Select the equivalent expression:
Please explain why it is changed from a fraction to a multiplication problem!
Answers
Answer:
On opening the bracket, we have (x^-28)/(x^56)
This is the same as (x^-28) . 1 / (x^56)
Following the law of indices 1/(x^a) = x^-a, we have 1 / (x^56) = (x^-56)
Hence (x^-28) . (x^-56)
Related Questions
Which of the following rational numbers is equivalent to a repeating decimal? a. 24/60 b. 30/64 c. 29/50 d. 35/60
Answers
Answer:
answer is D. 35/60
Step-by-step explanation:
35 divided by 60 is = 0.583333
which is a repeating decimal
Among the options, only a rational number (35/60) is equivalent to a repeating decimal. The correct answer is option (d).
To identify which of the given rational numbers is equivalent to a repeating decimal, we need to check their decimal representations.
a. 24/60 = 2/5 = 0.4 (terminating decimal, not repeating)
b. 30/64 = 15/32 = 0.46875 (terminating decimal, not repeating)
c. 29/50 = 0.58 (terminating decimal, not repeating)
d. 35/60 = 7/12 = 0.583333... (repeating decimal, as 3 repeats infinitely)
Among the options, only option d (35/60) is equivalent to a repeating decimal.
The repeating decimal representation is 0.583333... where the digit 3 repeats indefinitely.
This can be represented as 0.58(3).
The correct answer is option (d).
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Please helppp! I’ve been stuck for almost 45 minutes now.
Answers
The system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have a line showing the graph.
First, we have to calculate the equation of the line:
The horizontal line:
y = 3
The region represents the inequality:
y > 3
Second inequality line:
[tex]\rm \dfrac{x}{-2}+\dfrac{y}{3} < 1[/tex]
3x -2y < 1
Thus, the system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.
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Consider the equality xy=k. Write the following inverse proportion: y is inversely proportional to x. When y = 6, x = 3.
3/1 =k/6
1/6 = k/3
6/1 = 1/6
Answers
The correct expression for the inverse proportion is k/6 = 3/1
Inverse proportionsGiven the inequality xy = k
If y is inversely proportional to x, then;
y = k/x
Given that y = 6, and x = 3, then;
6 = k/3
Swap
k/3 = 6
k/6 = 3/1
Hence the correct expression for the inverse proportion is k/6 = 3/1
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Help I need this urgently please help!
Answers
Using translation concepts, the transformation is defined by:
J. A translation of triangle XYZ to the right.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the orientation of the triangle remains the same, hence it is a translation of the triangle to the right.
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Verify csc^2t-cos t sect= cot^2 t
Answers
Rewriting the left hand side,
csc²t - cost sec t
= (1/sin²t)-(cost)(1/cost)
= 1/sin²t - 1
= 1/sin²t - sin²t/sin²t
= (1-sin²t)/sin²t
= cos²t/sin²t
= cot²t
Step-by-step explanation:
assuming this is correct, you can really manipulate either side and you should arrive eventually arrive to same sides. But in this case you usually manipulate the more complex side. So I'll manipulate the left side.
Original Equation:
[tex]csc^2(t)-cos(t)*sec(t)=cot^2(t)[/tex]
Rewrite csc and sec, using the reciprocal identities:
[tex](\frac{1}{sin(t)})^2-cos(t)*\frac{1}{cos(t)}=cot^2(t)[/tex]
multiply cos(t) and 1/cos(t) and also distribute the exponent:
[tex]\frac{1}{sin^2t}-1=cot(t)^2[/tex]
Multiply 1 by sin^2(t)/sin^2(t)
[tex]\frac{1}{sin^2(t)}-\frac{sin^2(t)}{sin^2(t)}[/tex]
subtract the numerator
[tex]\frac{1-sin^2(t)}{sin^2(t)}[/tex]
Pythagorean Identity:
[tex]sin^2(t)+cos^2(t)=1[/tex]
subtract sin^2(t) from both sides
[tex]cos^2(t)=1-sin^2(t)[/tex]
Use this to rewrite the numerator:
[tex]\frac{cos^2(t)}{sin^2(t)}[/tex]
Rewrite using the reciprocal identities:
[tex]cot^2(t) = cot^2(t)[/tex]
Suppose a and b are independent events if p(a|b)=0.55 and p(b)=0.2, what is P(AnB)?
A. 0.275
B. 0.22
C. 0.11
D. 0.165
Answers
The value of the probability P(AnB) is 0.11
How to evaluate the probability?The given parameters are:
P(a|b)=0.55 and P(b)=0.2
The value of P(AnB) is calculated using:
P(AnB) = P(a|b) * P(b)
Substitute the known values
P(AnB) = 0.55 * 0.2
Evaluate the product
P(AnB) = 0.11
Hence, the value of the probability P(AnB) is 0.11
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Tom works at an aquarium shop on Saturdays. One Saturday, when Tom gets to work, he is asked to clean a 180-gallon reef tank. His first job is to drain the tank. He puts a hose into the tank and starts a siphon. Tom wonders if the tank will finish draining before he leaves work. He charts the amount of water remaining in the tank over time as shown in the table below.
Answers
Please find the question attached below.
The equation that models the decrease in water (in gallons) of the fish tank over time (in hours) is y = - 20x + 180.
We know that a linear equation with one variable is one that contains just one variable.
Here we have to find the appropriate equation that models the given chart.
For option A. :
y = - 40x + 140
At x = 2, y = - 40*2 + 140 = - 80 + 140 = 60 =/ 140
So this option is incorrect.
For option B.:
y = - 40x + 180
At x = 2, y = - 40*2 + 180 = - 80 + 180 = 100 =/ 140
So this option is incorrect.
For option C.:
y = - 20x + 140
At x = 2, y = - 20*2 + 140 = - 40 + 140 = 100 =/ 140
So this option is incorrect.
For option D.:
y = - 20x + 180
At x = 2, y = - 20*2 + 180 = - 40 + 180 = 140
So this option is correct.
Therefore, the equation that models the decrease in water (in gallons) of the fish tank over time (in hours) is y = - 20x + 180. So, the last option is correct.
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What is the value of the logarithm below? (Round your answer to two decimal
places.)
log₂7
A. 0.58
B. 2.11
C. 0.85
D. 2.81
Answers
Kevin bought snacks for his team's practice. He bought a bag of popcorn for $1.60
and a 8-pack of juice bottles. The total cost before tax was $16.80. How much was
each bottle of juice?
URGENTTTT
Answers
Answer:
$1.90
Step-by-step explanation:
16.80 - 1.60 = 15.20, since we are finding the price of each bottle of juice.
1) Set up and equation equated to 15.20.
8x = 15.20
x = 15.20/8
x = 1.90
Therefore, each bottle of juice costs $1.90.
$15.20/8=$1.90
y=1x^(2)+10x+22 line of symmetry
Answers
Answer:
x = -5
Step-by-step explanation:
We can use the below formula to find the line of symmetry.
( x - a )² + b
Here,
line of symmetry = +a
Vertex = +b
And now let us take a look at the given equation.
y = x² + 10x + 22
To find the line of symmetry from the given equation we have to make the given equation as the given formula.
Let us use the completing square method for that.
y = x² + 10x + 22
Put zero instead of y.
x² + 10x + 22 = 0
x² + 10x = -22
x² + 10x + 25 = -22 + 25
( x + 5 )² = 3
( x + 5 )² -3 = 0
Therefore,
line of symmetry of the line is = -5
∴ x = -5
If two-thirds of a number is diminished by 8, the result is 32
Answers
Answer:
60
Step-by-step explanation:
Let's call the number A.
We are told that:
(2/3)A - 8 = 32
Multiply both sides by 3 and rearrange:
3*[(2/3)A - 8 = 32]
2A - 24 = 96
2A = 120
A = 60
CHECK:
Does (2/3) of 60 minus 8 equal 32?
(2/3)*(60) = 40
40 - 8 = 32
YES
The number is 60
The length of arc PR is 12 centimeters and its measure is 60° on circle O.
A circle with center O has two radii OP and OR is shown.
The area of sector POR is approximately
square centimeters, and the perimeter of sector POR is approximately
centimeters.
Answers
The area of sector POR is approximately equal to 68.76 square centimeters, and the perimeter of sector POR is approximately equal to 34.92 centimeters.
How to calculate the length of the arc?In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle is given by:
Length of an arc = 2πr × θ/360
Substituting the given parameters into the formula, the radius of this circle is given by;
12 = 2 × 3.142 × r × 60/360
12 = 2 × 3.142 × r × 1/6
72 = 6.284r
Radius, r = 72/6.284
Radius, r = 11.46 centimeters.
Now, we can calculate the area of sector POR:
Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = πr² × θ/360
Where:
r represents the radius.θ represents the central angle.Substituting the given parameters into the formula, we have;
Area of sector = 3.142 × 11.46² × 60/360
Area of sector = 3.142 × 131.3316 × 1/6
Area of sector = 68.76 square centimeters.
Next, we would calculate the perimeter of sector POR:
Perimeter of sector POR = 2r + Length of an arc
Perimeter of sector POR = 2(11.46) + 12
Perimeter of sector POR = 22.92 + 12
Perimeter of sector POR = 34.92 centimeters.
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Type the correct answer in each box. Use numerals instead of words.
What are the decimal expansions of the following numbers? Expand to four decimal places if the number is a repeating decimal.
3/9
2/5
7/8
4/6
Answers
5 x 20 = 100, so now our denominator is 100. Because we multiplied 5 by 20, we also have to multiply 2 by 20. This means that 2/5 is equal to 40/100. 40/100 is representative as 0.4.
3/9 as a decimal can convert to 33/99, which would give us 0.3333 as a repeating decimal.
7/8 as a decimal expansion would give us 0.875 because 100 divided by 8 is equal to 12.5 (which is representative of 1/8), and 12.5 x 7 is equal to 87.5. Because we multiplied 1/8 x 7, we get 7/8 which is less than a whole. Therefore, the only number to the left of the decimal point should be 0. Hence, we divide 87.5 by 100 and we get 0.875. That is our decimal conversion.
4/6 as a decimal expansion would be 0.6666. Why? Well, first we would divide 100 by 6 to get approximately 16.6666. Then, because this represents 1/6, we can multiply it by 4 to get 4/6, which equals about 66.6664. Again, 4/6 is not a whole number and is less than a whole number. Because of this, the only digit to the left of the decimal point would be 0. When we divide 66.6664 by 100, we get 0.6666 as a repeating decimal.
If you need to better understand, let me know and I will gladly assist you.
Find the following value.
Please help!!
Answers
Answer: f^-1(1) + f(-14) = 20, f^-1(-2) = 10
Step-by-step explanation:
When finding the inverse through a table of functions, we are doing the opposite of a function. For example:
If f(9) = 1, then, let me ask you, what is f^-1(1)? Well, that's just 9! You're basically doing the opposite.
An inverse through a table of functions is basically you trying to figure out what x-value did you input to get the f(x) value. A regular function is you trying to figure out what f(x) value did you get by inputting an x-value.
So, the inverse of f(1) is 9, and the regular function of -14 is equal to 11. We then add. 11+9 = 20.
The inverse of -2, like I said before, is you trying to find out the x value you put to get -2. Well looking at the table, it seems x was 10. Thus the inverse of -2 is 10.
EVALUATE (mn)(x) for x = -3.
Answers
The value of expression (m n)(x) for x=-3 by putting x=-3 is -3mn.
Given Expression (m n)(x) and we have to find the value for x=-3.
Expression refers to the combinations of numbers, symbols, variables. It is usually not present in equal to form. It is often solved for finding the overall relationship between variables. It is often expresses quantity of one variable and combination of some material.
The given expression is (mn)(x)
To find the value of expression for x=-3, we have to just put the value of x=-3
mn(x)=(mn)(-3)
=(mn)-3
=-3mn
Hence the value of expression (mn)(x) for x=-3 is -3mn.
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how long word it take to travel a distance of 200 km if it traveling at a velocity of 55km
Answers
I NEED HELP PLEASEEEEEE
Answers
Answer:
A. The function is always decreasing
Step-by-step explanation:
we read a graph from left to right, so we can always compare the increase/decrease of a function by seeing how an x value compares with an x value to the left
(I am aware that this paragraph is really confusing)
we can see that as x increases, from -∞ to 0,
y decreases in correspondence
and that as x increases, from 0 to ∞,
y decreases in correspondence also
So, even though the graph doesn't quite look like it, when x < 0; the function decreases, when x > 0; function decreases--so the function is always decreasing
hope this helps!! have a lovely day :)
Triangle lmn has sides measuring 7 meters and 6 meters and a perimeter of 16 meters. heron’s formula: area = startroot s (s minus a) (s minus b) (s minus c) endroot what is the area of triangle lmn? round to the nearest square meter. 3 square meters 9 square meters 28 square meters 34 square meters
Answers
Answer:
9 m²
Step-by-step explanation:
s = half the perimeter = (a+b+c)/2
the perimeter in our case is
a+b+c = 16
so, s = 16/2 = 8
and the sides are
7 m
6 m
16 - 7 - 6 = 3 m
therefore, we get
area = sqrt(8(8-7)(8-6)(8-3)) = sqrt(8×1×2×5) = sqrt(80) =
= 8.94427191... ≈ 9 m²
Answer: the answer is b
Step-by-step explanation:
please help me i dont understand this
Answers
Answer:
200.96 m^2
Step-by-step explanation:
The formula for the area of a circle is πr^2, where r is the radius of the circle and π is approximately 3.14. We know that the diameter is 16 meters, and the radius is always half of the diameter (the diameter connects two ends of the circle, while the radius connects one point to the center). Therefore, the radius of this circle is 8m. Now we have all the information we need. The area of this circle is (3.14)(8)^2 = 3.14*64 = 200.96 m^2 (area is always in squared units)
Answer:
200.96m²
Step-by-step explanation:
Area of a Circle: Pi×r²
where:
pi = 3.14
r = diameter / 2
= 16÷2
= 8
Area = 3.14 × 8 × 8
= 200.96m²
Using f(x) = -5x + 12, evaluate f (-2)
Answers
Answer:
22Step-by-step explanation:
f(-2) means that the "x" variable in the equation can be substituted for -2
So, we have
-5(-2) + 12
This equals 10 + 12 = 22
So, the answer is 22
What is the coefficient of m3 in the expression 4m + 7 + 3m3?
4
7
3
3 m 3
Answers
Answer:
3 is the coefficient of m3
On applying a load of 100 N to a wire of a cross-sectional area of 0.01 m2, a strain of 6.25×10-3 is produced. Find Young’s Modulus for the wire.
Answers
The young modulus of a wire with an area of 0.01 m², that strain 6.25 * 10⁻³ if a load of 100N is applied is 16000 N/m²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The young modulus is given as:
Young modulus = stress / strain = load / (area * strain) = 100 / (0.01 * 6.25 * 10⁻³) = 16000 N/m²
The young modulus of a wire with an area of 0.01 m², that strain 6.25 * 10⁻³ if a load of 100N is applied is 16000 N/m²
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12. Create a two-way relative frequency table (in decimals) for the data in Exercise 9. Communication Gender Male Femal e Total Text 150.0 Talk 72.0 36.0 Social Media Apps 28.0 32.0 Total 250.0 150.0 12. Create a two - way relative frequency table ( in decimals ) for the data in Exercise 9 . Communication Gender Male Femal e Total Text 150.0 Talk 72.0 36.0 Social Media Apps 28.0 32.0 Total 250.0 150.0
Answers
See below for the steps to the two-way relative frequency table
How to create the two-way relative frequency table?The table of values is given as:
Communication Gender Male Female Total
Text 150.0 82.0 232.0
Talk 72.0 36.0 108.0
Social Media Apps 28.0 32.0 60.0
Total 250.0 150.0 400.0
Start by dividing each cell by the column total
Male Female Total
Text 150.0/250 = 0.6 82.0/150 = 0.55 232/400 = 0.58
Talk 72.0/250 = 0.288 36.0/150 = 0.24 108/400 = 0.27
Social Media Apps 28.0/250 = 0.112 32.0/150 = 0.21 60/400 = 0.15
Rewrite properly as:
Male Female Total
Text 0.60 0.55 0.58
Talk 0.288 0.24 0.27
Social Media Apps 0.112 0.21 0.15
Total 1 1 1
The above represents the two-way relative frequency table
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Find the value of:
(3/4)²
a.9/16
b.6/8
c.6/4
d.9/4
Answers
Answer:
a
Step-by-step explanation:
(3/4) to the power of 2 means to multiply it by itself and so, 3/4 times itself is 9/16
Answer:
This is a - [tex]\dfrac{9}{16}[/tex]Step-by-step explanation:
Hello
[tex]\large\displaystyle\text{$\begin{gathered} \sf Apply \ the \ third \ exponent \ rule-: \bigg(\dfrac{x}{y}\bigg)^m=\dfrac{x^m}{y^m} \end{gathered}$}}[/tex]
Solve-:
[tex]\large\displaystyle\text{$\begin{gathered} \sf \bigg(\dfrac{x}{y}\bigg)^2= \dfrac{3^2} {4^2} =\boxed{\sf{\frac{9}{16}}} \end{gathered}$ }}[/tex]
[tex]\pmb{\tt{done \ !!}}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
Which of the following expressions are equivalent to -9/6?
A. 9/-6
B. -9/-6
C. None of the above
Answers
The expression that is equivalent to -9/6 is = 9/-6. That is option A.
What is a fraction?Fraction is represented by a numerator and a denominator which can be either positive or negative.
From the fraction given, -9/6. The numerator is 9 while the denominator is 6.
The expression that is equivalent to -9/6 is = 9/-6 and not -9/-6 because the negatives are cancelled out.
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Javed saves Rs 50 000 in a bank. The annual interest is 2.5%. How much money will Mr Javed have in the account after one year? Javed saves Rs 50 000 in a bank . The annual interest is 2.5 % . How much money will Mr Javed have in the account after one year ?
Answers
Step-by-step explanation:
PLEASE HELP NEED ANSWER ASAP NEED HELP WITH SPECIFICALLY NUMBER 5
Daniel stands on one side of a stream that is 400 feet wide. He wants to reach his campsite that is 1600 feet downstream on the opposite side. He decides he will swim to the boat ramp on the opposite side, which is part way downstream toward the campsite, then jog the rest of the way. The angle formed by Daniel’s swim path and the shore at the boat ramp is .
(Score for Question 1: ___ of 3 points)
1. Draw a labeled diagram of the scenario.
Answer:
(Score for Question 2: ___ of 4 points)
2. Daniel can swim at an average rate of 150 feet per minute. How many minutes does it take him to swim to the boat ramp? Round your answer to the nearest hundredth.
Answer:
(Score for Question 3: ___ of 3 points)
3. How far is the boat ramp from the campsite? Round your answer to the nearest hundredth.
Answer:
(Score for Question 4: ___ of 4 points)
4. Daniel can jog at 4 miles per hour. How many minutes does it take him to jog from the boat ramp to the campsite? Round your answer to the nearest hundredth.
Answer:
(Score for Question 5: ___ of 6 points)
5. Daniel arrives at his campsite out of breath from his swim and jog. His sister tells him that he should have swam to the boat ramp that is only 200 feet from the campsite and then jogged. She claims that he would have arrived quicker this way.
Is Daniel’s sister correct? Support your answer mathematically.
Answers
Answer:
yes
Step-by-step explanation:
she is right because if he had did as she said it could have been better
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter motor company claims that its new sedan, the libra, will average better than 32 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
Answers
Rejecting the null thesis means that;
There's sufficient substantiation to support the claim that the mean is lesser than 32 long hauls per gallon.
For thesis testing, the first thing to define is the null and indispensable thesis.
In thesis testing, especially one comparing two sets of data, the null thesis plays the devil's advocate and generally takes the form of the contrary of the proposition to be tested. It generally contains the signs = , ≤ and ≥ depending on the directions of the test. It generally maintains that, with arbitrary chance responsible for the outgrowth or results of any experimental study/ thesis testing, its statement is true.
The indispensable thesis generally confirms the proposition being tested by the experimental setup. It generally contains the signs ≠,< and> depending on the directions of the test. It generally maintains that significant factors other than arbitrary chance, affect the outgrowth or results of the experimental study/ thesis testing and affect in its own statement.
For this question, Carter Motor Company claims that its new hydrofoil, the Libra, will total better than 32 long hauls per gallon in the megacity. And since this is talking distance covered per gallon of energy, better means that the new hydrofoil will total further than 32 long hauls per gallon.
So, the null thesis negating this claim would be that there is not significant substantiation to conclude that the normal of the new hydrofoil will be more or lesser than 32 long hauls per gallon.
That is, the new normal will be lower than or equal to 32 long hauls per hour.
And the indispensable thesis will confirm the claim that there's significant substantiation to conclude that the normal of the new hydrofoil will be more or lesser than 32 long hauls per gallon.
Mathematically,
The null thesis is represented as
H ₀ μ ≤ 32 long hauls per gallon
The indispensable thesis is given as
Hₐ μ> 32 long hauls per gallon
So, after the thesis test has been conducted, rejecting the null thesis means accepting the indispensable thesis and its statement that there's significant substantiation to conclude that the normal of the new hydrofoil will be more or lesser than 32 long hauls per gallon.
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help me solve this!!!
Answers
Answer:
C
Step-by-step explanation:
Here we can see this is a bit of an trial and error, let's go through the options individually.
To find whether the ordered pair satisfies the equation, we will substitute x and y into the equation. To have the ordered pair to satisfy the equation, the value must be 7.
A) Given x = -5 , y = 3,
[tex]-5x+3y= - 5(-5)+3(3)\\=25+9\\= 34\\34 \neq 7[/tex]
Therefore this pair does not satisfy the equation.
B) Given x = 2, y = -1,
[tex]-5x+3y = -5(2)+3(-1)\\= -10-3\\=-13\\-13 \neq 7[/tex]
Therefore this pair does not satisfy the equation.
C) Given x = 7, y = 14,
[tex]-5x+3y = -5(7)+3(14)\\= -35 + 42\\= 7[/tex]
Therefore this pair satisfy the equation.
D) Given x = -2, y =[tex]-\frac{13}{5}[/tex],
[tex]-5x+3y = -5(-2)+3(-\frac{13}{5} )\\=-10-\frac{39}{5} \\=-17.8 or -17\frac{4}{5} \\-17.8\neq 7[/tex]
Therefore this pair does not satisfy the equation.
need help solving for x
Answers
Answer:
x = 4
Step-by-step explanation:
the two angles you see are alternate exterior angles, meaning they are equal to eachother.
32x + 2 = 33x - 2
subtract so that x is on one side. 33 - 32 = 1, so the equation would be
2 = x - 2
add 2 to both sides.
4 = x
hope i helped.
Answer:
x = 16x
Step-by-step explanation:
32x divided by 2 equals 16x
33x minus 2 also equals 16x
Since the numbers are the same for both equations X equals 16x