Select the correct answer from the drop-down menu.Find the polynomial,{4'" is the solution set of
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Let P(x) be the polynomial such that the given set is its solution set.
Now notice that:
[tex]\begin{gathered} x=-\frac{1}{3}\Rightarrow x+\frac{1}{3}=0\Rightarrow3x+1=0, \\ x=4\Rightarrow x-4=0. \end{gathered}[/tex]Therefore (x-4) and (3x+1) divide to P(x), then:
[tex]\begin{gathered} Exists\text{ k such that:} \\ P(x)=k(x-4)(3x+1). \end{gathered}[/tex]Simplifying the above result we get:
[tex]P(x)=k(3x^2-11x-4).[/tex]Setting k=1 we get that:
[tex]P(x)=3x^2-11x-4.[/tex]Answer: Second option.
Related Questions
Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?
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The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.
What is an earthquake?An earthquake simply means a rapid motion of the solid layer of the Earth.
In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.
Since the year is being discussed, the unit should be based on the year.
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a. Solve for c: E = mc^2
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ANSWER
[tex]\text{c = }\sqrt[]{\frac{E}{m}}[/tex]EXPLANATION
We want to solve for c in:
[tex]E=mc^2[/tex]To do that, we will make c the subject of the formula:
[tex]\begin{gathered} E=mc^2 \\ \Rightarrow\text{ }\frac{E}{m}=c^2 \\ Find\text{ the square root of both sides:} \\ \Rightarrow\text{ c = }\sqrt[]{\frac{E}{m}} \end{gathered}[/tex]We have solved for c.
Hey I need help on this math problem thank you
Answers
Answer:
From the image below we will bring out two coordinates we are going to use to calculate the rate of change of the graph
The coordinates are given below as
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(2,4) \\ (x_2,y_2)\Rightarrow(-2,0) \end{gathered}[/tex]Concept:
The rate of change will be calculated using the formula below
[tex]\begin{gathered} \text{rate of change =}\frac{change\text{ in y}}{\text{change in x}} \\ \text{rate of change}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{rate of change}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change}=\frac{_{}0-4_{}}{-2_{}-2_{}} \\ \text{rate of change}=\frac{-4}{-4} \\ \text{rate of change}=1 \end{gathered}[/tex]Hence,
The rate of change = 1
76. A company has hired 10 new employees, I men and 3 women. The company mustassign 5 of them to the morning shift, 3 of them to the swing shift, and the restof them to the graveyard shift.(a) (2 points) Find the prob that at least one man is assigned to the swing shift?
Answers
Answer:
[tex]\frac{2519}{2520}[/tex]Explanation:
Here, we want to get the probability that at least one man is assigned to the swing shift
From the question, 3 of the employees are assigned to the swing shift
Thus we have to calculate the probability of:
1 man , 2 men or 3 men
Mathematically, we have that as:
1 - p(all of the swing shift employees are women)
For the swing shift, for all them to be women, we will be selecting 3 out of 3 so the combination here is 3 C 3 which is 1
We now calculate the probability by dividing this value by the total number of possible ways
Mathematically, we have that as follows:
[tex]\frac{1}{10\text{ C 5 }\times\text{ 5 C 3 }^\times\text{ 1}}\text{ = }\frac{1}{2520}[/tex]This is the probability of placing all of the women on the swing shift
So, the probability that at least 1 man is assigned will be:
[tex]1-\text{ }\frac{1}{2520}\text{ = }\frac{2519}{2520}[/tex]Seventh grade > X.9 Reflections over the x- and y-axes: find the coordinates TF8 You have prizes to reveal The point D(-5, -3) is reflected over the y-axis. What are the coordinates of the resulting point, D'?
Answers
Answer
The coordinates of the resulting point, D' = (5, -3)
Explanation
When a given point with coordinates A (x, y) is reflected over the y-axis, the y-coordinate remains the same and the x-coordinate takes up a negative in front of it. That is, A (x, y) changes after being reflected across the y-axis in this way
A (x, y) = A' (-x, y)
So, for this question where the coordinate is D (-5, -3). it changes in the manner,
D (-5, -3) = D' (-(-5), -3) = D' (5, -3)
Hope this Helps!!!
What is the average rate of change over the interval [1,2]Type the numerical value for your answer as a whole number, decimal, or fractionMake sure answers are completely simplified
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To calculate the average rate of change over the interval [1,2] we need to identify the points in the extremes of the interval.
This points are (1,50) and (2,25).
We calculate the average rate of change as the slope:
[tex]r=\frac{y_2-y_1}{x_2-x_1}=\frac{25-50}{2-1}=-\frac{25}{1}=-25[/tex]Answer: the rate of change over [1,2] is -25.
solving rational equations 1[tex] \frac{9x}{x - 2} = 6[/tex]2[tex] \frac{7}{x + 2} + \frac{5}{x - 2} = \frac{10x - 2}{x {}^2{ - 4} } [/tex]3[tex] \frac{ x - 1}{2x - 4} = \frac{2x - 2}{3x} [/tex]step by step instructions please thank you
Answers
the given expression is.,
[tex]\frac{9x}{x-2}=6[/tex][tex]\begin{gathered} 9x=6x-12 \\ 9x-6x=-12 \\ 3x=-12 \\ x=-\frac{12}{3} \\ x=-4 \end{gathered}[/tex]also, the given expression is,
[tex]\frac{7}{x+2}+\frac{5}{x-2}=\frac{10x-2}{x^2-4}[/tex][tex]\begin{gathered} \frac{7x-14+5x+10}{x^2-4}=\frac{10x-2}{x^2-4} \\ 12x-4=10x-2 \\ 12x-10x=4-2 \\ 2x=2 \\ x=\frac{2}{2}=1 \\ x=1 \end{gathered}[/tex]Determine the sum of the infinite geometric series
1/2-1/3+2/9-…
A. -1/2
B. the sum cannot be determined
C. 1/3
D. 3/10
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We (B) cannot determine the sum of the given infinite geometric series (1/2-1/3+2/9-…).
What is infinite geometric series?A geometric series is one where each pair of consecutive terms' ratios is a fixed function of the summation index. The ratio is a rational function of the summation index in a more general sense creating what is known as a hypergeometric series.The result of an infinite geometric sequence is an infinite geometric series. There would be no conclusion to this series. The infinite geometric series has the general form a₁ + a₁r + a₁r² + a₁r³ +..., where r is the common ratio and a1 is the first term.So, the sum of 1/2-1/3+2/9-…
We can easily observe that the terms of the following given series are not in a series or in a particular sequence.Then, it is not possible to find the sum of this given series.Therefore, we (B) cannot determine the sum of the given infinite geometric series (1/2-1/3+2/9-…).
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Classify the triangle formed by the side lengths as right, acute, or obtuse. 11 13 23
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The triangle of side lengths 11, 13 and 23 is obtuse triangle.
Since none of the sides are equal.
The original price of a sweater is $48. The sale price is 80%. What is the sale price of the sweater?
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48 x 0.8
= $34.40
Final price would be $40-$34.40= $9.60
Which transformations can be used to carry ABCD onto itself? The point ofrotation is (3,2). Check all that apply.у5DС321АВ012345
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The point of rotation is (3, 2). We would subtract this origin from each vertex. Let us consider vertex D(1, 3). Subtracting, we have (1 - 3, 3 - 2) = (- 2, 1).
if we rotate it 180 degrees, we have (- - 2, - 1) = (2, - 1). If we add the vertex again, it becomes (- 2 + 3, 1 + 2) = (1, 3). If we reflect it over the line, y = 2, we have (3, 2)
The correct options are
B. Rotate 180 degrees
D) reflection over the line, y = 2
Letters a, b, c, and d are angle measures. Which should equal 105° to prove that fll g? Фа Ob n b 75° 0 d g f Mark this and return Save and Exit Next Submit
Answers
in the given figure,
the sum of exterior angle 75 and d will be 180
we have 75 + d = 180
d = 180 - 75
d = 105 degrees,
thus, the correct answer is option D
Hello I will send a picture of my equation I need help on.
Answers
Answer:
p = -5
Explanation:
Given the expression
p + 5p - 2p + 4p = -40
6p - 2p + 4p = -40
6p + 2p = -40
8p = -40
Divide both sides by 8
8p/8 = -40/8
p = -5
Hence the value of p is -5
what is the domain and range of arccosine?Thanks!
Answers
Solution:
What is the domain and range of arccosine?
The function is
[tex]f(x)=\cos^{-1}(x)[/tex]The graph of the function is shown below
From the graph above;
The domain of the function is
[tex]-1\leq x\leq1[/tex]The range of the function is
[tex]0\leq y\leq\pi[/tex]5x^2+2x-3 and x+4 how do I find the area
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You have a rectangle with the followinf expressions for its sides:
w: width = 5x² + 2x - 3
h: height = x + 4
In order to calculate the area of the rectangle, you use the following formula for the area:
A = w*h
By replacing w and h by the given algebraic expressions you have:
A = (5x² + 2x - 3)(x + 4) use distribution property
A = 5x²(x) + 5x²(4) + 2x(x) + 2x(4) - 3(x) - 3(4) simplify
A = 5x³ + 20x² + 2x² + 8x - 3x - 12 simplify similar terms
A = 5x³ + 22x² + 5x - 12
Hence, the total area of the figure is 5x³ + 22x² + 5x - 12
for each triangle identify a base and corresponding height use them to find the are
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A)
For this tringle we can turn the figure like this:
now we have two right triangles and we can calulate the base of the first triangle with the sin law
[tex]\begin{gathered} \frac{\sin (90)}{3}=\frac{sin(a)}{2.5} \\ \sin (a)=\frac{2.5\sin (90)}{3} \\ \sin (a)=0.8 \\ a=\sin ^{-1}(0.8)=53º \end{gathered}[/tex]the angle b is going to be:
[tex]\begin{gathered} 180=90+53+b \\ b=180-90-53 \\ b=37 \end{gathered}[/tex]Now the base is going to be:
[tex]\begin{gathered} \frac{\sin(90)}{3}=\frac{\sin(37)}{\text{base}} \\ \text{base}=\frac{3\sin (37)}{\sin (90)}=1.8 \end{gathered}[/tex]and the base of the secon triangle is going to be:
[tex]\text{base}2=7.2-1.8=5.4[/tex]And the area of the triangles is going to be:
[tex]A1=\frac{base\times2.5}{2}=\frac{1.8\times2.5}{2}=2.25[/tex][tex]A2=\frac{base2\times2.5}{2}=\frac{5.4\times2.5}{2}=6.75[/tex]so in total the area is going to be:
[tex]A1+A2=2.25+6.75=9[/tex]B)
the procedure is similar, first we turn the tiangle like this:
the angle a is going to be:
[tex]\begin{gathered} \frac{\text{sin(a)}}{4.8\text{ }}=\frac{\sin (90)}{6} \\ \sin (a)=\frac{4.8\sin (90)}{6}=0.8 \\ a=\sin ^{-1}(0.8) \\ a=53º \end{gathered}[/tex]the angle b is going to be:
[tex]\begin{gathered} 180=90+53+b \\ b=180-90-53 \\ b=37º \end{gathered}[/tex]now the base is going to be:
[tex]\begin{gathered} \frac{\sin (37)}{base}=\frac{sen(90)}{4.8} \\ \text{base}=\frac{4.8\sin (37)}{\sin (90)} \\ \text{base}=2.8 \end{gathered}[/tex]and the base of the other triangle will be:
[tex]\text{base}2=5-2.8=2.2[/tex]And the area of the triangles will be:
[tex]\begin{gathered} A1=\frac{base\times4.8}{2}=\frac{2.8\times4.8}{2}=6.72 \\ A2=\frac{base2\times4.8}{2}=\frac{2.2\times4.8}{2}=5.28 \end{gathered}[/tex]And the total area will be:
[tex]A1+A2=6.72+5.28=12[/tex]Write the coordinates of the vertices after a reflection over the line y=-x
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The coordinates of the vertices after a reflection over the line y=-x are (y, -x)
How to determine the coordinates?From the question, the transformation rule is given as
Reflection over the line y=-x
There are four types of transformation,
These transformations are
DilationRotationReflectionTranslationEach of these transformations have their rule, and they are represented as
Reflection: reflection across linesDilation: k(x, y)Rotation: rotation by anglesTranslation: (x + h, y + k)So, we have
Reflection over the line y=-x
When represented as a coordinate, the coordinate is
(x, y) = (y, -x)
Hence, the coordinates are (y, -x)
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A small company produces baseball and racquetball by the function B(x)=-6x^2+2,556x-106,878. The profit made from the racquetball products can be represented by the function R(x)=-x^2+293x-16,770. If x is the total number of products made, which function best describes P(x), the profit the company makes from these two products?
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profit made from the baseball products
[tex]B(x)=-6x^2+2556x-106878[/tex]Profit made from the racquetball products
[tex]R(x)=-x^2+293x-16770[/tex]Profit made from those 2 products is
[tex]\begin{gathered} P(x)=-6x^2-x^2+2556x+293x-106878-16770 \\ P(x)=-7x^2+2849x-123648 \end{gathered}[/tex]help pleasesjjsnsbsbbbsbs
Answers
Student asking the same question for third time in less than ten minutes. Can't help him or her out with additional information to complete the exercise.
Closing the session!
Classwork Area of Algebra Tiles 1 An If the side lengths of a tile can be measured exactly, then the area of the tile can be calculated by multiplying these two lengths together. The area is measured in square units. For example, the tile at right measures 1 unit by 5 units, so it has an area of 5 square units. 1 The next tile at right has one side length that is exactly one unit long. If the other side length cannot have a numerical value, what can it be called? ?
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The other side of a tile can be called as width of hte tile
Convert each angle in radians to degrees 3π/4
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we have only to change pi by 180, and solve the multiplication
[tex]\frac{3\pi}{4}\rightarrow3\cdot\frac{180}{4}=135^{\circ}[/tex]There's a roughly linear relationship between the number of times a species of cricketwill chirp in one minute and the temperature outside. For a certain type of cricket,this relationship can be expressed using the formula I = 0.3lc + 36, where Trepresents the temperature in degrees Fahrenheit and c represents the number oftimes the cricket chirps in one minute. What is the meaning of the I'-value whenc= 148?
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The function T = T(c) tells us the temperature based on the number of times c the cricket has chirped in one minute. In other words, if we plug c = 148 in the formula we get:
[tex]\begin{gathered} T(c)=0.31c+36 \\ T(148)=0.31\times(148)+36 \\ T(148)=81.88^oF \end{gathered}[/tex]That means if the cricket chirps 148 times per minute, the temperature must be 81.88 ºF.
Answer: The expected temperature in degrees Farenheit if the cricket has chirped 148 times perminute.
Match the following reasons to the statements given.Given:ABEF isEBDCProve:ACDF is
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Solution
For this case we can do the following:
2. Part of lines FE and AB
4. Transitive
1. Given
5. Definition of parallelogram
3. Opposite sides of a parallelogram are II
Liz attended class every day since she started school as a kindergarten. She said she has been in school for about 1,000 days.What numbers could be the actual number of school days if Liz rounded to the nearest ten?4 grade student
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Solution.
Given that Liz attended class every day since she started school as a kindergarten and that she said she has been in school for about 1000 days (by rounding up the actual number of days to the nearest ten)
The actual number is a number that when rounded up, we would arrive at 1000.
This number falls between the numbers 995 and 1004.
Answer: Any of the numbers below could be the actual number:
995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004
* Use the digits 0, 2, and 5 to write all of the three-digit numbers that fit each
description. You can repeat digits in a number.
multiples of 2
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The 3-digit multiples of 2 using 0, 2, and 5 are:
250502520What are multiples?A multiple in science is created by multiplying any number by an integer. In other words, if b = na for some integer n, known as the multiplier, it can be said that b is a multiple of a given two numbers, a and b. This is equivalent to stating that b/a is an integer if an is not zero. In mathematics, multiples are the results of multiplying an integer by a given number. Multiples of 5 include, for instance, 10, 15, 20, 25, 30, etc. Numerous 7s include 14, 21, 28, 35, 42, 49, etc.So, 3-digit multiples of 2 using the digits 0, 2, and 5 are:
3 digits multiples of 2:
250502520Therefore, the 3-digit multiples of 2 using 0, 2, and 5 are:
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Zach can buy a dozen pencils for $1.89, 24 pencils for $3.60, or 36 pencils for $5.49. What is the best buy?
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To know which one is the best option we have to divide the cost in the number of pencils so:
[tex]\frac{1.89}{12}=0.16[/tex]the second option is:
[tex]\frac{3.60}{24}=0.15[/tex]the thert option is:
[tex]\frac{5.49}{36}=1.16[/tex]So the best option is the second option
Write vector h= 8i – 11j in vector component form.
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Solution:
Given the vector h;
[tex]h=8i-11j[/tex]The vector in component form is;
[tex]h=<(8,-11)>[/tex]evaluate the following function for f(-2) .f(x)=3x+12
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Given :
[tex]f(x)=3x+12[/tex]WE need to find the value of f(-2)
So, substitute with x = -2
[tex]f(-2)=3\cdot-2+12=-6+12=6[/tex]So, the value of f(-2) = 6
And if you can step by step on how to do it
Answers
The radius of the cylinder is r=3 cm.
The height of the cylinder is h=7 cm.
The expression for the volume of the cylinder is,
[tex]V=\pi r^2h[/tex]Substituting the given values in the above equation,
[tex]\begin{gathered} V=\pi(3\operatorname{cm})^2(7\operatorname{cm}) \\ =\frac{22}{7}\times9cm^2\times7\operatorname{cm} \\ =198cm^3 \end{gathered}[/tex]Thus, option (C) is the correct solution.
Draw the graph of the line that is parallel to Y -3 = 1/3(x+2) and goes through the point (1, 7)
Answers
Explanation:
We are required to draw the graph of the line that is parallel to y-3=1/3(x+2) and goes through the point (1, 7).
Given the equation of the line:
[tex]y-3=\frac{1}{3}(x+2)[/tex]Compare the equation with the slope-point form of a line:
[tex]$$y-y_1=m(x-x_1)$$[/tex]• The slope of the line, m=1/3
,• In addition, the line goes through the point (1,7)
Substitute these values into the point-slope form given above:
[tex]y-7=\frac{1}{3}(x-1)[/tex]Finally, graph the line by looking for another point in addition to point (1,7):
When x=-2
[tex]\begin{gathered} y-7=\frac{1}{3}(x-1) \\ y-7=\frac{1}{3}(-2-1) \\ y-7=\frac{1}{3}(-3) \\ y-7=-1 \\ y=-1+7 \\ y=6 \\ \implies(-2,6) \end{gathered}[/tex]Join the points (1, 7) and (-2, 6) to plot the line.
Answer:
The graph showing the two points is attached below:
Note:
For comparison purposes and to show that the two lines are parallel, the other graph is added below: