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The following results for the algebraic equation according to algebra properties are listed below:
x⁴ + 2 · x² · y² + y⁴ x⁴ + 4 · x² · y² x² · (x² + 4 · y²)How to expand an algebraic equationIn this problem we find an algebraic equation that must be expanded and simplified by means of algebra properties. Now we proceed to present the complete procedure. First, write the complete expression:
(x² + y²)² + 2 · x² · y² - y⁴ = x² · (x² + 4 · y²)
Second, expand the perfect square binomial:
x⁴ + 2 · x² · y² + y⁴ + 2 · x² · y² - y⁴ = x² · (x² + 4 · y²)
Third, use distributive property and add similar terms:
x⁴ + 4 · x² · y² = x² · (x² + 4 · y²)
Fourth, use distributive property once again:
x² · (x² + 4 · y²) = x² · (x² + 4 · y²)
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Related Questions
Male bullies are often: Question 5 options: below average in verbal assertiveness. above average in verbal assertiveness. above average in size. smaller than average in size.
Answers
Express in standard form :
42634.7
Answers
Answer:
ans is 42635 when expressed in standard form
Step-by-step explanation:
The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x^2 – 3
y > –x^2 + 2
Answers
The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution
How to modify the graphsFrom the graph, we have:
f(x) = x² - 3
g(x) = -x² + 2
Next, we change the equations to inequalities as follows:
y ≤ x² - 3
y > -x² + 2
To modify the graph, we then perform the following transformations:
Shift the function g(x) down by 2 unitsReflect across the x-axisShift the function g(x) down by 3 unitsHow to identify the solution setAfter the modifications in (a), we have:
y ≤ x² - 3 and y > -x² + 2
Substitute y > -x² + 2 in y ≤ x² - 3
-x² - 2 ≤ x² - 3
This gives
2x² ≤ - 1
Divide by 2
x² ≤ - 0.5
The square root of numbers less than 0 is a complex number
Hence, the set of inequalities do not have a solution
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Ralph Warren purchased 27 shares of stock at 16 3/8 per share. He paid a $27.50 brokerage fee. He later sold all 27 shares at 17 5/8 and paid a $28.75 brokerage fee. (36) What was his total cost for the stock including his brokerage fee? (37) What did he receive from the sale of the stock after he paid the brokerage fee? (38) Did he have a capital gain or loss? (39) How much was the gain or loss? (40) What was the net change from 16 3/8 to 17 5/8?
Answers
Based on the number of shares that Ralph Warren purchased, the total cost of the stock was $469.63. The amount he received from sales was $447.13. The capital loss was $22.50.
What was the gain on the sale of the shares?The cost of the stock was:
= (27 x 16³/₈) + 27.50
= $469.63
The amount received from sales:
= (27 x 17⁵/₈) - 28.75
= $447.13
This capital gain (loss):
= 447.13 - 469.63
= -$22.50
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In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$
Answers
The measure of angle D in the convex pentagon ABCDE is 132°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the measure of angle D, hence:
angle A = x - 40.
∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angle in a pentagon)
3(x - 40) + 2x = 540
x = 132°
The measure of angle D in the convex pentagon ABCDE is 132°
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Identify the range of the function shown in the graph.
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Solve this please!!!
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Answers:
i) [tex]\sf (x + 2)(x+ 3)[/tex]
ii) [tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Factorize expression's:
i.
[tex]\sf (x + 1)^2 + 3(x + 1) + 2[/tex]
apply perfect square and distributive method
[tex]\sf (x^2 + 2(x)(1) + 1^2) + 3x + 3 + 2[/tex]
expand
[tex]\sf x^2 + 2x + 1 + 3x + 3 + 2[/tex]
collect like terms
[tex]\sf x^2 + 2x + 3x + 3 + 2 + 1[/tex]
add/subtract like terms
[tex]\sf x^2 + 5x + 6[/tex]
breakdown
[tex]\sf x^2 + 3x + 2x+ 6[/tex]
factor common term
[tex]\sf x(x + 3) + 2(x+ 3)[/tex]
collect into groups
[tex]\sf (x + 2)(x+ 3)[/tex]
ii.
[tex]\sf (9x^2 + 9x - 4)(9x^2 + 9x - 10) - 72[/tex]
breakdown
[tex]\sf (9x^2 + 12x - 3x - 4)(9x^2 + 15x - 6x - 10) - 72[/tex]
factor common term
[tex]\sf (3x(3x + 4) -1( 3x + 4)) ( (3x(3x + 5)- 2(3x +5) )- 72[/tex]
collect like terms
[tex]\sf (3x -1)( 3x + 4) (3x- 2)(3x +5) - 72[/tex]
expand
[tex]\sf 81x^4+162x^3-45x^2-126x-32[/tex]
factor
[tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Answer:
[tex]\textsf{1.} \quad (x+3)(x+2)[/tex]
[tex]\textsf{2.} \quad (3x+1)(3x+2)(9x^2+9x-16)[/tex]
Step-by-step explanation:
Question 1
[tex]\textsf{Given expression}: \quad(x+1)^2+3(x+1)+2[/tex]
[tex]\textsf{Let }u=(x+1) \implies u^2+3u+2[/tex]
[tex]\textsf{To factor }\:\:u^2+3u+2:[/tex]
Rewrite the middle term as u + 2u:
[tex]\implies u^2+u+2u+2[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+1)+2(u+1)[/tex]
Factor out the common term (u+1):
[tex]\implies (u+2)(u+1)[/tex]
Replace [tex]u[/tex] with [tex](x+1)[/tex] :
[tex]\implies (x+1+2)(x+1+1)[/tex]
Simplify:
[tex]\implies (x+3)(x+2)[/tex]
Question 2
[tex]\textsf{Given expression}: \quad (9x^2+9x-4)(9x^2+9x-10)-72[/tex]
Expand:
[tex]\implies 9x^2(9x^2+9x-10)+9x(9x^2+9x-10)-4(9x^2+9x-10)-72[/tex]
[tex]\implies 81x^4+81x^3-90x^2+81x^3+81x^2-90x-36x^2-36x+40-72[/tex]
Collect like terms:
[tex]\implies 81x^4+81x^3+81x^3-90x^2+81x^2-36x^2-90x-36x+40-72[/tex]
Combine like terms:
[tex]\implies 81x^4+162x^3-45x^2-126x-32[/tex]
Use the Factor Theorem:
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
[tex]\begin{aligned}\implies f \left(-\dfrac{1}{3}\right) & =81\left(-\dfrac{1}{3}\right)^4+162\left(-\dfrac{1}{3}\right)^3-45\left(-\dfrac{1}{3}\right)^2-126\left(-\dfrac{1}{3}\right)-32\\ & = 1-6-5+42-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 1) is a factor.
[tex]\begin{aligned}\implies f \left(-\dfrac{2}{3}\right) & =81\left(-\dfrac{2}{3}\right)^4+162\left(-\dfrac{2}{3}\right)^3-45\left(-\dfrac{2}{3}\right)^2-126\left(-\dfrac{2}{3}\right)-32\\ & = 16-48-20+84-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 2) is a factor.
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(ax^2+bx+c)[/tex]
Compare the coefficient of x⁴ and the constant to find a and c:
[tex]\implies 3 \cdot 3 \cdot a=81 \implies a=9[/tex]
[tex]\implies 2c=-32 \implies c=-16[/tex]
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(9x^2+bx-16)[/tex]
Expand:
[tex]\implies f(x)=81x^4+(81+9b)x^3-(126-9b)x^2-(144-2b)x-32[/tex]
Compare the coefficient of x³ to find b:
[tex]\implies 81+9b=162 \implies b=9[/tex]
Therefore, the fully factorized expression is:
[tex]\implies (3x+1)(3x+2)(9x^2+9x-16)[/tex]
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. A scale factor of 2 is applied to the dimensions of the prism. What effect will this have on the volume
Answers
The volume of the prism would be enlarged by a factor of 8
How to determine the effect?The scale factor is given as:
k = 2
Let the initial volume be v and the final volume be V.
The relationship between both volumes is
V = k^3 * v
This gives
V = 2^3 * v
Evaluate
V = 8v
Hence, the volume of the prism would be enlarged by a factor of 8
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If a line has a slope of 1/3 and passes through the point (1,-2) which ff points also lies on the line a) -2,-5 b) -2,1 c) 4,-1 d) 4,10
Answers
Answer: c
Step-by-step explanation:
The equation of the line is
[tex]y+2=\frac{1}{3}(x-1)\\\\y+2=\frac{1}{3}x-\frac{1}{3}\\\\y=\frac{1}{3}x-\frac{7}{3}[/tex]
To determine which point lies on the line, we can substitute in the x coordinate and see if the equation gives the same y-coordinate.
If x = 2, then the equation of the line gives that y = -5/3.If x = 4, then the equation of the line gives that y = -1.Therefore, the answer is c.
True or False: Both equations have 'no solutions'.
15x +4-2x = 3(6x + 5)
(2x-8)=(8x+36)
Answers
Answer:
False
Step-by-step explanation:
They both have 1 solution
15x + 4 = 3(6x +5)
15x +4 = 18x + 15 Multiple everything in the parentheses by 3.
4 = 3x + 15 Subtract 15 x from both sides
-11 = 3x Subtract 15 from both sides
-11/3 = x Divide both sides by 3
There is only one solution for this equation.
2x -8 = 8x + 36
-8 = 6x + 36 Subtract 2x from both sides
--44 = 6x Subtract 36 from both sides
-44/6 = x Divide both sides by 6.
There is only one solution for this equation.
Answer:
false
Step-by-step explanation:
They both have solutions
Meredith is 160 cm tall. Jane’s height is 90% of Meredith’s height. How tall is jane?
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What is 90% of 160
9/10 times x/160
Cross multiply: 10x= 1440
Divide by 10 x=144
pls help >>> How many solutions does the quadratic
function represented on this graph have?
Answers
Answer:
Zero real number solutions
Step-by-step explanation:
Doesn't intercept the x-axis -> No real solutions
Find the slope of the line passing through the vertex and the y-intercept of the quadratic function
[tex]f(x) = 5x{}^{2} + 20x - 7 [/tex]
Answers
Find y intercept
y=5(0)²+20(0)-7y=0-7y=-7Point(0,-7)
Find vertex
x coordinate
-b/2a-20/10-2y coordinate
y=5(4)-40-7y=-27Vertex at (-2,-27)
Slope
m=(-27+7)/-2-0m=-20/-2m=10Answer:
10
Step-by-step explanation:
VertexThe x-coordinate of the vertex of a quadratic equation in the form
[tex]f(x)=ax^2+bx+c\quad \textsf{is} \quad -\dfrac{b}{2a}[/tex]
Given function:
[tex]f(x)=5x^2+20x-7[/tex]
[tex]\implies a=5, \quad b=20, \quad c=-7[/tex]
x-coordinate of the vertex
[tex]\implies -\dfrac{b}{2a}=-\dfrac{20}{2(5)}=-2[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the function:
[tex]\begin{aligned}\implies f(-2) & =5(-2)^2+20(-2)-7\\& = 5(4)-40-7\\& = 20-47\\& = -27\end{aligned}[/tex]
Therefore, the coordinates of the vertex are (-2, -27).
y-interceptThe y-intercept is when the curve crosses the y-axis, so when x = 0.
To find the y-coordinate of the y-intercept, substitute x = 0 into the function:
[tex]\begin{aligned}\implies f(0) & =5(0)^2+20(0)-7\\& = 0 + 0-7\\& = -7\end{aligned}[/tex]
Therefore, the coordinates of the y-intercept are (0, -7).
SlopeTo find the slope of the line passing through the vertex and the y-intercept, simply substitute the found points into the slope formula:
[tex]\implies \sf slope=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-27-(-7)}{-2-0}=\dfrac{-20}{-2}=10[/tex]
Therefore, the slope of the line passing through the vertex and the y-intercept of the given quadratic function is 10.
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Match each function with the expression representing its inverse function.
1. x - 4
2. x + 4
3. 0.25x
4. x
5. -2x
6. 2x
A. g ( x ) = -0.5 x
B. h ( x ) = 4 x
C. y = x - 4
D. ƒ( x ) = x/2
E. k ( x ) = x
F. p ( x ) = x + 4
Please help!!
Answers
Answer:
A matches with 5.B matches with 3.C matches with 2.D matches with 6.E matches with 4.F matches with 1.Step-by-step explanation:
To find the inverse of a function [tex]f(x)[/tex], we let [tex]f(y)=x[/tex] and then solve again for y.
For example, using [tex]g(x)=-0.5x[/tex], we will let [tex]g(y)=x[/tex], giving [tex]x=-0.5y[/tex]. This means that [tex]y=-2x[/tex], and thus [tex]g^{-1}(x)=-2x[/tex].
Using similar logic, we see that:
A matches with 5.B matches with 3.C matches with 2.D matches with 6.E matches with 4.F matches with 1.Pick the correct answer.
Help me please thanks so much
Answers
Area of square = l * w
L = 22; W = 22
Area of square = 484
Area of circle = pi * r^2
r = 11
Area of circle = 121 pi
Area of shaded region = Area of square 1 area of circle
So… 484 - 121 pi
Evaluate 2x for each value of x. Write your answers in simplest form. Show your work!
1. x = 1/4
2. x = 1/3
3. x = 1/2
4. x = 1/6
5. x = 1/7
6. x = 1/8
7. x = 2/3
8. x = 3/4
Answers
1. 1/2
2.2/3
3. 1
4. 1/3
5. 2/7
6. 1/4
7. 4/3
8. 3/2
How to evaluate the valueTo find 2x of the vale of x, we have to multiply the value of 'x' by 2
1. x = 1/4
[tex]2x = 2 * \frac{1}{4}[/tex] ⇒ [tex]\frac{2}{4}[/tex] ⇒[tex]\frac{1}{2}[/tex]
2. x = 1/3
[tex]2x = 2 * \frac{1}{3}[/tex] ⇒[tex]\frac{2}{3}[/tex]
3. x = 1/2
[tex]2x = 2* \frac{1}{2}[/tex] ⇒ [tex]\frac{2}{2}[/tex] ⇒ [tex]1[/tex]
4. x= 1/6
[tex]2x = 2* \frac{1}{6}[/tex] ⇒ [tex]\frac{2}{6}[/tex] ⇒ [tex]\frac{1}{3}[/tex]
5. x = 1/ 7
[tex]2x = 2 * \frac{1}{7}[/tex] ⇒ [tex]\frac{2}{7}[/tex]
6. x = 1/8
[tex]2x = 2 * \frac{1}{8}[/tex] ⇒ [tex]\frac{2}{8}[/tex] ⇒ [tex]\frac{1}{4}[/tex]
7. x = 2/3
[tex]2x = 2 * \frac{2}{3}[/tex] ⇒ [tex]\frac{4}{3}[/tex]
8. x = 3/4
[tex]2x = 2 * \frac{3}{4}[/tex] ⇒ [tex]\frac{6}{4}[/tex] ⇒ [tex]\frac{3}{2}[/tex]
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If the ratio of the measures of corresponding sides of two similar is 4:9, then the ratio of their perimeter is
Answers
Answer:
4 : 9
Step-by-step explanation:
ratio of corresponding sides and ratio of perimeter are equal
then ratio of perimeter = 4 : 9
can someone please help me with this problem?
Answers
X =3/5pie
Than we cross multiplication
X=(3/5pie multiply 360) all divide be two pie
Than x=108
For what values of o is tan o undefined?
Answers
Answer:
90 is the right answer
Step-by-step explanation:
because it give the value pf o is tan o
in a school, the ratio of the number of boys to the number of girls is 2:3 and the ratio of the number of girls to the number of teachers is 7:3. what is the ratio of the number of students to the number of teachers
Answers
Answer:
35:9
Step-by-step explanation:
The ratios can be combined by making the common element be represented by the same number.
Adjusted ratiosThe common element in the two ratios is the number of girls. In the first ratio, girls are represented by 3 ratio units. In the second ratio, they are represented by 7 ratio units. Multiplying the first ratio by 7 and the second ratio by 3 will make the number of girls the same in both.
boys : girls = 2 : 3 = 14 : 21
girls : teachers = 7 : 3 = 21 : 9
Then the extended ratio can be written ...
boys : girls : teachers = 14 : 21 : 9
The number of students is the total of the numbers of boys and girls, so we have ...
students : teachers = (14 +21) : 9
students : teachers = 35 : 9
Angle G is a circumscribed angle of circle E. Major arc FD measures 280°.
Circle E is shown. Line segments F E and D E are radii. A line is drawn to connect points F and D. Tangents F G and D G intersect at point G outside of the circle. Major arc F D measures 280 degrees.
What is the measure of angle GFD?
40°
50°
80°
90
Answers
The measure of angle GFD of the circumscribed circle is; A: 40°
How to find the measure of angle of a circumscribed circle?From the figure, we can apply the arc angles summation formula to get;
Major angle ∠FED + Minor angle ∠FED = 360°
We are given that Major arc FD measures 280°. Thus;
280° + Minor angle ∠FED = 360°
Minor angle ∠FED = 360° - 280°
Minor angle ∠FED = 80°
Also, we know that;
∠FED + ∠FGD = 180°
Thus, putting ∠FED = 80° gives us;
80° + ∠FGD = 180°
Subtract 80° from both sides using subtraction property of equality to get;
∠FGD = 180° - 80°
∠FGD = 100°
Now, GF and GD are the tangents to the circle from the same point G. Thus, we can say that;
GD = GF
Therefore,
∠FDG = ∠GFD = x
(This is because ∠FDG and ∠GFD are the angles opposite to equal sides.
In triangle FGD, we have sum of interior angles = 180°
Therefore, we have the expression;
∠FDG + ∠FGD + ∠GFD = 180° (due to the fact that sum of angles in a triangle is equal to 180°)
x + 100° + x = 180°
2x = 180° - 100°
2x = 80°
x = 40°
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Answer:
40
Step-by-step explanation:
I did a thing and it worked
the market price of article is rs 3000. a discount of 30% was agreed. find the sale price of the article and the amount of discount.
Answers
Answer: 2400
Step-by-step explanation:
3000 x 20/100 = 600
Discount = 600
Sale price of the article: 3000-600 = 2400
F(x)=4x^3+7x^2x-1. G(x)=4x-2 find (f-g)(x)
Answers
Answer:
4x^3 + 7x^2 - 3x + 1
Step-by-step explanation:
BTW your question, there is a sign misssing
1. Find the product using Suitable Property a) 55×99
Answers
Answer:
5445
Step-by-step explanation:
We can use distributive property. a*(b - c) = (a*b) - (a *c)
99 = 100 - 1
55 * 99 = 55 * (100 - 1)
= 55*100 - 55*1
= 5500 - 55
= 5445
A circle is formed when a plane slices through a cone. Which of the following describes the relationship between the plane and the cone
Answers
The plane is parallel to the base of the cone describes the relationship between the plane and the cone
A circle is a spherical form without boundaries or edges or we can say that A circle is a closed, curved object with two dimensions in geometry.
The produced cross-section is a circle when a plane slices a cone such that the plane is parallel to the base of the cone.
Ellipse is the shape that is produced when a plane cuts a cone at an angle such that it misses the base or the vertex. (As shown in figure)
Hence A circle is formed when a plane slices through a cone and the plane is parallel to the base of the cone
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What is the value of x?
Use the triangle to answer the question.
Enter your answer in the box.
x =
Answers
A shipment of 60 highly sensitive accelerometers is to be accepted or rejected based on the testing of 5 chosen randomly from the lot. The shipment will be rejected if more than 1 of the 5 fail. It is known that 10% of the shipment does not meet the specifications. Let X denote the number of units that fail. What is the standard deviation of the distribution
Answers
Using the binomial distribution, it is found that the standard deviation of the distribution is of 0.67.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The parameters are:
n = 5, p = 0.1.
Hence the standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5 \times 0.1 \times 0.9} = 0.67[/tex]
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which situation is most likley to show a constant rate of change
Answers
Option B. The situation that would be more likely to show a constant rate of change would be B. The distance traveled by a truck driving at a constant speed compared with time.
How to solve for the rate of changeThis is the factor that is used to determine if there is a decrease or an increase in a given factor.
A good way to d this is by the use of time and speed to compare the distance that is being traveled.
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Complete question
Which situation is most likely to show a constant rate of change?
A. The weight of a child compared with its age in months
B. The distance traveled by a truck driving at a constant speed compared with time
C. The cost of a new car compared with the number of tires it has
D. The outside temperature compared with the time of day
Given cos(x)=1/2, what is the value of cos(x+pi)?
Answers
Answer:
-1/2
Step-by-step explanation:
cos(x+pi) = -cos(x), so the answer is -1/2.
can someone show me way of solving this
Answers
Step-by-step explanation:
[tex]f(x) = ln( \frac{1}{x} ) [/tex]
To find the derivative, notice we have a function 1/x inside of another function, ln(x)
We use what we call the chain rule,
It states that
derivative of a '
[tex] \frac{d}{dx} f(g(x)) = f '(g(x)) \times \: g '(x)[/tex]
Here f is ln(x)
f is 1/x
So first, we know that
[tex] \frac{d}{dx} ( ln(x) = \frac{1}{x} [/tex]
so
[tex]f'(g(x)) = \frac{1}{ \frac{1}{x} } [/tex]
We know that
[tex]g'(x) = - \frac{1}{ {x}^{2} } [/tex]
So we have
[tex]x \times - \frac{1}{ {x}^{2} } = \frac{ - 1}{x} [/tex]