Answers
If you perform the synthetic division, you'll get what you see in the attached image.
The final answer is [tex]2x^2+3x+11+\frac{20}{x-3}[/tex]
Note: the quotient is 2x^2+3x+11; the remainder is 20. The remainder is found by the last item in the bottom row. The coefficients of the quotient are the remaining other values in the bottom row.
Related Questions
what is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16? y = –4 y = –2 y = 4 y = 6
Answers
It's always a good idea to use parentheses for clarity; it reduces or removes the need for guessing.
Here is my interpretation of your equation:
-8/2y-8=5/y+4 - 7y+8/y^2-16 becomes
-8 / (2y-8) = 5 / (y+4) - 7y + 8 / (y^2-16) (note use of parentheses)
Factoring all of the denominators results in:
-8 / [2(y-4)] = 5 / (y+4) - 7y + 8 / [(y-4)(y+4)]
The LCD is 2(y-4)(y+4). You must multiply each and every term in the above equation by this LCD to clear fractions:
-8(y+4) = 5(2)(y-2) - 7(y+4)(y-4) + 8/2
Then -8y - 32 = 10y -20 -7y^2 + 4
I believe the "-7y^2" term is incorrect.
In retrospect, you could simply substitute each of the given answers (y-values), one at a time, to determine which, if any, makes the equation true:
-8 / (2y-8) = 5 / (y+4) - 7y + 8 / (y^2-16) (note use of parentheses)
Let's test y = 4. Is this a solution? Subst. 4 for y in the above equation, we get:
-8 / (8-8) and several more terms. No, 4 is not a solution, because
-8 / (0) is undefined. Eliminate y = 4 as a solution. Try y = -4 and the other given possible solutions. Do any of them make this equation true?
Answer:
d. 6
Step-by-step explanation:
just took the pretest:) have such a fantastic day loves, you're doing AMAZING!
What is the reason for each step in the solution of the inequality?
−2(x+3)−4>4x+30
Select the reason for each step from the drop-down menus.
2nd picture is drop down box answers.
Answers
-2x - 6 - 4 > 4x + 30 : distributive property
-2x - 10 > 4x + 30 : combine like terms
-6x - 10 > 30 : subtraction property
-6x > 40 : addition property
x < -20/3 : division property
[tex]-2x - 6 - 4 \ \textgreater \ 4x + 30[/tex] : Distributive property
[tex]-2x - 10 \ \textgreater \ 4x + 30[/tex] : Combine like terms
[tex]-6x - 10 \ \textgreater \ 30[/tex] : Subtract
[tex]-6x \ \textgreater \ 40[/tex] : Add
[tex]x \ \textless \ - \dfrac{20}{3} [/tex] : divide
What is the answer to this question ?
Answers
your answer is A
Jeff invests an amount at 4% interest compounded annually. After 3 years, he has $1687.30. What was the original amount Jeff invested?
$1500
$1200
$1450
$750
Answers
:
To find the effect of 4% annual interest over 3 years, take 1.04 and raise it to the third power:
1.04³ = 1.125
Divide the final amount, 1687.30 by 1.125 to find the principal amount:
1687.30 ÷ 1.125 = ~1500
Answer is A.
Two numbers total 53 and have a difference of 25. Find the two numbers.
Answers
and
have a difference (x - y) of (=) 25.
So, x + y = 53 and x - y = 25.
Solve one equation for a variable. We'll solve for x in the first equation.
x + y = 53 Subtract y from both sides
x = 53 - y
Substitute x for (53 - y) in the second equation.
x - y = 25 Substitute (53 - y) in the x spot
53 - y - y = 25 Combine like terms (-y and -y)
53 - 2y = 25 Subtract 53 from both sides
-2y = -28 Divide both sides by -2
y = 14
Now, find x by plugging this y-value (14) into the first equation.
x + y = 53 Substitute y for 14
x + 14 = 53 Subtract 14 from 53
x = 39
Check both of your answers by plugging them into the original equations.
x + y = 53 Plug in your numbers (39 and 14)
39 + 14 = 53 Add
53 = 53
x - y = 25 Plug in your numbers (39 and 14)
39 - 14 = 25 Subtract
25 = 25
So, your answers are x = 39 and y = 14 .
Lakeya makes cupcakes to sell at her friend's lemonade stand. She sold 24 cupcakes and sold them for $3 each. Write a number sentence using the variable m to represent the total amount of money she made.
Answers
because she sold 24 cupcakes for $3 then you would multiply 24 and 3 to get the amount of money she made
Simplify 6 - 23 + (-9 + 5) · 2
A. -10
B. -12
C. 6
D. -8
I've been told the answer is A. -10, but I need to know how to get that answer.
Thanks.
Answers
at least u tried to help but the answer is -10 bro
In an x-y plot of an experiment what is usually plotted on the x axis?
a. the independent variable, which is the parameter that was manipulated.
b. th
Answers
PLZ HELP I WILL MAKE YOU BRAINLIEST!! IT IS GOOD FOR YOUR PROFILE!
Rewrite as a square or a cube:
1 11/25
Answers
= (6/5)^2
Answer:
1 11/25 = 36/25
= (6/5)^2
Step-by-step explanation:
What is 164% of 25? I have no idea and im in the middle of a test XDDD
Answers
What is the area of a triangle with verticies at (-2,1), (2,1) and (3,4)
Answers
notice, is just a triangle with a base of 4, and an altitude of 3.
A boat was sailing for 4 hours and covered 224 miles. A jet is ten times as fast as the boat. Find the jet’s speed.
Answers
224 ÷ 4 = 56
56 mi/1 h
Next, you would multiply the number of miles the boat traveled, 56, by 10.
56 x 10 = 560
The jet flew 560 mi/per hour
I hope this helps!
56 x 10 = 560 miles per hour
You swim 121 out of 1,000 meters. How can you write this as a decimal
Answers
0.121
The number in decimal form will be 0.121 meters.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that you swim 121 out of 1,000 meters. The decimal for the number will be written by dividing the number by 1000.
Decinmal form = 121 / 1000
Decimal form = 0.121 meters
Therefore, the decimal form of the number will be 0.121 meters.
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How many times does 1/2 fit into 30
Answers
30 ÷ [tex] \frac{1}{2} [/tex]
To divide by a fraction, multiply by its reciprocal (find reciprocal by flipping the fraction)
Ex. 30 * 2
Multiply 30 by 2 to get 60.
equivalent ratios number 1 to 50
Answers
Ordering Least to greatest 2 9/11, 4/5, 2.91, 0.9
Answers
Help Algebra Question
Answers
0 4
- 6 1
3 -4
Rember row times column.
=>
a11 = 4*0 + 0*(-3) = 0
a12 = 4*1 + 0*1 = 4 + 0 = 4
a21 = -1*0 + 2*(-3) = 0 - 6 = -6
a22 = -1*1 + 2*1 = -1 + 2 = 1
a31 = -3*0 + (-1)*(-3) = 0 + 3 = 3
a32 = -3*1 + (-1)*1 = -3 - 1 = -4
John throws a rock straight down with speed 12 m/s from the top of a tower. the rock hits the ground after 2.37 s. what is the height of the tower? (air resistance is negligible)
Answers
The tower is 28.44 meters tall.
Simplyfy (x - 5 / x^3 + 27) + (2 / x^2 - 9)
Answers
[tex]\bf \cfrac{x-5}{x^3+27}+\cfrac{2}{x^2-9}\implies \cfrac{x-5}{x^3+3^3}+\cfrac{2}{x^2-3^2} \\\\\\ \cfrac{x-5}{(x+3)(x^2-3x+3^2)}+\cfrac{2}{(x-3)(x+3)}\\\\\\ \cfrac{x-5}{(x+3)(x^2-3x+9)}+\cfrac{2}{(x-3)(x+3)} \\\\\\ \textit{so, we'll use the LCD of }(x-3)(x+3)(x^2-3x+9) \\\\\\ \cfrac{(x-3)(x-5)~~+~~(x^2-3x+9)2}{(x-3)(x+3)(x^2-3x+9)} \\\\\\ \cfrac{x^2-8x+15~~+~~2x^2-6x+18}{(x-3)(x+3)(x^2-3x+9)}\implies \cfrac{3x^2-14x+33}{(x-3)(x+3)(x^2-3x+9)}[/tex]
How does the throughput of pci express version 3.0 compare to pcie version 2.0?
Answers
How would you express as a unit rate: morag typed 60 words in one minute
Answers
I'm not sure what else you need to do as this answer is already in unit rate.
Hope This Helps You!
Good Luck :)
- Hannah ❤
Morag would be typing at a rate of 60 words per minute (wpm) in order to type 60 words in one minute.
What is Unit conversion?A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).
To express Morag's typing speed as a unit rate, we would divide the number of words by the number of minutes.
Therefore, the unit rate for Morag typing 60 words in one minute would be 60 words per minute (60 wpm).
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How do you solve an inequality
Answers
Answer:
you solve an inequality by doing the inverse equation on each side of the equation.
Step-by-step explanation:
A 27 oz bottle of a new soda costs $2.25. What is the unit rate, rounded to the nearest tenth of a cent?
Answers
1 / x =
Divide 2.25 by 27 to get
.08 dollars per ounce
The unit rate is the cost per ounce of soda. By dividing the total cost by the total ounces, we get the price per ounce in dollars ($0.08333), and converting this to cents gives us $8.3 cents per ounce.
Explanation:The term unit rate refers to a rate in which the second term is 1. In this case, we want to find out how much 1 ounce of soda costs.
First, you want to divide the total cost of the bottle by the total ounces in the bottle. So you divide $2.25 by 27. The answer you get is the price of one ounce of soda in dollars. When calculating it, you get approximately $0.08333.
To get the rate in cents, convert the dollars to cents by multiplying by 100 (since 1 dollar is 100 cents). The answer ($8.33) is the cost of one ounce to the nearest tenth of a cent.
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how many solutions are in 6x+4x-6=24+9x
Answers
To solve this, first combine like terms.
6x + 4x - 6 = 24 + 9x
10x - 6 = 24 + 9x
Then move all like terms to one side.
10x - 9x = 24 + 6
x = 30
x=30
..........
Hi, How do you find the first and second derivatives of the function.
y=(x^2-7/63x) (x^4+1/x^3)
I think for the first derivative dy/dx it's 2/63x-3/63x^-3+4/9x^-5 but I'm not sure, and I have no clue for the second derivative d^2y/dx^2.
Answers
The first hand derivative of the function is [tex]6x^5 - \frac{35}{63}x^4 - \frac{1}{x^2} - \frac{4}{63x^3}[/tex] and the second derivative is [tex]30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]. To find the first derivative, apply the product rule to the given function. Then, differentiate the first derivative to obtain the second derivative. Simplify each step carefully.
To find the first derivative of the given function [tex]y = \left( x^2 - \frac{7}{63}x \right) \left( x^4 + \frac{1}{x^3} \right)[/tex], we'll use the product rule, which states that if [tex]y = u(x) \cdot v(x)[/tex], then [tex]y' = u' \cdot v + u \cdot v'[/tex].
First, define u(x) and v(x) as following:
[tex]u(x) = x^2 - \frac{7}{63}x = x^2 - \frac{1}{9}x[/tex][tex]v(x) = x^4 + \frac{1}{x^3}[/tex]Compute u'(x):
[tex]u'(x) = 2x - \frac{1}{9}[/tex]Compute v'(x):
[tex]v'(x) = 4x^3 + (-3)x^{-4} = 4x^3 - \frac{3}{x^4}[/tex]Apply the product rule: [tex]y' = u' \cdot v + u \cdot v'[/tex]
Thus,
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex]Simplify this expression step-by-step to find the first derivative.
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= \left(2x \cdot x^4 + 2x \cdot \frac{1}{x^3} - \frac{1}{9} \cdot x^4 - \frac{1}{9} \cdot \frac{1}{x^3} \right)[/tex][tex]&\quad + \ \left( x^2 \cdot 4x^3 - x^2 \cdot \frac{3}{x^4} - \frac{1}{9}x \cdot 4x^3 + \frac{1}{9}x \cdot \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= 2x^5 + \frac{2}{x^2} - \frac{1}{9}x^4 - \frac{1}{9x^3} \\[/tex] [tex]&\quad + \ 4x^5 - \frac{3}{x^2} - \frac{4}{9}x^4 + \frac{1}{3x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{1}{x^2} - \frac{5}{9}x^4 + \frac{2}{9x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{5}{9}x^4 - \frac{1}{x^2} + \frac{2}{9x^3}[/tex]To find the second derivative, differentiate the first derivative, carefully differentiating each term:
[tex]y'' &= \frac{d}{dx}\left( 6x^5 \right) - \frac{d}{dx}\left( \frac{5}{9}x^4 \right) - \frac{d}{dx}\left( \frac{1}{x^2} \right) + \frac{d}{dx}\left( \frac{2}{9x^3} \right) \\[/tex][tex]y''[/tex] [tex]&= 30x^4 - \frac{5}{9} \cdot 4x^3 - \left( -2x^{-3} \right) + \left( -\frac{2}{9} \cdot 3x^{-4} \right) \\[/tex][tex]y''[/tex] [tex]&= 30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]So, for the function [tex]y = \left( x^2 - \frac{7}{63}x \right) \left( x^4 + \frac{1}{x^3} \right)[/tex], we have:
First derivative [tex](y')[/tex] [tex]&= 6x^5 - \frac{5}{9}x^4 - \frac{1}{x^2} + \frac{2}{9x^3}[/tex]Second derivative [tex](y'')[/tex] [tex]&= 30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]Find the gradient of the function at the given point. function point f(x, y, z) = x2 + y2 + z2 (3, 9, 8)
Answers
Answer:
[tex]\displaystyle \nabla f(3, 9, 8) = 6 \hat{\i} + 18 \hat{\j} + 16 \hat{\text{k}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Multivariable Calculus
Differentiation
Partial DerivativesDerivative NotationGradient: [tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]
Gradient Property [Addition/Subtraction]: [tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]
Gradient Property [Multiplied Constant]: [tex]\displaystyle \nabla \big[ \alpha f(x) \big] = \alpha \nabla f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x, y, z) = x^2 + y^2 + z^2[/tex]
[tex]\displaystyle P(3, 9, 8)[/tex]
Step 2: Find Gradient
[Function] Differentiate [Gradient]: [tex]\displaystyle \nabla f = \frac{\partial}{\partial x} \Big( x^2 + y^2 + z^2 \Big) \hat{\i} + \frac{\partial}{\partial y} \Big( x^2 + y^2 + z^2 \Big) \hat{\j} + \frac{\partial}{\partial z} \Big( x^2 + y^2 + z^2 \Big) \hat{\text{k}}[/tex][Gradient] Rewrite [Gradient Property - Addition/Subtraction]: [tex]\displaystyle \nabla f = \bigg[ \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial x}(y^2) + \frac{\partial}{\partial x}(z^2) \bigg] \hat{\i} + \bigg[ \frac{\partial}{\partial y}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial y}(z^2) \bigg] \hat{\j} + \bigg[ \frac{\partial}{\partial z}(x^2) + \frac{\partial}{\partial z}(y^2) + \frac{\partial}{\partial z}(z^2) \bigg] \hat{\text{k}}[/tex][Gradient] Differentiate [Derivative Rule - Basic Power Rule]: [tex]\displaystyle \nabla f = 2x \hat{\i} + 2y \hat{\j} + 2z \hat{\text{k}}[/tex][Gradient] Substitute in point: [tex]\displaystyle \nabla f(3, 9, 8) = 2(3) \hat{\i} + 2(9) \hat{\j} + 2(8) \hat{\text{k}}[/tex][Gradient] Evaluate: [tex]\displaystyle \nabla f(3, 9, 8) = 6 \hat{\i} + 18 \hat{\j} + 16 \hat{\text{k}}[/tex]∴ the gradient of the function at the given point is <6, 18, 16>.
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Topic: Multivariable Calculus
Unit: Directional Derivatives
Kristina invests $5,000 at 15% simple interest for 2 years.How much interest did Kristina earn over the 2 years?
Answers
SI = PRT/100
=( 5000 × 15 × 2)/100
= 50×15×2= 1500$
Calculate the mean of the number set 5 10 12 4 6 11 13 5
Answers
5+10+12+4+6+11+13+5 then divide that by 8
The answer to your question is: 8.25
Write a problem saying a single load of laundry cost $2 and a double load costs $4 the machine only accept quarters what is the answer
Answers
The problem is: A laundromat charges $2 for a single load of laundry and $4 for a double load. The machine only accepts quarters. How many quarters are needed to wash two double loads of laundry?
To solve this problem, we first need to determine the total cost of washing two double loads. Since each double load costs $4, two double loads will cost 2 * $4 = $8.
Next, we need to determine how many quarters are in $8. Since there are 4 quarters in a dollar, there are 4 * 8
= 32 quarters in $8.
Therefore, 32 quarters are needed to wash two double loads of laundry
How do i know that the variable x has a uniform distribution function?