Use synthetic division to find the quotient and remainder when2x^3+ 9x^2- 8x+ 4 is divided by x - 2
Answers
Solution:
Given;
[tex]\frac{2x^3+9x^2-8x+4}{x-2}[/tex]Using Synthetic division;
Thus, the solution is;
[tex]\frac{2x^{3}+9x^{2}-8x+4}{x-2}=2x^2+13x+18+\frac{40}{x-2}[/tex]The quotient is;
[tex]2x^2+13x+18[/tex]The remainder is;
[tex]18[/tex]
Related Questions
solve 2x^2+5x-3>0 quadratic inequalities
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The solution set of the inequality 2 · x² + 5 · x - 3 > 0 is (- ∞, - 3) ∪ (1 / 2, + ∞).
How to solve a quadratic inequality
Herein we find a quadratic inequality, whose solution set can be found by factoring the expression and determine the interval where the expression is greater than zero. Initially, we use the quadratic formula to determine the roots of the quadratic function:
2 · x² + 5 · x - 3 = 0
x₁₂ = [- 5 ± √[5² - 4 · 2 · (- 3)]] / (2 · 2)
x₁₂ = (- 5 ± 7) / 4
x₁ = 1 / 2, x₂ = - 3
Then, the factored form of the inequality is:
(x - 1 / 2) · (x + 3) > 0
In accordance with the law of signs, we must look for that intervals such that: (i) (x - 1 / 2) > 0, (ii) (x + 3) > 0, (ii) (x - 1 / 2) < 0, (x + 3) < 0. Then, the solution set of the quadratic inequality is:
Inequality form - x > 1 / 2 ∨ x < - 3
Interval form - (- ∞, - 3) ∪ (1 / 2, + ∞)
The solution set of the inequality is (- ∞, - 3) ∪ (1 / 2, + ∞).
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You roll a die. What is the probability that you’ll get a number less than 3?0.3330.50.6670.75
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Recall that the numbers in a die are 1,2,3,4,5,6.
[tex]S=\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Hence the number of possible outcomes is 6.
[tex]n(S)=6[/tex]We need a number less than 3. Let A be this event.
[tex]A=\mleft\lbrace1,2\mright\rbrace[/tex]The favorable outcome is 2.
[tex]n(A)=\mleft\lbrace1,2\mright\rbrace[/tex]Since there are 1,2 less than 3 in a die.
[tex]P(A)=\frac{Favourable\text{ outcomes}}{\text{Total outcomes}}=\frac{n(A)}{n(S)}[/tex]Substitute n(A)=2 and n(S)=6, we get
[tex]P(A)=\frac{2}{6}=\frac{1}{3}=0.333[/tex]Hence the required probability is 0.333.
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Solve the inequality
-1/3x - 12 > 21 or -6x + 10 < -2
x < ? or x > ?
solve for both
Answers
Answer:
x < 2 or x > -11
Step-by-step explanation:
b. 1. add 12 to both sides to get -1/3x > 33
2. multiply by -3/1 to both sides to get x > -11
a. 1) subtract 10 to both sides
2) divide by -6 to both sides
5 Which equations have the same value of x as 6 2 3 -9? Select three options. -9(6) 5x+4=-54 5x+4=-9 5x=-13 5X=-58
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The given equation is-
[tex]\frac{5}{6}x+\frac{2}{3}=-9[/tex]If we multiply the equation by 6, we would have the same value for the variable x since we are multiplying the same number on each side. So, the second choice is an equivalent equation to the given one.
Let's multiply by 6.
[tex]\begin{gathered} 6\cdot\frac{5}{6}x+6\cdot\frac{2}{3}=-9\cdot6 \\ 5x+4=-54 \end{gathered}[/tex]So, the third expression is also an equivalent expression.
Then, let's subtract 4 on each side.
[tex]\begin{gathered} 5x+4-4=-54-4 \\ 5x=-58 \end{gathered}[/tex]The last choice is also an equivalent expression.
Therefore, the right choices are 2, 3, and 6.Find the sum of the arithmetic series 31+37 +43 +49 +... where n=8,OA. 416B. 1668OC. 832D. 834Reset Selection
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} a_1=31 \\ n=8 \\ d=37-31=6 \end{gathered}[/tex]STEP 2: Write the formula for finding sum of arithmetic series
STEP 3: Find the sum of the series
By substitution,
[tex]\begin{gathered} S_8=\frac{8}{2}[2(31)+(8-1)6] \\ S_8=4(62+42) \\ S_8=4(104)=416 \end{gathered}[/tex]Hence, the sum is 416
A rectangular garden plot measure 3.1 meters by 5.6 meters as shown Find the area of the garden in square meters
Answers
Given:
Length(l) of the garden is 3.1 meters
Width(w) of the rectangular garden is 5.6 meters
[tex]\begin{gathered} \text{Area of the garden=}l\times w \\ =3.1\times5.6 \\ =17.36 \end{gathered}[/tex]Area of the garden is 17.36 square meters.
Hey everybody! Can somebody help me solve this problem? I don't need a big explanation just the answer and a brief explanation on how you get it! Look at photo for problem.
Answers
Given the ordered pairs:
(-12, -16), (-3, -4), (0, 0), (9, 12)
Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:
[tex]y=k\cdot x[/tex]Using the ordered pairs:
[tex]\begin{gathered} -16=-12k\Rightarrow k=\frac{4}{3} \\ -4=-3k\Rightarrow k=\frac{4}{3} \\ 0=0\cdot k\text{ (this means that it is correct)} \\ 12=9k\Rightarrow k=\frac{4}{3} \end{gathered}[/tex]We conclude that the constant of variation is:
[tex]k=\frac{4}{3}[/tex]15 points?Solve for A 5/A = P A = ???? That’s all it saysPlease state what A is.
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2. The product of two consecutive odd numbers is 143. Find the numbers. (Hint: If the first odd number is x, what is the next odd number?)
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Step-by-step explanation:
we have the 2 numbers x and (x+2).
x × (x + 2) = 143
x² + 2x = 143
x² + 2x - 143 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case this is
x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
x1 = -1 + 12 = 11
x2 = -1 - 12 = -13
so, we have 2 solutions : 11 and 13, -13 and -11
11× 13 = 143
-11×-13 = 143
Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
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A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
A gift box is 12 inches long 8 inches wide and 2 inches high how much wrapping paper is needed to wrap the gift box
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Given that a box is 12 inches long 8 inches wide and 2 inches high, the area of wrapping paper needed to wrap the gift box is equal to the total surface area of the box.
[tex]\begin{gathered} \text{length l =12 inches} \\ \text{width w = 8 inches} \\ \text{ height h = 2 inches} \end{gathered}[/tex]The total surface area of the box can be calculated using the formula;
[tex]undefined[/tex]The graph models the heights, in feet, of two objectsdropped from different heights after x seconds.Which equation represents g(x) as a transformation off(x)?y45+O g(x) = f(x) -5O g(x) = f(x-5)O g(x) = f(x) + 5O g(x) = f(x + 5)40+35y = f(x)30-25+20-15+10+5+ly = g(x)0.5 1.0 1.5 20
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For this problem we know that y=f(x) at x=0 is 5 units above y=g(x). So then the best solution for this case it seems to be:
[tex]f(x)=g(x)+5[/tex]And solving for g(x) we got:
[tex]g(x)=f(x)-5[/tex]Exercise 2 Find a formula for Y in terms of X
Answers
Given:
y is inversely proportional to square of x.
The equation is written as,
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ y=\frac{c}{x^2}\ldots\ldots\ldots c\text{ is constant} \end{gathered}[/tex]Also y = 0.25 when x = 5.
[tex]\begin{gathered} y=\frac{c}{x^2} \\ 0.25=\frac{c}{5^2} \\ 25\times0.25=c \\ c=\frac{25}{4} \end{gathered}[/tex]So, the equation of y interms of x is,
[tex]y=\frac{25}{4x^2}[/tex]When x increases,
[tex]\begin{gathered} \lim _{x\to\infty}y=\lim _{x\to\infty}(\frac{25}{4x^2}) \\ =\frac{25}{4}\lim _{x\to\infty}(\frac{1}{x^2}) \\ =0 \end{gathered}[/tex]Hence, the value of x increases then y decreases.
A website recorded the number y of referrals it received from social media websites over a 10-year period. The results can be modeled by y = 2500(1.50), where t is the year and 0 ≤ t ≤9.Interpret the values of a and b in this situation.O a represents the number of referrals after 9 years; b represents the growth factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the decay factor of the number of referralseach year.O a represents the number of referrals after 9 years; b represents the decay factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the growth factor of the number ofreferrals each year.What is the annual percent increase?The annual percent increase is%.
Answers
In this problem
we have an exponential growth function
[tex]y=2500(1.50)^t[/tex]where
a=2500 ----> initial value of the number of referrals at the start of the model
b=1.50 ---> the base of the exponential function (growth factor of the number of referrals each year
therefore
The answer Part 1 is the last option
Part 2
Find out the annual percent increase
we know that
b=1+r
b=1.50
1.50=1+r
r=1.50-1
r=0.50
therefore
r=50%
The annual percent increase is 50%Identify the values of a, b, and c for the quadratic equation given:y=-x2 +9a =b =C=
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Question:
Solution:
A quadratic Equation in Standard Form is given by the following formula:
[tex]ax^2+bx\text{ + c = 0}[/tex]now, the given equation is
[tex]y=-x^2+9[/tex]this is equivalent to:
[tex]f(x)=-x^2+9[/tex]According to the Quadratic Equation in Standard Form, we can conclude that
[tex]a\text{ = -1}[/tex][tex]b\text{ = 0}[/tex]
and
[tex]c\text{ = 9}[/tex]solver for r: C=2(pie)r
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We have the following equation:
[tex]C=2\pi r[/tex]We want to rewrite it in a way 'C' is a function of 'r'. We can accomplish that, if we divide both sides by 2pi.
[tex]2\pi r=C\Rightarrow r=\frac{C}{2\pi}[/tex]From this, we have our result.
[tex]r=\frac{C}{2\pi}[/tex]One angle measures 140°, and another angle measures (5k + 85)°. If the angles are vertical angles, determine the value of k.
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The value of k when one angle measures 140°, and another angle measures (5k + 85)° and if the angles are vertical angles is 11.
What is vertical angles?
Vertical angles are angles opposite each other where two lines cross.
Note: Vertical angles are equal.
To calculate the value of k, we use the principle of vertical angle
From the question,
140 = (5k+85)°Solve for k
5k = (140-85)5k = 55Divide both side by the coefficient of k (5)
5k/5 = 55/5k = 11Hence, the value of k is 11.
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what is the area if one of the triangular side of the figure?
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Compound Shape
The shape of the figure attached consists on four triangles and one square.
The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:
[tex]A_t=\frac{BH}{2}[/tex]Calculating:
[tex]A_t=\frac{12\cdot10}{2}=60[/tex]The area of each triangle is 60 square cm.
Now for the square of a side length of L=12.
The area of a square of side length a, is:
[tex]A_s=a^2[/tex]Calculate the area of the square:
[tex]A_s=12^2=144[/tex]The total surface area is:
A = 60*4 + 144
A= 240 + 144
A = 384 square cm
suppose that you have two square garden plots: One is 10’ x 10’ and the other is 15 x 15’. You want to cover both gardens with a 1 inch layer of mulch. If the 10 x 10 garden took 3 1/2 bags of mulch, could you calculate how many bags of mulch you need for the 15 x 15 garden by setting up the following proportion 3.5/10 = X/15. explain clearly why or why not. If the answer is no is there another proportion that you could set up? it may help you to make drawings of the Gardens
Answers
Answer:
Step-by-step explanation:
This question can be solved using a rule of three.
For each configuration, we need the perimeter and the amount of bags of mulch.
For a square of side s, the perimeter is P = 4s
If the 10 x 10 garden took 3 1/2 bags of mulch:
10x10 means that s = 10.
So the perimeter is:
P = 4*10 = 40
The number of bags of mulch is:
3 1/2 = 3 + (1/2) = 3 + 0.5 = 3.5
15 x 15 garden
15x15 means that s = 15.
The perimeter is: P = 4*s = 4*15 = 60.
The number of bags is X.
Now applying the rule of three:
With the number of bags and the perimeter.
3.5 bags - 40'
X bags - 60'
Now we apply cross multiplication:
[tex]undefined[/tex]Find the minimum weight resistance possible for A 230 pound man
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Hello there. To find this minimum weight resistance, we need to convert the percentage value to decimals and multiply it by the weight of the person.
8% converted to decimals is equal to 0.08.
Now, multiply it by the weight of the 230 pound man
0.08 * 230 = 18.4 pounds
This is the minimum weight resistance this U gym offers to the customers.
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,where t is measured in seconds.(A)(i) Find the average velocity over the time interval [3,4].Average Velocity = ___ meters per second(ii) Find the average velocity over the time interval [3.5,4].Average Velocity=____meters per second(iii) Find the average velocity over the time interval [4,5].Average Velocity= ____meters per second(iv) Find the average velocity over the time interval (4,4.5] Average Velocity = ____meters per.(B) Find the instantaneous velocity when t=4.Instantaneous velocity= ____ meters per second.
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Given
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,
Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water, Marla's eye-level is 5.5 feet, and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, tothe nearest foot?
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SOLUTION
Let us make a diagram to interpret the question
from the diagram above, we can make the right-angle triangle as follows
So we can use SOHCAHTOA to solve this. The opposite side to the angle 52 degrees is 45.5 ft, this is gotten by adding the height of the cliff to Maria's height from her feet to her eyes.
The adjacent side is d, that is the distance from the seal to the cliff, so we have
[tex]\begin{gathered} TOA\text{ tan}\theta\text{ = }\frac{opposite}{adjacent} \\ tan52\degree=\frac{45.5}{d} \\ cross\text{ multiply, we have } \\ tan52\degree d=45.5 \\ d=\frac{45.5}{tan52} \\ d=35.54849 \end{gathered}[/tex]Hence the answer is 36 foot to the nearest foot
$(20) = 4x^2+ 5x – 3 g(x) = 4x^3 – 3x^2 + 5 Find (f + g)(x)
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The value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
The given functions are f(x)=4x²+ 5x - 3 and g(x)=4x³ - 3x² + 5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, (f+g)(x)=f(x)+g(x)
= 4x²+ 5x - 3+4x³ - 3x² + 5
= 4x³+4x²- 3x²+5x+5-3
= 4x³+x²+5x+2
Therefore, the value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
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What is the slope of the line that passes through the points (6,-10) and (3,-13)? Write in simplist form
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Use the slope formula to find the slope of a line that goes through two points:
[tex]\begin{gathered} \text{Coordinates of two points}\rightarrow\text{ }(x_1,y_1),(x_2,y_2) \\ \text{Slope of a line through those points}\rightarrow m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitute the coordinates (6,-10) and (3,-13) into the slope formula:
[tex]\begin{gathered} m=\frac{(-13)-(-10)}{(3)-(6)} \\ =\frac{-13+10}{3-6} \\ =\frac{-3}{-3} \\ =1 \end{gathered}[/tex]Therefore, the slope of a line that passes through those points, is 1.
3. An equation that crosses the y-axis at -5 and crosses the x-axis at 24. An equation that crosses the y-axis at -5 and crosses the x-axis at -65. An equation that crosses the y-axis at -5 and crosses the point (2,3)
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We need to find the equation of the line which:
• crosses the y-axis at -5
,• crosses the x-axis at 2
The y-axis cutting point is (0,-5)
The x-axis cutting point is (2,0)
The equation of line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-axis cutting point
m is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
y_2 = 0
y_1 = -5
x_2 = 2
x_1 = 0
So, slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0--5}{2-0}=\frac{0+5}{2}=\frac{5}{2}[/tex]We got m, we also know b.
The y cutting point is -5, so b = -5
The equation is:
[tex]y=\frac{5}{2}x-5[/tex]The graph would look like:
More clear version:
Graph the line with the given slope m and y-intercept b.
m = 4, b = -5
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Answer:
Step-by-step explanation:
What we know:
m = 4, b = -5
y = mx + b where m is the gradient/slope and b is the y-intercept
Substitute m and b values:
y = 4x + -5 which is the same as y = 4x - 5
Substitute all x values to find y coordinate:
When x = -7, y = (4 x -7) - 5 = -33
When x = -6, y = (4 x -6) - 5 = -29
When x = -5, y = …
Continue for all x values
An 80% confidence interval for a proportion is found to be (0.27, 0.33). Whatis the sample proportion?
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Step 1
Given;
Step 2
When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).
[tex]\begin{gathered} Sample\text{ proportion=}\hat{p} \\ \hat{p}\pm margin\text{ error=cofidence interval} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} Let\text{ }\hat{p}=x \\ Margin\text{ of error=y} \\ x-y=0.27 \\ x+y=0.33 \end{gathered}[/tex]checking properly, the sample proportion =0.30, because
[tex]\begin{gathered} 0.30-0.03=0.27 \\ 0.30+0.03=0.33 \end{gathered}[/tex]Answer; Option D
[tex]0.30[/tex]Which points are included in the solution Set of the systems of equations graphed below?
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Given:
Required:
We need to find the points are included in the solution
Explanation:
Recall that the solution of the system of inequalities is the intersection region of all the solutions in the system.
The points G and F lie inside the intersection.
The points in the solution are G and F.
Final answer:
Points F and G.
Find the interval in which the following quadratic is decreasing.
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The quadratic is decreasing in the interval in which the y values decrease with the increase in x values.
In the interval, (-∞, 0), the y values decrease with increase in x values.
Hence, the quadratic is decreasing in the interval (-∞, 0),
Convert the function p(x) = 2(x – 4)(x + 3)
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Expanding the expression,
[tex]\begin{gathered} p(x)=2(x-4)(x+3) \\ \rightarrow p(x)=2(x^2+3x-4x-12) \\ \rightarrow p(x)=2(x^2-x-12) \\ \rightarrow p(x)=2x^2-2x-24 \end{gathered}[/tex]We get that:
[tex]p(x)=2x^2-2x-24[/tex]