Answers
Given the polynomial function:
[tex]x^3-2x^2-x+2[/tex]Group the functions:
[tex](x^3-2x^2)-(x-2)[/tex]Factor out the greatest common factor from the parenthesis
[tex]\begin{gathered} x^2(x-2)-1(x-2) \\ (x^2-1)(x-2) \end{gathered}[/tex]Simplify fully to have:
[tex]\begin{gathered} (x^2-1)(x-2) \\ \lbrack(x^2-1^2)\rbrack(x-2) \\ (x+1)(x-1)(x-2) \end{gathered}[/tex]This gives the factored form of the given polynomial.
Related Questions
I need help converting to logarithmic equation e^-t = 125
Answers
Apply ln to both sides:
Ln e^-t = ln 125
Ln e (125) = -t
in a survey of 800 college students 800, it is found that:274 are majoring in english,156 are majoring in mathematics and422 are majoring in at least one of english and mathematics.A. How many of the 800 are majoring in both english and mathematics?B. how many are majoring in mathematics only?
Answers
A. There are 17 students that are majoring in both english and mathematics
B. There are 139 students that are majoring in mathematics only
Explanation:Given that 274 are majoring in english, n(E) = 274
156 are majoring in mathematics, n(M) = 156
422 are majoring in at least one of english and mathematics, n(E U M) = 422
We have:
A. The number of students that are majoring in both english and mathematics is obtained as follows:
[tex]\begin{gathered} n(E\cap M)=n(E)+n(M)-n(E\cup M) \\ \\ =274+165-422 \\ \\ =17 \end{gathered}[/tex]B. The number of students that are majoring in mathematics only is obtained as follows:
[tex]\begin{gathered} n(M\text{ only\rparen=}n(M)-n(M\cap E) \\ \\ =156-17 \\ =139 \end{gathered}[/tex]A. Identify the two points located on the graph and explain what they represent in the context of this situation. B. Approximately how much money will sheryl earn if she works 9 hours?
Answers
Graphs
The amount of money Sheryl makes is modeled in the graph shown.
A.
There are two points located on the graph.
The first point is at (0, 0) and represents the condition where Sheryl has not worked (0 hours) and has not earned a dollar ($0). This means she only gets paid per hour worked.
The other point at (1, 13) (approximately) represents the fact that Sheryl earned $13 for an hour worked.
B.
The graph does not show Shery's earnings for 9 hours, but we can use the result in part A to find that out.
If she makes $13 in an hour worked, then she should earn $13 * 9 = $117 for 9 hours of work.
taxes :2.69 * 10 ^ 5 square miles Rhode Island:1.21 * 10 ^ 3 square miles Determine the differences in square miles between the area Texas and the area Rhode Island. write your answer in scientific notation
Answers
Explanation:
The difference is:
[tex]2.69\cdot10^5-1.21\cdot10^3[/tex]To solve this we need the exponent of 10 be the same for both terms of the substraction. It is better is we change the exponent of the area of Texas, by moving the decimal point two places to the right:
[tex]2.69\cdot10^5-1.21\cdot10^3=269\cdot10^3-1.21\cdot10^3[/tex]Now we can substract the numbers and leave the 10³ out:
[tex]269\cdot10^3-1.21\cdot10^3=(269-1.21)\cdot10^3=267.79\cdot10^3[/tex]Scientific notation has always only one place with a number before the decimal point. Therefore 267.79x10³ is not in scientific notation, we have to move the decimal point two places to the left and add 2 to the exponent of 10:
Answer:
The difference is 2.6779 x 10⁵ square miles
The population of one country changed from 23 million to 54 million. Use the information to find the unknown values in the bar diagrams a = L.347 b
Answers
The population of one country changed from 23 million to 54 million. Use the information to find the unknown values in the bar diagrams a = L.347 b
y
Claire took part in a cross country race
and completed the course in 1 hour and 12
minutes. Her average speed for the race
was a sound 17.5 km per hour. What was
the distance that she ran
Answers
Claire who took part in a cross-country race ran 21 km in 1 hour and 12 minutes.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Claire took part in a cross-country race and completed the course in 1 hour and 12 minutes which is (1 + 12/60) = (1 + 1/5) = 6/5 = 1.2 hours.
Her average speed for the race was 17.5 km per hour.
∴ The total distance she ran is,
= (17.5×1.2) km.
= 21 km.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ1
Find X and RDB:
X =
RDB =
Answers
[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]
8. Select the equation that has no real solution.12x + 15 = 12x - 157x +21= 21-5x-25 = 5x + 2512x+ 15 = 3(4x+5)
Answers
We will have that the equation with no real solution is:
[tex]12x+15=12x-15[/tex]Because:
[tex]12x-12x=-15-15\Rightarrow0\ne-30[/tex]Use the GCF and the Distributive property to find the sum.
Answers
Notice that both numbers 26 and 29 are divisible by 13:
[tex]\begin{gathered} \frac{26}{13}=2 \\ \frac{39}{13}=3 \end{gathered}[/tex]thus, we can write the sum 26 + 39 like this:
[tex]26+39=13(2+3)[/tex]What is the surface area of a right square pyramid with height of 3 centimeters and a base that measures 8 centimeters by 8 centimeters?
Answers
Okay, here we have this:
Considering the provided measures, we are going to calculate the requested surface area, so we obtain the following:
So to calculate the surface area we will use the following formula:
A = a(a + √(a^2 + 4h^2))
A = 8 cm(8cm + √((8 cm)^2 + 4(3 cm)^2))
A = 8 cm(8cm + √(64 cm^2 + 4*9 cm^2))
A = 8 cm(8cm + √(64 cm^2 + 36 cm^2))
A = 8 cm(8cm + √(100 cm^2))
A = 8 cm(8cm + 10 cm)
A = 8 cm(18 cm)
total surface areaA = 144 m^2
Finally we obtain that the total surface area is equal to 144 m^2
when Thanos snapped his fingers in Avengers endgame he put a circular hole in this Square what is the area of the Shaded region last left?
Answers
Calculate the area of the square (A1), and then subtract the area of the circle (A2).
Square area = side length ^2
A1 = 12^2 = 144 ft2
Area of a circle = π r^2
where:
r= radius = diameter /2 = 12/2 = 6
Replacing:
A2 = π 6^2 = 113.09 ft^2
Area of the shaded region = A1- A2 = 144-113.09 = 30.92 ft2
find the area of the white region ...blue region has a 150 degree triangle with 7cm side and the circle has a radius of 7
Answers
First, let's find the area circular sector:
[tex]A=\frac{r^2\theta}{2}[/tex]Where:
r = radius = 7cm
θ = angle (in radians) = 5/6 π
so:
[tex]\begin{gathered} A=\frac{7^2(\frac{5}{6}\pi)}{2} \\ A=\frac{245}{12}\pi \end{gathered}[/tex]Now, let's find the area of the triangle, that triangle is an isosceles triangle, so, we can use the following formula in order to find its area:
[tex]\begin{gathered} At=\frac{1}{2}s^2\cdot\sin (\theta) \\ \end{gathered}[/tex]where:
s = one of the equal sides = 7
θ = angle = 150
so:
[tex]\begin{gathered} At=\frac{1}{2}(7^2)\sin (150) \\ At=\frac{49}{4} \end{gathered}[/tex]Therefore, the area of the white region will be, the area of the circular sector minus the area of the isosceles triangle, so:
[tex]Area_{\text{ }}of_{\text{ }}the_{\text{ }}white_{\text{ }}region=\frac{245}{12}\pi-\frac{49}{4}=51.9cm^2[/tex]Which equation can be used to find the area of the figure below? 10 16 FA = (598)+(168) GO A=()+(108) HOA = (1+ (6 - 8) 3 A = (6 - 8)+(108) Bducano
Answers
The given figure is the combination of a triangle and rectangle.
In the given
Determine the slope of the line between (-6,13) and (1,11)
Answers
We can find the slope using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Let:
[tex]\begin{gathered} (x1,y1)=(-6,13) \\ (x2,y2)=(1,11) \\ \end{gathered}[/tex]Therefore:
[tex]m=\frac{11-13}{1-(-6)}=\frac{-2}{7}=-\frac{2}{7}[/tex]Answer:
[tex]-\frac{2}{7}[/tex]At a sale this week, a suit is being sold for $174.80. This is a 62% discount from the original price.What is the original price?
Answers
Let x be the original price then we can set up the following equation:
[tex]\begin{gathered} x(1-0.62)=174.80 \\ \text{solving for x we get} \\ x=\frac{174.80}{(1-0.62)}=\frac{174.80}{0.38}=460 \end{gathered}[/tex]Answer: $460.
Ivanna is on her way home in her car. Her drive is 12 miles long. She has finished one-fourth of the drive so far. How far has she driven?miles
Answers
Fractions
Ivanna has to drive 12 miles. She has already driven 1/4 so far.
The distance she has driven is:
[tex]\frac{1}{4}\cdot12=\frac{12}{4}=3[/tex]Ivanna has driven 3 miles so far
Miguel drove for 8 hours at a constant rate. He drove a total of 424 miles.Donna also drove at a constant rate. This table shows the number of miles she had driven in different numbers of hours.How do the unit rates compare?Select from the drop-down menus to correctly complete the statement.Miguel has a Choose... greater or less unit rate of change than Donna because Choose... 48 mph or 53 mph or 424 mph or 432 mph is greater than Choose... 48 mph or 53 mph or 424 mph or 432 mph
Answers
As Miguel drove a total of 424 miles in 8 hours, at a constant rate, then the unit rate of change can be calculated as:
[tex]M=\frac{424miles}{8hours}=53\text{ miles/hour}[/tex]Now, Donna also drove at a constant rate, and we have a table of values, by dividing the miles driven in the corresponding time, the unit rate of change is:
[tex]D=\frac{144miles}{3hours}=\frac{288miles}{6hours}=\frac{432miles}{9hours}=48\text{ miles/hour}[/tex]As can be seen, Miguel has a greater unit rate of change than Donna because 53 mph is greater than 48 mph.
a rectangle with a base of 6 and height of 4 has been scaled with a scale factor of 3. what is the area of the scaled copy?
Answers
We have a rectangle of base 6 and height 4. We have a rectangle like this:
Now, we have a scale factor of 3. We need to multiply each side by 3:
Now the rectangle has a height of 12 and a base of 18.
The area of a rectangle is h*b. Then, the area of the scaled copy is:
[tex]A=12\cdot18\Rightarrow A=216[/tex]Therefore, the scaled copy has an area of 216 square units.
At an important meet, Hassan won the men's 400 meters in 47.36 seconds. Hassan ran an average rate of__ meters per minnearest hundredth
Answers
506.78 meters per min
Explanation:distance = 400 m
time = 47.36 seconds
The result is meant to be in meters/min
We need to convert the seconds to minute:
60 seconds = 1 min
47.36 seconds = 47.36/60 = 0.7893
The average rate will be distance divided by time
[tex]\begin{gathered} \text{Average rate =}\frac{400}{0.7893} \\ \text{Average rate =}\frac{400}{0.7893}\text{ = }506.7782 \\ \\ \text{Average rate = }506.78\text{ meters per min (nearest hundredth)} \end{gathered}[/tex]Can you pls help me with this question thank you
Answers
I) We have to convert the temperature from Celsius to Farenheit, using the formula:
[tex]F=\frac{9}{5}\cdot C+32[/tex]The temperature in the Poconos is 15 °C, so we have C = 15. We can then calculate the temperature as:
[tex]\begin{gathered} F=\frac{9}{5}\cdot15+32 \\ F=27+32 \\ F=59 \end{gathered}[/tex]The temperature in Canada is 5 °C, so we can calculate the temperature in Farenheit as:
[tex]\begin{gathered} F=\frac{9}{5}\cdot5+32 \\ F=9+32 \\ F=41 \end{gathered}[/tex]II) We have to find the expression for the cost for each hotel in function of "n", the number of nights.
Holiday inn costs $80 per night plus $10 for parking.
We can express the total cost in function of n as:
[tex]undefined[/tex]if B D equals b c b d equals 5x - 26 BC equals 2x + 1 and a C equals 43 find a b
Answers
Given the information
BD=BC
where
BD= 5x-26
BC=2x+1
then
[tex]5x-26=2x+1[/tex][tex]5x-2x=1+26[/tex][tex]3x=27[/tex][tex]x=\frac{27}{3}=9[/tex]Since
AB= AC-BC
where
BC=2x+1
BC= 2(9)+1 = 19
AC=43
[tex]AB=43-19=24[/tex]witch is an equation in point slope form the given point and slope point (1, 9) point 5
Answers
The formula for equation of line pasing through point (x_1,y_1) with slope m is,
[tex]y-y_1=m(x-x_1)[/tex]Substitute point and slope in the equation to obtain the equation of line.
[tex]\begin{gathered} y-9=5(x-1) \\ y-9=5x-5 \\ y=5x+4 \end{gathered}[/tex]So equation of line is y=5x+4.
which one is X value the proceeds from a carwash are directly proportional to the number of cars washed. The total after 9 cars with $180. How much can be raised if 60 cars were washed
Answers
Answer:
$1200 would be raised if 60 cars were washed.
Step-by-step explanation:
This question can be solved using a rule of three.
The total after 9 cars was of $180. How much would be raised with 60 cars washed?
9 cars - $180
60 cars - $x
Applying cross multiplication
9x = 180*60
9x = 10800
x = 10800/9
x = 1200
$1200 would be raised if 60 cars were washed.
Step 1 of 2: Reduce the rational expression to its lowest terms 3x - 9/3 - xStep 2 of 2: Find the restricted values of X, if any, for the given rational expression.
Answers
Step 2.
There are not restricted values because because it's possible to simplify the expression and there is not a denominator.
richard can break up a fight in 12 minutes, harold can break up a fight in 5 minutes how long will it take them to solve it together pls help
Answers
SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Time for Richard to break up a fight =12 minutes } \\ \text{Time for harold to break up a fight =5 minutes } \end{gathered}[/tex]Let the time at which both of them work be
[tex]R[/tex]Then
The individual rate will be
[tex]\begin{gathered} \text{Richard}=\frac{1}{12} \\ \text{And } \\ \text{Harold}=\frac{1}{5} \end{gathered}[/tex]Then
[tex]\frac{1}{12}+\frac{1}{5}=\frac{1}{R}[/tex]Simplifying fraction, we have
[tex]\begin{gathered} \frac{5+12}{60}=\frac{1}{R} \\ \text{Then} \\ \frac{17}{60}=\frac{1}{R} \end{gathered}[/tex]Hence
[tex]\begin{gathered} R=\frac{60}{17} \\ R=3.53 \end{gathered}[/tex]Therefore
It will take both of them 3.53 minutes to solve it together
The expression to represent the decrease in temperature then the explanation and it’s meaning
Answers
The expression would be:
[tex]\frac{10}{1000}\cdot x[/tex]Where x are the meters climbed.
For 2,000 m we'll have:
[tex]\frac{10}{1000}\cdot2000\rightarrow20[/tex]A 20°C decrease in temperature.
Find the exact value of s in the given interval that has the given circular function value.
Answers
Recall that:
[tex]\tan x=\frac{\sin x}{\cos x}\text{.}[/tex]Therefore:
[tex]\tan s=1\Leftrightarrow\frac{\sin s}{\cos s}=1.[/tex]Then:
[tex]\sin s=\cos s\text{.}[/tex]Now, notice that:
[tex]\sin s-\cos s=-\sqrt{2}\cos (s+\frac{\pi}{4}).[/tex]Then:
[tex]-\sqrt[]{2}\cos (s+\frac{\pi}{4})=0.[/tex]Therefore:
[tex]\cos (s+\frac{\pi}{4})=0.[/tex]Then:
[tex]\begin{gathered} s+\frac{\pi}{4}=\frac{\pi}{2}+n\pi, \\ s+\frac{\pi}{4}=\frac{3\pi}{2}+n\pi\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} s=\frac{\pi}{4}+n\pi, \\ s=\frac{5\pi}{4}+n\pi\text{.} \end{gathered}[/tex]Since:
[tex]s\in\lbrack\pi,\frac{3\pi}{2}\rbrack^{},[/tex]we get that:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]Answer:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]The back of Toms property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 120 feet of fencing available, what is the maximum possible area of the pasture?
Answers
Suppose that the sides of the rectangle have lengths x and y, and that the measure of the side parallel to the creek is y, as shown in the drawing below
The total length of the fence, according to the drawing, is:
[tex]2x+y[/tex]Since there is 120 feet of fencing available, then:
[tex]\begin{gathered} 2x+y=120 \\ \Rightarrow y=120-2x \end{gathered}[/tex]On the other hand, the area A of the pasture, is equal to the base 120-2x times the height x:
[tex]\begin{gathered} A=x(120-2x) \\ =2x(60-x) \end{gathered}[/tex]Find the maximum value of the 2nd degree polynomial for A. Since A has roots at x=0 and x=60, the maximum value is found at x=(60+0)/2=30.
Then, the maximum possible area of the pasture can be found by plugging in x
Convert the following units as indicated.2,250 watts to horsepower (Round answer to the nearest thousandth.)
Answers
The question given is to convert
[tex]2250\text{ watts to horse power}[/tex]From a conversion calculator,
[tex]1\text{ horse power = }745.699872\text{Watt}[/tex]Therefore,
[tex]1\text{ watts = }\frac{1}{745.699872}\text{horse power}[/tex]Therefore,
2250 watts will be
[tex]\begin{gathered} =2250\times\frac{1}{745.699872} \\ =\frac{2250}{745.699872}\text{horse power} \\ =3.0172997\text{ horse power} \\ \approx to\text{ the nearest thousandth} \\ =3.017\text{ horsepower} \end{gathered}[/tex]Hence,
The final answer = 3.017 horse power
How would you do this type of problem and what would the increasing and decreasing interval be
Answers
y-intercept is the point in the y-axis that the graph intersects.
From the figure, the graph intersects at point (0, 3)
The y- intercept is (0, 3)
x-intercept is the point in the x-axis that the graph intersects.
Since the graph does not intersects the x-axis, the x-intercept does not exist
Vertex is a point on the graph that is a maximum or a minimum.
The vertex of the graph which is the lowest point as shown in the figure is at point (1, 2)
And this is a minima, since it is the lowest point.
Domain is the set of x-values that exist in the graph, the graph is going infinitely to the left and to the right, therefore the domain is (-∞, ∞)
Range is the set of y-values that exist in the graph, the y values starts from the vertex which is the lowest point at (1, 2) going upward.
So the range is all real numbers greater than or equal to 2. [2, ∞)
End behavior is the behavior of the function at large positive and negative values of x.
when x goes positive infinity, f(x) goes to positive infinity
As x ⇒ ∞, f(x) ⇒ ∞
when x goes negative infinity, f(x) goes to negative infinity
As x ⇒ -∞, f(x) ⇒ -∞
Decreasing interval occurs when the graph is going down, and increasing interval occurs when the graph is going up.
Decreasing interval will be (-∞, 1]
Increasing interval will be [1, ∞)