I need to figure out the easiest way to solve this and apply the method to every problem
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The function is given as,
[tex]f(x_{)=-3x^2-7x}[/tex]It is asked to find the value of the expression,
[tex]f(7)[/tex]This can be obtained by replacing 'x' by 7 in the given expression of the function,
[tex]f(7)=-3(7)^2-7(7)[/tex]Resolve the parenthesis,
[tex]\begin{gathered} f(7)=-3(49)-49 \\ f(7)=-147-49 \end{gathered}[/tex]Simplify the terms further,
[tex]f(7)=-196[/tex]Thus, the value of the expression f(7) is obtained as,
[tex]=-196[/tex]Related Questions
You deposit $400 into a savings account that earns interest annually. The function g(x) = 400(1.05)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[0, 400]
[0, ∞)
[400, ∞)
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Answer:
Step-by-step explanation:
The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits.
Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.
Principal - $400
rate of interest is compounded annually
g(x) = 400( 1.03)ˣ equation 1.
Formula used
A = P( 1 + r )ⁿ
here n = x
Solution:
Putting the value of n, and principal in the formula
A = P( 1 + r )ⁿ ................... equation 2
now comparing both equation 1 and equation 2,
400( 1.05)ˣ = 400( 1 + r )ˣ
( 1.05)ˣ = ( 1 + r )ˣ
1.05 = 1 + r
r = 1.05 - 1
r = 0.05
r % = 0.05 × 100
r % = 5 %
thus, the constant percent rate of change = 5 %
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I need help on answering 3. (d) I have two choices it can be which is false and sometimes true.
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Question:
Solution:
If x represents a positive integer, then the point x is a natural number, that is, x is greater than zero, in particular, if x is a number greater than zero it can be a number greater than any number after zero. For example, it can be greater than 1.
Then the question d is ALWAYS TRUE.
Consider the following word problem:Two planes, which are 1180 miles apart, fly toward each other. Their speeds differ by 40 mph. If they pass each other in 2 hours,what is the speed of each?Step 1 of 2: Use the variable x to set up an equation to solve the given problem. Set up the equation, but do not take steps to solve it.
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So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:
[tex]\begin{gathered} 2v+40\frac{mi}{h}=\frac{1180mi}{2h}=590\frac{mi}{h} \\ 2v=590\frac{mi}{h}-40\frac{mi}{h}=550\frac{mi}{h} \\ v=\frac{550\frac{mi}{h}}{2}=275\frac{mi}{h} \end{gathered}[/tex]Then we get:
[tex]v+40\frac{mi}{h}=275\frac{mi}{h}+40\frac{mi}{h}=315\frac{mi}{h}[/tex]Then the speeds of the planes are 275mph and 315mph.
Suppose you open a bank account and deposit $50. Then, every month you deposit $20. Write anequation that relates the total number of dollars deposited, T, and the month, m.Which equation below relates the total number of dollars deposited, T, and the month, m?
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Let:
T = Total number of dollars deposited
m = Number of months
b = Initial deposit
So:
[tex]\begin{gathered} T(m)=20m+b \\ where \\ b=50 \\ so\colon \\ T(m)=20m+50 \end{gathered}[/tex]9 - 6 - 19 c) y - 12 OC p = b) y 24 c) = 9
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x=70, y= -50 and x=80
1) Let's solve each equation, plugging in the given value for x
y=5x -300
a) y=50
y=5x -300 Plug y=50
50=5x -300 Add 300 to both sides
50+300=5x
350 = 5x Divide both sides by 5
x=70
b) x = 50
y=5x -300 Plug x=50
y=5(50) -300 Distribute the factor
y= 250 -300
y= -50
c) y=100
y=5x -300 Plug y=100
100 = 5x -300 Add 300 to both sides
400 = 5x
x =80
Hence, the answer is
x=70, y= -50 and x=80
a triangle with an area of 8 in^2 is dilated by a factor of 3. the area of the dilated triangle is ___ in^2(no image included)
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we have:
[tex]A=\frac{1}{2}(b\times3)(h\times3)=\frac{1}{2}(9bh)=\frac{9}{2}bh[/tex]therefore:
[tex]A=72[/tex]answer: 72 in^2
hello can you help me with this question and this a homework assignment
Answers
Problem
Solution
For this case we can use the Cosine law and we have:
[tex]\cos (c)=\frac{a^2+b^2-c^2}{2ab}=\frac{35^2+56^2-33^2}{2\cdot35\cdot56}=0.8346938776[/tex][tex]\cos (b)=\frac{a^2+c^2-b^2}{2ac}=\frac{35^2+33^2-56^2}{2\cdot35\cdot33}=-0.356[/tex][tex]\cos (a)=\frac{c^2+b^2-a^2}{2cb}=\frac{33^2+56^2-35^2}{2\cdot33\cdot56}=0.8116883117[/tex]And then we can find the angles with the arcos like this:
[tex]<\gamma=ar\cos (0.8346938776)=33.42[/tex][tex]<\beta=ar\cos (-0.356)=110.85[/tex][tex]<\alpha=ar\cos (0.8116883117)=35.74[/tex]Can you see the new values for gamma and alfa
You and 2
2
friends have a job cleaning houses. You split the total money you make so that you each get the same amount. On the first day, you earn $93
$
93
. The second day, you earn $75
$
75
. The third day, you earn $108
$
108
. How much money do you each get for 3
3
days of work?
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The amount of money that each person would get for the three days of work is $92.
How much would each person get?The first step is to add all the money earned on the three days together. Addition is the process of determining the sum of two or more values.
Total amount earned in the 3 days = amount earned on the first day + amount earned on the second day + amount earned on the third day
= $93 + $75 +$108 =$276
The next step is to divide the total amount of money earned in the three days by the total number of people that would share the money. Division is the process of determining the quotient of a number.
The amount of money gotten by each person = total earnings / total number of people
$276 / 3 = $92
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n=39; i = 0.039; PMT = $196; PV =?
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Given the Present Value (PV) formula
[tex]PV=PMT\times\frac{1-(\frac{1}{(1+i)^n})}{i}[/tex]Write out the parameters
[tex]\begin{gathered} PV=\text{?} \\ n=39 \\ i=0.039 \\ \text{PMT=\$196} \end{gathered}[/tex]Substitute the following values in the present value formula to find the PV
[tex]PV=196\times\frac{1-(\frac{1}{(1+0.039)^{39}})}{0.039}[/tex][tex]PV=196\times\frac{1-0.2249021697}{0.039}[/tex][tex]PV=196\times\frac{0.7750978303}{0.039}[/tex][tex]\begin{gathered} PV=196\times19.87430334 \\ PV\approx3895.36 \end{gathered}[/tex]Hence, the Present Value (PV) is approximately $3895.36
I will attach a picture to this question so you can understand it better.
Answers
Here are the given information:
1. 7 red beads for every 4 blue beads
2. total of 44 beads (red and blue)
Find: the number of red beads
Solution:
We can solve this in two ways. We can solve this using proportion or we can solve this by counting.
Let's start counting first. Let's say 7 red beads and 4 blue beads is 1 set. So, for every set, we already have 7 + 4 = 11 beads in total.
First set = 7 red bead + 4 blue beads = 11 beads
Second set = 7 red bead + 4 blue beads = 11 beads
Third set = 7 red bead + 4 blue beads = 11 beads
Fourth set = 7 red bead + 4 blue beads = 11 beads
If we add all the 4 sets, we have a total of 44 beads. If we add all the RED beads only, we get 7 red beads x 4 sets = 28 red beads.
Therefore, Lily used 28 red beads.
Now, using proportion, we can have this equation:
[tex]\frac{7\text{red beads}}{4\text{blue bead}}=\frac{x\text{ red beads}}{(44-x\text{ red)blue beads}}[/tex]where x = the total number of red beads and we got 44 - x as the number of blue beads.
The next thing that we need to do here is to solve for x.
1. To solve for x, do cross multiplication first.
[tex]7(44-x)=4x[/tex]2. Multiply 7 to the numbers inside the parenthesis.
[tex]308-7x=4x[/tex]3. Add 7x on both sides of the equation.
[tex]\begin{gathered} 308-7x+7x=4x+7x \\ 308=11x \end{gathered}[/tex]4. Lastly, divide both sides by 11.
[tex]\begin{gathered} \frac{308}{11}=\frac{11x}{11} \\ 28=x \end{gathered}[/tex]As we can see, the value of x = 28. Lily used 28 red beads.
Find the equation of a line that is parallel to the line x = 10 and contains the point (-8,1)the equation of the line is =
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The given line is x = 10, which is a vertical line. All vertical lines have the form x = k, where k is a real number.
So, a parallel line passing through (-8,1) would be x = -8.
Hence, the answer is x = -8.Find f(-4) and f(3) for the following funxripnf(x)=3x
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Given the function:
[tex]f(x)=3x[/tex]• You need to substitute this value of "x" into the function:
[tex]x=-4[/tex]And then evaluate, in order to find:
[tex]f(-4)[/tex]You get:
[tex]f(-4)=3(-4)[/tex][tex]f(-4)=-12[/tex]Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]• Substitute this value of "x" into the function:
[tex]x=3[/tex]Then:
[tex]f(3)=3(3)[/tex]Evaluate, in order to find:
[tex]f(3)[/tex]You get:
[tex]f(3)=9[/tex]Hence, the answer is:
[tex]\begin{gathered} f(-4)=-12 \\ f(3)=9 \end{gathered}[/tex]Triangle ABC is similar to triangle DEF. Find the measure of side DE. Round youranswer to the nearest tenth if necessary.C7BF27E15DAD
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Given:
Triangle ABC is similar to triangle DEF.
[tex]\frac{DE}{AB}=\frac{EF}{BC}[/tex][tex]\begin{gathered} \frac{DE}{15}=\frac{27}{7} \\ DE=\frac{27}{7}\times15 \\ DE=57.9 \end{gathered}[/tex]the table below shows changes in the population densities of the zebra and you knew I'd muscles from 1991 to 2015, in six-year intervals.1. based on the data shown in the table calculate the percent change in the population density of zebra mussels from 1997 to 2003
Answers
The table below shows changes in the population densities of the zebra and you knew I'd muscles from 1991 to 2015, in six-year intervals.
1. Based on the data shown in the table calculate the percent change in the population density of zebra mussels from 1997 to 2003
_____________________
1997 (3 250)
2003 (2 500)
Percentage change= 100 *(new value- old value)/old value
Percentage change = 100 *(2500- 3250)/ 3250 = 100* (-0.2308)
Percentage change = -23.08%
__________________________________
Answer
The percent change in the population density of zebra mussels from 1997 to 2003 is -23.08%
There was a decrease of 23. 08%
A hot chocolate recipe calls for 2.5 gallons of milk. How many quarts of milk are needed for the recipe
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Answer: 10
Step-by-step explanation: a gallon has 4 quarts, 4x2.5=10
10 quarts is 2.5 gallons.
Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary.5,−2,45,...5,−2, 54 ,...Sum of a finite geometric series:Sum of a finite geometric series:Sn=a1−a1rn1−rS n = 1−ra 1 −a 1 r n
Answers
Solution:
Given:
[tex]5,-2,\frac{4}{5},\ldots[/tex]To get the sum of the first 7 terms, the formula below is used;
[tex]S_n=\frac{a_1-a_1r^n}{1-r}[/tex]where;
[tex]\begin{gathered} n=7 \\ a_1\text{ is the first term = 5} \\ r\text{ is the co}mmon\text{ ratio=}\frac{-2}{5} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} S_n=\frac{a_1-a_1r^n}{1-r} \\ S_7=\frac{5-5(-\frac{2}{5})^7}{1-(-\frac{2}{5})} \\ S_7=\frac{5-5(-0.4)^7}{1+\frac{2}{5}} \\ S_7=\frac{5-5(-0.0016384)}{1+0.4} \\ S_7=\frac{5+0.008192}{1.4} \\ S_7=\frac{5.008192}{1.4} \\ S_7=3.57728 \end{gathered}[/tex]Therefore, the sum of the first 7 terms is 3.57728
Consider the following relation: (1,12) ,(3, 8) , (3, 11) , (6, 9) , (7, 11) . Whichordered pair could be removed so thatthe relation is a function?Group of answer choices
Answers
Answer: Rajesh Kumar
Step-by-step explanation I took the wok to poland
The pyramid has a square base with side
length 2 cm and height 3 cm. What is the
volume of the chocolate to the nearest
tenth?
A 12 cm
B 6 cm3
C 4 cm
D 2 cm
E 1.3 cm3
Answers
The radius of cylinder is r = 3 in.
The height of cylinder is h = 10 in.
The formula for the volume of cylinder is,
[tex]V=\pi\cdot(r)^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cylinder.
[tex]\begin{gathered} V=\pi\cdot(3)^2\cdot10 \\ =282.743 \\ \approx282.7 \end{gathered}[/tex]So volume of cylinder is 282.7 in^3.
Option H is correct.
Hello I would like to know what is the answer to the question 3/4x 3 < 6
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The director of an alumni association for a small college wants to determine whether there is any type of relationship between an alum’s contribution (in dollars) and the number of years the alum has been out of school. The data follow.
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----------------------------
b)
[tex]\begin{gathered} X=4 \\ \hat{y}(4)=-50.43919(4)+453.17568 \\ \hat{y}(4)=-201.75676+453.17568 \\ \hat{y}(4)=251.41892 \end{gathered}[/tex]Find the values of x and y
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Since the "x" values are vertical angles, and so are the "y" values, you must make them equal. If this is confusing, look at steps below (The order of solving the "x" or "y" values don't matter. I will write both ways down (in point form --> [tex](x,y)[/tex] and as just "x=..." "y=..."
First step is to make the "y" values equal each other
[tex]5y = 7y-34\\-2y = -34\\2y = 34\\\\y=17[/tex]
Next to solve make the "x" values equal each other
[tex]8x+7 = 9x-4\\-x = -11\\x = 11[/tex]
Final Answer:
[tex](11,17)[/tex]
x = 11; y = 17
Hope this helps :)
5 1/7 * 4 2/3 equals
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We have to solve this operation with mixed numbers.
We can solve this applying the distributive property or by converting the mixed numbers into fractions.
We will solve this converting the numbers into fractions:
[tex]\begin{gathered} (5+\frac{1}{7})\cdot(4+\frac{2}{3}) \\ \frac{5\cdot7+1}{7}\cdot\frac{4\cdot3+2}{3} \\ \frac{35+1}{7}\cdot\frac{12+2}{3} \\ \frac{36}{7}\cdot\frac{14}{3} \\ \frac{36}{3}\cdot\frac{14}{7} \\ 12\cdot2 \\ 24 \end{gathered}[/tex]Answer: 24
determin wether true or false. (2 points) True False The functions f(x) = x – 5 and g(x) = -3x + 15 intersect at x = 5. The functions f (x) = 3 and g(x) = 11 – 2. intersect at x = 3. O The functions f (x) = x + 3 and g(x) = -x + 7 intersect at x = 2. The functions f (x) = {x – 3 and g(x) = -2x + 2 intersect at x = -2.
Answers
To find the intersection point between f(x) and g(x) we will equate their right sides
[tex]\begin{gathered} f(x)=x-5 \\ g(x)=-3x+15 \end{gathered}[/tex]Equate x - 5 by -3x + 15 to find x
[tex]x-5=-3x+15[/tex]add 3x to both sides
[tex]\begin{gathered} x+3x-5=-3x+3x+15 \\ 4x-5=15 \end{gathered}[/tex]Add 5 to both sides
[tex]\begin{gathered} 4x-5+5=15+5 \\ 4x=20 \end{gathered}[/tex]Divide both sides by 4 to get x
[tex]\begin{gathered} \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Then the first one is TRUE
For the 2nd one
f(x) = 3, and g(x) = 11 - 2x
If x = 3, then substitute x by 3 in g(x)
[tex]\begin{gathered} g(3)=11-2(3) \\ g(3)=11-6 \\ g(3)=5 \end{gathered}[/tex]Since f(3) = 3 because it is a constant function and g(x) = 5 at x = 3
That means they do not intersect at x = 3 because f(3), not equal g(3)
[tex]f(3)\ne g(3)[/tex]Then the second one is FALSE
For the third one
f(x) = x + 3
at x = 2
[tex]\begin{gathered} f(2)=2+3 \\ f(2)=5 \end{gathered}[/tex]g(x) = -x + 7
at x = 2
[tex]\begin{gathered} g(2)=-2+7 \\ g(2)=5 \end{gathered}[/tex]Since f(2) = g(2), then
f(x) intersects g(x) at x = 2
The third one is TRUE
For the fourth one
[tex]f(x)=\frac{1}{2}x-3[/tex]At x = -2
[tex]\begin{gathered} f(-2)=\frac{1}{2}(-2)-3 \\ f(-2)=-1-3 \\ f(-2)=-4 \end{gathered}[/tex]g(x) = -2x + 2
At x = -2
[tex]\begin{gathered} g(-2)=-2(-2)+2 \\ g(-2)=4+2 \\ g(-2)=6 \end{gathered}[/tex]Hence f(-2) do not equal g(-2), then
[tex]f(-2)\ne g(-2)[/tex]f(x) does not intersect g(x) at x = -2
The fourth one is FALSE
A father is buying cheeseburgers for his children. Each cheeseburgercosts $3.50. He spends $17.50 on cheeseburgers. Which equation canyou use to determine how many cheeseburgers he bought?O 17.50 = 3.50cO 3.50 = 17.500O 3.50 + 17.50 =cO 17.50 -3.50 = C« PreviousNext
Answers
Each cheese burger costs $3.50
c reprsents the number of cheese burgers
$17.50 is the total cost spent on c cheeseburgers
If you multiply the value of each cheeseburger by the number bought, you'll obtain the total cost:
3.50c=17.50
The correct option is number 1
Frank makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
Answers
The equation will be
P = 8h
here, P = total pay
h= working hours.
Bell Ringer -- Find the distance of each side of the triangle: A(-10, 6) B(-6, 9) C(-6, 6)
Answers
Answer:
It is c) (-6, 6)
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units. Where has the point moved to?
Answers
Given
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units.
To find:
Where has the point moved to?
Explanation:
It is given that,
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units.
That implies,
Since starting at 0 on a number line, a point is moved 21 units.
Then,
[tex]0+21=21[/tex]Also, then 53 units.
Then,
[tex]21+53=74[/tex]Also, then 721 units.
Then,
[tex]74+721=795[/tex]And, finally negative-50 units.
Then,
[tex]\begin{gathered} 795+(-50)=795-50 \\ =745 \end{gathered}[/tex]Hence, the point is moved to 745.
Takashi is driving to his grandmother's house. he is driving at a constant speed and will not make any stops along the way. Takashi’s distance in miles from his grandmother’s house h hours after leaving can be described by equationA. Identify and interpret the independent variable? B. Identify and interpret the coefficient? C. Identify and interpret the constant term ?D. Identify and interpret the dependent variable?
Answers
Let's begin by listing out the information given to us:
To calculate Takashi's distance from his grandmother's house is given by the formula:
[tex]\begin{gathered} distance=speed\cdot time \\ h=v\cdot t \end{gathered}[/tex]Independent variable refers to the variable that stands by itself and whose value is not affected by the other
Dependent variable refers to the variable whose value is affected by the value of another variable
A. The distance (h) does not change irrespective of Takashi's speed, hence it is the independent variable
B. The coefficient is the speed (v)
C. The constant is time (t)
D. The speed (v) changes with variation in time, hence it is the dependent variable
A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annual interest is $590
Answers
If a total of $6000 is invested, part at 5% and remainder at 10%, then the amount invested on 10% interest is $5800 and the amount invested on 5% interest is $200
The total amount = $6000
Consider the amount invested on 10% interest as x
The amount invest on 5% interest = (6000-x)
The the equation will be
x×(10/100) + (6000-x)(5/100) = 590
0.1x + 0.05(6000-x) = 590
0.1x + 300 - 0.05x = 590
0.05x +300 = 590
0.05x = 590-300
0.05x = 290
x = 290/0.05
x = $5800
The amount invested on 10% interest = $5800
The amount invested on 5% interest = 6000-5800
= $200
Hence, if a total of $6000 is invested, part at 5% and remainder at 10%, then the amount invested on 10% interest is $5800 and the amount invested on 5% interest is $200
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Operations in Scientific NotationWrite two numbers in scientificnotationFind their sum, difference, product& quotient
Answers
Solution:
Let the two numbers be
[tex]20\text{ and 10}[/tex]In scientific notation, the numbers are
[tex]\begin{gathered} 20=2\times10^1 \\ 10=1\times10^1 \end{gathered}[/tex]The sum of the numbers will be
[tex]=(2\times10^1)+(1\times10^1)=10^1(2+1)=10^1(3)=3\times10^1[/tex]Hence, the sum is
[tex]3\times10^1[/tex]The difference between the two numbers will be
[tex]=(2\times10^1)-(1\times10^1)=10^1(2-1)=10^1(1)=1\times10^1[/tex]Hence, the difference is
[tex]1\times10^1[/tex]The product of the numbers will be
[tex]=(2\times10^1)\cdot(1\times10^1)=(2\times1)(10^{1+1})=2(10^2)=2\times10^2[/tex]Hence, the product is
[tex]2\times10^2[/tex]The quotient of the numbers will be
[tex]=\frac{2\times10^1}{1\times10^1}=\frac{2}{1}\times(10^{1-1})=2(10^0)=2\times10^0[/tex]Hence, the quotient is
[tex]2\times10^0[/tex]