3. Simplify the expression (x3 - 5x2 + 7x - 12) = (x – 4) using long division. Show your work.
Answer:
Answers
Answer:
x^2-x+3
Step-by-step explanation:
(x^3-5x^2+7x-12)÷(x-4)
x^3−5x^2+7x−12
Factors of 12,
1,2,3,4,6,12
Substitute 4 into x. Since the result is 0, x-4 is a factor..
4^3−5×4^2+7×4−12=0
x-4
x^2 -x 3
x-4 | x^3 -5x^2 7x -12
x^3 -4x
-x^2 7x -12
-x^2 4x
3x -12
3x -12
x^2−x+3
(x^2−x+3)(x−4)
x−4
(x^2−x+3)
Answer = x^2-x+3
Hopes this helps
Related Questions
What is the slope of the linear function graphed
below?
Answers
Answer:
y=2x+2
Step-by-step explanation:
The slope of the function is going up by 2 every time.
What is 12/9 in simplest form
Answers
Explanation)
You’d have to find the common factor of 12 and 9
How to factor 3x³+3x²-36
Answers
Answer:
[tex]3(x - 2) (x^2 + 3x + 6)\\[/tex]
Step-by-step explanation:
Firstly, divide all parts of the equation by 3:
[tex]3x^3 + 3x^2-36[/tex]
[tex]3(x^3 + x^2-12)[/tex]
Now focus on the equation:
[tex]x^3 + x^2-12[/tex]
We know that the equation can be factored using x so we know that (x +- unknown) is the factor. We need to find the easiest way to factor this, lets find the factors of 12:
1 12
2 6
3 4
1 and 12 won't work so let's try 2 and 6, initially start as a negative 2:
[tex]\frac{ x^3 + x^2 - 12}{x - 2}[/tex] = [tex]x^2 + 3x + 6[/tex]
We can confirm this is simplified by multiplying together:
[tex](x - 2) (x^2 + 3x + 6)[/tex]
[tex]x* x^2 = x^3\\x * 3x = 3x^2\\x * 6 = 6x\\-2 * x^2 = -2x^2\\-2 * 3x = 6x\\-2 * 6 = -12[/tex]
= [tex]x^3 + x^2 - 12[/tex]
Meaning it is simplified.
Now, put the equations together:
[tex]3(x - 2) (x^2 + 3x + 6)\\[/tex]
Hope this helps!
What is the product of 14.5×100
Answers
Answer:
1450
Step-by-step explanation:
Any number times 10 goes up one value.
ones become tens, and tens become hundreds etc..
87x10=870
And a number times 100 goes up two values.
23.5x100= 2350
hope this helped ;)
Step-by-step explanation:
you don't have a calculator ? with that you would have gotten the answer immediately.
so you had to write the question in here, need to wait for an answer, ...
but actually, this is very easy to solve even without a calculator, as this is how our decimal numbers work : based on powers of 10.
multiplying by 100 moves the decimal point 2 positions to the right (and fill up with zeros where necessary) :
14.5 × 100 = 1450
a multiplication by 10 moves the decimal point 1 position to the right.
a multiplication with 1000 3 positions to the right. and so on.
a division by 100 moves the decimal point 2 positions to the left (and fill up with zeros where necessary). and so on.
80 precent of games is 32 games
Answers
Answer:
If you are asking for the whole number of game it is 40
Step-by-step explanation:
Choose the scientific notation for 800.
O 8 x 10
O 8 x 102
O 8 x 103
O 8 x 100
Answers
Answer:
O [tex]8 * 10^2[/tex]
Step-by-step explanation:
Hope it helps
Peace out
^^ ^-^ :) ;) ~-~
help dududidihendhhejrjfjf
Answers
Answer:
x = − 8
Step-by-step explanation:
Factor then solve to find the complex solutions.
Q1: The first three stages of a pattern are shown below. Each stage of the pattern is made up of small squares. Each small square has an area of one square unit. Stage 1 Stage 2 (a) Draw the next two stages of the pattern. (b) The perimeter of Stage 1 of the pattern is four units. The perimeter of Stage 3 Stage 2 of the pattern is 12 units. Find a general formula for the perimeter of Stage n of the pattern, where # EN. (c) Find a general formula for the area of Stage n of the pattern, where E N. (d) What kind of sequence (arithmetic, quadratic, geometric, or none of these) do the areas follow? Justify your answer.
Answers
9514 1404 393
Answer:
a) see attached for the drawings
b) p = 8n -4
c) a(n) = 4n(n -3) +13 for n > 1; a(1) = 1
d) none
Step-by-step explanation:
a) The overall dimensions of the next two stages of the pattern will be 7×7 and 9×9. Excluding the 4 "ears", the central squares are 5×5 and 7×7. The drawings are shown in the attachment.
__
b) The sequence of perimeter values is ...
4, 12, 20, 28, 36, ...
This is an arithmetic sequence with a common difference of 8. A suitable formula for the perimeter p of stage n is ...
p = 8n -4
__
c) The sequence of area values is ...
1, 5, 13, 29, 53, ...
The first differences are ...
4, 8, 16, 24, ...
and the second differences are ...
4, 8, 8, ...
At no level are the differences "common", so this sequence cannot be described by a polynomial function. After the first one, the second differences are common, so the sequence after the first term can be described by a quadratic function.
The function describing the sequence must be defined in two parts:
[tex]a(n)=\begin{cases}1&\text{ for $n = 1$}\\4n(n-3)+13&\text{ for $n>1$}\end{cases}[/tex]
__
d) Because the function must be piecewise defined, the area sequence is not any of the types of sequences listed. After the first term, it is a quadratic sequence.
_____
Additional comment
The leading coefficient of the quadratic formula for the area sequence is half the second difference. When 4n² is subtracted from the sequence of areas, the remaining arithmetic sequence has a common difference of -12. In order to bring the total of these quadratic and arithmetic sequences up to the correct area value, 13 must be added. This formula would give a(1) = a(2) = 5, which is not the correct value for a(1). Hence, that must be defined separately.
Calculate A woman is walking at a rate of 0.5
m/s. Her mass is 62 kg. Calculate the woman's
kinetic energy in joules.
Answers
Answer:
7.75J
Step-by-step explanation:
kinectic energy formula = 1/2mv²
m mass
v velocity
1/2 x 62 x 0.5² = 7.75
A woman is walking at a rate of 0.5m/s. Her mass is 62 kg. The woman's kinetic energy in joules:
K.E. = 7.75 kgm²/s²
What is Kinetic Energy?
The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
Given,
Mass = 62kg
Velocity = 0.5m/s
The formula for Kinetic Energy is :
K.E. = 1/2 m v².
K.E. = 1/2 (62)(0.5)²
K.E. = 1/2 (62)(0.25)
K.E. = 1/2 (15.5)
K.E. = 15.5/2
K.E. = 7.75 kgm²/s²
or
K.E. = 7.75 joules
Hence, he woman's kinetic energy in joules, K.E. = 7.75 kgm²/s²
To learn more about Kinetic Energy click on the link
https://brainly.com/question/8101588
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help pls aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
x=3
Step-by-step explanation:
y = mx + b
m = (y2 - y1)/(x2 - x1)
m = (8+4)/(3-3) = 12/0 = UD
x = 3
Determine if the sequence is arithmetic 7,9,11,13,15…
If so, find the common difference
b. What would be a30
Answers
Answer:
65
Step-by-step explanation:
a. since we add 2 to each term in this sequence, the difference between one term and the next is a constant. therefore, it's an arithmetic sequence
b. in this case, a = 7 and d =2
the equation would be a30 = 7 + (30-1)2
solving this gives us 65
A box of candy has 7 red pieces, 3 orange, 2 yellow, and 8 blue pieces. You get to
pick two pieces of candy. If you reach into the box without looking, what is the
probability that you will pick a blue piece, not replace it an then a red piece of
candy?
Answers
There are 20 pieces of candy. First, you find the probability of drawing a blue piece which is 8/20 which is reduced to 4/5. Then you find the probability of drawing a red piece. Since you have removed a blue piece, there are now 19 pieces instead of 20. So, the probability of drawing a red piece is 7/19. Since the question is asking the probability of drawing a blue piece THEN a red piece you multiply the two fractions together since they are dependent upon each other. So, (4/5)(7/19)= 28/95.
Hope this helped. :)
Match the expression with it's simplified version:
Answers
Answer:
they are already matched
Step-by-step explanation:
Answer: (x^7)/(x^4) = x^3, x^(-3) = 1/(x^3), x^0 = 1, (x^4)/(x^3) = x
Step-by-step explanation:
Dividing two exponents with the same base can be simplified by subtracting the exponents. Thus (x^7)/(x^4) is the same as x^(7-4), or x^3.
A negative exponent is the same as the reciprocal of the positive exponent. x^-3 is the same as 1/(x^3).
Anything with an exponent of 0 is equal to 1.
Again, when dividing two exponents, if they have the same base, you can just subtract the exponents. (x^4)/(x^3) = x^(4-3) = x^1 = x.
if your monthly salary is $1,015.00 what percentage of your monthly salary is used on paying your rent.
Rent: $443.50
Answers
Answer:
43%
Step-by-step explanation:
443.50 divided by 1015 is 0.43 when rounded; 0.43 as a fraction is 43%. So therefore, the answer is 43%.
If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 6, how small can f(6) possibly be?
Answers
Answer:
[tex]f'( x ) = \frac{f(b) - f(a)}{b - a} \\ = \frac{f(6) -f(a)}{6 - 1} \\ 3\leqslant \frac{f(6) - 10}{5} \\ 15\leqslant f(6) - 10 \\ f(6) \geqslant 15 + 10 \\ f(6) \geqslant 25[/tex]
Answer:
25
Step-by-step explanation:
Our "best" case is when [tex]f'(x) = 3[/tex] everywhere - if it changes it means [tex]f(x)[/tex] will grow faster. But if [tex]f'(x)[/tex] is constant, it means [tex]f(x)[/tex] is the straight line [tex] y-10 = 3 (x-1) [tex], which passes through the point (6, 25)
Holly buys a $22 shirt for 20% off. The tax rate in her city is 6.5%. What is the total amount she paid for the shirt? Round to the nearest cent.
Answers
Answer:
$18.74
Step-by-step explanation:
To find the sale price:
22 * 0.2 = 4.4
22 - 4.4 = 17.6
or, you can just multiply by 0.8, so you wont need to subtract later
22 * 0.8 = 17.6
Then, you need to find the tax amount:
17.6 * 6.5 = 1.144
17.6 + 1.144 = 18.744
Round
18.74
write the ratio $12 dollars 3 tickets as a unit rate
Answers
Answer:
20 pesos lang
Step-by-step explanation:
kami 5 pesos per ticket kayo 12 dollar
In a state's Pick 3 lottery game, you pay $1.35 to select a sequence of three digits (from 0 to 9), such as 966. If you select the same sequence of three digits that are drawn, you win and collect $394.46
What is the probability?
If you win what is your net profit?
Find the value?
Answers
Answer:
How old are you
Step-by-step explanation:
A figurine of a lighthouse is shown. if the actual lighthouse is 30feet wide, how tall is the lighthouse
Answers
Answer:
30× 60 ( 3×2= 6 + tens= 60 )= minimum- 180 fery
pls help
which trend line properly describes the data relationship in the scatterplot?
Answers
Answer:
The 2nd one
Step-by-step explanation:
The trend line properly describes the data relationship in the scatterplot is plot A.
What is Trend line?A trend line is also known as a line of best fit, and it is used to illustrate the behaviour of a set of data to assess if it is in a given pattern. So, a trend line is an analytical technique that is frequently used in conjunction with a scatter plot to determine whether or not there is a relationship between two variables.
As, per the plots.
The scatter plot A have the points distributed symmetrically on the both side of line.
Also, straights lines are negatively correlated with scatter points.
Learn more about Trend line here:
https://brainly.com/question/22601112
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List all subsets of the set {A, B, C} using proper notation
Answers
Answer:
subset of {A, B, C} = { }, {A}, {B}, {C}, {A,B}, {B,C},{C,A}
Hope that my answer is helpful to you
A water tank is a cube of side 2m the depth of water in it is60cm. What is the volume of water in the tank?
Answers
Answer:
Step-by-step explanation:
The base is made of a square that is 2 meters by 2 meters.
Base = 4 m^2
The height of the water is 60 cm
60 cm// 100 cm/meter = 0.6 meters
Volume = Base * height
Base = 4m^2
height = 0.6 m
Volume = 4 * 0.6 = 2.4 m^3
A drilling machine can drill 12 holes in 6 minutes. If the machine drills holes at a constant speed, it can drill
holes in 25 minutes. HELPPP
Answers
Answer:
The machine can drill 50 holes in 25 minutes!
Explanation:
6 by 4 is 24, which in this context will be 24 minutes. Therefore, multiply 12 by 4 to get the sum of 48. Then, to find the remaining 1 minute, divide 12 by 6 to get 2 which is the amount of holes per minute. Add 2 to 48 and that is your answer!
x + 4y = 23
-2x + 3y = -2
Answers
Answer:
(x, y) = (7, 4)
Step-by-step explanation:
I find a graphing calculator to give a solution quickly and easily.
(x, y) = (7, 4)
__
Here, we can solve the first equation for x, then substitute into the second.
x = 23 -4y
-2(23 -4y) +3y = -2 . . . . . substitute for x
-46 +8y +3y = -2 . . . . . eliminate parentheses
11y = 44 . . . . . . . . . . . collect terms
y = 4 . . . . . . . . . . . . divide by the coefficient of y
x = 23 -4·4 = 7 . . . . use the expression for x to find x
(x, y) = (7, 4)
How simplify -8/3 devided by -2/6
Answers
Answer:
The answer is 8
Step-by-step explanation:
-8/3 divided by -1x2 / 3x2
-8/3 divded by -1/3
-8/3 x 3 / 3 x -1 = -8/-1 = 8 x -1 + 0 / -1
= 8
So your answer is 8
Please mark Brainliest I answered First
Solve the inequality graphically.
3-* > 6*
a. x < 1
b.X>1
C.X>0
d. x <0
Answers
Answer:
Simplify the expression.
−
729
Step-by-step explanation:
your wlecome
If the sales tax rate is 8.9%, how much tax will be paid on a $457 tv?
State your answer in terms of dollars, rounded to the nearest cent (hundredth).
Do not include a $ sign with your response.
Answers
What is the slope of the line that passes through the points (4, 10)(4,10) and (1, 10) ?(1,10)? Write your answer in simplest form.
Answers
Answer:
0
Step-by-step explanation:
Slope = Δy/Δx
Slope = 10-10/4-1
Slope = 0/3
Slope = 0
It is a Horizontal Line
-Chetan K
What algebraic property is T - 6 = -4
Answers
—————————————————————
Answer:
subtraction to addition algebraic expression.
Step-by-step explanation:
Which values of a, b, and c represent the answer in simplest form?
7/9 * 4/9 = a b/c
Answers
Answer:
Option 2: A=1, B=3, C=4
Step-by-step explanation:
7/9÷4/9 = 7/9*9/4cancel 9 on each side=7/4= 1 3/4