Answer:
2^(8/9) in²
Step-by-step explanation:
Make use of the identity ...
... (a^b)^c = a^(bc)
Here, you have a=2, b=4/9, c=2. There is an additional factor (units of inches) inside the parentheses on the left. For that, you use the identity
... (ab)^c = a^c·b^c
In this case a = 2^(4/9), b = in, c = 2.
So, the working of your problem is ...
... Area = (side length)^2 = (2^(4/9) in)^2 = (2^(4/9))^2 in^2
... = 2^(4/9·2) in^2 = 2^(8/9) in^2
A metalworker has a metal alloy that is 20% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 52% copper alloy?
The metalworker should use
_______ of the metal alloy that is 20% copper and ___ kilograms
of the metal alloy that is 60% copper
(Type whole numbers.)
I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.
That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.
_____
Using an equation
If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...
... 0.60x + 0.20(100 -x) = 0.52·100
... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20
... x = 32/0.40 = 80 . . . . . kg of 60% alloy
... (100 -80) = 20 . . . . . . . .kg of 20% alloy
the original price of the sweater is 18.00 dollares. the sale price is 20% OFF THE ORIGINAL PRICE .what is the amount off the original price?
Answer:
The amount off the original price is $3.6.
Step-by-step explanation:
The original price of the sweater = $18.00
Amount off on the sweater = 20% of the original price of the sweater
=[tex]18.00\times\frac{20}{100}=$3.6[/tex]
The cost of the sweater on the sale = $18.00 - $3.6 = $14.4
The amount off the original price is $3.6.
The sum of 7 times a number and 9 is 5 . Use the variable c for the unknown number.
c - the number
The sum of 7 times a number and 9 is 5:
[tex]7c+9=5[/tex] subtract 9 from both sides
[tex]7c=-4[/tex] divide both sides by 7
[tex]\boxed{c=-\dfrac{4}{7}}[/tex]
Solve the equation.
x + 7/8 = 4
A. x = 4 7/8
B. x = -3 1/8
C. x = -4 7/8
D. x = 3 1/8
Answer:
D. x = 3 1/8
Step-by-step explanation:
x + 7/8 = 4
The first step is to subtract 7/8 from each side
x + 7/8 - 7/8 = 4 - 7/8
x = 4 - 7/8
We need to borrow from the 4. It become 3 8/8
x = 3 8/8 - 7/8
x = 3 1/8
Answer:
I believe the answer would be D.
Step-by-step explanation:
Solve the equation.
-3 2/5 + b = 8 1/5
A. b = 5 3/5
B. b = 11 3/5
C. b = 4 4/5
D. b = 11 1/5
Answer:
B. b = 11 3/5
Step-by-step explanation:
-3 2/5 + b = 8 1/5
The first step is to isolate b by adding 3 2/5 to each side
-3 2/5+ 3 2/5 + b = 8 1/5 + 3 2/5
b = 8 1/5 + 3 2/5
b = 8+3 + 1/5+2/5
b = 11 3/5
You have towels of three sizes. The length of the first is 3 /4 m, which makes up 3/ 5 of the length of the second. The length of the third towel is 5 /12 of the sum of the lengths of the first two. What part of the third towel is the second?
Answer:
9/10
Step-by-step explanation:
In ratio units, the relative lengths of the first, second, and third towels are ...
... 1 : 3/5 : (5/12)·(1 +3/5)
... = 1 : 3/5 : 2/3
Then the fraction the second towel is of the third towel is ...
... (3/5)/(2/3) = (3/5)·(3/2) = 9/10
answer:
the answer is 2/3
Please explain your answer!
Answer:
C none of the above
Step-by-step explanation:
-7 / -f
We know that a negative divided by a negative is a positive
-1/-1 * 7/f
1* 7/f
7/f
HELP!! will give points for brainliest
Denise earns $60 per day, plus $15 for each new customer she signs up. What is an explicit function rule for the amount Denise earns in a day, assuming that she signs up n customers?
an=
Answer:
f(x) = 60 + 15n
Step-by-step explanation:
if the start off amount is 60, so we can simply start it with 60 + ...
If she gets 15 for each customer, and the amount of customers is equal to n, then this can be written by 15n ( 12 * n )
Simply put these two parts together:
60 + 15n
So in a function:
f(x) = 60 + 15n
Use the table of values to identify the mathematical model that would best fit the data.
y = -4.2x +34
Step-by-step explanation:The differences between adjacent y-values are -4.2 for all data points given, so the data is best modeled by a linear function with a slope of -4.2. The value for x=0 (the y-intercept) will be 4.2 higher than the value for x=1, so will be 34.
Thus the model can be ...
... y = -4.2x + 34
_____
Comment on the attached graph
The graph shows an attempt to model the data with a quadratic function (the first on your answer list). The result is that the x² coefficient is zero, and the model is the equation of a line (as shown above).
Answer:
Linear
Step-by-step explanation:
I got it from passing a quiz
Mr. O'Conell spends 15% of his salary on food. He then spends 24% of it on transportation and saves the remaining $1,830. What is his salary?
Answer:
what do i do if my math skills are bad
Step-by-step explanation:
Let the Salary of Mr. O'Conell be : S
Given : Mr. O'Conell spends 15% of his Salary on Food
[tex]\mathsf{\implies 15\%\;of\;Salary(S) = (\frac{15}{100} \times S) = 0.15 \times S}[/tex]
Given : Mr. O'Conell spends 24% of his Salary on Transportation
[tex]\mathsf{\implies 24\%\;of\;Salary(S) = (\frac{24}{100} \times S) = 0.24 \times S}[/tex]
Given : After Spending on Food and Transportation, He saves $1830
Money Spent on Food + Money spent on Transportation + Remaining Money should be Equal to his Total Salary
[tex]\mathsf{\implies 0.15S + 0.24S + 1830 = S}[/tex]
[tex]\mathsf{\implies 0.39S + 1830 = S}[/tex]
[tex]\mathsf{\implies S - 0.39S = 1830}[/tex]
[tex]\mathsf{\implies 0.61S = 1830}[/tex]
[tex]\mathsf{\implies S = \frac{1830}{0.61} }[/tex]
[tex]\mathsf{\implies S = 3000}[/tex]
Mr. O'Conell's Salary is $3000
To finish an order in time the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. In how many days was the company supposed to finish the order?
Answer:
9 days.
Step-by-step explanation:
If the company produced 20 more items than 40 items each day, then it must have produced 60 items each day.
Though you're probably expected to write an equation, it's easiest to solve this through educated guess and check.
If there were 120 items to be produced, the company would be required to do it in 3 days (120 items, 40 items/day) but completed it in 2 days (120 items, 60 items/day). In this case, they finished their order 1 day early. But the problem states that they finished 3 days early. So we guess 3 times 120 items, or 360 items. Checking this, they should have finished their order in 9 days (360 items, 40 items/day) but they finished in 6 days (360 items, 60 items/day). 6 is three less than 9, so our guess of 360 items was correct. We have shown that the company should have finished the order in 9 days.
If you had to use an equation:
Let the desired number of days be x. Then, the company finished its order in x - 3 days. Since number of items produced is the number of days times items per day, and it doesn't change:
number of items = 40 items/day * x days = 60 items/day * (x - 3) days
40x = 60(x - 3) = 60x - 180
180 = 20x
x = 9
9 days is the desired answer.
Answer:
9
Step-by-step explanation:
Which proportion is true and why?
Answer:
D
Step-by-step explanation:
a) correct is 3/4.5=4/6; b) correct is 3.2/2.4=4/3; c) correct is 4/3.2=3/2.4; d) this is correct answer.
After joining two pieces of a picture frame together, a frame maker checks her work by measuring the diagonal (see the illustration). The sides of the frame form a right angle and the measurements are as follows: a = 12 in. and b = 5 in.
Write an equation of the line that passes through a pair of points: -2,-2 and 5,-5
Answer:
The equation of the line would be y = -3/7x - 20/7
Step-by-step explanation:
To start finding the line of this equation, you need to find the slope. You can do this using the slope equation.
m(slope) = (y2 - y1)/(x2 - x1)
m = (-2 - -5)/(-2 - 5)
m = (-2 + 5)/(-2 - 5)
m = 3/-7
m = -3/7
Now that we have the slope, we can use that and either point in point-slope form to get the equation.
y - y1 = m(x - x1)
y + 5 = -3/7(x - 5)
y + 5 = -3/7x + 15/7
y = -3/7x - 20/7
To find the equation of the line that passes through (-2, -2) and (5, -5), calculate the slope, apply it to the point-slope form using one of the points, then simplify to slope-intercept form, resulting in y = (-3/7)x - 20/7.
To find the equation of the line that passes through the points (-2,-2) and (5,-5), we first need to calculate the slope of the line. The slope (m) can be found using the formula:
m = (y_{2} - y_{1}) / (x_{2} - x_{1})
Substituting our points into the formula:
m = (-5 - (-2)) / (5 - (-2)) = (-5 + 2) / (5 + 2) = -3 / 7
Next, we use the point-slope form of a line's equation which is y - y1 = m(x - x1). Let's use the first point (-2, -2):
y - (-2) = (-3/7)(x - (-2))
Now we simplify and write the equation in slope-intercept form (y = mx + b):
y + 2 = (-3/7)x - 6/7
Subtract 2 from both sides of the equation to solve for y:
y = (-3/7)x - 6/7 - 14/7
y = (-3/7)x - 20/7
The equation of the line that passes through the points (-2,-2) and (5,-5) is y = (-3/7)x - 20/7.
If f(x) = x3 – x2 – 3, which of the following is equal to g(x) = f(2 – x)?
–x3 + 5x2 – 8x + 1
–x3 + 7x2 – 16x – 15
x3 + 5x2 + 8x + 1
x3 – 7x2 + 16x – 15
Answer:
-x^3+5x^2-8x+1, which is choice A
======================================
Work Shown:
f(x) = x^3 - x^2 - 3
f(x) = (x)^3 - (x)^2 - 3
f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)
f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2
f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3
f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4
f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5
f(2-x) = -x^3+5x^2-8x+1
----------
note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.
note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2
note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.
note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.
note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2
Answer:
–x3 + 5x2 – 8x + 1
–x3 + 7x2 – 16x – 15
x3 + 5x2 + 8x + 1
x3 – 7x2 + 16x – 15
Step-by-step explanation:
–x3 + 5x2 – 8x + 1
–x3 + 7x2 – 16x – 15
x3 + 5x2 + 8x + 1
x3 – 7x2 + 16x – 15
At a high school, the probability that a student is a senior is 0.25. The probability that a student plays a sport is 0.15. The probability that a student is a senior and plays a sport is 0.10. What is the probability that a randomly selected student plays a sport, given that the student is senior?
A. 0.10
B. 0.15
C. 0.66
D. 0.40
Please explain
Use the definition of conditional probability:
[tex]P(\text{sports}\mid\text{senior})=\dfrac{P(\text{sports AND senior})}{P(\text{senior})}[/tex]
We know that 0.10 of students belong to both categories, and that 0.25 of students are seniors, so
[tex]P(\text{sports}\mid\text{senior})=\dfrac{0.10}{0.25}=0.40[/tex]
Answer:
0.40
Step-by-step explanation:
The figure shows the graphs of the functions y=f(x) and y=g(x). the four indicated points all have integer coordinates. If g(x) = f(x) +k, what is the value of k?
Answer:
k = -2
Step-by-step explanation:
The graph clearly shows the y-intercept of f(x) as being 4, and that of g(x) as being 2. Thus, g(x) = f(x) -2 = f(x) +k.
Subtracting f(x) from that equation, you get k = -2.
_____
Check
g(x) is displaced 3 units to the right of f(x). The slopes of both f(x) and g(x) are 2/3, so a displacement of 3 units right is equivalent to a displacement of 2 units down. k represents the vertical translation, so is -2.
The value of k is found by examining the vertical distance between the graphs of y=f(x) and y=g(x) at the same x-coordinate. Without the visual graphs or specific points, the exact value of k cannot be provided.
Explanation:The student is asking about the relationship between two functions, where g(x) is related to f(x) by the addition of a constant k.
To find the value of k, one would typically examine the vertical distance between the two function graphs at any given x-coordinate, since g(x) = f(x) + k. Without the graphical information provided, it is not possible to determine the exact value of k.
However, typically if you have two functions with graphs that are vertically shifted versions of each other, and you know two corresponding points on each graph with integer coordinates, you can subtract the y-values of these points to find k.
Simplify. 3.3÷(0.8−3)−0.5 Enter your answer in the box.
Answer:
-2
Step-by-step explanation:
3.3÷(0.8−3)−0.5
First think of PEMDAS
So first do parenthese
(0.8-3)=-2.2
3.3÷-2.2-0.5
Now do division
3.3/-2.2=-1.5
and now subtraction
-1.5-0.5=-2
What is the value of this expression (29+18)+(17-8) / 8
48 1/8
Step-by-step explanation:As written, it is evaluated as ...
... 47 + 9/8 . . . . . . . . parentheses are evaluated first
... = 47 + 1 1/8 . . . . . . then division
... = 48 1/8 . . . . . . . . then addition
_____
A decent calculator will evaluate this for you according to the order of operations. A Google or Bing search box will do that, too.
Math Help
Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. (5 points)
f(x) = 4.7 ⋅ 1.09x
A) Exponential decay function; 109%
B) Exponential growth function; 0.09%
C) Exponential growth function; 109%
D) Exponential growth function; 9%
the tale-tell fellow is the base of the exponent ˣ.
if that number is less than 1, is a decay factor, if it's more than 1, is growth.
1.09 is cleary more than 1, so is growth, at what rate?
[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &P\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0.0r\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ f(x)=4.7(1.09)^x\implies f(x)=4.7(1+\stackrel{\stackrel{r}{\downarrow }}{0.09})^x \\\\\\ r=0.09\implies \stackrel{\textit{converting it to percentage}}{r=0.09\cdot 100}\implies r=\stackrel{\%}{9}[/tex]
Exponential functions are mostly used to represent growth of population.
The true option is: (d) Exponential growth function; 9%
The function is given as:
[tex]\mathbf{f(x) = 4.7 \cdot 1.09^x}[/tex]
An exponential function is represented as:
[tex]\mathbf{f(x) = a \cdot b^x}[/tex]
By comparison:
[tex]\mathbf{b = 1.09}[/tex]
When b is greater than 1, then the function is a growth function.
Next, we calculate the constant percentage rate of growth (r)
If b is greater than 1, then:
[tex]\mathbf{b = 1 + r}[/tex]
Substitute 1.09 for b
[tex]\mathbf{1 + r = 1.09}[/tex]
Subtract 1 from both sides
[tex]\mathbf{r = 0.09}[/tex]
Express as percentage
[tex]\mathbf{r = 0.09 \times 100\%}[/tex]
[tex]\mathbf{r = 9\%}[/tex]
Hence, the growth rate is 9%
Hence, the true option is: (d) Exponential growth function; 9%
Read more about exponential growth and decay functions at:
https://brainly.com/question/14355665
A construction crew is lengthening a road. The road started with a length of 59 miles, and the crew is adding 4 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.
Answer:
The total length of the road after the crew has worked 31 days is 183 miles.
Step-by-step explanation:
As given
A construction crew is lengthening a road.
The road started with a length of 59 miles, and the crew is adding 4 miles to the road each day.
let L represent the total length of the road (in miles).
let D represent the number of days the crew has worked.
Than the equation becomes
L = 59 + 4D
Now find out the total length of the road after the crew has worked 31 days.
D = 31 days
Put in the equation
L = 59 + 4 × 31
= 59 + 124
L = 183 miles
Therefore the total length of the road after the crew has worked 31 days is 183 miles.
A motorboat, that has speed of 10 km/hour in still water, left a pier traveling against the current of the river. Forty-five minutes after the boat left the pier, the motor of the boat broke, and the boat began drifting with the current. After three hours of drifting with the current, the boat was back at the pier where it had started. What is the speed of the current of the river?
Answer:
2 km/h
Step-by-step explanation:
distance = speed × timetime = distance/speedLet c represent the speed of the current of the river in km/h. Then the speed of the boat upstream is (10-c). In 3/4 hour, the distance traveled upstream is ...
... distance upstream = (3/4)·(10 -c)
The time taken to travel the same distance downstream is given as 3 hours. The speed in that direction is c, so we have ...
... 3 = distance upstream/c = (3/4)(10 -c)/c
Multiplying this equation by 4c, we get ...
... 12c = 3(10 -c)
... 15c = 30 . . . . . . . . add 3c
... c = 2 . . . . . . . . . . . divide by 15
The speed of the river current is 2 km/h.
Answer:
2km/h
Step-by-step explanation:
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
Answer:
34
Step-by-step explanation:
3 + 4 = 7
34 with reversed digits is 43
43 - 34 = 9
Solve for x and y if: 2x + 3y = 5 and 3x + 4y = 4
[tex]\left\{\begin{array}{ccc}2x+3y=5&|\text{multiply both sides ny 3}\\3x+4y=4&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x+9y=15\\-6x-8y=-8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad \boxed{y=7}\\\\\text{put the value of y to the first equation}\\\\2x+3(7)=5\\\\2x+21=5\qquad\text{subtract 21 from both sides}\\\\2x=-16\qquad\text{divide both sides by 2}\\\\\boxed{x=-8}\\\\Answer:\ \boxed{x=-8\ and\ y=7}[/tex]
The area of a square is 361 square yards. How long is each side of the square?
Answer:
19 yards
Step-by-step explanation:
A square has 4 equal sides, thus its area is given by the formula below.
[tex]\boxed{\text{Area of square}=\text{side}^2}[/tex]
Substitute the area of the square into the formula:
361= side²
Square root both sides:
Length of each side
= [tex]\sqrt{361}[/tex]
= 19 yards
To learn more about area of square, check out: https://brainly.com/question/4988011
please answer quickly
Answer:
Option C is correct.
The value of x nearest to tenth is, 21.4 units
Step-by-step explanation:
In a given right angle triangle;
by definition of tangent ratio i,e [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]
[tex]\tan 25^{\circ} = \frac{10}{x}[/tex]
[tex]0.46630765815 = \frac{10}{x}[/tex]
or
[tex]x = \frac{10}{0.46630765815} = 21.4450692[/tex] units
Therefore, the value of x nearest to tenth is, 21.4 units
Which answer is the explicit it rule for the sequence 12.5, 11,9.5,8,6.5,5
A. an=14+1.5n
B. An=13-1.5n
C. an=14.5-1.5n
D. an=14 -1.5n
D. an = 14 - 1.5n
Step-by-step explanation:Selection D is the only one that works to give a1 = 12.5.
The explicit rule for the given sequence is option D, an = 14 - 1.5n, which indicates starting from 14, subtract 1.5 times the position of the term (n).
Explanation:To determine the explicit rule for the given sequence 12.5, 11, 9.5, 8, 6.5, 5, we can observe that the sequence is decreasing by 1.5 each time. Knowing this, we can try to find a relationship between the position of each term (n) and its value (an).
Let's consider the first term when n=1. We need a starting point (initial value when n=1) that degreases by 1.5 for each subsequent term. We can see that the first term of the sequence (12.5) is 1.5 less than 14, so we subtract 1.5 from 14 to define the first term: 14 - 1.5*1 = 12.5. Thus, for any term n, the value would be 14 - 1.5*n.
Therefore, the correct explicit rule is given by option D: an = 14 - 1.5n.
Of items produced by a factory, 40% come from line i and 60% from line ii. eight percent of the items produced on line i and 10% of the items produced on line ii are defective. an item is chosen at random. find the probability that it is not defective.
Answer:
Step-by-step explanation:
I don't know how is to speak it English correctly but is the teoreme of whole probability
P(A1)=0.08*0.4=0,032 is probability to choose defective item line I
P(A2)=0.1*0.6=0.06 is probability to choose defective item line II
P(B)=P(A1)+P(A2)=0,032+0.06=0.092 probability to choose defective item
P(C)=1-P(B)=0.908 the probability that it is not defective
Use properties of exponents to simplify the following expression.
Help!!!Math!! Please explain how you got your answer.
the simplified expressions are:
1. [tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]
2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]
3. [tex](2/3) * (x^2 / y) * (1/z^7)[/tex]
4. [tex](2/3x^2) * yz[/tex]
5. [tex](2x^4 * y) / (3z)[/tex]
Let's simplify each of the given expressions using properties of exponents:
1. [tex](2x^4 * y^-4 * z^-3) / (3x^2 * y^-3 * z^4)[/tex]
To simplify this expression, you can use the properties of exponents that state when you divide two terms with the same base, you subtract the exponents:
[tex](2x^4 / 3x^2) * (y^-4 / y^-3) * (z^-3 / z^4)[/tex]
Now, simplify each term separately:
[tex](2/3) * (x^(4-2)) * (y^(-4-(-3))) * (z^(-3-4))[/tex]
[tex](2/3) * x^2 * y^(-1) * z^(-7)[/tex]
The simplified expression is
[tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]
2. [tex](3x^2 * y^2 * z^4) / 2[/tex]
To simplify this expression, simply divide each term by 2:
[tex](3x^2 / 2) * (y^2 / 2) * (z^4 / 2)[/tex]
The simplified expression is:
[tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]
3. [tex](2x^2) / (3y * z^7)[/tex]
To simplify this expression, divide each term in the numerator by 3y and each term in the denominator by 3y:
[tex](2x^2) / (3y * z^7) = (2x^2 / 3y) * (1 / z^7)[/tex]
The simplified expression is:
[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]
4. [tex](2yz) / (3x^2)[/tex]
To simplify this expression, divide each term in the numerator by 3x^2:
[tex](2yz) / (3x^2) = (2 / 3x^2) * yz[/tex]
The simplified expression is:
[tex](2/3x^2) * yz[/tex]
5. [tex](2x^4 * y) / (3z)[/tex]
This expression is already in a relatively simple form, and there are no common factors to further simplify it.
So, the simplified expressions are:
1. [tex](2/3) * x^2 * (1/y) * (1/z^7)\\[/tex]
2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]
3.[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]
4. [tex](2/3x^2) * yz[/tex]
5. [tex](2x^4 * y) / (3z)[/tex]
Learn more about Exponents here:
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Today's newspaper contains a 20%-off coupon at Old Army. The $100 jacket that you want was already reduced by 40%. What as the final price that you paid for the jacket?
a.
$48
b.
$46
c.
$42
d.
$40
Answer:
Answer is: D. $40
Step-by-step explanation:
20+40=60
100-60=40
Answer:
A 48
Step-by-step explanation: