \frac{9}{16}=\frac{9}{16} \\ \\ \frac{3}{8}=\frac{2\cdot3}{2\cdot8}=\frac{6}{16} \\ \\ \frac{1}{4}=\frac{4\cdot1}{4\cdot4}=\frac{4}{16} \\ \\ \frac{5}{8}=\frac{2\cdot5}{2\cdot8}=\frac{10}{16} \end{gathered}[/tex]So, the answer will be the arrange will be:
[tex]\begin{gathered} \frac{4}{16},\frac{6}{16},\frac{9}{16},\frac{10}{16} \\ \\ \frac{1}{4},\frac{3}{8},\frac{9}{16},\frac{5}{8} \end{gathered}[/tex]
A student was measuring water in a graduated cylinder. The student read the amount of water at 20 ml. The actual amount of water in the graduated cylinder was 17 ml, What is the approximate percent error?
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Recall that percent error is given by the formula:
[tex]|\frac{real\text{ value-measured value}}{\text{real value}}|\cdot100[/tex]Therefore in our case this becomes:
[tex]|\frac{17-20}{17}|\cdot100=|\frac{3}{17}|\cdot100\approx17.65[/tex]Therefore the rounded (to two decimals) answer is : 17.65 %
Each month Mark‘s phone company charges a flat fee of $12 plus $0.05 per minute his bill for last month was $18 how many minutes did Marty talk on the phone last Month
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Given:
Flat fee = $12
Per minute charge = $0.05
Total bill for last month = $18
To find the number of minutes, we have the equation:
18 = 12 + 0.05M
Where M represents number of minutes
Let's solve for M:
Subtract 12 from both sides:
18 - 12 = 12 - 12 + 0.05M
6 = 0.05M
Divide both sides by 0.05:
[tex]\begin{gathered} \frac{6}{0.05}=\frac{0.05M}{0.05} \\ \\ 120\text{ = M} \end{gathered}[/tex]Therefore, Marty spent 120 minutes talking on the phone last month.
ANSWER:
120 minutes
Thomas runs 34 of a mileevery day for 5 days. Howfar has he run total?
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Guven:
Miles per day = 34 miles
Number of days = 5 days
To find the total distance(miles), we have:
Total distance = distance covered per day x Number per days
= 34 x 5 = 170 miles
Therefore, the total distance he has covered is 170 miles
ANSWER:
170 miles
Which interval notation represents a function with a domain of all real numbers greater than -3 and less than 6?A.) -2
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The domain is the values of x, and if we want x to fit the inequalities they gave us, we have that
[tex]-3\leq x<6[/tex]QUESTION 16Find anequation of the circle that satisfies the given conditions.Radius 6 and center (3.-5)
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A circle can be represented by the following equation:
[tex]\mleft(x-h\mright)^2+(y-k)^2=r^2[/tex]Where the radius is r and the center is (h, k).
Using the radius 6 and the center (3, -5), we have that:
[tex]\begin{gathered} (x-3)^2+(y-(-5))^2=6^2 \\ (x-3)^2+(y+5)^2=36 \end{gathered}[/tex]So the equation of the circle that satisfies radius = 6 and center = (3, -5) is:
(x-3)^2 + (y+5)^2 = 36
I need help to find the indicated operation:g(n)= 2n-2h(n)= n^2+3nFind (g×h)(n)
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Composition of functions:
You combine two functions bycomposition by using one of the functions to substitute the independient variable in the other one.
To find (g o h)(n) you substitute the n in the function g(n) for the function h(n):
[tex](g\circ h)(n)=2(n^2+3n)-2[/tex]Simplify:
[tex](g\circ h)(n)=2n^2+6n-2[/tex]What is the domain and range of y=-1/2x+3
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For the function
[tex]y=-\frac{1}{2}x+3,[/tex]the range is all the values y can have and the domain is all the possible values that x can take.
In our function there seems to be no restriction on what values x and y can take—our function is defined for all real values of x and y — therefore, the domain and the range of our function is all real numbers.
Drag each figure to show if it is similar to the figure shown or why it is not similar.
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It is found that all the figures in the options except the fourth figure are similar to the given figure.
What are geometric shapes called?Geometric forms are figures in mathematics that depict the shape of items we observe in our daily lives. Shapes are the forms of things in geometry that have boundary lines, angles, and surfaces. There are several sorts of 2d and 3d shapes.
The given figure is a rectangle with dimensions 4 feet and 8 feet for length and breadth respectively.
We need to determine similar figure from the given options.
The first figure has a rectangle shape with different dimensions which is similar to given figure.
The second figure is also similar to given figure as it is also a rectangle with different dimensions.
By looking at the third figure, we can see that it has same rectangle shape and dimensions as the given figure which is 4 feet and 8 feet for length and breadth respectively.
The fourth figure is not a rectangle so it is not similar to the given figure.
Also, the last figure is a rectangle with different dimensions so it is similar to given figure.
Thus, we conclude that all the figures in the options except the fourth figure are similar to the given figure.
Learn more about shapes here:
https://brainly.com/question/25965491
#SPJ1
Find the area of the shaded region.3112Note: Use either the pi button on your calculator or 3.14 for pi. Round to the nearest tenth.
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The area of a sector of a circle can be calculated by using the formula:
[tex]A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ where }\theta\text{ is the angle in degrees and r is the radius}[/tex]The total area of a circle can be calculated as:
[tex]A_{total}=\pi\cdot r^2\text{ where r is the radius}[/tex]To find the area of the shaded region, you need to calculate the total area of the circle and then subtract the area of the non-shaded region, as follows:
[tex]\begin{gathered} A_{total}=\pi\cdot r^2\text{ The given value for r is 3} \\ A_{total}=\pi\cdot3^2\text{ } \\ A_{total}=\pi\cdot9 \\ A_{total}=3.14\cdot9 \\ A_{total}=28.3 \end{gathered}[/tex]Now let's calculate the area of the non-shaded region:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ the given values for }\theta=112\text{ and r=3} \\ A=\frac{112}{360}\cdot\pi\cdot3^2\text{ } \\ A=0.31\cdot3.14\cdot9 \\ A=8.8 \end{gathered}[/tex]The area of the shaded region will be:
[tex]\begin{gathered} A_{SR}=A_{total}-A \\ A_{SR}=28.3_{}-8.8 \\ A_{SR}=19.5 \end{gathered}[/tex]Which is more 1163 millimeters or 1meters?
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Given : 1163 millimeter and 1 meters
We need to compare between them
First make both numbers at the same units :
1163 millimeter
1 meters = 1000 millimeters
So, 1163 millimeters > 1000 millimeters
So, 1163 millimeters is more than 1 meters
Solve for Time Principle $2,000Interest $480Rate 8%
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ANSWER:
t = 3
STEP-BY-STEP EXPLANATION:
Given:
Principle (P) = 2000
Interest (I) = 480
Rate (r) = 8% = 0.08
The simple interest formula is the following:
[tex]I=P\cdot r\cdot t[/tex]We substitute each value and solve for t, like this:
[tex]\begin{gathered} 480=2000\cdot 0.08\cdot \:t \\ \\ t=\frac{480}{2000\cdot0.08}=\frac{480}{160} \\ \\ t=3 \end{gathered}[/tex]Therefore, the time would be 3 periods (it depends on the interest rate if it is annual, monthly, etc.)
How many tablespoons of blue paint should Elena mix with 6 cups of white paint and blue paint? How many batches would this make?
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According to the given graph, 2 cups of white paint are in the same ratio as 6 tablespoons of blue paint.
So, if she has 6 cups of white paint, we just have to multiply the number of tablespoons by 3.
[tex]6\times3=18[/tex]So, Elena needs 18 tablespoons of blue paint.Additionally, this would make three batches because the given ratio is being multiplied by 3.Mars is about 142 million miles from the sun. The earth is about 93,000,000 miles from the sun. How much farther from the sun is Mars than the earth? Express the answer in scientific notation State the letter of the correct answer. A.) 235x10 B.) 2.35x107 C) 4.9x10 D.) 49x107
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D)
1) Let's visualize it to better understand this
2) Let's pick the distance between Mars and the Sun, and subtract it by the distance (Earth-Sun):
[tex]142,000,000-93,000,000=49,000,000=49\cdot10^6\text{ or 4.9 }\cdot10^7[/tex]3) So Mars is 4.9 x 10^7 miles farther from the sun than the Earth.
Students were asked to prove the identity (cot x)(cos x) = csc x − sin x. Two students' work is given.Part A: Did either student verify the identity properly? Explain why or why not.Part B: Name two identities that were used in Student A's verification and the steps they appear in.
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Part A
Looking at the work done by each student, both students verified the identity properly because the trigonometric identities were properly applied where necessary, the steps were clear, mathematical operations were applied correctly and at the end, both sides of the equation were the same.
Part B
Looking at student's A verification,
In step 3, the pythagorean identity was used
In step 5, the reciprocal identity was used
solve for y in the equation below
2 4y = 9
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Answer:9/24
Step-by-step explanation
A piece of wire 32 cm long is cut into two pieces, each to be bent to make a square. The length of a side of one square is to be 4 cm longer than the length of a side of the other How should the wire be cut?The length of the shorter piece of wire is :
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Let P1 represent the perimeter of the larger square and let P2 represent the perimeter of the smaller square. Since the piece of wire is 32 cm long and both squares are made of this wire, we have the following:
[tex]P_1+P_2=32[/tex]Now let x be the length of the side of the smaller square. Since the larger square has sides 4cm longer than the length of the side of the other square, we have the following:
[tex]\begin{gathered} P_1=4(x+4) \\ P_2=4x \end{gathered}[/tex]using these expressions on the first equation and solving for x, we get:
[tex]\begin{gathered} 4(x+4)+4x=32 \\ \Rightarrow4x+16+4x=32 \\ \Rightarrow8x=32-16=16 \\ \Rightarrow x=\frac{16}{8}=2 \\ x=2 \end{gathered}[/tex]we have that x = 2. Then, the length of the shorter piece of wire will be the perimeter of the smaller square, therefore, the length of the shorter piece of wire is P2 = 4(2) = 8 cm
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. f((x) = (x + 1)(x + 4)(x + 5)^5
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Answer:
The graph falls to the left and rises to the right.
Explanation:
Given f(x) defined below:
[tex]f\mleft(x)=(x+1)(x+4)(x+5)^5\mright?[/tex]We are to determine the end behavior of the polynomial using the Leading Coefficient Test.
When using the Leading coefficient test, the following rule applies:
• When the ,degree is odd, and the ,leading coefficient is positive,, the graph falls to the left and rises to the right.
,• When the ,degree is odd, and the ,leading coefficient is negative,, the graph rises to the left and falls to the right.
,• When the ,degree is even, and the ,leading coefficient is positive,, the graph rises to the left and right.
,• When the ,degree is even, and the ,leading coefficient is negative,, the graph falls to the left and right.
Back to our function, f(x):
[tex]\begin{gathered} f(x)=(x+1)(x+4)(x+5)^5 \\ \text{Degree}=7\text{ (Odd)} \\ \text{Leading Coefficient = 1 (Positive)} \end{gathered}[/tex]From the first rule above, we can conclude that the graph falls to the left and rises to the right.
A graph of f(x) is attached which confirms this end behavior.