determine if x-3 is a factor of f(x)=x^3-x^2-5x-3
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
(x - 3) is a factor of the given function
Step-by-step explanation:
Given function:
[tex]\implies f\:\!\:(x)=x^3-x^2-5x-3[/tex]
If (x - 3) is a factor of the given function then [tex]f\:\!\:(3) = 0[/tex]
Substitute x = 3 into the function and solve:
[tex]\implies f\:\!\:(3)=(3)^3-(3)^2-5(3)-3[/tex]
[tex]\implies f\:\!\:(3)=27-9-15-3[/tex]
[tex]\implies f\:\!\:(3)=0[/tex]
Therefore, as [tex]f\:\!\:(3) = 0[/tex] then (x - 3) is a factor of the given function.
Related Questions
Can someone please help me? I’ll give brainliest to the first person who gets it right
Answers
Answer:
128 degrees
Step-by-step explanation:
B = D
B = 128
Therefore, D = 128
This shape has these characteristics:
⇒ there are two sets of parallel sides
⇒ This shape is a parallelogram
Since this shape is a parallelogram:
⇒ meaning that angles opposite to each other
⇒ equal in measure
Since ∠B and ∠D are opposite each other
⇒ ∠D = 125°
Answer: ∠D = 125°
Hope that helps!
Gold has a density of 19.32 grams per cubic centimeter. How much does one-half of a cubic centimeter weigh? Gold has a density of 19.32 grams per cubic centimeter . How much does one - half of a cubic centimeter weigh ?
Answers
Substituting into the formula [tex]d=\frac{m}{v}[/tex],
[tex]19.32=\frac{m}{0.5}\\\\m=\boxed{9.66 \text{ grams}}[/tex]
square root of 12-square root of 8
Answers
Answer:
please tell me if im wrong!
Step-by-step explanation:
answer: 16 √ 3
Answer:
24√2
Step-by-step explanation:
if I'm correct the equation is
(√12)^2(√8)
we expand the surds
(√4x3)^2 (√4x2)
(2√3)^2 (2√2)
(4x3) (2√2)
12x2√2 =
24√2
If the sum of a number and eight is doubled the result is five less than the number find the number
Answers
Answer: -21
Step-by-step explanation:
Let the number be x.
Then, this means 2(x+8)+5=x.
2x+16+5=x [distributive property]2x+21=x [combine like terms]x+21=0 [subtract x from both sides]x= - 21 [subtract 21 from both sides]Alina has $20 in her account she wants to purchase a purse shoes that cost $45 if the line makes the purchase which ener will represent the amount of money in the line of the account
Answers
The line represent the amount of money in the line of the account will be x + y = 45.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Alina has $20 in her account she wants to purchase a purse, shoes that cost $45.
If the line makes the purchase, Then the line represent the amount of money in the line of the account will be
x + y = 45
where x be the price of purse and y be the price of shoe.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
A quadratic equation is an equation whose leading coefficient is of the second degree. The correct options are A, B, and E.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Roots of the quadratic equation:
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The complete question is:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot
8(x2 + 2x + 1) = 3 + 1
8(x2 + 2x) = –3
If we simplify the given options, then the option that is correct is,
A.) 8(x² + 2x + 1) = –3 + 8
8x² + 16x + 3 = 0
B.) 8x² + 16x + 3 = 0
[tex]x = \dfrac{-16\pm\sqrt{16^2-4(8)(3)}}{2(8)}\\\\x = -1 \pm \dfrac{\sqrt{10}}{4}\\\\x = -1 \pm \sqrt{\dfrac{10}{16}}\\\\x= -1 \pm \sqrt{\dfrac{5}{8}}[/tex]
E.) 8(x² + 2x) = –3
8x² + 16x + 3 = 0
Hence, the correct options are A, B, and E.
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14)
Given a circle with a radius of 5, which equation expresses it as the ratio of the circumference of a circle to its diameter?
A)
B)
C)
D)
sin
- 7
10
216
C
Answers
Answer: 10
Step-by-step explanation: The diameter is twice the radius
Clara is building a triangular garden. She wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long.
What expression could she write to determine the perimeter of the triangle if s represents the length of the shortest side?
Answers
The garden's perimeter = 3+2s+12+s.
The simpler version of the expression = 15+3s.
The variable's frequency in the abbreviated statement is 3.
Calculation of a triangle's perimeter:The triangle's perimeter is equivalent to the sum of its edges, where a, b, and c are its sides.
Let the triangle's longest edge be 'a'shorter one to be 's'the opposite side 'b'With the information provided, the formula will become 'a = 3+2s'
and 'b' is also 12 ft.
Triangle perimeter =the total of its edges
= a + b + s
= 3 + 2s + 12 + s
= 15 + 3s
As a result, the garden's perimeter = 3+2s+12+s.
Therefore,the simpler version of the formula is 15+3s.
The variable's coefficient in the abbreviated statement is 3.
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Suppose a bag contains a set of 10 tiled letters: M, T, O, A, T, P, J, A, K, A You draw a tile from the bag, and record the letter and leave it on the table. You shake up the bag, and draw another tile out of the bag. Calculate the probability you will select the letter M on the first draw and the Letter T on the second draw?
Answers
Answer:
1/90
Step-by-step explanation:
Comment
To begin with, there are 10 tiles.. You draw one and don't replace it. Then you draw another tile from the 9 that remain. The job is to figure out the probability of that happening.
You have a 1/10 chance of drawing the M.
But now there are only 9 tiles left and you have a 1 in 9 chance of drawing a T
Solution
P(M,T) = 1/10 * 1/9 = 1 / 90
You have a 1 in 90 chance of getting the two tiles in the order you have specified.
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Answers
Using translation concepts, the sequence that is used to obtain the translated image is:
Reflection over the y-axis.Shift right of one unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
For all the vertices, the transformations follow the given pattern:
(x,y) -> (-x,y) -> (-x + 1, y).In the step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, in step (-x,y) -> (-x + 1, y), the function is shifted right one unit.
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If the ordered pair (-5/2, y) lies on the graph of y=7-2x, find the value of y.
19/2
012
02
Answers
The correct answer is option B which is the value of Y will be 12.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
If the ordered pair (-5/2, y) lies on the graph of y=7-2x,
The value of Y will be calculated as:-
Y = 7 - 2x
Y = 7 - 2 ( -5/2 )
Y = 7 - ( - 5 )
Y = 7 + 5
Y = 12
Therefore the correct answer is option B which is the value of Y will be 12.
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The price of a Delta airline ticket from Los Angeles to Boston increased to $440. This is a 15% increase. What was the old fare?
Answers
Explanation: you would have to divide the $440 which is your right now price with the 15% increase that was put so then you would find out the actual number of how much was added which comes out to be( $66)!!
Hope this helps!!^^^^
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8
What is 11 - 2³?
Answers
Answer:
[tex]11 - 2 {}^{3} [/tex]
[tex]11 - 8[/tex]
[tex]3[/tex]
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants. Calculate the average rate of change (slope) for the number of Burger King restaurants over this time period.
PLS HELP ME
Answers
Slope of the given data is 579.88
What is Slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.
Here, given data;
x₁ = 2009 y₁ = 12078 burger
x₂ = 2017 y₂ = 16717 burger
Now, Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (16717 - 12078) / (2017 - 2009)
Slope = 4639 / 8
Slope = 579.88
Thus, Slope of the given data is 579.88
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Find the truth set of each predicate.
Answers
The truth set for each predicate are:
a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
b) d ∈ { 1, 2, 3, 6}
c) x ∈ { [-2, -1] U [1, 2]}
d) x ∈ {-2, -1, 1, 2}
How to find the truth set of each predicate?
We only need to find the sets of values such that the statements are true.
a)
We want to find vales of d, such that d is an integer, and 6/d is an integer.
Here the possible values of d will be:
d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
Which are all the factors of 6, so all these integers divide 6.
b) Same as before, but this time the domain is a positive integer, so now the truth set will be:
d ∈ { 1, 2, 3, 6}
c) We want to find real values of x such that:
1 ≤ x² ≤ 4
If we apply the square root to the 3 sides, we get two inequalities:
-√1 ≥ x ≥ -√4
√1 ≤ x ≤ √4
Simplifying:
-1 ≥ x ≥ -2
1 ≤ x ≤ 2
So the truth set is:
x ∈ { [-2, -1] U [1, 2]}
c) Same as before, but now we only have integer solutions, so the truth set is:
x ∈ {-2, -1, 1, 2}
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Fill in the blank. In the triangle below, y=? Round your answer to two decimal places.
Answers
Answer:
z= 38°
Step-by-step explanation:
z= 90(from right angle)+52=142
180-142=38°
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.3
B.5
C.7
D.9
E.4
Answers
If you bought a stock last year for a price of $66, and it has gone down 13.9% since then, how much is the stock worth now, to the nearest cent?
Answers
The stock worth now, to the nearest cent, is $58.14.
How to find the current worth of stock?The current worth of stock = initial price of stock+increase in the price of stocks
If you bought stock last year for a price of $66, and it has gone down 13.9% since then,
Let X be the worth of stock;
66 × 100 = (13.5% + 100%) × X
6600 = 113.5X
X = 6600/113.5
X = 58.14458
X = $58.14
Hence, The stock worth now, to the nearest cent is $58.14.
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Select the correct answer from each drop-down menu. y 11 10 Weight (kilograms) 9 00 7 CO 5 3 2 1 5 6 7 Age (months) The scatter plot shows the weight of a child each month. 1 rights reserved 2 3 4 The birth weight of the child is V X 8 9 10 11 kilograms. The child gains an average of per month. Select the correct answer from each drop - down menu . y 11 10 Weight ( kilograms ) 9 00 7 CO 5 3 2 1 5 6 7 Age ( months ) The scatter plot shows the weight of a child each month . 1 rights reserved 2 3 4 The birth weight of the child is (blank) kilograms . The child gains an average of(blank) per month .
Answers
Answer:
its wrong answer and question
S
2
Question 10 of 10
What is the value of p?
90
125
OA. 125°
O B. 55°
O C. 45°
O D. 35°
SUBMIT
Answers
Answer:
D
Step-by-step explanation:
You do 180-125 to find the angle (because its a straight line) and then you get 55, then you have a right angle so you have 90 and then you do:
55+90+p=180
and then you get
145 +p=180
180-145=35
p=35
What is the reciprocal of (10xyz)/(40xyz)
Answers
Answer:
4
Step-by-step explanation:
10xyz/40xyz
the xyz would cancel out
leaving 10/40.
10/40 would then simplify to 1/4 (divide by 10)
1/4
The reciprocal of 1/4 is 4
To check:
1/4 * 4 = 1
The scatter plot shows the relationship between the mass of a tree and the total mass of the vegetation within 100 square meters of the tree.
Answers
The regression equation is given by [tex]\overline{y}=50-0.01x[/tex]
We have given that,
The scatter plot shows the relationship between the mass of a tree and the total mass of the vegetation within 100 square meters of the tree.
What is the formula for slope?The slope =change in y/change in x
We have given the two points (100,40) and (25000,2)
Therefore the slope of the given point is,
[tex]=\frac{25-40}{2500-1000} \\=-0.01[/tex]
The y-intercept is the value of y when x=0 this implies that y=50
Therefore the regression equation is given by
[tex]\overline{y}=50-0.01x[/tex]
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Move the slider on the graph on the right to graph each function:
For the function: y = StartRoot x minus 7 EndRoot + 1
The domain is : x ≥
The range is: y ≥
Answers
Answer:
domain: x ≥ 7 . . . [7, ∞) in interval notationrange: y ≥ 1 . . . [1, ∞) in interval notationStep-by-step explanation:
You want the domain and range of the function y = √(x -7) +1.
DomainThe domain is the horizontal extent of the graph. The graph of the given function extends to the right from x=7, which is included in the solution set.
The domain is x ≥ 7.
RangeThe range is the vertical extent of the graph. The graph of the given function extends upward from y=1, which is included in the solution set.
The range is y ≥ 1.
Answer: domain: 7
range: 1
Step-by-step explanation:
Given 4 c 5 not-equals 0 and c is a real number, what is the multiplicative inverse of 4 c 5 not-equals 0 0 1 startfraction 1 over 4 c 5 end fraction startfraction 1 over 4 c endfraction 5
Answers
The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)
Complete questionGiven 4c + 5 ≠ 0 and c is a real number, what is the multiplicative inverse of 4c + 5
How to determine the multiplicative inverse?The expression is given as:
4c + 5
The multiplicative inverse of an expression x is 1/x
This means that:
The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)
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Find the equation of a line that contains the points (−2,−4) and (−5,4). Write the equation in slope-intercept form, using fractions when required.
Answers
The equation would be y+ 3/8x+9/4.
Lets try to explain in the further steps to calculate the equation,
Slope formula: (y₂ - y₁) / (x₂ - x₁)
First, plug in these values of the two given points.
[tex]= > (-5+2) / (4+4)\\= > -3/8[/tex]
Slope = -3/8
To find the equation of the line, (y- y1) = m* (x-x1)
So by putting the values into the above equation we get,
[tex]= > (y-4) = -3/8(x+5)\\= > y-4 = -3/8x - 15/8\\= > y + 3/8x + 4 - 15/8\\= > y + 3/8x + 9/4[/tex]
Hence the equation is [tex]y+ 3/8x+9/4.[/tex]
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Karen runs 7 miles in 50 minutes. At the same rate, how many miles would she run in 75 minutes?
Answers
Answer :
10.5 miles
Given :
7 miles in 50 mins
Step-by-step explanation :
Calculate how many miles in 1 minute :
Divide both by 50 :
7/50 miles in 1 minute
To work out 75 minutes we multiply both by 75 :
75 × 7/50 =
10.5
Therefore our final answer is 10.5 miles
Hope this helped and have a good day
Express the division form of a+bi (1+3i) divided by (2+i)
Answers
Help me with this question please!! :)
Answers
Answer: 9516793/9765625
Step-by-step explanation:
We can subtract the probability none of them have been vaccinated from 1.
If 52% of people are vaccinated, then 48% of people are not vaccinated.
Thus, the probability is [tex]1-(0.48)^{5} =\frac{9516793}{9765625}[/tex]
9x+9y=9. Solve for Y
Answers
Answer:
y = 1 - x
Step-by-step explanation:
9x + 9y = 9 ( divide through by 9 )
x + y = 1 ( subtract x from both sides )
y = 1 - x
Answer:
y = 1 - x
Step-by-step explanation:
9x + 9y = 9
First, take 9x to the right side.
9y = 9 - 9x
9y = 9 ( 1 - x )
Divide both sides by 9.
y = 1 - x
The scatter plot shows a correlation between the years and the rainfall in centimeters in Tennessee.
The line of regression models that correlation.
Enter a number to complete each statement.
please help
Answers
Answer:
7
4
Step-by-step explanation:
The actual values are shown on the given graph as blue points.
The line of regression is shown on the given graph as the red line.
From inspection of the graph, in the year 2000 the actual rainfall was 43 cm, shown by point (2000, 43). It appears that the regression line is at y = 50 when x is the year 2000.
⇒ Difference = 50 - 43 = 7 cm
In 2000, the actual rainfall was 7 centimeters below what the model predicts.
From inspection of the graph, in the year 2003 the actual rainfall was 44 cm, shown by point (2003, 40). It appears that the regression line is at y = 40 when x is the year 2003.
⇒ Difference = 44 - 40 = 4 cm
In 2003, the actual rainfall was 4 centimeters above what the model predicts.
