Answer:
[tex]y=\left(x^2-\dfrac{9}{2}\right)^2-\dfrac{65}{4}[/tex]
Step-by-step explanation:
To put this in vertex form, we need to create a perfect square polynomial within the right side of the equation.
[tex]y=x^2-9x+4[/tex]
[tex]y=\left(x^2-9x + \left(-\dfrac{9}{2}\right)^2\right)+4 - \dfrac{81}{4}[/tex]
[tex]y=\left(x^2-\dfrac{9}{2}\right)^2+4 - \dfrac{81}{4}[/tex]
[tex]y=\left(x^2-\dfrac{9}{2}\right)^2-\dfrac{65}{4}[/tex]
#11 i
Graph the polygon with the given vertices and its image after the given rotation about point A.
A(-2,-5), B(-7, 3), C(-4, 3), D(-1, -3); 270° counterclockwise.
Check the picture below.
Cheng is thinking a of a number
what number is Cheng thinking of ?
cheng thinking ;
I multiply my number by 100,hen divide by 10,then multiply by 1000.
My answer is 170'000
Is Cheng's answer is correct or incorrect
The number is 17
Let the number = x
From the question, we have
(x*100)/10*1000 = 170000
x = 17
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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paula is transferring photo files to an external hard drive to free up storage on her phone. The size of the files on her external hard drive in megabytes is give F , where F=38+6t and t is the time in seconds since the transfer began. how many megabytes of files are transferred to her hard drive every second
Every second, 44 megabytes of files will be transferred to her hard drive.
The size of the files on her external hard drive in megabytes is given F, where F = 38 + 6t and t is the time in seconds since the transfer began.
The function is below
F = 38 + 6t ....(i)
To determine the number of megabytes of files transferred to her hard drive every second
Substitute the value of t = 1 in the equation (i), and solve for F
F = 38 + 6(1)
F = 38 + 6
F = 44
So the number of megabytes of files = 44
Therefore, every second, 44 megabytes of files will be transferred to her hard drive.
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*URGENT + 100 POINTS*
A right triangle is shown in the graph.
right triangle on coordinate plane with hypotenuse labeled t and one endpoint of hypotenuse at r comma s and the other endpoint at x comma y, vertical line from point x comma y and horizontal line from r comma s that meet at right angle of triangle, horizontal dotted line from point r comma s to point s on y axis, horizontal dotted line from point x comma y to point y on y axis, vertical dotted line from point r comma s to point r on x axis, and vertical dotted line from right angle to point x on x axis
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points)
Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points)
Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points)
Answer:
Part A
[tex](x-r)^2+(y-s)^2=t^2[/tex]
where:
(r, s) is the center of the circle.(x, y) is a point on the circle.t is the radius of the circle.Part B
Domain = [-3, 17]
Range = [-14, 6]
Part C
Point (9, 1) is inside the border of the circle.
Step-by-step explanation:
Part A[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given triangle:
a = x - rb = y - sc = tSubstitute these values into the formula to derive the standard equation of the circle:
[tex]\boxed{ (x-r)^2+(y-s)^2=t^2}[/tex]
where:
(r, s) is the center of the circle.(x, y) is a point on the circle.t is the radius of the circle.Part BGiven the center of the circle (r, s) is (7, -4) and the radius (t) is 10.
The domain of the circle is the x-value of the center minus and plus the radius:
[tex]\begin{aligned}\implies \textsf{Domain}&=[r-t,r+t]\\&= [7-10, 7+10] \\&= [-3, 17]\end{aligned}[/tex]
The range of the circle is the y-value of the center minus and plus the radius:
[tex]\begin{aligned}\implies \textsf{Range}&=[s-t,s+t]\\&=[-4-10, -4+10]\\& = [-14, 6]\end{aligned}[/tex]
Part CSubstitute (r, s) = (7, –4) and t = 10 into the derived equation from part A:
[tex]\implies (x-r)^2+(y-s)^2=t^2[/tex]
[tex]\implies (x-7)^2+(y-(-4))^2=10^2[/tex]
[tex]\implies (x-7)^2+(y+4)^2=100[/tex]
Substitute the given point (9, 1) into the equation:
[tex]\begin{aligned}\implies (9-7)^2+(1+4)^2&=2^2+5^2\\&=4+25\\&=29\end{aligned}[/tex]
As 29 < 100, the point (9, 1) is inside the border of the circle.
How many terms are in this expression?
6w + 7x
Answer:
2
Step-by-step explanation:
6w is a term
7x is a term
which represents a rotation of 189
degrees?
(X,y) -> (-X,-y)
(X,y) -> (X,-y)
(X,y) -> (y,X)
(X,4) -> (-X,4)
The required rotation of the 180° is given by, (X,y) -> (-X,-y), option A is correct and the required translation is given by (x + 6, y - 2), option D is correct.
Given that,
To determine which option shows the rotation of 180°, and translation of right 6 units and down 2 units.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
Here,
For the rotation of the 180°, the given coordinate undergoes the change in direction so the required coordinate after 180° rotation is given as (-x, -y).
Now, for the translation of 6 units right we must add x with 6 and for 2 units down we must subtract y by 2, the required translation is given as(x + 6, y -2).
Thus, the required rotation of the 180° is given by, (X,y) -> (-X,-y), and the required translation is given by (x + 6, y - 2).
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What are all the real and complex solutions of x3 + 2x2 + 36x = –72? Round to the nearest tenth if necessary.
The roots of the equation x³ + 2x² + 36x + 72 = 0 are ( -2 , -6i , +6i )
What is Factorizing?
Brackets should be expanded in the following ways:
For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket
For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.
Given data ,
Let the equation be x³ + 2x² + 36x = -72
Adding 72 on both sides , we get
x³ + 2x² + 36x + 72 = 0
Now , on simplifying we get
Take the common factor x² in first two terms and 36 in last two terms
So ,
x² ( x + 2 ) + 36 ( x + 2 ) = 0
Now , taking ( x + 2 ) as common factor , we get
( x² + 36 ) ( x + 2 ) = 0
So , for the equation to be 0 , either ( x + 2 ) = 0 or ( x² + 36 ) =0
And , we can find the solutions to the equation as
x + 2 = 0
Subtracting 2 on both sides , we get
x = -2
So , one solution is -2
Now ,
( x² + 36 ) =0
Subtracting 36 on both sides , we get
x² = -36
x = √ ( -36 )
x = ± 6i
So , we got two more solutions as -6i and +6i
Hence , the roots of the equation are -2 , -6i and +6i
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please help. I don't get it.
Step-by-step explanation:
what is the problem to solve ?
I assume we need to calculate the area of the whole figure ?
in any case, we have a problem :
a rhombus is a tilted square, a special parallelogram, as it has 4 equal sides.
that would mean all 4 sides of that central rhombus are 5 in.
that would make both triangles equilateral triangles (all 3 sides are equally long : 5 in).
but in order for a right-angled triangle to have the Hypotenuse = 5 in and the height (= left leg) = 4 in, that must make the right leg
5² = 4² + leg²
25 = 16 + leg²
9 = leg²
leg = 3 in
and so, the baseline of the large triangle 2×3 = 6 in.
and not 5 in, which must be the top and base line of the rhombus.
so, the whole problem definition is wrong.
the only solution when accepting the given lengths, is that the triangle sides are NOT a straight extension of the rhombus sides.
the triangle side is the Hypotenuse of the smaller internal right-angled triangle
side² = 4² + (5/2)² = 16 + 6.25 = 22.25
side = 4.716990566... in
anyway, the area of each of the large triangles is
baseline×height / 2 = 5×4/2 = 10 in²
we have 2 triangles = 2×10 = 20 in²
the area of the rhombus is
baseline×height = 5×4 = 20 in²
please note that the area of a rhombus is also
diagonal1 × diagonal2 / 2
but that applies only, when we have the lengths of the diagonals. both approaches give the same result, of course.
so, the whole area is
20 + 20 = 40 in²
hi thank you for seeing this
Each pair of angles should be matched with the correct property (theorem) as follows:
e. Vertical Angles: Angles 7 and 6.
a. Alternate Exterior Angles: Angles 1 and 8.
g. Alternate Interior Angles: Angles 4 and 5.
h. Corresponding Angles: Angles 2 and 6.
d. Supplementary Angles: Angles 6 and 8.
What are parallel lines?Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude such as Angles 1 and 8.
What is the alternate interior angles theorem?The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent such as Angles 4 and 5.
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Solve the following system of linear equations by graphing:
4x + 2y = -4
4x + 2y = -20
Graph the linear equations by writing the equations in slope-intercept form:
y= ___x + ___
y= ___x + ___
Identify the appropriate number of solutions. If there’s a solution, give the point.
Answer:
No solution. The lines are parallel
Step-by-step explanation:
I graphed with Desmos. It is a free.
Find the inverse of the function.
y = x² + 4x + 4
I pretty much understand the concept on how to do this. Somebody on here already asked this exact question and got responded with a step by step answer, but I need someone to go more in depth. The part that confuses me most is the x² + 4x, how exactly do I write that out? The person who answered the other guy's question solved it by saying, "y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation
y = (x+2)(x+2)". Where in the world did the (x+2)(x+2) come from?.. The video I'm learning from did not do that once whilst solving these problems. I really hope someone can help.
Inverse of the function is -2+x
What do you mean by inverse function?
A function that returns the initial value for which a function has produced an output is known as an inverse function. If f(x) is a function that produces the value y, then [tex]f^{-1}(y)[/tex] the inverse function of y, will provide the value x.
The function's inverse, represented by , [tex]f^{-1}[/tex] returns the original value that was used to create the output (x).
Given function is y = x² + 4x + 4
To find the inverse function, we need to express x as a function of y:
Substitue y=x
⇒ x = [tex]y^{2}+4y+4[/tex]
Substract x from the above equation we get,
[tex]y^{2}+4y+4[/tex] - x = 0
Solve the above equation using quadratic formula we get,
y = [tex]\frac{-4+\sqrt{16-4(4-x)} }{2}[/tex] [tex]=\frac{-4+\sqrt{16-16+4x} }{2}[/tex] = [tex]\frac{-4+2x}{2}=-2+x[/tex]
Similarly, y = -2-x
Therefore, [tex]f^{-1}=[/tex] -2+x , -2-x
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Question in file please help!!!!
Answer:
Step-by-step explanation:
Ok:
Area of circle:
A=πr^2
1. Apply to question!
5^2π=
25π/4: Since it is a 1/4 of the circle
6.25π
Answer: 6.25π or 6.25 pie
Answer:
about 19.63496 m^2
Step-by-step explanation:
this is 1/4 of a circle so we find the are of the full circle
pi(r)^2
pi(5)^2
pi25
78.53982
Divide by 4
78.53982/4
19.63496
Hopes this helps please mark brainliestC
Make the subject of
x − 5 = t
This is the initial tableau of a linear programming problem. Solve by the simplex method.
x 1
x1
x 2
x2
s 1
s1
s 2
s2
s 3
s3
z
1
3
3
1
0
0
0
12
2
4
4
0
1
0
0
2
2
1
1
1
0
0
1
0
4
minus
−2
minus
−1
0
0
0
1
0
Question content area bottom
Part 1
The maximum is
enter your response here
when
x 1
x1
equals
=
enter your response here
,
x 2
x2
equals
=
enter your response here
,
s 1
s1
equals
=
11
11,
s 2
s2
equals
=0, and
s 3
s3
equals
=
3
3.
The solution of linear programming problem is the maximum value is 2, x_1 = 1, x _2 =0.
What is linear programming problem?
The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation. The objective function may have a number of variables that must meet a set of linear inequalities known as linear constraints. These variables may also be subject to conditions. The following scenarios, such as manufacturing difficulties, diet problems, transportation challenges, allocation problems, and so on, can be solved optimally using the linear programming problems.
After first iteration,
Negative minimum Z_j-C_j is -2 and its column index is 1. So, the entering variable is x_1.
Minimum ratio is 1 and its row index is 2. So, the leaving basis variable is S_2.
∴ The pivot element is 2.
Entering =x_1, Departing =S_2, Key Element =2
After second iteration:
Since all Z_j-C_j≥0
Hence, optimal solution is arrived with value of variables as :
x_1=1,x_2=0
Max Z=2
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Write the equation of a sine function that has the given characteristics.
Amplitude: 4
Period: 3pie
Answer:
y = 4 sin(2x/3)
Step-by-step explanation:
The parent function for sine functions is: y = a sin b(x - c) + d
"a" defines amplitude/vertical dilation
"b" defines the change to the period/horizontal dilation
"c" defines the phase shift/horizontal translation
"d" defines the midline/vertical translation
We can already set "a = 4" because 4 is the amplitude.
However, to include the period into the function, we have to take note of the parent sine function already having a period of 2π.
This means: 2π/b = period
2π/period = b
2π/3π = b
2/3 = b
Knowing the "a" and "b" values, we can set up the equation:
y = 4 sin(2x/3)
No horizontal/vertical translations were applied, so "c" and "d" are both zero.
A quadratic function
y
=
f
(
x
)
y=f(x) is plotted on a graph and the vertex of the resulting parabola is
(
−
5
,
6
)
(−5,6). What is the vertex of the function defined as
g
(
x
)
=
f
(
x
−
2
)
g(x)=f(x−2)?
Step-by-step explanation:
g(x) = the original function at x-2.
just means it is the same function as the original function, just moved 2 units to the right.
just think about it :
e.g.
g(3) is the same as the originated function at x=1.
g(4) is the same as the original function at x=2.
...
so, everything that happened for the original function at x, happens now for g at x+2.
therefore, again, things move 2 units to the right (positive x direction) .
that means the vertex "moves" from
(-5, 6) to (-3, 6)
the vertex of g(x) = (-3, 6)
let f(x) = x-1 graph g(x)=f(3/4x)
The graph of the function g(x) after putting the value in function f(x) is attached with the answer.
What is function?
A relation b/w a collection of inputs and outputs is known as a function. A function is a relationship between inputs in which each input is connected to precisely one output.
Given function: f(x) = x-1
we have to find: g(x)=f(3/4x)
Putting the value of f(x) in g(x),
g(x) = 3/4x - 1
Now, the graph of the function (3/4)x - 1 is attached in the question.
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Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=9.9 and x = 8.7 and passes through the point ( 0, 8.5 )
Answer:
ft HD st he do it to we if do ks do just bc
A rectangular plece of carpet covers 180 yd². The width is 7 yd less than the length. Find the length and width.
Round your answers to the nearest tenth of a yard.
The length is approximately
yd.
The width?
THE LENGTH AND WIDTH WILL BE = length: 5.7 yd
width: 1.7 yd.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.We are aware of the quantity of apples and the amount of money in the aforesaid problem.According to our question-
w(w +4) = 10
w² +4w = 10 . . . . . eliminate parentheses
w² +4w +4 = 14 . . . . . . add the square of half the w-coefficient to complete the square
(w +2)² = 14 . . . . . . . . . rewrite as a square
w +2 = √14 . . . . . . . . . take the square root
2 = -2 +√14 ≈ 1.7 . . . . yards (width)
Then the length is 4 more yards than this, so is ...
length = 1.7 +4 = 5.7 . . . yards
The length and width are 5.7 and 1.7 yards, respectively.
In the attached graph, we let x represent the length. As you can see, the magnitudes of the two zeros are width and length.
HENCE,THE LENGTH AND WIDTH WILL BE = length: 5.7 yd width: 1.7 yd.
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a store sells a $400 microscope after a markup of 32% what is the price of the microscope at the store
A 32% mark up means that the price goes up by 32 percent. The way to find this is by finding 132% of $400.
1.32 x 400 = $528.
I hope this helps!
The price of the microscope after the markup of 32% at the store will be equal to $528.
What is Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the given data in the question,
Price of microscope = $400
Markup percentage = 32%
Increase in price = 400 × 32/100
= $128.
Price after markup will be,
$400 + $128 = $528.
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NEED REALLY BADLY WILL GIVE 50 POINTS D: What is the product in simplest form -2/11 3/4
Answer:
-3/22
Step-by-step explanation:
Hope this helps!
Answer: [tex]-\frac{3}{22}[/tex]
Step-by-step explanation:
To find the product, multiply the two fractions:
[tex]-\frac{2}{11} *\frac{3}{4} =-\frac{2*3}{11*4} =-\frac{6}{44} =-\frac{3}{22}[/tex]
Which values from the given replacement set make up the solution set of the inequality?
2b≥6; {1, 2, 3, 4}
Responses
{1, 2, 3}
left curly bracket 1 comma 2 comma 3 right curly bracket
{1, 2}
left curly bracket 1 comma 2 right curly bracket
{3, 4}
left curly bracket 3 comma 4 right curly bracket
{2, 3, 4}
PLS HURRY AHHH
{3, 4} are the values which make up the solution set of the inequality
2b ≥ 6.
Given, an inequality
2b ≥ 6.
Now, we have to find the solution set of the given inequality,
2b ≥ 6
On dividing both the sides by 2, we get
2b/2 ≥ 6/2
b ≥ 3
So, the solution set of the given inequality, be
the values of b must be greater than or equal to 3.
So, Option (3) i.e. {3 , 4} is the solution set of the inequality.
Hence, {3, 4} are the values which make up the solution set of the inequality 2b ≥ 6.
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A stockbroker charges a 1.5% commission to sell shares of a stock for a client. Find the value of stock sold by a broker if the commission was $420.
Answer:
value of stock =1.5% × 420?= 6.3
Please help these lessons are confusing me
Answer: y-9 = 17(x+7)
Step-by-step explanation:
We will use the second coordinate point to use in the equation and the first coordinate (-8, -8) to figure out the slope of this line.
Answer:
y-9=17x+119
Step-by-step explanation:
given points (-8,-8) & (-7,9)
let's take (-7,9) as (x1,y1) and (-8,-8) as (x2,y2)
now for finding out equation through two points, we use
[tex] \frac{x-x_{1} }{x_{1}-x_{2} } =\frac{y-y_{1} }{y_{1}-y_{2} } [/tex]
So accordingly, we input the values
[tex] \frac{x-(-7) }{-7-(-8)} } =\frac{y-9 }{9-(-8) } [/tex]
[tex] \frac{x+7 }{-7+8} } =\frac{y-9 }{9+8 } [/tex]
[tex] \frac{x+7 }{1} } =\frac{y-9 }{17 } [/tex]
[tex] 17(x+7) = y-9 [/tex]
[tex] 17x+119 = y-9 [/tex]
find the values of x, y, and z.
To find x, you would do 180-36-63, which would be 81.
Then you would do 180-81 to find z, which is 99.
To find y, would do do 180-99-13, which is 68.
Answer:
x=81
y=68
Z=99
Step-by-step explanation:
to find x we have to remember the rule that all 3 angles sum up to be 180 in a triangle
So we use this to find x
180-(63+36)=x
180-99=x
81=x
Now to find z since it is on a flat plane you just subtract 81 from 180 to find z
180-81=z
99=z
Now to find y we add all the angles of the second triangle and then subtract that sum by 180
180-(13+99)=y
180-112=y
68=y
Hopes this helps please mark brainliest
Choose the pair of numbers that is not a solution to the given equation. . (1, 2) (0, ) (4, 3)
The pairs of numbers given, (1, 2) is not a solution.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y= 2x+1 /3
Now, First value of x = 0
y= 2(0)+1 /3
y= 1/3
i.e., (0, 1/3)
and, Second value of x = 1
y= 2(1)+1 /3
y= 5/3
i.e., (1, 5/3)
and, Third value of x = 4
y= 2(4)+1 /3
y= 9/3
y=3
i.e., (4, 3)
Hence, from the pairs of numbers given, (1, 2) is not a solution.
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A right triangle has a leg that measures 7 in. The angle opposite this side measures
62°. What is the length of the hypotenuse of this triangle? Round to the nearest tenth.
(Remember to include the correct units in your answer)
Please help
The hypotenuse of the right triangle is 7.93 inches.
According to the question,
We have the following information:
A right triangle has a leg that measures 7 in. The angle opposite this side measures 62°.
Now, the hypotenuse can be easily found using the trigonometric function.
(More to know: in a right triangle, we can use the Pythagoras theorem. This theorem can not used in any other triangle.)
We will use sin 62 to find hypotenuse.
Sin 62 = perpendicular/hypotenuse
Hypotenuse = perpendicular/sin 62
Hypotenuse = 7/0.88295
Hypotenuse = 7.93 inches
Hence, the hypotenuse of the right triangle is 7.93 inches.
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I need the Answer Options are also given
The simplified form of the expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex] after evaluating is equal to [tex]\sqrt[3]{2}[/tex]
What are Powers?
A power is created when a number is multiplied by itself. A power is typically represented by a base number and an exponent. The multiplier is revealed by the base number while the exponents, which are little numbers written above and to the right of base numbers, indicate how many times the base number has been multiplied.If a number is written as 6 to the power of 2, it is represented as, [tex]6^{2}[/tex]. Here, 6 is the base and 2 is the power.Steps to Combine and Simplify Exponents
The three basic rules of exponents used to combine the exponents and simplify the expression are as follows:
[tex]a^{m} \times a^{n} =a^{m+n}[/tex] -----(1)[tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex] -----(2)[tex](a^{m})^{n} =a^{m \times n}[/tex] ------(3)Here, we have to simplify and evaluate the given expression using the rules of exponents.
We have the given expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex] -------(4)
Using the exponents rules, [tex](a^{m})^{n} =a^{m \times n}[/tex] and [tex](a \times b)^{m}=a^{m} \times b^{m}[/tex] in the above expression, we get
[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3} } \times 3^{\frac{2}{3} } \times 2^{3 \times \frac{1}{3} } }{2^{\frac{2}{3} } \times 2^{\frac{2}{3} } \times 3^{\frac{2}{3} }}[/tex]
Simplifying further using (1) and (2), we get (4) as,
[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3}}}{2^{\frac{2}{3}+\frac{2}{3} }} \times \frac{3^{\frac{2}{3} } }{3^{\frac{2}{3} }} \times 2^{1} \\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =\frac{2^{\frac{2}{3}}}{2^{\frac{4}{3} }} \times 2^{\frac{2}{3}-\frac{2}{3} } \times 2\\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{\frac{2}{3}-\frac{4}{3} } \times 2^{0} \times 2[/tex]
We know that, [tex]a^{0} =1[/tex]
So, further simplifying we get
[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{-\frac{2}{3} } \times 1 \times 2\\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = 2^{-\frac{2}{3}+1 } \\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=2^{\frac{1}{3}}\\ \imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=\sqrt[3]{2}[/tex]
Therefore, the simplied form of the given expression is [tex]\sqrt[3]{2}[/tex]
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How do you solve this problem step-by-step? 15(40-9)x3+6
Answer:
The answer to this problem is 1401.
Step-by-step explanation:
By using the order of operations listed here, we can solve the problem very easily.
EVALUATE IN PARENTHESES [tex]40-9[/tex]: 40 minus 9 is 31, so now the problem is 15(31) x 3 + 6
MULTIPLY/DIVIDE [tex]15(31)*3[/tex]: X times Y can be [tex]X*Y[/tex] or [tex]X (Y)[/tex]. This evaluates to [tex]15*31*3[/tex] which is 1395.
ADD/SUBTRACT: The problem now is just [tex]1395+6[/tex] which evaluates to a total of [tex]1401[/tex].
A $26,000 car is on sale for 5% off with 3% tax. Interpret the change of the price as a percentage. Round to the nearest hundredth.
The new price of the car is $25441.
How to calculate the price?Given that the $26,000 car is on sale for 5% off with 3% tax.
The discount will be:
= 5% × $26000
= $1300
The tax will be:
= 3% × ($26000 - $1300)
= 3% × $24700
= $741
The new price will be:
= Amount - Discount + Tax
= $26000 - $1300 + $741
= $25441
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