Rewrite (4x4 + 8x2 + 3)/(4x2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.
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ANSWER
(x² + 2) + 3/4x²
EXPLANATION
Since the divisor is a single-term polynomial, to write the answer in the requested form, we can distribute the divisor into each of the terms of the dividend,
[tex]\frac{4x^4+8x^2+3}{4x^2}=\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}[/tex]And simplify,
[tex]\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}=(x^2^{}+2)^{}+\frac{3}{4x^2}[/tex]Hence, the answer is (x² + 2) + 3/4x².
Related Questions
Select the correct answer.In triangle ABC, AB = 12, BC = 18, and m B = 75° what are the approximate length of side AC and measure of A?O AAC = 18.9;m SA = 66.99OB.OC.AC = 20.3 m A = 34.8°AC = 18.9: m A = 37.8°AC = 20.31 m A = 58.9°ODResetNext
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Draw the triangle ABC.
Determine the length of side AC.
[tex]\begin{gathered} (AC)^2=(AB)^2+(BC)^2-2\cdot AB\cdot BC\cdot\cos B \\ =(12)^2+(18)^2-2\cdot12\cdot18\cdot\cos 75 \\ =356.190 \\ AC=\sqrt[]{356.19} \\ =18.87 \\ \approx18.9 \end{gathered}[/tex]So side AC is equal to 18.9 m.
Determine the measure of angle A.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{18.9}{\sin75}=\frac{18}{\sin A} \\ \sin A=\frac{18}{18.9}\cdot\sin 75 \\ A=\sin ^{-1}(0.9199) \\ =66.9 \end{gathered}[/tex]So mesure of angle A is 66.9 degree.
Which of the following expressions represents the simplified version of the expression below
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we have the expression
[tex](5x^3y^2-3xy+2)+(2x^3y^2-3x^2y^2+4xy-7)[/tex]step 1
Combine like terms
so
[tex](5x^3y^2+2x^3y^2)+(-3xy+4xy)+(2-7))-3x^2y^2[/tex][tex](7x^3y^2)+(xy)+(-5)-3x^2y^2[/tex]therefore
the answer is the second optiongraphing a parabola of the form y=ax squared 2
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The graph of the parabola given by the equation:
[tex]y=\frac{1}{4}x^2[/tex]has a vertex when y=0 which happens iff
[tex]\begin{gathered} \frac{1}{4}x^2=0 \\ x^2=0 \\ x=0 \end{gathered}[/tex]Therefore the graph is:
The vertex has coordinates (0,0). Now, two points to the left of the vertex that are on the parabola have coordinates (-2,1) and (-4,4). Two points that are to the right of the parabola have coordinates
Got cut off while saying thanks to last tutorial t bg at helped me.
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We are given the following equation.
[tex]A=p+prt[/tex]we are asked to find an equation for "t". To do that, we are going to solve for "t", first by subtracting "p" on both sides, like this:
[tex]\begin{gathered} A-p=p-p+prt \\ A-p=prt \end{gathered}[/tex]Now we will divide both sides of the equation by "pr"
[tex]\begin{gathered} \frac{A-p}{pr}=\frac{prt}{pr} \\ \frac{A-p}{pr}=t \end{gathered}[/tex]A thus we found a relationship for "t".
Find the general equation of the circle having a diameter with endpoints at A(-2,3) and B(4,5).
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The equation of a circle whose center is (a, b) and which has a radius r is given as:
(x - a)² + (y - b)² = r²
For the circle with endpoints at A(-2,3) and B(4,5).
The center (a, b) of the circle is calculated as:
[tex]\begin{gathered} a=\frac{-2+4}{2} \\ a=\frac{2}{2} \\ a=1 \\ b=\frac{3+5}{2} \\ b=\frac{8}{2} \\ b=4 \end{gathered}[/tex]The center, (a, b) = (1, 4)
The diameter(D) of the circle is the distance between the endpoints A(-2,3) and B(4,5).
[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(4-(-2))^2+(5-3)^2} \\ D=\sqrt[]{(4+2)^2+2^2} \\ D=\sqrt[]{6^2+2^2} \\ D=\sqrt[]{36+4} \\ D=\sqrt[]{40} \end{gathered}[/tex]The diameter of the circle = √40
Radius = Diameter / 2
r = d/2
r = √40 / 2
Substituting a = 1, b = 4, and r = √40 / 2 into the general equation of a circle:
[tex]\begin{gathered} (x-1)^2+(y-4)^2=(\frac{\sqrt[]{40}}{2})^2 \\ (x-1)^2+(y-4)^2=\frac{40}{4} \\ (x-1)^2+(y-4)^2=\text{ 10} \end{gathered}[/tex]The general equation of the circle is:
[tex](x-1)^2+(y-4)^2=\text{ 10}[/tex]If 14 people want to share 24 oranges equally, how many oranges will each person get?
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Given data:
The total number of oranges is: 24
The total number of people is: 14
The expression to calculate the number of oranges a person has is,
[tex]\begin{gathered} \frac{Total\text{ number of oranges}}{\text{Total number of people}}=\frac{24}{14} \\ =1+\frac{5}{7} \\ =1.714\text{ oranges.} \end{gathered}[/tex]Thus, each person gets 1 orange and 5/7 of an orange.
1. Write an equation of the line that is parallel to the linewhose equation is 4y + 9 = 2x and passes through thepoint (7,2)
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First let's put the equation 4y + 9 = 2x in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. So we have that:
[tex]\begin{gathered} 4y+9=2x \\ 4y=2x-9 \\ y=\frac{2x-9}{4} \\ y=\frac{1}{2}x-\frac{9}{4} \end{gathered}[/tex]The slope of this equation is 1/2. In order to the second line be parallel to this line, it has to have the same slope. Also, since the second line passes through the point (7, 2), we have:
[tex]\begin{gathered} y=\frac{1}{2}x+b \\ (7,2)\colon \\ 2=\frac{1}{2}\cdot7+b \\ 2=\frac{7}{2}+b \\ b=2-\frac{7}{2}=\frac{4-7}{2}=-\frac{3}{2} \end{gathered}[/tex]So the second equation is:
[tex]y=\frac{1}{2}x-\frac{3}{2}[/tex]Select the correct answer.378Convert4 to rectangular form.OA.Y = -1OB.y = 1O C.y =O D.O E.I = -1
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The Solution.
Assuming the radius is 1.
[tex]x=\cos (\frac{3\pi}{4})=-\sin (\frac{3\pi}{4})[/tex]Therefore,
[tex]\begin{gathered} x=-y \\ or \\ y=-x \end{gathered}[/tex]So, the correct answer is option D
11. You want to tape five posters on a wall so that the spaces between posters are the same. You alsowant the spaces at the left and right of the group of posters to be three times the space between anytwo adjacent posters. The wall is 15 feet wide and the posters are 1.5 feet wide.a. Draw a diagram that represents theb. Write and solve an equation to find howsituation.to position the posters.
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Let's use the variable x to represent the spaces between posters.
So the spaces at the left and right of the group will be 3x.
Drawing the diagram, we have:
Writing an equation to solve for x, we have:
[tex]\begin{gathered} 3x+3x+1.5+1.5+1.5+1.5+1.5+x+x+x+x=15 \\ 6x+7.5+4x=15 \\ 10x+7.5=15 \\ 10x=15-7.5 \\ 10x=7.5 \\ x=\frac{7.5}{10} \\ x=0.75 \end{gathered}[/tex]So the space between each pair of posters is 0.75 feet.
Find the unit price. If necessary, round your answer to the nearest cent. You would enter an answer like $0.49/pound, the value (like 0.49) in the first box and the appropriate unit (like pound) in the second boX $8.39 for 12 kg
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For a determined product you can buy 12Kg for $8.39. To determine how much 1Kg of said product costs, you can apply cross multiplication to calculate it:
If 12 Kg cost $8.39
1 Kg costs $x:
[tex]\begin{gathered} \frac{8.39}{12}=\frac{x}{1} \\ \frac{8.39}{12}=x \\ x=0.699\cong0.70 \end{gathered}[/tex]The cost is $0.70/Kg
10. (09.02 MC)Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?[p and q are integers) (5 points)
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To transform
[tex]x^2+8x+15=0[/tex]Make it a perfect square
since 8x/2 = 4x, then
We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1
[tex]\begin{gathered} x^2+8x+(15+1)-1=0 \\ x^2+8x+16-1=0 \end{gathered}[/tex]Now we will make the bracket to the power of 2
[tex]\begin{gathered} (x^2+8x+16)-1=0 \\ (x+4)^2-1=0 \end{gathered}[/tex]Add 1 to both sides
[tex]\begin{gathered} (x+4)^2-1+1=0+1 \\ (x+4)^2=1 \end{gathered}[/tex]The answer is C
Find the reference angle for a rotation of 334º.
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We are asked to find the reference angle for a standard angle of 334°
Recall that the reference angle is the angle that is measured with respect to the x-axis.
First, we need to find out in which quadrant the given standard angle lies.
334° lie in the 4th quadrant (180° to 360°)
So, the reference angle can be found as
[tex]\begin{gathered} \theta^{\prime}=360\degree-\theta \\ \theta^{\prime}=360\degree-334\degree \\ \theta^{\prime}=26\degree \end{gathered}[/tex]Therefore, the reference angle is 26°
given expression :4x-2y=11find the missing coordinate in ordered pair (-3,?)
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Equations
We are given the equation:
4x - 2y = 11
And it's required to find the missing coordinate in the ordered pair (-3, ?).
The first coordinate is x=-3, thus we need to calculate the y-coordinate by solving the equation for y, using the value of x.
Substituting:
4(-3) - 2y = 11
Operating:
-12 - 2y = 11
Adding 12:
-2y = 23
Dividing by -2:
y = 23/(-2)
y = -23/2
The ordered pair is:
[tex](-3,-\frac{23}{2})[/tex]The radius of a circle is 7 in. Find its area in terms of pi
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Answer:
49π
Step-by-step explanation:
πr^2 <---- The formula for the area of a circle.
let "a" represent area of the circle.
a = π × 7^2
Simplify by the use of the exponent.
7^2 = 49
Your answer:
49π
A Ferris wheel has a radius of 12 meters and takes 16 seconds to complete one full revolution. The seat you are riding in, takes 4 seconds to reach the top which is 28 meters above the ground. Write a sine or cosine equation for the height of your seat above the ground as a function of time.
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EXPLANATION
Given that the wheel has a radius of 12 meters and it takes 16 seconds to complete one full revolution, if we call t to the time in seconds and since the top of the wheel is 28 meters above the ground, the bottom is 4 meters above the ground.
Now, we need to consider that the equation that applies is the following:
[tex]height=16-12\cos \theta[/tex]As theta is the angle between the radius from the center of the wheel to the bottom and the rider's coordinate, we need to represent the angle as a function of the time. We have that it takes 16 second to complete one full revolution, this means that the wheel rotates 360 degrees in 16 seconds. Now, we can use the angular velocity: w= 360/16 = 22.5 degrees/s
Then, we need to represent the angular velocity in radians, as 360 degrees is 2π radians, the obtained angular velocity would be: w = 2π/16 = π/8 rad/s
Hence the appropiate equation as a function of the time would be as follows:
[tex]h=16-12\cdot\cos (\frac{\pi t}{8})[/tex]
each student in a class received some textbooks one third of these were english books which expresión shows how manys english books each student received
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Let x be the total number of books each student recieved, since one third of them is an english book we have that the expression is:
[tex]\frac{1}{3}x[/tex]The peak of Mt. Whitney in California is 14,494 feet above sea level. Write this number as an integer.
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The peak of the mountain is 14, 494 ft above sea level therefore the number can be represented as follows as an integer
[tex]+14,494\text{ feet}[/tex]The mountain is plus 14,494 ab
Flnd the value of x for the triangle or rectangle. Then find the length of the sides of the triangle or rectangle.Q1: Perimeter = 18 meters Q2: Perimeter = 23 feet
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The perimeter of a rectangle is given by:
P = 2w + 2h
Where:
w = width = 2x
h = height = x
P = 18
Replacing the data into the equation:
18 = 2(2x) + 2(x)
18 = 4x + 2x
18 = 6x
Solving for x:
x = 18/6
x= 3
Therefore:
w = 2(3) = 6m
h = 3m
---------------------------------------------------------------------------------
P = x + 2x + (x + 3)
23 = 3x + x + 3
23 = 4x + 3
Solving for x:
23 - 3 = 4x
20 = 4x
20/4 = x
5 = x
Therefore its sides are:
x = 5 ft
2x = 2(5) = 10ft
x + 3 = 5 + 3 = 8ft
Rewrite the following equation in slope-intercept form.6x+y=12Write your answer using integers, proper fractions, and improper fractions in simplest form.
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According to the given data we have the following equation:
6x+y=12
To rewrite the following equation in slope-intercept form we would have to make the following steps:
6x+y=12
Move 6x to the other side, by doing this it would change its sign
So,
y=-6x + 12
So, equation in slope-intercept form would be y=-6x + 12
find the volume of a hemisphere when the diameter is 24 cm. Leave answer in terms of Pi. I had the answer of 1152 which is not correct.
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Explanation
the volume of a hemisphere is given by:
[tex]\text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot r^3[/tex]where r is the radius
then
[tex]\begin{gathered} Diameter=2\text{radius} \\ \frac{\text{Diameter}}{2}=r \\ \frac{24\text{ cm}}{2}=r \\ r=12\text{ cm} \end{gathered}[/tex]now, replace.
[tex]\begin{gathered} \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot r^3 \\ \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot(12\operatorname{cm})^3 \\ \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot1728cm^3 \\ \text{Volume}_{hemisphere}=1152\text{ }\pi cm^3 \end{gathered}[/tex]so, the answer is
[tex]\text{Volume}_{hemisphere}=1152\text{ }\pi cm^3[/tex]I hope this helps you
Completing the square can be use to find the minimum value of the function represented by the equation y=x^2+4x+7. Where is the minimum value of the function located?
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Given:
[tex]y=x^2+4x+7[/tex]Find: the manimum value of the function.
Explanation:
[tex]\begin{gathered} y=x^2+4x+7 \\ y^{^{\prime}}=2x+4 \\ y^{^{\prime}}=0 \\ 2x+4=0 \\ x=-2 \end{gathered}[/tex]ar x=-2,
the function will be
[tex]\begin{gathered} y=x^2+4x+7 \\ y(-2)=(-2)^2+4(-2)+7 \\ =4-8+7 \\ =11-8 \\ =3 \end{gathered}[/tex]Find the volume of the triangular pyramid to the nearest whole number.HighlightA)181 in 3B)361 in 3722 inD)1,082 in 3what's the answer
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the volume of a pyramid is
[tex]V=\frac{1}{3}Ah[/tex]where A is the area of the basis and h is the height of the pyramid.
[tex]A=\frac{12.3\text{ in }\times10\text{ in}}{2}=61.5in^2[/tex]Then the volume is
[tex]\begin{gathered} V=\frac{1}{3}(61.5in^2)(17.6in) \\ =360.8in^3 \end{gathered}[/tex]Then rounding the number, the answer is B).
Good morning I could really use some help solving this problem!
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If the new line passes through the point (-6, 2), let's use x = -6 and y = 2 in the equation and then solve it for 'a':
[tex]\begin{gathered} y=\frac{1}{2}x+a\\ \\ 2=\frac{1}{2}(-6)+a\\ \\ 2=-3+a\\ \\ a=2+3\\ \\ a=5 \end{gathered}[/tex]Therefore the value of 'a' is 5.
Please answer all. How do you determine the dose-specific response of a drug given f(x)?
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__________________
Just replace in value of x in the function
f(0.1) = 100* (0.1)^2 / ((0.1)^2 + 0.17) = (1)/(0.18) = 5.56
f(0.1) = 5.56
f(0.8) = 100* (0.8)^2 / ((0.8)^2 + 0.17) = (64)/(0.81)= 79.01
f(0.8) = 79.01
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derivative of a quotient
Q(x)= f(x)/g(x)
Q'(x)= (f'(x)*g(x) - f(x)*g'(x)) / (g(x) ^2)
[tex]Q^{\prime}\mleft(x\mright)=\frac{f^{\prime}\mleft(x\mright)\cdot g\mleft(x\mright)-f\mleft(x\mright)\cdot g^{\prime}\mleft(x\mright)}{g\mleft(x\mright)^2}[/tex]_____________________________
If f(x) = 100* (x^2) / (x^2 + 0.17),
f'(x)= 100 * ( 2x* (x^2 + 0.17) - 2x*x^2 ) / (x^2 + 0.17)^2
f'(x)= 100 * ( 2x^3 + 2x* 0.17 - 2x^3 ) / (x^2 + 0.17)^2
f'(x)= 100 * ( 2x* 0.17 ) / (x^2 + 0.17)^2
f'(x)= 34*x/ (x^2 + 0.17)^2
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Just replace in value of x in the function
f'(0.1)= 34*(0.1)/ (0.1^2 + 0.17)^2
f'(0.1)= 3.4/ (0.18)^2
f'(0.1)= 104.9
f'(0.8)= 34*(0.8)/ (0.8^2 + 0.17)^2
f'(0.8)= 27.2/ (0.81)^2
f'(0.8)= 41.46
I don’t know the answer for this one and others I need help
Answers
x = 1, y = 3
Explanation:The given system of equations is:
y = 4x - 1.......................(i)
y - 2x = 1..................(ii)
Substitute equation (i) into equation (ii)
4x - 1 - 2x = 1
4x - 2x = 1 + 1
2x = 2
x = 2/2
x = 1
Substitute x = 1 into equation (i)
y = 4x - 1
y = 4(1) - 1
y = 4 - 1
y = 3
The solution to the system of equations is x = 1, y = 3
(U.LL.2) A perfectly cube-shaped smelly candle has a volume of 125 cubic kilometers. What is the area of each side of the smelly candle?
Answers
25 square kilometers
Explanation
the volume of a cube is given by:
[tex]\begin{gathered} \text{Volume}=\text{side}\cdot\text{side}\cdot\text{side} \\ \text{volume}=(side)^3 \end{gathered}[/tex]Step 1
Let
volume = 125 cubic kilometers
Step 2
replace and solve for "side"
[tex]\begin{gathered} \text{Volume= side}^3 \\ 125km^3=side^3 \\ \text{cubic root in both sides} \\ \sqrt[3]{12}5km^3=\text{ }\sqrt[3]{side^3} \\ 5\text{ km= side} \end{gathered}[/tex]Step 3
now, we have the length of a side, to find the area, make
Area of a square is
[tex]\begin{gathered} \text{Area= side }\cdot side \\ \text{Area}=side^2 \end{gathered}[/tex]replace to find the area
Let side = 5 km
[tex]\begin{gathered} \text{Area}=(5km)^2 \\ \text{Area = 25 km}^2 \end{gathered}[/tex]
A medicine is applied to a burn on a patient’s arm. The area of the burn in square centimeters decreases exponentially and is shown on the graph
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EXPLANATION
The function that represents the exponential decay is as follows:
[tex]f(x)=ab^x[/tex]Where a=initial amount and b= decay coefficient
Since the initial amount is 8cm^2, the is the value of the coefficient a is 8.
[tex]f(x)=8b^x[/tex]Now, we need to compute the decay rate:
We can obtain this by substituting two given values, as for instance (0,8) and (1,6) and dividing them:
[tex]\frac{6}{8}=\frac{8}{8}\frac{b^1}{b^0}[/tex]Simplifying:
[tex]\frac{3}{4}=0.75=b[/tex]The value of b is 3/4:
[tex]y=8\cdot0.75^x[/tex]1) There will be 3/4 of the burn area each week.
2) The equation representing the area of the burn, after t weeks will be the following:
[tex]y=8\cdot(\frac{3}{4})^x[/tex]3) After 7 weeks, the area will be represented by the following expression:
[tex]y=8\cdot(\frac{3}{4})^7[/tex]Computing the power:
[tex]y=8\cdot\frac{2187}{16384}=1.068cm^2[/tex]
Fill in the blanks to make the question number since true
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Sheliqua, this is the solution:
a. 13 divided by 5
13/5 = 2 3/5
b. 9/5
9 divided by 5
c. 7 divided by 8
7/8
d. 1 2/3
5/3
5 divided by 3
least to greatest [tex]\pi[/tex][tex] \frac{13}{4} [/tex]22/2[tex] \sqrt{12} [/tex][tex] - 2[/tex]3.07[tex] - 3.27[/tex]
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We have this number and we have to sort them from least to greatest.
We start by expressing them in decimals in order to compare them easily.
Take into account some of them are irrational, so they will be expressed approximately by a decimal (for example, pi).
Then, we have:
[tex]\begin{gathered} \pi\approx3.14 \\ \frac{13}{4}=3.25 \\ \frac{22}{2}=11 \\ \sqrt{12}\approx3.46 \\ -2 \\ 3.07 \\ -3.27 \end{gathered}[/tex]The least will be the negative numbers of this group, so we start with the negative value with the most absolute value: -3.27.
Then, we continue with -2.
Then, we start with the positive values: 3.07, pi, 13/4, sqrt(12) and 22/2.
Then, we can write them in order as:
[tex]\begin{gathered} -3.27 \\ -2 \\ 3.07 \\ \pi \\ \frac{13}{4} \\ \sqrt{12} \\ \frac{22}{2} \end{gathered}[/tex]Which two European nations took control of the regions in the Middle East that had been controlled by the Ottoman Empire?d
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The two European nations took control of the regions in the Middle East that had been controlled by the Ottoman Empire are Britain and France.
The Ottoman Empire had long held the top position among Islamic nations in terms of geography, culture, and theology. Due to the division of the Ottoman Empire after the war, Western powers like Britain and France came to dominate the Middle East, and the modern Arab world and the Republic of Turkey were established.
The Turkish National Movement initiated opposition to these forces, but it did not extend to the other post-Ottoman states until the time of quick decolonization following World War II.
Learn more about Ottoman Empire on:
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