(x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].
What is a remainder theorem?Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a) that isn't essentially an element of the polynomial, you will find a smaller polynomial along with a remainder.
The Remainder Theorem: If (x-a) is a factor of the f(x) then f(a) = 0
Here,
f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex]
substitute a = 2
[tex]f(2)=3(2^{4}) -3(2) ^{3}-9(2)^{2}+5(2)-2[/tex]
= 48-24-36+10-2
= 32-36
f(2) = -4
f(2) [tex]\neq 0[/tex]
Hence, (x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].
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Find the sum of 8x^{2}-x+98x
2
−x+9 and 8x^{2}-5x+58x
2
−5x+5.
Answer: 16x^2+144x+18
Step-by-step explanation:
The sum of two given expressions is 16x²-6x+14.
What is addition of algebraic expression?Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.
The given expressions are 8x²-x+9 and 8x²-5x+5.
Now, sum =8x²-x+9+8x²-5x+5
Group like terms and simplify, we get
(8x²+8x²)+(-x-5x)+(9+5)
= 16x²+(-6x)+14
= 16x²-6x+14
Therefore, the sum of two given expressions is 16x²-6x+14.
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Triangle rst is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures? δrst ≅ δacb δrst ≅ δabc δrst ≅ δbca δrst ≅ δbac.
Triangle RST is rotated 180° about the origin, and then translated up 3 units. Then , ΔRST ≅ ΔBAC
We know that To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).
Thus, The coordinates of triangle RST becomes
R (1,1) → R'(-1,-1)
S (3,4) → S'(-3,-4)
T(-5,0) → T'(5,0)
Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)
R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B
S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A
C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C
As rotation and translation both are rigid transformation that maps only congruent figures.
Therefore, ΔRST ≅ Δ BAC
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The cost of renting a canoe to use on River Y costs $.40 The cost of renting a canoe to use on River Z costs $5 per hour plus a $15 deposit. The total cost, c, of renting a canoe on either river for n hours can be represented by an equation. Write and graph a system to find how many hours you have to rent a canoe for the cost to be the same on both rivers.
Answer:
y=40 z= 5h+15
5 hours to make the same amount of money
Step-by-step explanation:
40-15=25
25/5=5
hope this helped
What is 1 as a power of 10
Answer:
Step-by-step explanation:
1 to the 10th power is 1.
DOI HAVE TO DISTRIBUTE?
2+5(x+3)-3(x-4)=x+2(2x+4)
Answer:
Yes, you have to distribute.
Step-by-step explanation:
2+5(x+3)-3(x-4)=x+2(2x+4)
2+5x+15-3x+12=2(2x+4)
Add the Numbers
2+5x-3x=2(2x+4)
Combine Like Terms, Then you can rearrange the terms for simplification. You should end up with an exation looking like this:
2x+29=5x+8
Subtract 29 from both sides. Simplify, then subtract 5x from both sides.
2x-5x=5x-21-5x
Simplify, then Divide both sides by the same factor. Simplify once more then you should have
x=7
Hope this helps ;)
f(x) = 1x g(x) = x − 4 Can you evaluate (g ○ f)(0)?
The evaluation of the composite function (g o f)(0) is -4
How to solve composite function?A composite function is generally a function that is written inside another function.
Therefore, let's solve the composite function below:
f(x) = 1x
g(x) = x - 4
Let's find (g o f)(0)
Therefore,
(g o f)(x) = g(f(x))
Hence,
(g o f)(0) = g(f(0))
f(0) = 1(0) = 0
Therefore, let's substitute f(0) in g(x)
(g o f)(0) = 0 - 4
(g o f)(0) = - 4
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What is m
Enter your answer in the box.
A=(3x-35)
B=(x-35)
c=x
The measure of angle A is found as 115 degrees.
What is described as the term triangles?A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle is a type of polygon.A triangle is made up of three sides. The sides of triangle ABC are AB, BC, and CA.The angle made by any 2 sides of a triangle, signified by the symbol, is the angle of the triangle. There are three angles in a triangle. ABC, BCA, and CAB are the 3 angles of a triangle ABC. These angles also are known as B, C, and A, in that order.A vertex is the point at which two sides of such a triangle intersect. There are three vertices in a triangle. The vertices of triangle ABC are A, B, and C.For the given question, the values of the angles are given.
A=(3x-35)
B=(x-35)
c=x
We know that the sum of all angles in a triangle is 180.
A + B + C = 180
Put the values;
3x-35 + x-35 + x = 180
Simplifying;
5x - 70 = 180
5x = 250
x = 50
Put the values in the angles;
Angles A = 3×50 - 35
Angles A = 115
Thus, the measure of angle A is found as 115 degrees.
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which equation describes the line that is perpendicular to y=1/3x+2
Answer:
y= -3x+1
Step-by-step explanation:
Write an expression for the volume of a cube with a side of length 3z^5 Simplify your expression
The volume of the cube is 27[tex]z^{15}[/tex]
A cube is a three dimensional shape having 6 square faces , all the faces are of equal length , breadth and height.
Here we have to find the volume of a cube
The length of the side is 3[tex]z^{5}[/tex].
The formula for the volume of the cube = a³
where a is the length of the side.
Substituting the value of a we get,
The volume of the cube = (3[tex]z^{5}[/tex])³
= 27[tex]z^{15}[/tex]
Therefore the volume of a cube is 27[tex]z^{15}[/tex].
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Suppose that R and S are points on the number line If RS= 10 and R lies at 13 where could S be located
Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at
323'What is a number line?A number line is a sequence of numbers arranged at a particular pattern in a straight line
How to find the point of S if R lies at point 13Information gotten form the question have it that"
RS= 10
R lies at 13
In a number line if R lies in point 13 and RS = 10 then we solve as follows
R + | 10 |
13 + 10 = 23
13 - 10 = 3
Hence R lies at point 3 or 13
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Intelligence Quotient (IQ) scores are often reported to be normally distributed with 100.0 and standard deviation = 15.0. A random sample of 57 people is taken.
What is the probability that the mean IQ score of people in the sample is less than 987 Round your answer to 4 decimal places, if necessary.
A measure of the probability that the sample's average IQ is below 987 is 44.70 %.
Why are z-scores important?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean.
Do z scores have p values?The Z-standard score's deviation measure, which the p-value is, can be regarded of as a percentile expression. So they do have p-values.
Given: IQ scores are frequently described as having a normal distribution with a mean of 100.0 and a standard deviation of 15.0. A sample of 57 persons is chosen at random.
Z-score = (X- μ)/σ
= (98-100)/15
= -0.1333
P value for this z score equals 0.4470 which is 44.70 %
Therefore, the probability that the average IQ of the sample's population is lower than 987 is 44.70 %.
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Here is an unlabeled rectangle, followed by other quadrilaterals that are labeled.
a. Select ALL quadrilaterals that are scaled copies of the unlabeled rectangle.
The quadrilateral named D, H, and E will be the scaled copies of the unlabeled rectangle.
A quadrilateral may be defined as a closed figure having four sides whereas a rectangle is a type of quadrilateral which has four sides in which any two sides are equal and the other two sides are also equal. The interior angles are 90°. The scale factor may be defined as the ratio of two dimensions such that one figure is large, and another is small. The scale factor is done due to the unpractical measurement of any figure. For example, if a figure is a scale copy of the scale factor of 6/2 it means 2 is converted into 6. Now, from the question If any figure is a scaled copy, then all dimensions must be enlarged with the same factor it means length and width both must be enlarged with the same factor. So, the unlabeled rectangle has 4 grid lengths and 2 grid widths. In H length is 8 grids and width are 4 which is the multiplication of 2 by 4 and 2. Quadrilateral D and E also follow the same.
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The Great Games Company sells 9/20 of its games through its online store. What percent of the games are sold online?
If the Great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%
The fraction of games sells through the online store = 9/20
Here we have to convert the simple fraction to the percentage
Simple fraction is a fraction that consist of whole number numerator and denominator. The top term in the simple fraction is called the numerator and bottom term is called denominator
The percentage is defined as the number that is expressed as the fraction of 100. It is represented by the percentage sign "%"
To convert simple fraction to percentage, multiply the simple fraction by 100
The percent of games are sold online = (9/20)×100
= 45%
Hence, if the great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%.
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10.8 divided by 0.09
Answer: 120
Step-by-step explanation:
[tex]\displaystyle\\10.8:0.09=\\\\\frac{10.8}{0.09}=\\\\\frac{10.8(100)}{0.09(100)}=\\\\\frac{1080}{9} =\\\\\frac{9(120)}{9}=\\\\120[/tex]
pls help its urgent!!
1/2 - 9/4x = -2/3 solve for x and simplify your answer as much as possible
Hello!
So, we are given the following to solve:
[tex]\frac{1}{2}- \frac{9}{4}x=- \frac{2}{3}[/tex]
To solve this, subtract [tex]\frac{1}{2}[/tex] from both sides.
[tex]\frac{1}{2} -\frac{9}{4}x- \frac{1}{2} =-\frac{2}{3} -\frac{1}{2}[/tex]
Simplify.
[tex]-\frac{9}{4}x= -\frac{7}{6}[/tex]
Multiply both sides by 4.
[tex]4(-\frac{9}{4}x)=4(-\frac{7}{6})[/tex]
Simplify.
[tex]-9x=-\frac{14}{3}[/tex]
Divide both sides by -9.
[tex]\frac{-9x}{-9}= \frac{-14/3}{-9}[/tex]
Finally, simplify.
[tex]x=\frac{14}{27}[/tex]
Hope this helps!
DONT IGNORE PLEASE HELP
Answer:
y = 5
Step-by-step explanation:
the equation of a horizontal line, parallel to the x- axis is
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (- 5, 5 ) and (0, 5 ) with y- coordinates 5 , then
y = 5 ← equation of line
Graph the polygon with the given vertices and its image after a reflection in the line y=-x . A(0, -3), B(2, 2), C(5,\0)
The reflection of a coordinate about the y = x will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5).
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
It is known that,
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
Therefore,
A(0, -3) → A'(-3,0)
B(2, 2) → B'(2,2)
C(5,0) →C'(0,5)
Hence "The reflection of a coordinate about the y = x will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5)".
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1
10
To solve this problem, ask the question
= ?
How many tenths are in 4/5?
How many fifths are in 1/10?
How many tenths are in 1/5?
How many fifths are in 5?
There are 8 tenths in 4/5, There are five fifths in 1/10, there are 2 tenths in 1/5, there are 25 fifths in 5.
What is tenths and fifths?The digit that follows the decimal has the place value of tenth. It stands for the digit's 1/10 position.
The fifth of a number is obtained by multiplying five occurrences of the number n together: n5 = n n n n. A number's fourth power or its square by its cube can likewise be used to create fifth powers.
a) Given 4/5, multiply the numerator and denominator by 2 to obtain the tenths. We get =4/5 2/2 =8/10 =8(1/10). Similarly, in 1/5, calculate the tenths in 1/5.
c) 525/25 = 25 is the fifth in 5.
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A pendulum is 45cm long. When the pendulum swings it travels along the arc of the circle and covers a distance of 27.5cm. Calculate the size of the angle which the pendulum travels.
The angle which the pendulum travels is 0.61 radian
What is central angle of circle ?Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disk in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases.
Given that :A pendulum is 45cm long. When the pendulum swings it travels along the arc of the circle and covers a distance of 27.5cm.
Central Angle =[tex]\frac{length of arc}{Radius}[/tex]
= [tex]\frac{27.5}{45}[/tex]
=0.61 radian
The angle which the pendulum travels is 0.61 radian
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A woman has a total of $8,000 to invest. She invests part of the money in an account that pays 11 % per year
and the rest in an account that pays 12% per year. If the interest earned in the first year is $920, how much did
she invest in each account?
Answer:
Step-by-step explanation:
art I 5.00% per annum ------------- Amount invested =x
Part II 9.00% per annum ------------ Amount invested = y
8000
Interest----- 520.00
Part I 5.00% per annum ---x
Part II 9.00% per annum ---y
Total investment
x + 1 y= 8000 -------------1
Interest on both investments
5.00% x + 9.00% y= 520
Multiply by 100
5 x + 9 y= 52000.00 --------2
Multiply (1) by -5
we get
-5 x -5 y= -40000.00
Add this to (2)
0 x 4 y= 12000
divide by 4
y = 3000
Part I 5.00% $ 5000
Part II 9.00% $ 3000
CHECK
5000 --------- 5.00% ------- 250.00
3000 ------------- 9.00% ------- 270.00
Total -------------------- 520.00
Find two functions F and G such that (f°g) (x) = h(x).
This operation is equivalent to:
[tex](f\circ g)(x)=f(g(x))[/tex]It is like a function inside a function. So, we can look for parts in h(x) that are common and call that the function inside.
As we can see, h(x) have terms with x + 4, so if we call:
[tex]g(x)=x+4[/tex]We can see that h(x) becomes:
[tex]h(x)=(g(x))^2+2g(x)[/tex]And if we substitute g(x) by x, we will get the expression of the ouside function f(x):
[tex]f(x)=x^2+2x[/tex]This way, we have:
[tex](f\circ g)(x)=(g(x))^2+2g(x)=(x+4)^2+2(x+4)=h(x)[/tex]So, the functions are:
[tex]\begin{gathered} g(x)=x+4 \\ f(x)=x^2+2x \end{gathered}[/tex]Dale has 33 carnival tickets. Its costs 7 tickets to ride the roller coaster. How many rides can he take?
Trigonometry Question!
Second Question: Calculate the value of X.
Show work needed.
Answer:
0.026 is the value of x.
Step-by-step explanation:
sinx=p÷h
sinx=5.3÷8.2
sinx=sin0.02......
x=0.02°
b. If Mark stays where he is and Mandy walks to him, how far must she walk?
Mandy must to walk a distance of 24.73 units towards Mark.
Given:
Mark is standing at 35th Street and 21st Avenue, so his location can be determined using the coordinates (35,21)
Mandy is positioned at 59th Street and 15th Avenue, hence her position's coordinates are as follows: (59,15).
We must now determine the distance Mandy must travel if Mark stays where he is and walks to meet him.
We can use the distance formula to determine this:
D = [tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} -y_{1})^{2} } }[/tex]
Here,
(x₁, y₁) = (35, 21)
(x₂, y₂) = (59, 15)
Then,
D = [tex]\sqrt{(59-35)^{2}+(21-15)^{2} }[/tex]
D = [tex]\sqrt{24^{2} +6^{2} }[/tex]
D = [tex]\sqrt{576+36}[/tex]
D = √612
D = 24.73
That is,
Mandy must to walk a distance of 24.73 units towards Mark.
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Consider the points on a line segment in the coordinate plane A(-2, -4) and B(0, 8). What is the
distance from the midpoint to the origin?
A √8
B √5
C √10
D √2
The distance from the midpoint to the origin is [tex]\sqrt{5}[/tex].
What is midpoint?
Midpoint is the point that is in the middle pf the line, and to calculate midpoint the formula is
[(x)1 + (x)2]/2, [(y)1 + (y)2]/2
given coodinates are (-2, -4) and (0, 8)
midpoint = (-2+0/2, 8-4/2)
=(-1, 2)
to find the distance from the midpoint to origin.
d= [tex]\sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_{2} )^2} }[/tex]
the points are (-1,2) and (0,0)
d = [tex]\sqrt{(-1)^2+(2)^2}[/tex]
d = [tex]\sqrt{5}[/tex]
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ASAP!!!
2 1/4x + 1/2x = 44
Solove for X and include all steps to get branliest.
Answer:
16
Step-by-step explanation:
→ Add the fractions
[tex]2\frac{1}{4} +\frac{1}{2} =\frac{9}{4} +\frac{1}{2} =\frac{9}{4} +\frac{2}{4} =\frac{11}{4}[/tex]
→ Equate to 44
[tex]\frac{11}{4} x=44\\[/tex]
→ Multiply both sides by 4
11x = 176
→ Divide both sides by 11
x = 16
what is 1+13⋅2+52−3+15−3
Answer:
88
Step-by-step explanation:
multiply 13 by 2 = 26
then add by 1 52 and 15
= 94
then subtract 94-6
88
Remember use Dmas while solving
Please help asap
Word definitions you can use
Rigid Transformations
Sequence of Transformations
Translations (slide) -
Reflection (flip)
The best description for the sequence of transformation used is; Rigid Transformations.
What is the type of transformation?
In mathematics, a rigid transformation is defined as a geometric transformation of a defined Euclidean space that does not change or preserves the Euclidean distance that is between every pair of points. Examples of this rigid transformations are rotations, translations, reflections e.t.c
Now, from the given transformation, the first thing to notice is that the transformation does not change the distance between pair of points in the diagram. Secondly, it is neither only a translation nor reflection as it is more than one transformation that was used and so it can be described as a rigid transformation.
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Write the answer in the blank.
What number is 350 more than 400?
Answer:
Step-by-step explanation:
We are looking for a new number which is 350 more than 400.
We will get the new number by adding 350 to 400.
We write it down as:
400+350=750
Therefore your answer is; 750
Answer: 750
Step-by-step explanation: You add both of them 350+400...