The simplest form of the expression [tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}[/tex] is yx³.
The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).
A fraction is a number that has been expressed as a quotient by dividing the numerator by the denominator. Both are integers in a simple fraction. In a complex fraction, a fraction can be found in either the numerator or the denominator.
An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions joined by an equal sign form an equation.
Consider the expression,
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}[/tex]
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=\frac{x^{\frac{1}{3} }}{y^{-1}}[/tex]
We know, x⁻¹ = 1/x
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=(yx^{\frac{1}{3} })^{9}[/tex]
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=(y^{9})(x^{\frac{1}{3}\times 9})[/tex]
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=(yx^{3})[/tex]
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what is the inverse of (x) = [tex]\sqrt{x+9}[/tex] x[tex]\geq[/tex] -9
f−1(x)=(x−9)2, x≥9
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals left parenthesis x minus 9 right parenthesis squared, , , x is greater than or equal to 9
f−1(x)=−(x−9)2, x≤9
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative left parenthesis x minus 9 right parenthesis squared, , , x is less than or equal to 9
f−1(x)=x2−9, x≥0
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals x squared minus 9, , , x is greater than or equal to 0
f−1(x)=x2−9, x≤0
The inverse of [tex]f[/tex], denoted [tex]f^{-1}[/tex], is such that
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given [tex]f(x)=\sqrt{x+9}[/tex], we have
[tex]f\left(f^{-1}(x)\right) = \sqrt{f^{-1}(x) + 9} = x[/tex]
Solve for [tex]x[/tex].
[tex]\sqrt{f^{-1}(x) + 9} = x[/tex]
[tex]\left(\sqrt{f^{-1}(x) + 9}\right)^2 = x^2[/tex]
[tex]f^{-1}(x) + 9 = x^2[/tex]
[tex]f^{-1}(x) = x^2 - 9[/tex]
Note that [tex]f(x)\ge0[/tex], so we must also have [tex]f\left(f^{-1}(x)\right) = x \ge 0[/tex]. This makes the third choice the correct one.
What volume in milliliters, of a 60% hydrochloric acid solution must be added to 100ml of a 30% hydrochloric acid solution to make a 36% hydrochloric acid solution?
Answer:
Since 30% of 100 ml = .3*100 = 30 ml
60 % of X ml = .6x which we are trying to solve
add
(X+100).36 = 30+.6x
.36x+36 = 30+.6x
so
6 = .24x
x = 25 ml
Step-by-step explanation:
I hope this helps you
a chessplayer won 32 of the games he played if the ratio of wins to lossses was 8:3 how many games did he play total
Answer:
Step-by-step explanation:
i don't know if this is right but here is how i would do it.
Wins: Losses = 8:3 = 32: 12 = 32 wins + 12 losses = 44 games played.
How do you solve this −6x−16<2x
Answer:
x >-2
Step-by-step explanation:
subtract 2x from both sides
-6x - 16 - 2x < 0
subtract 2x from 6x
-8x - 16 < 0
add 16 to both sides
-8x < 16
divide by -8
x> -2
The atoms of a certain element each contain 11 protons and 1 valence electron. Which statement correctly identifies this element and describes its chemical reactivity?
The correct option is D). The element is sodium, and it is highly reactive.
What type of atom has 11 protons?The atomic number of the element sodium (Na) is 11. It means that the sodium has 11 protons in total and because it is neutral it has 11 number of electrons.
Valence electrons (VE) refers to the electrons that usually presents in the outer shell of an atom. Thus, the sodium has only 1 valence electron.
Basically, the mass number of an element tells about the number of protons and neutrons in an atom and sodium is the atom that has 11 atomic number.
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Complete question:- The atoms of a certain element each contain 11 protons and 1 valence electron. Which statement correctly identifies this element and describes its chemical reactivity?
A The element is sodium, and it is highly reactive.
B The element is fluorine, and it is not very reactive.
C The element is sodium, and it is not very reactive.
D The element is fluorine, and it is highly reactive.
Kinsley went rock climbing at Red River Gorge. At noon, she was at an elevation of 76 feet. Then, she climbed 28 feet higher to reach the peak.
What was Kinsley's elevation at the peak?
Answer:
Step-by-step explanation:
28 + 76=
104
Her elevation is 104 at the peak.
Find the total amount given the original price and tax rate. Round to the nearest cent if necessary
$31.69, 6%
The total amount including the tax rate is found as $34.
What is defined as the percentage?A percentage is a fraction of a whole articulated as just a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the fraction of the total by the total and multiply by 100.For the stated conditions in the question.
The original amount = $31.69.
The tax rate is 6%.
The total mount will be the sum of original amount and tax price.
First calculated the tax price;
6% of 31.69 = 6×31.69/100
6% of 31.69 = 1.9014
Tax price = $1.9014.
Total price = original amount + tax price
Total price = $31.69 + 1.9014
Total price = 33.5914
Total price = $34 (Round to the nearest cent.)
Thus, the total amount is estimated as $34.
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After three quarters of the season has past, the Tigers basketball tean has won 48 out of 72 games. How many of the remaining games must they win in order to win more than 70% of all their games this season?
Answer: at least 3 more games
Step-by-step explanation:
70% of 72 is 50.4
50.4 - 48 = 2.4
Because one can't win only a fourth of a game, you need to round up. Bringing us to at least 3 more games to win
Can someone please help me really quick
The amount of the shed that Jack would have built when Kyle finishes the shed is 8/25.
How much shed would Jack have built?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 8/25. 8 is the numerator and 25 is the denominator.
When Kyle finishes building the shed, he would have finished building a fraction of 1/1 of the shed. S
So, the amount of shed, that Kyle still needs to build to complete the shed is 1 ÷ 5/8
= 1 x 8/5 = 8/5
The amount of shed that Jack will have built when Kyle finishes the shed is:
8/5 x 1/5 = 8/25
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please just solve this, I'm confused.
The quotient of each of the expressions are:
a. 1⅖ / -1/5 = -7
b. -0.4 ÷ 0.25 = 1.6
c. 7/8 ÷ -3/4 = -7/6
d. 0.7 ÷ -1 1/6 = -0.6
How to Find the Quotient?Quotient is the result you get after dividing one quantity by another. For example, the quotient of a and b is a/b.
Find the given quotient as shown below:
a. 1⅖ / -1/5
Convert mixed fraction to improper fraction
7/5 / -1/5
Change the division sign to multiplication and turn the fraction upside down
7/5 × (-5/1)
= -(7 × 5)/(5 × 1)
= -(7 × 1)/(1 × 1)
= -7/1
= -7
b. -0.4 ÷ 0.25
-0.4/0.25
= 1.6
c. 7/8 ÷ -3/4
Change the division sign to multiplication and turn the fraction upside down
7/8 × -4/3
= -(7/8 × 4/3)
= -(7 × 4)/(8 × 3)
= -(7 × 1)/(2 × 3)
= -7/6
d. 0.7 ÷ -1 1/6
0.7 ÷ -7/6
Change the division sign to multiplication and turn the fraction upside down
0.7 × -6/7
0.1 × -6/1
= 0.1 × -6
= -0.6
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P = IV
●
Here is what you know about the baseball field parking lot situation.
There are 9 lamp posts connected to this circuit.
Each lamp post has a 400 watt lamp installed.
The circuit is 120-volt and 20-amp.
Here is what you don't know, but can figure out:
How many watts does 9
lampposts require?
How many lamposts could this
circuit handle? HELP
Answer:
1M
Step-by-step explanation:
HOPE ITS HELP!! PLEASE STAY ALIVE!! :D
solve for r -17= 2/3r
Answer:r=51
Step-by-step explanation:
Answer:
r = 51
Step-by-step explanation:
r - 17 = [tex]\frac{2}{3}[/tex] r ( multiply through by 3 to clear the fraction )
3r - 51 = 2r ( subtract 2r from both sides )
r - 51 = 0 ( add 51 to both sides )
r = 51
Ruth's new lunch box is only 5 centimeters in height, so it fits in her backpack along with all her books. The lunch box has 3 sections for different types of food. The length and width of the lunch box are 22 centimeters and 14 centimeters. What is the volume of Ruth's new lunch box?
The volume of Ruth's new lunch box is 1,540 cm³.
What is the volume?The volume is a measure of an object occupied in a three-dimensional space.
Volume is a three-dimensional quantity that measures the capacity of a shape or the amount of three-dimensional space a closed figure can occupy.
The formula for computing a volume is height x length x width.
Data and Calculations:Height = 5 cm
Length = 22 cm
Width = 14 cm
Volume = 1,540 cm³ (5 x 22 x 14)
Thus, the volume of Ruth's new lunch box, showing the three-dimensional space within, is 1,540 cm³.
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Ill need asap please
D. 37.8204
A negative absolute value is always positive.
Answer:
d) 37.8204
Step-by-step explanation:
Given that,
→ |-18.531| + |-19.2894|
Let's solve the problem,
→ |-18.531| + |-19.2894|
→ 18.531 + 19.2894
→ 37.8204
Thus, option (d) is correct.
Solve one step equalities using multiplication & division
X/2 = 17/1
Answer:
[tex] \sf \: x=34[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
x/2 = 17/1
Step 1: Cross-multiply.
x/2 = 17/1
x*(1)=(17)*(2)
x=34
Fill in the tables and create a recursive and explicit equation for all three questions.
Answer:okay
Step-by-step explanation:hm
a group of 10 people have gotten together to play basketball. they will begin by dividing themselves into two teams of 5 players each. one team will wear red uniforms and the other will wear blue uniforms. in how many ways can this be done?
Answer:
9!
Step-by-step explanation:
Because a person who switch with 9 people, then another person switch with 8 people (because the first person was already counted), then another person who switch with 7 people (becsuse the first and the second person was already counted)... and you will get 9!. 9! is 9 factorial which is 9×8×7×6×5×4×3×2×1. :)
Mike drove a nail 2.5 in. long through a board 0.75 in. thick into a post. How far did the nail go into the post?
Answer:
1.75 inches deep into the post
Step-by-step explanation:
First, you do 2.5 - 0.75 which is 1.75 in
The answer is 1.75 in
Hope this helps!
simplify -2(-3 - x) + 6x
Answer:
0.75
Step-by-step explanation:
1. distribute the 2 into the perenthesis
2. combine like terms
3. simplify on both sides
19 1/5 - 11 1/11?????????
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{19\frac{1}{5}}\implies \cfrac{19\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{96}{5}} ~\hfill \stackrel{mixed}{11\frac{1}{11}}\implies \cfrac{11\cdot 11+1}{11}\implies \stackrel{improper}{\cfrac{122}{11}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{96}{5}~~ - ~~\cfrac{122}{11}\implies \stackrel{\textit{using the LCD of 55}}{\cfrac{(11)96~~ - ~~(5)122}{55}}\implies \cfrac{1056~~ - ~~610}{55} \\\\\\ \cfrac{446}{55}\implies {\LARGE \begin{array}{llll} 8\frac{6}{55} \end{array}}[/tex]
In 11 years, John's age will be 5 less than 5 times his current age. How old is he?
If xrepresents John's current age, which of the following equations could be used to solve this problem?
Answer:
x=4
Step-by-step explanation:
Find the area of the polygon with th
Ay
7.
A(-2,3)
-4
C(-2,-3)
4
2
-2
4-
2'
4 X
B(3, -3)
The area of the triangle is 15 square units after using the distance formula.
What is a distance formula?
It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
It is given that:
The triangle is shown on the coordinate plane.
Using the distance formula:
The height of the triangle:
[tex]\rm AC=\sqrt{(-2+2)^2+(-3-3)^2}[/tex]
AC = 6 units
Again using the distance formula:
[tex]\rm BC =\sqrt{(3-(-2))^2+(-3-(-3))^2}[/tex]
BC = 5 units
The area of the triangle = (1/2)6x5
The area of the triangle = 15 square units
Thus, the area of the triangle is 15 square units after using the distance formula.
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A cell phone company charges its customers $40 each month for owning a cell phone plan and $0.25 for
each minute the customer talks on the phone. These costs are modeled by the following equation:
C=25m +40, where Crepresents the total cost of the bill and m represents the number of minutes the
customer talked on the phone that month. Given this equation, how many minutes would the customer
have to talk on the phone for their monthly bill to be $84.25? (Hint: plug in 84.25 for the total cost, C, and
solve for the unknown, m).
Answer:
The customer would have 177 minutes to talk on the phone for their monthly bill to be 84.25
Step-by-step explanation:
Point of correction it's not C=25m +40 but it is
C=0.25m +40
Where,
C = $84.25➟ 84.25 = 0.25m + 40
Let's solve your equation step-by-step.
84.25=0.25m+40
Step 1: Flip the equation.
0.25m+40=84.25
Step 2: Subtract 40 from both sides.
0.25m+40−40=84.25−40
0.25m=44.25
Step 3: Divide both sides by 0.25.
0.25m/0.25 = 44.25/0.25
m=177
∴ The customer would have 177 minutes to talk on the phone for their monthly bill to be 84.25
- The flag of Equatorial Guinea contains an isosceles triangle.
(Recall that an isosceles triangle contains two angles with the
same measure.) If the measure of the third angle of the trian-
gle is 30° more than twice the measure of either of the other
two angles, find the measure of each angle of the triangle.
(Hint: Recall that the sum of the measures of the angles of a
triangle is 180°.)
Please show me step by step how you got the answer, Thanks
The measure of each angle of the triangle is 40°, 40° and 100°.
What is the triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.Given:
In an isosceles triangle two of the three angles measure the same.
Let the two angles be equal to x.
The third angle is 20 more than twice the measure of either angle, which means 2x+20.
The angles of a triangle add up to 180 degrees.
(x)+(x)+(2x+20)=180
4x+20=180
4x=160
x=40 degrees
So, the two angles measure 40° each and the third angle would be,
2x+20
=2*40+20
=100°
Therefore, the measure of each angle of the triangle is 40°, 40° and 100°.
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What is the x value of the solution to the system shown?
2y = 2x + 12
2-y=4
Answer:
[tex]x = -8[/tex]
Step-by-step explanation:
[tex]\begin{cases}2y = 2x + 12\\2-y = 4\end{cases}[/tex]
It would be easier to start with the second equation.
[tex]2 - y = 4 \text{ // Add y and subtract 4}\\\to 2 - y - 4 = 4 - y - 4\\\to -2 = y[/tex]
From here, we can substitute [tex]y = -2[/tex] into the first equation, to solve for [tex]x[/tex].
[tex]2(-2) = 2x + 12\\\to -4 = 2x + 12 \text{ // Subtract 12 on both sides}\\\to -4 - 12 = 2x + 12 - 12\\\to -16 = 2x \text{ // Divide by 2}\\\to -\frac{16}2 = \frac{2x}2\\\to -8 = x[/tex]
In the figure below, AD and AB are tangent to the circle centered at O. The segment DB passes through the center of the circle. Given that AD=10.6 and DB=5.6, find DC.
The length of DC found using Pythagorean theorem given AD = 10.6 and DB = 5.6 and AD and AB are tangent of circle O, is DC = 1.6
How can Pythagorean theorem be used to find DC?The given parameters are;
The tangents of circle O = AD and AB
The segment passing through O = DB
AD = 10.6
DB = 5.6
Required; The length of DC
Solution;
According to Pythagorean theorem, we have;
AB = √(10.6² - 5.6²) = 9
AB = AC = 9
AD = DC + AC
Which gives;
10.6 = DC + 9
DC = 10.6 - 9 = 1.6
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find the constant of proportionality on this graph
PLEASE HELP GIVING BRAINLIEST :))
Answer:
I think the constraint of proportionality is 25 because each dot it increases buy 25.
I also believe that at 10 the total should be at 225.
Which number sentence represents 8 times as many as 9
Answer:
72
Step-by-step explanation:
this number sentence will be represented as,
72 is 8 times as many as 9
how do i right it please help
The contrapositive statement is:
If x ≠ 2, then x^2 ≠ 4
And it is false.
How to write the contrapositive statement?
First, we have two propositions:
p = "x^2 = 4"
q = "x = 2"
The contrapositive statement is:
¬q → ¬p
The negation of the propositions are:
¬q = "x ≠ 2"
¬p = "x^2 ≠ 4"
Then the contrapositive statement with the given propositions is:
If x ≠ 2, then x^2 ≠ 4
Now, is this statement true?
No, because we can have:
x = -2 (which is different than 2, so the hypothesis is true)
and x^2 = (-2)^2 = 4
Then the conclusion is false, so the statement is false.
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Jack is in a marathon. He rides his bike 64 miles in 4 hours. How many miles does Jack ride his bike per hour?
Answer: 16mph
Step-by-step explanation:
64 miles divided by the 4 hours comes out to 16 per hour
Answer: 16 miles per hour