For this case we must find the roots of the following equation:
[tex]3x ^ 2-4x + 2 = 0[/tex]
We have that the roots will come from:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 3\\b = -4\\c = 2[/tex]
Substituting the values:
[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (3) (2)}} {2 (3)}\\x = \frac {4 \pm \sqrt {16-24}} {6}\\x = \frac {4 \pm \sqrt {-8}} {6}\\x = \frac {4 \pm \sqrt {-1 * 8}} {6}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 2}} {6}\\x = \frac {4 \pm2i \sqrt {2}} {6}\\x = \frac {2 \pmi \sqrt {2}} {3}[/tex]
We have two complex roots:
[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]
Answer:
[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]
A: what is the discriminators for the quadratic equation?
B:based on the discriminant which statement about the number and type of solutions in the equation is correct?
[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]
Answer:
0
Step-by-step explanation:
Descriminator is calculated by the following formula:
b*b - 4 * a * c, where a,b,c are the numbers in equitation.
Factored form of x^12 y^16+1
Answer:
B
Step-by-step explanation:
let's recall that
1² = 1
1⁴ = 1
1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1
[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{12}y^{18}+1\implies x^{4\cdot 3}y^{6\cdot 3}+1^3\implies (x^4)^3(y^6)^3+1^3\implies (x^4y^6)^3+1^3 \\[2em] [x^4y^6+1][(x^4y^6)^2-(x^4y^6)(1)+1^2]\implies (x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]
A couple finds that they are experiencing debt problems and decide to find a credit counseling agency. What are three (3) things that the couple should find out about an agency before they allow the agency to represent them?
Answer:
This is an odd question...
The couple should find out the following:
1.) is the agency legitimate?
2.) Will they be doing a hard inquiry on our credit history? if so, this could affect our current credit score
3.) Will they charge me to review my current credit reports?
Three things that should be considered about a credit agency are : Credibility and Reliability, Financial Efficiency, Accreditation and Acclamation
Given - The couple are facing debt issues. They need a credit counselling agency.
While choosing an agency, they should be careful about the following aspects of respective agency.
Credibility & Reliability - ie how trustworthy they are Financial Efficiency - denotes their competence in handling with funds Accreditation and Acclamation - represents the recognition and public image held by the agency.To learn more, refer https://brainly.com/question/1430582?referrer=searchResults
Find the measure of a in the picture please
Answer:
a = 44 degrees
Step-by-step explanation:
Triangle AOB is an isosceles triangle.Angle A and B are same.All three angles of a triangle are equal to 180 degrees.angle 0 + angle a + angle b = 180 degrees
angle b = angle a
92 + a + b = 180 degrees
92 + 2a = 180 degrees
a = 44 degrees
!!
What is the position of F on the number line below? write your answer as a fraction or mixed number
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
There are 4 steps to complete to go from 0 to 1. Hence each step is:
1 out of 4, or simply [tex]\frac{1}{4}[/tex]
F is located at the 3rd mark, which will be [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}[/tex]
Hence, F is located at [tex]\frac{3}{4}[/tex]
Answer:
F is on [tex]\frac{3}{4}[/tex] on the number line
Step-by-step explanation:
Notice in the image that between 0 and 1 there are 4 subdivisions.
Then divide.
[tex]\frac{1}{4} = 0.25[/tex].
Each subdivision is equal to 0.25 units.
Point F is in the third subdivision.
This means that the distance between 0 and F is:
[tex]\frac{1}{4}*3 = \frac{3}{4} = 0.75[/tex].
Finally F is on [tex]\frac{3}{4}[/tex] on the number line
HELP!!Use the figure to decide the type of angle pair that describe <6 and<4.
Angle 6, an acute angle, measures below 90 degrees, reflecting a sharp inclination. Angle 4, a right angle at precisely 90 degrees.
In the geometric configuration, Angle 6 is characterized as an acute angle, signifying that its measure falls between 0 and 90 degrees. Acute angles are typically associated with sharp inclinations, emphasizing a compact angular span. On the other hand, Angle 4 is identified as a right angle, precisely measuring 90 degrees.
Right angles are distinctive for their perpendicular alignment, forming the cornerstone of rectangular shapes and providing structural stability. The significance of Angle 4 lies in its pivotal role in defining perpendicularity within geometric constructs.
This geometric interplay showcases the diversity of angles, with acute angles like Angle 6 emphasizing sharpness and right angles like Angle 4 embodying orthogonality, contributing to the intricacies and precision inherent in geometric relationships.
Factor this trinomial completely.
2x2 + 8x + 6
Answer:
[tex]2 {x}^{2} + 8x + 6 \\ 2( {x}^{2} + 4x + 3) \\ = 2( {x}^{2} + x + 3x + 3) \\ = 2(x + 1)(x + 3)[/tex]
Answer:
the answer is correct, just backwards. thanks for your help!
Step-by-step explanation:
Dion is performing a hypothesis test in which the population mean is 92 and the standard deviation is 2. His sample size is 7 with a mean of 93.5. Which of the following correctly depicts the z-statistic for this data?
a. 0.28. b.0.36. c.1.98. d.2.63
Answer:
Step-by-step explanation:
Answer:
Answer is 1.98
You're welcome.
What is the exact distance from (−1, 4) to (6, −2)?
Answer:
The exact distance is √(29) or 29^(1/2)
Step-by-step explanation:
Find the answer using the distance formula (aka the Pythagorean theorem)
d=√(x1+x2)^2+(y1+y2)^2)
d=√(-1+6)^2+(4+-2)^2), Solve for d:
d= √((25)+(4))
d=√(29)
Answer:
[tex]\sqrt{35}[/tex]
Step-by-step explanation:
To calculate the distance (d) use the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)
d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]
= [tex]\sqrt{7^2+(-6)^2}[/tex]
= [tex]\sqrt{49+36}[/tex] = [tex]\sqrt{85}[/tex] ← exact value
The figure shows the letter M and four of its transformed images—A, B, C, and D: Which of the four images was formed by a reflection of the letter M?
Answer:
Correct answer is figure D.
Step-by-step explanation:
According to the attached image Figure D is correct option.
In a reflection transformation, all the points of an object are reflected or flipped. It is a type of transformation where the new image is the mirror image of the original and x-coordinates and y-coordinates changes the place.
Figure A is rotation and translation and Figure B and C are translation
Thus the correct option is Figure D....
If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. True or False?
Answer:
False
Step-by-step explanation:
This statement states that If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.
This is a false statement.
Lets recall the properties of a parallelogram to understand the concept. The definition says that a quadrilateral is said to be a parallelogram if its opposite angles are congruent and two consecutive angles are supplementary.
Therefore the statement is false....
The expression on the left side of an equation is shown below. 3x+9= []
If the equation has no solution, which expression can be written in the box on the other side of the equation?
A. –9
B. –3
C. 3x
D. 3x + 9
Answer:
C. 3x
Step-by-step explanation:
The first two choices give 1 solution each.
The last choice gives an infinite number of solutions.
Choice C. gives no solution.
3x + 9 = 3x
Subtract 3x from both sides.
9 = 0
Since 9 = 0 is false, equation 3x + 9 = 3x has no solution.
The expression can be written in the box on the other side of the equation as C. 3x.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given expression is
3x + 9 = _
Subtract 3x from both sides;
9 = 0
Since 9 = 0 is false,
The equation 3x + 9 = 3x has no solution.
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A rectangular prism has a volume of 300 ft. If the base measures 5 ft by 8 ft, what is the height of the prism?
40 ft
13 ft
23.1 ft
7.5 ft
Answer:
7.5 ft
Step-by-step explanation:
Volume of a prism is V = L*W*H.
In this case, the volume is V = 300 ft^3 (not 300 ft). Therefore,
300 ft^3 = L*W*H = (8 ft)(5 ft)(height)
Solving for the height, H, we get:
300 ft^3
H = --------------- = 7.5 ft
40 ft^2
Answer:
7.5 ft
Step-by-step explanation:
Vole is the length time the width times the height
V = l*w*h
Substituting what we know
300 = 5*8*h
300 = 40h
Divide each side by 40
300/40 =40h/40
7.5 =h
If g of x equals x squares minus 1, find g of 2
Answer:
g(2) = 3
Step-by-step explanation:
g(x) = x² - 1.
Substituting 2 for x in this formula, we get:
g(2) = 2² - 1, or g(2) = 3
Answer:
g(2) =3
Step-by-step explanation:
g(x) = x^2 -1
Let x=2
g(2) = 2^2 -1
=4-1
=3
Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be [tex]m = 2.[/tex]
[tex]y = 2x + b[/tex]
We substitute the given point to find b:
[tex]2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4[/tex]
Finally the line is:
[tex]y = 2x + 4[/tex]
Answer:
[tex]y = 2x + 4[/tex]
Answer:
y = 2x + 4.
Step-by-step explanation:
The slope = the slope of y = 2x - 3 which is 2.
Using the point-slope form:
y - y1 = 2(x - x1)
Using the point (-1, 2):
y - 2 = 2(x - -1)
y = 2x + 2 + 2
y = 2x + 4 is the answer.
Which of the following is the equation of a line that passes through (-2,1) and (-4,-3)?
Answer:
The equation is y= 2x+5
Step-by-step explanation:
Lets find the slope of the line through the points (-2,1) and (-4,-3).
where x1 = -2, y1= 1, x2= -4, y2 = -3.
Now apply slope formula:
m= y2-y1/ x2-x1
m= -3-1/-4-(-2)
m = -4/-4+2
m= -4/-2
Divide the term by 2:
m = 2
Now we will apply point slope formula:
y-y1 = m (x-x1)
Now substitute the values in the formula:
y-1=2(x-(-2))
y-1 =2(x+2)
y-1=2x+4
Now combine the constants:
y= 2x+4+1
y=2x+5
So the equation is y= 2x+5 ....
1.) Which system of equations below give the solution (-1,-2)?
(1)
(3)
y = x - 3
y = -x - 1
y = -x - 3
y = x - 1
(2)
y = x - 3
(4)
y = -x - 3
y=-x-1
y = x - 1
Answer:
y = -x - 3
Step-by-step explanation:
Plug in -1 for x and your result will come out to 1 because of that double negative [-(-1) = 1]. Next, deduct 3 from 1 to get -2.
I am joyous to assist you anytime.
Given the diagram below what is tan 60?
A. [tex]\sqrt{3}[/tex]
What is triangle and its properties?In the Geometry, the triangle is a 3-sided polygon that consists of 3 edges and 3 vertices. The most important property of the triangle is that the sum of the internal angles of the triangle is = to 180 degrees. its property is known as angle sum property of triangle.
We have been given the image of the right triangle and we are asked to find the value of the tan(60) for our given triangle
from we know that tangent represents the relation between opposite or adjacent of the right triangle.
[tex]tan = \frac{opposite}{adjacent}[/tex]
We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we could conclude that our given triangle is 30-60-90 triangle.
from the sides corresponding to 30-60-90 triangle equals to[tex]x,x\sqrt{3}[/tex] and [tex]2x[/tex] , so the adjacent side for our given triangle will be,
[tex]x\sqrt{3} =8 \sqrt{3\\\\\\[/tex]
[tex]\frac{x \sqrt{3} }{\sqrt{3} } =\frac{8\sqrt{3} }{\sqrt{3} }[/tex]
[tex]x=8[/tex]
Upon substituting these values on above formula we will get,
[tex]tan( 60^{0} ) = \frac{8\sqrt{3} }{8} \\tan( 60^{0})=\sqrt{3}[/tex]
hence, the value of tan(60) is [tex]\sqrt{3}[/tex]and option B is the correct choice.
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what is 1 1/4÷ by 3 4/5
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}[/tex]
Answer:
1/3
Step-by-step explanation:
covert the mixed number to an improper fraction
1x4+1 / 4
any expression multiplied by 1 remains the same
4+1 / 4
Add the numbers
5 / 4
Dividing is equivalent to multiplying with the reciprocal value
5 / 4 x 1 / 3 x 4 / 5
reduce the numbers with greatest common divisor 5
1 / 4 x 1 / 3 x 4
reduce the numbers with greatest common divisor 4
1 /3
What is the name of the property given below?
If a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.
Answer:
This is the zero product rule.
Step-by-step explanation:
a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.
This is the zero product rule.
It shows that for the product to be zero, at least one factor must be zero
If a*b= 0: It shows that one of the factor is zero or may be both the factors are zero that is why their resultant product is 0....
The legs of a right triangle measure 5 centimeters and 12 centimeters. What
is the length of the hypotenuse?
Answer:
13
Step-by-step explanation:
Using pythag the. , we see the rule a2+b2=c2 (Square)
so, a2=25, b2= 144,
25+144=c2
c2=169
sqrt=13
Which fraction is equivalent to 20%?
1/20
2/20
4/20
5/20
Answer:
4/20
Step-by-step explanation:
20 %
Percent means out of 100
20/100
Divide top and bottom by 10
2/10
We want the denominator to be 20 so multiply the top and bottom by 2
4/20
For this case we must find a fraction equivalent to 20%
We have to:
[tex]\frac {1} {20} =[/tex] 0.05 * 100% = 5%
[tex]\frac {2} {20} =[/tex] 0.1 * 100% = 10%
[tex]\frac {4} {20} =[/tex] 0.2 * 100% = 20%
[tex]\frac {5} {20} =[/tex] 0.25 * 100% = 25%
Thus, the correct option is option C, [tex]\frac {4} {20}[/tex]Answer:
[tex]\frac {4} {20}[/tex]
Option C
What must be a factor of the polynomial function f(x) graft on the coordinate plane below
Answer:
The correct answer option is B. (x - 1).
Step-by-step explanation:
We are to determine the factor of the polynomial function [tex]f(x)[/tex] which is graphed on the given coordinate plane.
We know that if the zeros (or intercepts) of an equation are [tex] r _ 1 [/tex] and [tex] r _ 2 [/tex] then the factors for this equation will be [tex] ( x - r _ 1 ) [/tex] and [tex]( x - r _ 2 ) [/tex].
From the graph, we can see that it intercepts the x axis at [tex]1[/tex] and [tex]6[/tex]. So the roots will be [tex](x-1)[/tex] and [tex](x-6)[/tex].
Therefore, the correct answer option is B. (x - 1).
Answer: SECOND OPTION.
Step-by-step explanation:
We can verify each option by making eac equal to zero and solving for "x":
First option
[tex]x-3=0\\x=0+3\\x=3[/tex]
The first option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=3[/tex].
Second option
[tex]x-1=0\\x=0+1\\x=1[/tex]
The second option is a factor of the polynomial function, because the parabola intersects the x-axis at [tex]x=1[/tex].
Third option
[tex]x+1=0\\x=0-1\\x=-1[/tex]
The third option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-1[/tex].
Fourth option
[tex]x+3=0\\x=0-3\\x=-3[/tex]
The fourth option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-3[/tex].
Find the answer to each word problem.
29. Diane bought 48 bottles of water. Ewan
bought 60 bottles. The water came in
packs of the same number of bottles.
What is the greatest number of bottles
that could be in a pack?
Answer:
Step-by-step explanation:
This is a way of asking you what the highest common factor is. So factor into primes and find the highest that is between them.
48: 2 * 2 * 2 * 2 * 3
60: 2 * 2 * 3 * 5
The answer is Bolded and underlined.
HCF: 2 * 2 * 3
HCF: 12
The greatest number that could be in a pack is 12
List all the perfect squares between 1 and 250
Answer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
Step-by-step explanation:
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 =49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
11 x 11 = 121
12 x 12 = 144
13 x 13 = 169
14 x 14 = 196
15 x 15 = 225
Which statements about the hyperbola are true? Check all that apply.
The center is located at (0, 0).
There is a vertex at (–6, 0).
The transverse axis of the graph is vertical.
The foci are located within the rectangular reference box.
The directrices are vertical lines.
Answer:
True options: 1, 2 and 5
Step-by-step explanation:
From the given diagram, you can see that the center of the hyperbola is placed at the origin, so first option is true (see attached diagram for definition of center, vertices, foci, i.e.)
There are two vertices of the hyperbola, they are placed at (-6,0) and (6,0), so second option is true.
The transverse axis is the segment connecting vertices, this segment is horizontal, so option 3 is false.
The foci are not placed within the rectangular reference box, so this option is false.
The directrices are vertical lines with equations [tex]x=\pm \dfrac{a}{e}[/tex], so this option is true.
Answer:1 2 5
Step-by-step explanation:
Find the first five terms of the sequence in which a(1) = –10 and a(n) = 4a(n) – 1 + 7, if n ≥ 2.
options:
A –33, –125, –493, –1965, –7853
B 11, 15, 19, 23, 27
C 47, –10, –33, –125, –493
D –10, –33, –125, –493, –1965
Answer:
hello : answer: A
Step-by-step explanation:
a(1) = –10 and a(n) = 4a(n– 1) + 7, if n ≥ 2.
n=2 : a(2)=4a(1)+7 a(2) =4(-10)+7 = -33
n=3 : a(2)=4a(2)+7 a(3) =4(-33)+7 = -125
n=4 : a(2)=4a(3)+7 a(4) =4(-125)+7 = -493
n=5 : a(2)=4a(4)+7 a(5) =4(-493)+7 = -1965
n=6 : a(2)=4a(5)+7 a(6) =4(-1965)+7 = -7853
What is the following product ^3sqrt16x^7*^3sqrt12x^9
Answer:
4x^5\sqrt[3]{3x}
Step-by-step explanation:
Given
[tex]\sqrt[3]{16x^7}\left(\sqrt[3]{12x^9}\right)\\\sqrt[3]{4^{2} x^7}\sqrt[3]{4(3)x^9}\\ 4^\frac{2}{3} . x^\frac{7}{3} . 4^\frac{1}{3} . 3^\frac{1}{3} . x^\frac{9}{3}\\ 4^\frac{2+1}{3} . 3^\frac{1}{3}. x^\frac{9+7}{3} \\4^\frac{3}{3} . 3^\frac{1}{3}. x^\frac{16}{3}\\ 4\sqrt[3]{3x^16}[/tex]
[tex]4\sqrt[3]{3} . x^\frac{16}{3} \\4\sqrt[3]{3} . x^\frac{15}{3} .x^\frac{1}{3} \\4\sqrt[3]{3} . x^5 .x^\frac{1}{3} \\4x^5\sqrt[3]{3x}[/tex] !
Answer:
The expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex]
Required
Products of both
To do this, we have to apply the laws of indices,
Follow the highlighted steps
Step 1: Multiply both parameters directly
Since they both have the same roots, they can be multiplied directly according to the law of indices
[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] becomes
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex]
Step 2: Apply the 1st law of indices
First law of indices states that
[tex]x^{a} * x^{b} = x^{a + b}[/tex]
So, [tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] becomes
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7} * x^{9} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7+9} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{16} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{192 * x^{16} }[/tex]
Step 3: Rewrite the expression
[tex]\sqrt[3]{192 * x^{16} }[/tex] = [tex]({192 * x^{16} })^{\frac{1}{3} }[/tex]
Step 4: Expand the Expression in bracket
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]({64 * 3* x^{15} * x^{1} })^{\frac{1}{3} }[/tex]
Break down into bits
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]64^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3}) ^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3*\frac{1}{3}}) * 3^\frac{1}{3} * (x^{15}*^\frac{1}{3}) * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 * 3^\frac{1}{3} * (x^{5}}) * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 (x^{5}})* 3^\frac{1}{3} * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3^\frac{1}{3} * x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3x)^\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * \sqrt[3]{3x}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Hence, the expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Solve by factoring or finding square roots
x^2-1=0
Answer:
{1,-1}
Step-by-step explanation:
Let's do both!
Factoring!
x^2-1 is a difference of squares.
The formula for factoring a difference of squares is: u^2-v^2=(u-v)(u+v).
So the factored form of x^2-1 is (x-1)(x+1).
So we want to solve the equation x^2-1=0 which is equivalent to solving
(x-1)(x+1)=0.
If you have A*B=0 then either A=0 or B=0.
So in our case we have x-1=0 or x+1=0.
Now we just solve the equations.
x-1=0 can be solved by adding 1 on both sides giving us x=1.
x+1=0 can be solved by subtracting 1 on both sides giving us x=-1.
Square root!
When you want to use square roots, you have to have a perfect square containing the variables and a constant. We have that here.
We have x^2-1=0 which is equivalent to x^2=1. You could get this last equation by adding one on both sides of x^2-1=0.
Anyway, once you have the square part equals the constant, all you have to do is square root both sides to get rid of the square on the variable part.
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]\sqrt{x^2}=\sqrt{1}[/tex]
[tex]x=\pm \sqrt{1}[/tex] It leads to two answers because [tex]\sqrt{x^2}=|x|[/tex].
[tex]x=\pm 1[/tex]
The solution to the equation x^2-1=0 is x = 1 or x = -1.
Explanation:To solve the equation x^2-1=0 by factoring or finding square roots, we can start by rearranging the equation to get x^2=1. This means that the square of x is equal to 1. To find the square root of both sides, we take the square root of 1, which gives us x=±1. So the solution to the equation is x = 1 or x = -1.
Learn more about Solving quadratic equations here:https://brainly.com/question/32403169
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Ms. Jackson has 32 students. She needs to order a set of books for her class.
Each box has 12 books. How many boxes must she order to make sure each
student gets a book?
Answer:
3
Step-by-step explanation:
12 times table= 12,24,36..
if we have 24 books then not everyone can get a book.
it's best to get the 3 boxes of 36 as everyone can get one. As my teacher always said, the more the better.