1. x - 3 is not a factor
2. The remainder is 32.
1. How to determine if x - 3 is a factor of 2x³ - 4x² - 6?Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.
So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then
p(3) = 0
So, substituting x = 3 into the equation, we have
p(3) = 2x³ - 4x² - 6
= 2(3)³ - 4(2)² - 6
= 2(27) - 4(4) - 6
= 54 - 16 - 6
= 54 - 22
= 32
Since p(3) ≠ 0.
x - 3 is not a factor
2. What is the remainder?Since p(3) = 32,
The remainder is 32.
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You will have $ in ten years if you set aside $500 a year at 10%.
Compound interest: $8,765.58
( 9 times 10 to the power of -7) (5 times 10 to the power of -4)
what is the answer to 2y=3x+4
Answer:
y = (3/2)x + 2
assuming that the question is to find y in its simplest form.
Step-by-step explanation:
2y=3x+4
(1/2)*(2y)= (1/2)*(3x+4)
y = (3/2)x + 2
Use inverse trigonometric functions to solve the following equations. If there is more than one solution, enter all solutions as a comma-separated list (like "1, 3"). If an equation has no solutions, enter "DNE".Solve tan(θ)=1 for θ (where 0≤θ<2π).θ=Solve 7tan(θ)=−15 for θ (where 0≤θ<2π).θ=
Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]How can you show two figures are congruent?
O Use the Third Angles Theorem.
O Use rigid transformations.
O Confirm they have the same symmetries.
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
What in mathematics is the congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.Use the Third Angles Theorem for two figures are congruent.
When two of a triangle's angles match up with two of another triangle's angles, the third angle must likewise match up.
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
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what are the roots of the equation ?-3x = -10x^2-4
Given the following Quadratic equation:
[tex]-3x=-10x^2-4[/tex]You can use the Quadratic formula to solve it:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, you need to add "3x" to both sides of the equation:
[tex]\begin{gathered} -3x+(3x)=-10x^2-4+(3x) \\ 0=-10x^2+3x-4 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} a=-10 \\ b=3 \\ c=-4 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2^{}-4(-10)(-4)}}{2(-10)} \\ \\ x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]Answer
Complex roots:
[tex]\begin{gathered} x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]Rewrite x4y2 − 3x3y3 using a common factor. 3xy(x3y − x2y) 3xy2(x2 − x2y) x2y(xy − 3xy2) x2y2(x2 − 3xy)
Answer:
(d) x²y²(x² − 3xy)
Step-by-step explanation:
You want to identify a rewrite of x⁴y² − 3x³y³ using a common factor among ...
3xy(x³y − x²y) 3xy²(x² − x²y) x²y(xy − 3xy²) x²y²(x² − 3xy)SimplifiedHere, we write the expanded form of the answer choices to see if any is a fit for the given expression.
3xy(x³y − x²y) = 3x⁴y² -3x³y²3xy²(x² − x²y) = 3x³y² -3x³y³x²y(xy − 3xy²) = x³y² -3x³y³x²y²(x² − 3xy) = x⁴y² -3x³y³ . . . . . . . matches the given expression__
Additional comment
The relevant rule of exponents is ...
(a^b)(a^c) = a^(b+c)
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Which of the following is used to identify outliers in a set of data?
1.5(IQR)
1.5(range)
2(mean)
2(median)
A) 1.5 (IQR) is used to identify outliers in a set of data.
What is the Interquartile range (IQR)?
The interquartile range is a measure of statistical dispersion, or the spread of the data, in descriptive statistics.
The middle 50%, fourth spread, or H-spread are additional names for the IQR.
It is described as the discrepancy between the data's 75th and 25th percentiles.
The interquartile range is the best tool to use to find all of your outliers (IQR).
Knowing the IQR makes it simple to identify outliers because it represents the middle portion of your data.
Find the median (middle value) of the lower half and upper half of the data before calculating the interquartile range (IQR).
Quartile 1 (Q1) and Quartile 3 are these values (Q3).
The IQR represents the variation between Q3 and Q1.
As it is given in the description itself, the interquartile range is the best tool to use to find all of your outliers (IQR).
Therefore, (A) 1.5 (IQR) is used to identify outliers in a set of data.
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The correct question is given below:
Which of the following is used to identify outliers in a set of data?
(A) 1.5(IQR)
(B) 1.5(range)
(C) 2(mean)
(D) 2(median)
P.s hopes this helps
a line that is parallel to y = 4 and passes through (-3,1)
Answer: I'm not sure what your options are, but a line the passes through -3,1, and is parallel to y=4, would be y=1
Step-by-step explanation:
Is the following process correct? If not, which step is where the error occurs, justify your answer. Then rework the problem to find the correct answer.
We are given the following absolute value equation
[tex]|4x-1|=5x+37[/tex]Let us solve the problem then we will compare it with the given solution.
[tex]\begin{gathered} |4x-1|=5x+37 \\ 4x-1=\pm(5x+37) \end{gathered}[/tex]Now we will solve for the positive and negative sign separately
[tex]\begin{gathered} 4x-1=5x+37 \\ 4x-5x=37+1 \\ -x=38 \\ x=-38 \end{gathered}[/tex][tex]\begin{gathered} 4x-1=-5x-37 \\ 4x+5x=-37+1 \\ 9x=-36 \\ x=\frac{-36}{9} \\ x=-4 \end{gathered}[/tex]Comparing it with the given solution, there is an error on the left-hand side step 2. (the sign of 38 should be positive but in the figure, it is shown negative)
Now let us substitute the obtained x values into the original absolute value equation and check if they satisfy the equation.
For x = -4:
[tex]\begin{gathered} |4(-4)-1|=5(-4)+37 \\ |-16-1|=-20+37 \\ |-17|=17 \\ 17=17 \end{gathered}[/tex]Hence, x = -4 is a valid solution.
For x = -38:
[tex]\begin{gathered} |4(-38)-1|=5(-38)+37 \\ |-152-1|=-190+37 \\ |-153|=-153 \\ 153\ne-153 \end{gathered}[/tex]Hence, x = -38 is not a valid solution.
The above is an example of an extraneous solution.
An extraneous solution is a solution that we get during the process of solving an equation but it is not really the solution meaning that it does not satisfy the equation!
Therefore, x = -4 is the only solution to the given equation.
x-intercepts of -14 and -2; passes through (-16, -8)
The equation of the parabola in intercept form exists
y = -2/7(x + 14)(x + 2).
What is meant by the equation of the parabola in intercept form?The intercept form exists y = a(x - r)(x - s), where r and s exists the x-intercepts on the graph. The intercept form will tell us if there exists two x-intercepts, one x-intercept, or no x-intercepts.
Let x-intercepts of -14 and -2; passes through (-16, -8)
The equation of the parabola in intercept form y = a(x - r)(x - s)
substitute the values in the above equation, and we get
-8 = a(-16 + 14)(-16 + 2)
simplifying the above equation, we get
-8 = a(-2)(-14)
-8 = 28a
a = -2/7
y =-2/7(x + 14)(x + 2)
Therefore, the equation of the parabola in intercept form exists
y = -2/7(x + 14)(x + 2).
The complete question is:
Write an equation of the parabola in intercept form X-intercepts of -14 and -2; passes through (-16, -8)
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Can you help me pls this was very hard for me
Given:
The equation is,
[tex]\frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}[/tex]Explanation:
Simplify the right hand side of equation.
[tex]\begin{gathered} -8x-3-\frac{53}{ax-2}=\frac{(-8x-3)(ax-2)-53}{ax-2} \\ =\frac{-8ax^2-3ax+16x+6-53}{ax-2} \\ =\frac{-8ax^2+(-3a+16)x-47}{ax-2} \end{gathered}[/tex]From left side and right side of equationn it can be observed that,
[tex]-8ax^2=24x^2\text{ and (-3a+16)x=}25x[/tex]Simplify the equation for a.
[tex]\begin{gathered} -8a=24 \\ a=\frac{24}{-8} \\ =-3 \end{gathered}[/tex]OR,
[tex]\begin{gathered} -3a+16=25 \\ -3a=25-16 \\ a=\frac{9}{-3} \\ =-3 \end{gathered}[/tex]So value of a is -3.
Option B is correct.
someone please help me!!!
Im going to answer for the first one.So angles 1 and 2 are corresponding angles and so they are equal because line k and line p and parellel
Which expression is equivalent to sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12)?
sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12) is equivalent to sin(-pi/2)
Define Trigonometric functions
A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.
We know the formula of sin(A - B) = sinAcosB - cosAsinB
And the given expression is
sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
Which is in the form of given formula of sin(A - B)
where, A = π/12 and B = 7π/12
put A and B values in sin(A - B),
sin(π/12 - 7π/12) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
sin(-6π/12) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
sin(-π/2) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
Hence, sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12) is equivalent to sin(-π/2).
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find the area of this question.
30pts.
Answer:
A=40, formula for area of a rectangle is a=L×W
Step-by-step explanation:
A=L×W = 10×4
Tara makes two batches of purple food coloring. The table show the number of drops of red and blue coloring she uses for each batch. Do the two batches use the same number of drops of red per drop of blue.
Given data:
The number of red drops for first batch are r=100.
The number of blue drops for first batch are b=20.
The number of red drops for second batch are r'=75.
The number of blue drops for second batch are b'=15.
The expression for the red per blue drop for first batch is,
n=r/b
Substitute the given values in the above expression.
n=100/20
=5
The expression for the red drop per blue drop of the second batch is,
n'=r'/b'
Substitute the given values in the above expression.
n'=75/15
=5
Thus, yes the ratio of red to the blue drop is same for both batches.
Tom surveyed 150 students at his school to find out each student's favorite color. His results are shown in the circle graph above. Candace asked 15 of her friends from the same school to choose their favorite color, and 5 people chose yellow. According to Tom's survey, how many of Candace's friends would have been expected to choose yellow?
We have that in Tom's survey he obtained that 20% of the students like the yellow color (see graph above).
Then, in Candance's (small) survey, she asked 15 friends. According to Tom's survey, Candance should have obtained that 20% of her friends like the yellow color.
Therefore, we need to find 20% of 15 (friends) to find the expected number of friends that Candance should have had using the results of Tom's survey. Then, we have:
[tex]\frac{20}{100}\cdot15=\frac{300}{100}=3[/tex]Hence, according to Tom's survey, Candance's friends would have been expected to be 3 to choose (of her 15 friends) yellow (3 is 20% of 15).
What is the equation of the line that passes through the point (-6,-3) and has a slope of 0?
which two county libraries charge the same penalty per week
Answer:
where's the rest of the question⁉️
yesterday han drove 1 hour longer than ian at an average speed 5 miles per hour faster than ian. jan drove 2 hours longer than ian at an average speed 10 miles per hour faster than ian. han drove 70 miles more than ian. how many more miles did jan drive than ian?
Total 150 miles Jan drove than Ian.
Set the time Ian traveled as I, and set Han's speed as H.
Therefore, Jan's speed is H+5.
We get the following equation for how much Han is ahead of Ian;
H + 5I = 70.
The expression for how much Jan is ahead of Ian is; 2 (H + 5) + 10I
This simplifies to: 2H + 10 + 10I
However, this is just 2(H + 5I) + 10
Substitute, from the first equation, H + 5I as 70
Therefore, the answer is 140 + 10, which is 150.
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Plot the ordered pair and state which quadrant or on which axis the point lies
Answer:
Explanation:
Given the ordered pair (-2, 4 1/2), where x = -2 and y = 4 1/2 = 9/2 = 4.5. Plotting this point, we'll have;
Note that quadrants are numbered in an anti-clockwise manner with the top right portion of the graph as Quadrant I. Looking at the plotted point, we can see that it lies in Quadrant II.
Simplify the expression. Assume that x is nonzero. Your answer should have only positive exponents. x to the power of negative 10 multiplied by x to the power of 6
The answer after simplifying the expression, [tex]x^{-10} *x^{6}[/tex], will be [tex]1/x^{4}[/tex].
According to the question,
We have the following expression:
[tex]x^{-10} *x^{6}[/tex]
Now, we know that if two numbers are being multiplied with the same base but different powers then their powers are added.
(More to know: if the numbers are in division with the same base but different powers then their powers are subtracted.)
So, we have:
[tex]x^{-10+6}[/tex]
[tex]x^{-4}[/tex]
Now, we know that if powers are in negative then the number can be inverted to make the power positive (because it is given that the answer should have only positive exponents).
[tex]1/x^{4}[/tex]
Hence, the value after solving the expression is [tex]1/x^{4}[/tex].
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Determine if the equation is linear. If so graph the function (x+y=1)
Answer:
The equation is linear
Step-by-step explanation:
Make the equation in y=mx+b form
which is y=-x+1 and because the x is not the first power it must be linear
Graph:
Use the graph of f below. Assume the entire function is graphed below.Find ƒ(−1).ƒ(−1) = 0ƒ(−1) = −3ƒ(−1) = −1ƒ(−1) = −5
Answer:
ƒ(−1) = −3
Explanation:
From the graph, we have the point (-1, -3).
This means that:
• When x=-1
,• The value of f(x)=-3.
Therefore, the value of f(-1) is -3.
n Bill's physics class, he had to solve the equation 6 = 12kx2 for k. Each step of his work is shown below.
The unknown value from the given linear expression is 1/4
Solving linear equationsAx+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.
When an equation is given in this format, finding both intercepts is rather simple (x and y).
Given the equation below;
6 = 12k * 2
6 = 24k
Divide both sides by 24
24k = 6
k = 6/24
k = 1/4
Hence the value of k from the given expression is 1/4
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there are grass in a farm and the same amount of grass is grown each day. it takes 10 days for 17 cows to eat all grass in the farm. it takes 12 days for 15 cows to eat all grass in the farm. how many days does it take for 7 cows to eat all grass in the farm?
7 cows will eat all the grass on the farm in 28 days
17 cows eat all the grass on the farm in 10 days
15 cows eat all the grass in the farm in 12 days
We can see a relationship between the number of cows and the number of days. A reduction of 2 cows leads to an increase in 2 days for the cows to eat the grass.
As a result, when we reduce the cows by 4 the increase in the number of days will be 8.
Hence, to reduce the cows from 15 to 7 we will reduce the number of cows by 8 resulting in an increase in 16 days for the grass on the farm to be eaten up
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What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
The lengths of the major and minor axis of the ellipse, [tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex] are;
Length of major axis; 4•√6Length of minor axis; 4•√3What is an ellipse in coordinate geometry?An ellipse describes the locus of a point on a curve, such that the sum of the distance from two focal points from the points on the curve is a constant.
The given given function of the ellipse can be presented as follows;
[tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex]
The above equation can be compared to the standard equation of an ellipse as follows;
[tex] \displaystyle{ \frac{ {(x - h)}^{2} }{ {b}^{2} } +\frac{ {(y - k)}^{2} }{ {a}^{2} } = 1}[/tex]
Where;
(h, k) = The coordinates of the center of the ellipse
a = The length of the semi major axis
b = The length of the semi minor axis
By comparison, we have;
(h, k) = (3, -4)
a = √(24) = 2•√6
b = √(12) = 2•√3
The length of the major axis = 2•a
The length of the minor axis = 2•b
The length of the major axis is therefore;
2•a = 2 × 2•√6 = 4•√6
The length of the minor axis is therefore;
2•b = 2 × 2•√3 = 4•√3
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A set of stickers contains 4 hearts for every 6 stars. Which choice contains an equivalent ratio of hearts to stars?
Select the correct answer. sean used cross multiplication to correctly solve a rational equation. he found one valid solution and one extraneous solution. if 1 is the extraneous solution, which equation could he have solved? a. the equation is = because 1 makes a denominator equal zero and is a solution of the equation derived from cross multiplying. b. the equation is = because 1 is a solution of both the original equation and the equation derived from cross multiplying. c. the equation is = is because 1 makes a numerator equal zero and is a solution of the equation derived from cross multiplying. d. the equation is = because 1 makes a denominator equal zero and is not a solution of the equation derived from cross multiplying.
The equation is = because 1 makes a denominator equal zero and is a solution of the equation derived from cross multiplying. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.
What is extraneous equation?An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.
We have to open the equation by using cross multiplication
10(3x - 3) = 15(x² - 1)
= 30x - 30 = 15x² - 15
we would have to factorize
30(x-1) = 15(x-1)(x+1)
We have to divide by 15(x-1)
2 = x + 1
take the like terms
2 -1 = x
x = 1
Hence the equation that has the extraneous solution is option a because the solution is 1.
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The triangle shown is dilated with scale factor =2 which is the image of vertex m after the dilation
ANSWER
(-4, 2)
(Option D)
EXPLANATION
The triangle in the picture is dilated with scale factor 2.
This simply means that the size of the triangle was increased by 2.
To do this, first, let us write out the cordinates of the vertices of the original triangle:
M(-2, 1)
P(2, -2)
A(3, 5)
To dilate this, we will multiply the cordinates by 2, they become:
M' (-4, 2)
P' (4, -4)
A' (6, 10)
Therefore, the vertex M on the image after the dilation is (-4, 2).
(Option D)
