Which of the following polynomials has a remainder of 24 when divided by x+2?
A. 4x3+2x2+5
B. 3x3+6x−2
C. −2x3+4x2+3x−2
D. x3−2x2−4x+1
Option C is the correct choice [tex]-2x^4+4x^2+3x-2[/tex],
Remainder of a polynomial by substitution
For a polynomial f(x) to give a remainder of 24 when divided by x + 2:
f(-2) = 24
By testing, substitute x = -2 into the equation [tex]-2x^4+4x^2+3x-2[/tex]
[tex]f(x) = -2x^3+4x^2+3x-2\\\\f(-2)=-2(-2)^3+4(-2)^2+3(-2)-2\\\\f(-2)=-2(-8)+4(4)-6-2\\\\f(-2)=16+16-8\\\\f(-2)=32-8\\\\f(-2)=24[/tex]
Since f(-2) = 24 when x = -2 is substituted into [tex]-2x^4+4x^2+3x-2[/tex], then [tex]-2x^4+4x^2+3x-2[/tex] has a remainder of 24 when divided by x+2
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Find 0 Round to the nearest degree.
OA. 68°
OB. 69°
OC. 22°
OD. 21°
Answer:
A
Step-by-step explanation:
[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]
Which geometric series results in a sum of -69, 905?
O A.
SOB.
O C.
O D.
10
k=0
(-4)*
- }(4) *
Σ-1(5)
k=0
Σ 1 (-5)*
k=0
The geometric series which result in a sum of -69,905 is: D. [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
The standard form of a geometric series.Mathematically, the standard form of a geometric series can be represented by the following expression:
[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]
Where:
a₁ is the first term of a geometric series.r is the common ratio.Also, the sum of a geometric series is given by:
[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]
For option A, we have:
r = -5, n = 8, a₁ = 1/4 = 0.25
[tex]S=\frac{0.25(1-(-5)^8)}{1-(-5)}[/tex]
S = -24,414.
For option B, we have:
r = 5, n = 12, a₁ = -1/4 = -0.25
[tex]S=\frac{-0.25(1- 5)^{12})}{1-5}[/tex]
S = -15,258789.
For option C, we have:
r = -4, n = 11, a₁ = 1/5 = 0.2
[tex]S=\frac{0.2(1-(-4)^{11})}{1-(-4)}[/tex]
S = -279,620.
For option D, we have:
r = 4, n = 10, a₁ = -1/5 = -0.2
[tex]S=\frac{-0.2(1-4^{10})}{1-4}[/tex]
S = -69,905.
In conclusion, the geometric series which result in a sum of -69,905 is [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
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Simplify.
Rewrite the expression in the form y^n.
(y^2)^3 =
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
So there is an exponent identity that states: [tex](x^b)^a = x^{a*b}[/tex] which means this question becomes: [tex](y^2)^3 = y^{2*3} = y^6[/tex].
Just so you completely understand why this works, it might help to express y^2, as what it truly represents: [tex]y^2=y*y[/tex]. So using this definition we can substitute it into the equation so it becomes: [tex](y*y)^3[/tex]. Now let's use the definition of exponents like we just did with the y, to redefine this in terms of multiplication: [tex](y*y)^3 = (y * y) * (y * y) * (y * y)[/tex]. We can just multiply all these out, and we get: [tex]y * y * y * y * y * y =y^6[/tex].
To make it a bit more general when we have the exponent: [tex]x^b[/tex] it can be expressed as: [tex](x*x*x...\text{ b amount of times})[/tex] now when we raise it to the power of a. we get: [tex](x * x * x...\text{ b amount of times})^a[/tex] which can further be rewritten using the definition of an exponent to become the equation: [tex](x*x*x\text... \text{ b amount of times}) * (x * x * x...\text{ b amount of times})...\text{ a amount of times}[/tex] which just simplifies to: [tex]x*x*x*x...\text{ a times b amount of times}[/tex]. Hopefully this makes the identity a bit more understandable
WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
last choice
Step-by-step explanation:
The domain is the set of x values: from -3 to 3.
The range is the set of y values: from 1 to 10.
Answer: last choice
I cant figure this out
The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the width, hence:
length = x + 2
The area of a rectangle is the product of its length and its width.
Area = length * width
Area = x(x + 2)
120 = x² + 2x
x² + 2x - 120 = 0
x = 10, length = 10 + 2 = 12
The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.
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Find the sum.
10+12+14+...+78
Answer:
1540
Step-by-step explanation:
This is an arithmetic progression.
a = first term = 10
Common difference = d = second term - first term
= 12 - 10
d = 2
Last term = l = 78
First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d
78 = 10 + (n -1) * 2
78 -10 = (n -1)*2
68 = (n -1) *2
68 ÷2 = n -1
34 = n - 1
34 + 1 = n
n = 35
There are 35 terms.
[tex]\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}}[/tex][tex]\sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}[/tex]
[tex]\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540[/tex]
Step-by-step explanation:
This is an arithmetic progression.
a = first term = 10
Common difference = d = second term - first term
= 12 - 10
d = 2
Last term = l = 78
First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d
78 = 10 + (n -1) * 2
78 -10 = (n -1)*2
68 = (n -1) *2
68 ÷2 = n -1
34 = n - 1
34 + 1 = n
n = 35
There are 35 terms.
\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}} \sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}
Sum =
2
n
(a+l)
\begin{gathered}\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540\end{gathered}
=
2
35
(10+78)
=
2
35
∗88
=35∗44
=1540
Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
O h(x) = x -4
O h(x) = 3/4x
O h(x) = 1/4x
Answer:
last answer:
h(x) = 1/4 x
Step-by-step explanation:
First, change f(x) to y.
f(x) = 4x
y = 4x
Then switch the x and y.
y = 4x
x = 4y
Last, solve for y.
x = 4y
x/4 = 4y/4
x/4 = y
y = x/4
This is the same as:
y = 1/4 x
h(x) = 1/4 x
Suppose you are saving your money to pay for a vacation for your family. so far, you have saved. you plan on saving more each month so you can pay for the vacation at the end of the year. assume that you save more each month than the previous month.
part a: write a formula that would show the amount you will have saved after year.
part b: if the vacation costs a total of , will you be able to pay for it after year?
part c: explain why or why not. show your work to support your answer.
440 repeat 11 more times.
400+(400*.1)=440 repeat 11 more times. Remember to use a new value each time.
Vacations can get expensive fast. The average cost per person for a week-long vacation is about $1,200 annually. So, if you've got a family of five, you'll need to sock away at least $6,000 for transportation, hotels, meals, and amusement parks.
Financial experts suggest that the average family vacation costs between 5-10% of your total income. If your family makes $40,000 per year then experts say your yearly family vacation budget should average between $2,000-$4000.
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math related!!!!! Pls help look at pic >>>>>
Julian wants to ride his bicycle 20.6 miles this week. He has already ridden 8 miles. If he rides for 3 more days, write and solve an equation which can be used to determine xx, the average number of miles he would have to ride each day to meet his goal.
Answer:
Step-by-step explanation:
Our equation will be 3x+8=20.6
3x=12.6
x=4.2
Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease. Suppose also that the incidence of the disease is 1%. If a person tests positive for the disease, what is the chance that they have the disease
If the test gives positive results for 95% of those having disease and correctly gives negative results for 90% of those who don't have disease and the incidence of the disease is 1% then the chance of having disease is 0.0105.
Given that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease.
We have to calculate the chance of having disease.
Probability that test is correct in determining the disease when person is suffering from it is 0.95.
Probability that test is not correct in determining the disease when person is suffering from it is 1-0.95=0.05.
Probability that test is correct in determining that the person is not suffering from disease when person is not suffering from it is 0.90.
Probability that test is not correct in determining that the person is not suffering from disease when person is not suffering from it is 1-0.9=0.10.
The chance of having disease is equal to incidence of disease multiplied by probabilities that the test has corectly determined disease when personis suffering from it and when test is not able to determine the disease when person is suffering from it.
Chance=0.01*0.95+0.01*0.10
=0.0095+0.001
=0.0105.
Hence the chance of having disease is 0.0105.
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When bowling, the scoring rule for a spare is 10 points and then the points scored in the next delivery. Group of answer choices True False
The given statement is True for the scoring rule in bowling.
Scoring Rule in Bowling
The number of frames in a game of bowling is ten. According to the scoring rule in bowling, the bowler will have two opportunities to use their bowling ball to remove as many pins as they can throughout each frame.
Every bowler will complete their frame in a predefined order before the next frame starts in games with more than one bowler, which is typical.
Rule for Spare
A bowler is given a strike if they can remove all 10 pins with their first ball. A spare is achieved when the bowler uses both of the two balls in a frame to remove all 10 pins.
Depending on whether the next two balls (for a strike) or the next ball (for a goal) are scored, bonus points are given for both of these (for a spare), as per the scoring rule.
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The following statistics describe the hourly wages paid by two firms. Firm A Firm B Sample size 50 40 Sample mean $16.5 $16 Population standard deviation $0.9 $0.85 The test statistic used to evaluate whether there is any significant difference between the mean hourly wages is:
The t-test statistic is used to evaluate whether there is any significant difference between the mean hourly wages.
What is t-test?To evaluate whether there is a statistically significant difference between the means of two variables, a t-test is an inferential statistic that is utilized.
A statistical test for assessing hypotheses is the t-test.
The difference between the means from each data set, the standard deviation of each group, and the total number of data values are the three basic data values needed to do a t-test.
There are independent and dependent T-tests.
The problem statement is established mathematically by using a sample from each of the two sets in the t-test. It presupposes that the two means are equal, which is the null hypothesis.
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What are the coordinates of vertex A of square ABCD
A(-1,-6)
B(-1,-2)
C(-1,6)
D(-2,1)
The given points on the final image A''B''C''D'', and the transformation gives;
The coordinates of the vertex A of square ABCD is the option;
D. A(-2, 1)
How can the coordinate of the point A on the pre-image be found?From the figure, we have;
A''(-5, -3), B''(-3, -1), C''(-1, -3), D''(-3, -5)
The given transformation is presented as follows;
[tex] T_{ (- 4 , \: - 1)} \circ \:R_ {( O , \: 90^{ \circ} )}[/tex]
The formula for a rotation of 90° about the origin is presented as follows;
(x, y) rotation of 90°→ (-y, x)Therefore;
(-y, x) reverse rotation of 90°→ (x, y)Therefore;
A''(-5, -3) → A'(-5 + 4, -3 + 1) = A'(-1, -2)
B''(-3, -1) → B'(-3 + 4, -1 + 1) = B'(1, 0)
C''(-1, -3) → C'(-1 + 4, -3 + 1) = C'(3, -2)
D''(-3, -5) → D'(-3 + 4, -5 + 1) = D'(1, -4)
A'(-1, -2) rotation of 90° reverse → A(-2, 1)The coordinates of the vertex A of square ABCD is therefore;
D. A(-2, 1)
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Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.
Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)
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What is the solution for the compound 5/2+x>1/3 or x+2 < -29/6
Answer:
x < -41/6 or x > -13/6.
Step-by-step explanation:
5/2+x>1/3
x > 1/3 - 5/2
x > 2/6 - 15/6
x > -13/6
x+2 < -29/6
x < -29/6 - 2
x < -41/6
The answer is x < -41/6 or x > -13/6.
Answer:
x > -13/6 or x < -41/6
Step-by-step explanation:
5/2+x>1/3 or x+2 < -29/6
x > 1/3 - 5/2 or x < -29/6 - 2
x > 2/6 - 15/6 or x < -29/6 - 12/6
x > -13/6 or x < -41/6
Manju and Arif are playing a game in which one of them thinks of a number from the grid shown
below and the other has to guess it using some clues that are given. Manju thinks of a number
and gives the following clues:
It is a multiple of 3.
It is even.
It is in the third row.
What is Manju's number?
The number from the grid that fulfills all the given clues is; 12
How to find the multiple of a number?
The grid is shown in the attached image.
Now, we are told that Manju and Arif are thinking of a number on the grid and the clues are;
It is a multiple of 3.
It is even.
It is in the third row.
Now, looking at the third row, we see the numbers as;
11, 12, 13, 14, 15
Now, the only number that fulfills all the given clues is 12.
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This figure represents a design found in a glass panel. ABCD is a rectangle with
midpoints X, Y, Z, and W. Emily states that the quadrilateral formed by the segments
that join the midpoints of the sides is a rhombus. Do you agree with her? Explain why
or why not.
Answer: Yes
Step-by-step explanation:
Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.
Fyodor and his three sons, Ivan, Dmitri and Alyosha, are standing exactly on the corners of a rectangular room. Fyodor is $3$ meters from Dmitri and $5$ meters from Ivan. What is the minimum possible distance that Fyodor could be from Alyosha, in meters
The minimum possible distance that Fyodor could be from Alyosha is 4 meters.
Given Information and Deduction
It is given that Fyodor is 3 meters in distance away from Dmitri and 5 meters from Ivan.
Now, since we know that the longest side of a right angle triangle formed by the dividing the rectangular room into two parts using a diagonal is the hypotenuse. Thus, if we want to find the minimum possible distance between Fyodor and Alyosha, we will have to assume that Ivan is standing diagonally opposite to Fyodor, as shown in the figure below.
Calculating the Minimum Distance
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Here, the hypotenuse is the distance between Fyodor and Ivan.
Perpendicular and the base are the distances between Fyodor and Dmitri, and Fyodor and Alyosha respectively.
⇒ base = √(hypotenuse)² -(perpendicular)²
⇒ base = √(5)²-(3)²
⇒ base = √(25-9)
⇒ base = √16
⇒ base = 4 meters
Therefore, the minimum possible distance between Fyodor and Alyosha is 4 meters.
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A score that is three standard deviations above the mean would have a z score of
a. -3
b. 3
c. 0
d. 1
The value of z-score for a score that is three standard deviations above the mean is 3.
In this question,
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
Let x be the score
let μ be the mean and
let σ be the standard deviations
Now, x = μ + 3σ
The formula of z-score is
[tex]z_{score} = \frac{x-\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{ 3\sigma }{\sigma}[/tex]
⇒ [tex]z_{score} = 3[/tex]
Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.
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PLEASE HELP IM SUPER STUCK
Answer:
27 cm³
Step-by-step explanation:
To find the volume, multiply the length, the width, and the depth together.
3*3*3=27
The volume of the cube is 27 cm³
Hope this helps!
The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M'?
Answer:
(-4,-4)
Step-by-step explanation:
If the point is moved 2 units to the rights then we add 2 to the x value: -6+2 = -4
(-4,-4)
For what value of mc009-1 is the function one-to-one?
(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)
2
5
11
13
Using the concept of an one-to-one function, it will be one-to-one for c = 13.
What is an one-to-one function?A function is said to be one-to-one if each output is mapped to only one input.
In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.
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120 is increased by b% then increased by 25%. What is the result?
Answer:
150 + 1.5d
Step-by-step explanation:
increase 120 by d%
d% = d/100
So, increasing 120 by d % means
120 + (d/100 * 120)
= 120 + 1.2d
Then increase this by 25%
= (120 + 1.2d) + 25/100(120 + 1.2d)
= 120 + 1.2d + (120+1.2d)/4
= 120 + 1.2d + 30 + 0.3d
= 120 + 30 + 1.2d + 0.3d
= 150 + 1.5d
8. A can do a piece of work in 16 days, B in 10 days. A and B work at it together for 6 days and then C finishes it in 3 days. In how many days could C have done it alone? (a) 120 days (c) 140 days (b) 130 days (d) 150 days
Answer: 120 days
Step-by-step explanation:
A can complete it in 16 days.
=100/16 =6.25%/day.
B has ten days to do it.
10% every day is equal to 100/10.
So they would each contribute 16.25 percent per day as a group.
then for six days,
16.25*6 =97.50percent
97.50% of the work has been finished, in other words.
The amount of work left is now 100-97.5 = 2.5.
C finishes up the remaining job in 3 days
3.5% in 3 days, to be exact.
Consequently, he will finish his entire project in 120 days.
[2.5 * 40 = 100 percent; 40 * 3 = 120 days]
Find the hourly rate of pay for each of the following jobs: a) Tamara owns a salon and earns R1050 for 6 hours and 15 minutes of work.
Answer:
₹168 per hour
Step-by-step explanation:
The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.
HoursWe know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...
(15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h
Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.
Hourly rateThe pay per hour is found by dividing pay by hours.
₹1050/(6.25 h) = ₹168/h
Tamara's hourly rate of pay is ₹168 per hour.
in order to solve the following system of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them?
4x-2y=7
3x-3y=15
The following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .
What is the solution of the given system of equation ?The two equations are given as -
4x-2y=7
3x-3y=15
First substituting the value of x from the first equation and then putting that value in the second equation for the following system of equation.
From first equation,
⇒ 4x = 7 + 2y
∴ x = (7 + 2y)/4
Putting this value of x in second equation,
⇒ 3*(7 + 2y)/4 - 3y = 15
⇒ 3*(7 + 2y) - 12y = 60
⇒ 21 + 6y - 12y = 60
⇒ -6y = 39
∴ y = -6.5
∴ x = (7 + 2y)/4 = -1.5
Thus x = -1.5 and y = -6.5
Therefore, the following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .
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Multiply two and six eighths multiplied by six.
A. fourteen and five eighths
B. sixteen and two eighths
C. sixteen and four eighths
D. seventeen and three eighths
Answer:
C . Sixteen and four eighths.
Step-by-step explanation:
2 6/8 * 6
= 22/8 * 6
= 6*22 / 8
= 132/8
= 16 4/8.
A desk is on sale for $595, which is 32% less than the regular price. What is the regular price?
Answer:
875
Step-by-step explanation:
1-0.32=0.68 so its 0.68 of its original price.
x*0.68=595 x is the original price
x=595/0.68
x=875
What are the plotting points?
Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V
-3|0+2|+4=-2
-3|1 +2|+4= -5
-3|2+2|+4= -8
-3|-1+2|+4=1
+3|-2+2|+4=1
Step-by-step explanation: