[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A=500\left(1+\frac{0.03}{1}\right)^{1\cdot 5}\implies A=500(1.03)^t[/tex]
Answer:
b
Step-by-step explanation:
Let event A = You buy a new umbrella on Friday. Which event is most likely to
be independent of A?
Answer:
B. You had a math test on Thursday
Step-by-step explanation:
B is most likely the answer because you would have a math test regardless of the weather. Teachers do stuff like that. Also I just took this quiz on APEX.
Last week, a coral reef grew 20.3 mm taller. How much did it grow in meters?
Answer:
0.0203 meters
Step-by-step explanation:
If a coral reef grew 20.3 mm taller, it grew 0.0203 meters taller.
20.3 mm = 0.0203 meters
The coral reef grew by 20.3 millimeters last week, which is equivalent to 0.0203 meters. This is calculated by dividing the millimeters by 1000, as there are 1000 millimeters in a meter.
Explanation:The amount of growth in the coral reef's height can be converted from millimeters to meters by using the conversion ratio of 1 meter being equal to 1000 millimeters. So, to find out how much the coral reef grew in meters, we would take the growth in millimeters (20.3 mm) and divide by 1000.
The calculation would be like this: 20.3 mm / 1000 = 0.0203 meters.
So, the coral reef grew by 0.0203 meters last week.
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9) A rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from
the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?
A) 130 m
B) 150 m
C) 160 m
D) 140 m
To solve for the distance from the base of the cliff, the time to hit the ground is calculated from the initial vertical velocity and the height of the cliff. The horizontal distance is then found by multiplying the time by the horizontal component of the initial velocity.
Explanation:To determine how far from the base of the cliff a bullet strikes the ground, we use the concepts of projectile motion. The initial velocity components are [tex]v_{0x} = 800 \cos(30^{\circ}) m/s[/tex] (horizontal component) and v_{0y} = [tex]800 \sin(30^{\circ}) m/s[/tex](vertical component downwards). The time it takes for the bullet to hit the ground can be found using the equation for vertical motion: y =[tex]v_{0y}t + \frac{1}{2}gt^2[/tex], where y is the height of the cliff, g is the acceleration due to gravity [tex](-9.8 m/s^2[/tex] since the bullet is moving downwards), and t is the time. Solving for t we get two possible times, but we choose the positive one. Once we have t, we can find the horizontal distance using x = v_{0x}t. Using these calculations, the appropriate distance from the base of the cliff can be determined.
what is a line of symmetry
Answer:
A line where you put it in the middle of the shape and see if it's symmetrical or the same. You fold the shape and if one side matches to other, that is symmetrical. That is the line of symmetry.
A line of symmetry divides a figure into two parts such that each part is the mirror image of the other. In other words, if we flip one side of the figure over the line of symmetry, it should match up exactly with the other side.
What is the change that occurs to the parent function f(x) = x^2 given the function f(x) = 2(x + 2)^2 + 1.
The graph is compressed by a factor of 2, moves 2 units to the right, and 1 unit up.
The graph is compressed by a factor of 2, moves 2 units to the left, and 1 unit up.
The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.
The graph is stretched by a factor of 2, moves 2 units to the right, and 1 unit up.
Answer:
The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.
Step-by-step explanation:
The base of the quadratic function is
[tex]f(x) = {x}^{2} [/tex]
We can transform this function to look narrower or wider.
Looking narrower is termed a stretch.
This happens when a>1
Looking wider is termed a compression.
This happens when 0<a<1
We can also
[tex]g(x) = a {(x + h)}^{2} + k[/tex]
+h moves the parent graph to the left by h units
-h moves the parent graph to the left by h units.
+ k moves the parent function up by k units
- k moves the parent function down by k units.
The change that occurs to
[tex]f(x) = {x}^{2} [/tex]
given
[tex]f(x) = 2( {x + 2)}^{2} + 1[/tex]
is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up
Therefore the last choice is the correct answer.
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 +6x +8 = 0
Answer:
Step-by-step explanation:
The roots are very clear on the graph. I have left them unlabeled so that you can put the two points in.
The points are (-4,0) and (-2,0)
The graph was done on desmos which you can look up. The box in the upper left corner was filled with
y = x^2 + 6x + 8
The equation of line CD is y = -2x - 2. What is the equation of a line parallel to line CD in slope-intercept form that contains point (4,5)?
Answer:
y=-2x+13
Step-by-step explanation:
Slope-intercept form of a line is y=mx+b where m is slope and b is y-intercept.
The slope of y=-2x-2 is -2 since m=-2.
A line that is parallel to the given line is going to have the same slope.
So we already know the equation we are looking for should be in the form y=-2x+b.
We just to need to find b.
We can use the given point on our line do that.
5=-2(4)+b
5=-8+b
8+5=b
13=b
So the equation is y=-2x+13.
Answer:
y = -2x+13
Step-by-step explanation:
The slope of the original line is -2 so you take that and plug it in with the points (4,5) in point slope form to get y-5 = -2(x-4), then you simplify to get y-5 = -2x+8 then y = -2x+13
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
x + 2y = 12
- x= -y-6
O A. (6.0)
O B. (8,2)
C. (9,3)
(7.1)
Answer:
The correct option is B....
Step-by-step explanation:
The given equation is:
x + 2y = 12 -----equation 1
- x= -y-6. -------equation 2
lets take equation 2:
-x=-y-6
Take minus as common on R.H.S
-x= -(y+6)
x=y+6 (Lets call it equation 3)
Substitute the value of x in the first equation:
x+2y=12
y+6+2y=12
Combine the like terms:
y+2y = 12-6
3y=6
Divide both the sides by 3
3y/3=6/3
y=2
Now substitute the value of y in equation 3:
x=y+6
x=2+6
x=8
Thus the solution set is (x,y){(8,2)}.
The correct option is B....
Answer:
B. (8,2)
Step-by-step explanation:
Apex
Hope this helps Have a nice day
Which choice is equivalent to the expression below?
Square root of -17
A.-3sqr of 3i
B.-sqr of 27
C.-3sqr of 3
D.3sqr of 3
E.3i sqr of 3
Answer:
d
Step-by-step explanation:
3×3×3 is 27 so that's the answer
John walked 9 5/8 mile at an average speed of 1 3/4 mile per hour how long did it take John to walk this distance
so, we know his average speed is 1¾ of a mile in 1 hour, so how long is it to cover 9⅝ miles then?
[tex]\bf \begin{array}{ccll} miles&hour\\ \cline{1-2} 1\frac{3}{4}&1\\\\ 9\frac{5}{8}&x \end{array}\implies \cfrac{~~1\frac{3}{4}~~}{9\frac{5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{1\cdot 4+3}{4}~~}{\frac{9\cdot 8+5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{7}{4}~~}{\frac{77}{8}}=\cfrac{1}{x}[/tex]
[tex]\bf \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{11}{~~\begin{matrix} 77 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} =\cfrac{1}{x}\implies \cfrac{2}{11}=\cfrac{1}{x}\implies 2x=11\implies x=\cfrac{11}{2}\implies x=5\frac{1}{2}[/tex]
The required time is 5.5 hours.
Simple linear equation:Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1.
It is given that,
Speed=[tex]1\frac{3}{4}[/tex] mile per hour.
Distane:=[tex]9\frac{5}{8}[/tex] mile
[tex]Time=\frac{Distance}{Speed}[/tex]
Now, substituting the given values into the above formula we get,
[tex]T=\frac{\frac{77}{8} }{\frac{7}{4} }\\ =\frac{77\times4}{8\times 7} \\=\frac{11}{2}\\ T=5.5 hour[/tex]
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Ellie wants to change her password which is ELLIE9 but with same letters and number. In how
many ways she can do that?
P = 256
P = 150
P = 200
P = 179
[tex]\dfrac{6!}{2!2!}-1=\dfrac{3\cdot4\cdot5\cdot6}{2}-1=180-1=179[/tex]
The number of passwords she can create is an illustration of permutations.
The number of ways to create the password is 179
The password is given as: ELLIE9
The number of characters in the password is:
[tex]n = 6[/tex]
L and E are repeated twice.
So, we have
[tex]L = 2[/tex]
[tex]E = 2[/tex]
The number of new passwords to create is then calculated as:
[tex]Passwords = \frac{n!}{L!E!} - 1[/tex] --- 1 represents the current password
This gives
[tex]Passwords = \frac{6!}{2!2!} - 1[/tex]
Expand
[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 \times 2!}{2! \times 2 \times 1} - 1[/tex]
[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 }{2 \times 1} - 1[/tex]
Simplify
[tex]Passwords = 180 - 1[/tex]
Subtract
[tex]Passwords = 179[/tex]
Hence, the number of ways to create the password is 179
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What is h(10) equal to? h:k→k^2-k
h(10)=[1]
[tex]h(k)=k^2-k\\\\h(10)=(10)^2-10=90[/tex]
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.
Answer:
[tex]a_n=9(4^{n-1})[/tex]
Step-by-step explanation:
we know that
In a Geometric Sequence each term is found by multiplying the previous term by a constant, called the common ratio (r)
In this problem we have
[tex]a_2=36\\ a_5=2,304[/tex]
Remember that
[tex]a_2=a_1(r)[/tex] -----> [tex]36=a_1(r)[/tex] -----> equation A
[tex]a_5=a_4(r)[/tex]
[tex]a_5=a_3(r^{2})[/tex]
[tex]a_5=a_2(r^{3})[/tex]
Substitute the values of a_5 and a_2 and solve for r
[tex]2,304=36(r^{3})[/tex]
[tex]r^{3}=2,304/36[/tex]
[tex]r^{3}=64[/tex]
[tex]r=4[/tex]
Find the value of a_1 in equation A
[tex]36=a_1(4)[/tex]
[tex]a_1=9[/tex]
therefore
The explicit rule for the nth term is
[tex]a_n=a_1(r^{n-1})[/tex]
substitute
[tex]a_n=9(4^{n-1})[/tex]
Answer:
an=9(4^n-1)
Step-by-step explanation:
ANSWER ASAP 20 POINTS AND GIVE EXPLANATION
Answer:
Option 2
Step-by-step explanation:
Given
B = (-6,1)
B' = (-3,-2)
Step 1: Substitute the original and translated coordinates into (x,y) => (x+a,y+b)
B(-6,1) => B'(-6+a , 1+b) = B'(-3,-2)
Step 2: Write two equations
-6+a = -3 => a = -3+6 = 3
1+b=-2 => b = -2-1 = -3
Hence, we can conclude that Indira wrote the equations wrong which was her first error.
Therefore, Option 2 is correct ..
Subtract (3x2 + 2x - 9) - (6x2 - 16). Write your answer as a polynomial
Answer:
The answer is -3x^2+2x+7 ....
Step-by-step explanation:
(3x2 + 2x - 9) - (6x2 - 16)
Open the parenthesis
Keep in mind that when you will open the parenthesis the signs of 2nd bracket will be multiplied by negative sign
3x^2+2x-9-6x^2+16
Arrange the terms:
3x^2-6x^2+2x+16-9
Solve the like terms:
= -3x^2+2x+7
Thus the answer is -3x^2+2x+7 ....
= (3x²+2x-9) - (6x²-16)
= 3x² + 2x - 9 - 6x² +16
= -3x² +2x + 7
While opening the brackets, make sure you change the signs accordingly. If there is a "-" sign outside the bracket then while opening the brackets, terms inside change their signs, which means "+" becomes "-" and vice versa.
lsaiah has $20 to spend on bowling he has four bowling alleys to choose from,and the price each charges for a game is shown in the table
He afford 5 games at bowling alley C.
What is comparison of numbers?Comparing Numbers means identifying a number that is smaller or greater than the rest. We can compare numbers using different methods such as on a number line, by counting, or by counting the number of digits, using place values of the numbers, etc.
According to the topic , we know
4 games at bowling alley B need to speed [tex]4 \times 5.25 = 21 > 20[/tex]
5 games at bowling alley C need to speed [tex]5 \times 3.75 =18.75 < 20[/tex]
5 games at bowling alley A need to speed [tex]5 \times 4.25 = 21.25 > 20[/tex]
6 games at bowling alley D need to speed [tex]6 \times 3.50 = 21 > 20[/tex]
So, the answer is 5 games at bowling alley C.
Option B is correct.
He afford 5 games at bowling alley C.
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a brokerage firm charges 1 1/4% if its fee on stock purchase was 400$ what was amount of purchase?
let's say the amount purchased was "x", so then that's the 100%.
if we know that 400 is the 1¼% and "x" is the 100%, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 400&1\frac{1}{4} \end{array}\implies \cfrac{x}{400}=\cfrac{100}{1\frac{1}{4}}\implies \cfrac{x}{400}=\cfrac{100}{\frac{1\cdot 4+1}{4}}\implies \cfrac{x}{400}=\cfrac{\frac{100}{1}}{\frac{5}{4}} \\\\\\ \cfrac{x}{400}=\cfrac{\stackrel{20}{~~\begin{matrix} 100 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{1}\cdot \cfrac{4}{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x}{400}=80\implies x=32000[/tex]
If F(x) = x - 1, which of the following is the inverse of F(x)?
O A. F'(x) = x + 1
O B. F1(x) = x
O c. Fl(x) = 1 - x
O D. F1(x) = x - 1
Answer:
A
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = x - 1 ( add 1 to both sides )
y + 1 = x
change y back into terms of x, hence
[tex]f^{-1}[/tex] (x ) = x + 1 → A
the correct (answer)
is A f1(x)=x+1
Write the equation of the line that passes through the points (0, -6) and (-4, 0).
Show how you arrived at your answer.
What would be the EQUATION? I’m confused. Please help.
Answer:
The slope is -3/2.
Step-by-step explanation:
Hint: slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex]
[tex]\displaystyle \frac{0-(-6)}{(-4)-0}=\frac{6}{-4}=\frac{6\div2}{-4\div2}=\frac{3}{-2}=-\frac{3}{2}[/tex]
[tex]\Large \textnormal{Therefore, the slope is -3/2.}[/tex]
Answer:
y=(-3/2)x+-6
or
y=(-3/2)x-6
Step-by-step explanation:
We are going to use slope-intercept form to find the equation for this line.
y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.
y-intercept means where it crosses the y-axis; the x will be 0 here. Look the question gives us the y-intercept which is -6.
So we already know b which is -6.
y=mx+-6
Instead of finding the slope using the slope formula which you could.
I'm going to plug in the point (-4,0) into y=mx+-6 to find m.
So replace x with -4 and y with 0 giving you:
0=m(-4)+-6
0=-4m-6
Add 6 on both sides:
6=-4m
Divide both sides by -4:
6/-4=m
Reduce the fraction:
-3/2=m
The slope is -3/2.
Again you could use the slope formula which says [tex]m=\frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line}[/tex].
This is the same thing as lining the points up vertically and subtracting the points vertically then putting 2nd difference over first difference. Like this:
( 0 , -6)
-( -4 , 0)
---------------
4 -6
The slope is -6/4 which is what we got doing it the other way.
So the equation with m=-3/2 and b=-6 in y=mx+b form is
y=(-3/2)x+-6
or
y=(-3/2)x-6
Use the figure to decide the type of angle pair that describes angle 3 and angle 2
Step-by-step explanation:
both are obtuse angles
and
angle 2 = angle 3
they are also alternative interior angles
In ABC, O is the centroid of the triangle and AO is 12.7 m. Find the length of OY and AY.
Answer:
[tex]\boxed{OY = 6.35 m} \\\boxed{AY=19.05 m}[/tex]
Step-by-step explanation:
The centroid of a triangle always cuts a triangle perfectly at 2/3.
What I mean by this is that the line that touches the tip of the triangle and touches the median of the base is cut into one third and its other part is cut into two thirds of the whole segment. This segment is AY.
Knowing this, I can tell that OY is 1/3 of the length of AO, which is given to be 12.7 m.
To find OY, make an equation where AO and OY add up to AY.
[tex]12.7+\frac{1}{3} x=x[/tex]The variable x represents the length of AY, and 1/3x represents the length of OY (because it is one-third of AY).
Solve the equation by subtracting 1/3x from both sides.
[tex]12.7=\frac{2}{3} x[/tex]Divide both sides by 2/3.
[tex]x=19.05[/tex]Now we know the length of AY (x). To find the length of OY substitute this value of x into 1/3x, which represents OY.
[tex]\frac{1}{3} (19.05)[/tex]
This gives us 6.35, which is the length of OY.
The final answers are:
OY = 6.35 mAY = 19.05 mA distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/h, by a bus at 60 km/h, a truck at 50 km/h, and a bicyclist at 20 km/h. How much time did each require to travel the entire distance? Explain why speed and the time needed to travel 150 km are inversely proportional quantities?
I need to know how to explain the last sentence.
Answer:
Motorcyclist: 2 hours
Bus: 2.5 hours
Truck: 3 hours
Bicyclist: 7.5 hours
Step-by-step explanation:
#23-6: The pool concession stand made $5,800 in June and $6,300 in July. What is the percent of increase in sales? Round the answer to the nearest tenth.
Answer:
8.6%
Step-by-step explanation:
To find the percent change, you will need to compute the positive difference and then divide the difference by the original (the older amount).
So the positive difference will be obtain by doing larger minus smaller:
6300
- 5800
-----------
500
The older amount was 5800.
So 500/5800 is the answer as a un-reduced fraction.
I'm going to reduce it by dividing top and bottom by 100:
500/5800 = 5/58
5/58 is the answer as a reduced fraction.
5 divided by 58 gives=0.086206897 in the calculator .
Approximately 0.0862 is the answer as a decimal.
To convert this to a percentage, multiply it by a 100:
8.62%
Rounded to the nearest tenths is 8.6%
-------------
So 5800+5800(.0862) should be pretty close to 6300 (not exactly though since we rounded).
5800+5800(.0862)=6299.96 using the calculator.
If the sides of one triangle are lengths 2, 4 and 6 and another triangle has sides of lengths 3,6 and
Answer:
True.
Step-by-step explanation:
If the sides of one triangle are lengths 2,4 and 6 and another triangle has sides of lengths 3,6 and 9 then the triangles are similar.
28
The elevation at ground level is O feet. An elevator starts 90 feet below ground level.
After traveling for 15 seconds, the elevator is 20 feet below ground level. Which
statement describes the elevator's rate of change in elevation during this 15-second
interval?
A
The elevator traveled upward at a rate of 6 feet per second.
The elevator traveled upward at a rate of 4 feet per second.
B
C
The elevator traveled downward at a rate of 6 feet per second.
D
The elevator traveled downward at a rate of 4 feet per second.
Step-by-step explanation:
If we graph elevation vs time, the rate of change is the slope of the line.
At t = 0, h = -90.
At t = 15, h = -20.
m = (-20 − (-90)) / (15 − 0)
m = 70/15
m = 4.67
The closest answer is B. The elevator traveled upward at a rate of 4 feet per second.
The population of a town doubled approximately every 5 years during the first several decades after it was founded. If the original population of the town was 39 people when it was founded in the year 1761, about how many residents were there in the year 1781? (Hint: the population doubled 4 times during this time period.)
Answer:
624 people
(I put two ways to look at the problem.)
Step-by-step explanation:
What is describe here is an exponential function of the form:
[tex]P=P_0 e^{kt}[/tex]
[tex]t[/tex] is the number of years after 1761.
[tex]P_0[/tex] is the initial population.
So t=0 represents year 1761.
t=1 represents year 1762
t=2 represents year 1763
....
t=20 represents year 1781.
So we have the doubling time is 5 years. This means the population will be twice what it was in 5 years. Let's plug this into:
[tex]P=P_0e^{kt}[/tex]
[tex]2P_0=P_0e^{k\cdot 5}[/tex]
Divide both sides by [tex]P_0[/tex]:
[tex]2=e^{5k}[/tex]
Convert to logarithm form:
[tex]5k=\ln(2)[/tex]
Multiply both sides by 1/5:
[tex]k=\frac{1}{5}\ln(2)[/tex]
[tex]k=\ln(2^{\frac{1}{5}})[/tex] By power rule.
So in the next sentence they actually give us the initial population and we just found k so this is our function for P:
[tex]P=39e^{\ln(2^{\frac{1}{5}})t}[/tex]
So now we plug in 20 to find how many residents there were in 1761:
[tex]P=39e^{\ln(2^{\frac{1}{5}})(20)}[/tex]
This is surely going to the calculator:
[tex]P=624[/tex]
Now if you don't like that, let's try this:
Year 0 we have 39 people.
Year 5 we have 39(2)=78 people.
Year 10 we have 78(2)=156 people.
Year 15 we have 156(2)=312 people.
Year 20 we have 312(2)=624 people.
Angelo has a credit score of 726. According to the following table, his credit rating
is considered to be which of these?
A.Good
B.Fair
C.Poor
D.Excellent
Answer is A
Answer:
A. good
Step-by-step explanation:
it is in the range of 660-749.
Answer:
"Good"
Step-by-step explanation:
"Good" is appropriate, because the score 726 is between 660 and 749.
Nick is solving the equation 3x2=20−7x with the quadratic formula.
Which values could he use for a, b, and c?
a = 3, b = −7 , c = 20
a = 3, b = 7, c = −20
a = 3, b = −20 , c = 7
a = 3, b = 20, c = −7
Answer: Second option.
Step-by-step explanation:
Given a Quadratic equation in the form:
[tex]ax^2+bx+c=0[/tex]
It can be solve with the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
In this case, given the Quadratic equation:
[tex]3x^2=20-7x[/tex]
You can rewrite it in the form [tex]ax^2+bx+c=0[/tex]:
- Subtract 20 from both sides of the equation:
[tex]3x^2-20=20-7x-20\\\\3x^2-20=-7x[/tex]
- Add [tex]7x[/tex] to both sides of the equation:
[tex]3x^2-20+7x=-7x+7x\\\\3x^2+7x-20=0[/tex]
Therefore, you can identify that:
[tex]a=3\\b=7\\c=-20[/tex]
Answer:
option B. a=3, b=7, c=-20
I just took the test :)
Step-by-step explanation:
which is equivalent to..... algebra II engenuity
Answer:
The correct answer is second option option
9¹/⁸ ˣ
Step-by-step explanation:
Points to remember
Identities
ᵃ√x = = x¹/ᵃ
√x = x¹/²
(xᵃ)ᵇ = xᵃᵇ
To find the correct option
It s given that,
(⁴√9)¹/² ˣ
By using the above identities we can write,
(⁴√9)¹/²ˣ = (9¹/⁴)¹/²ˣ [ since ⁴√9 = 9¹/⁴]
= 9⁽¹/⁴ * ¹/²⁾ ˣ
= 9¹/⁸ ˣ
Therefore the correct answer is second option option
9¹/⁸ ˣ
What is sqrt12x^8/sqrt3x^2 in simplest form
[tex]\bf \cfrac{\sqrt{12x^8}}{\sqrt{3x^2}}~~ \begin{cases} 12=&2\cdot 2\cdot 3\\ &2^2\cdot 3\\ x^8=&x^{4\cdot 2}\\ &(x^4)^2 \end{cases}\implies \cfrac{\sqrt{2^2\cdot 3(x^4)^2}}{\sqrt{3x^2}}\implies \cfrac{2\stackrel{x^2}{~~\begin{matrix} x^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 2x^2[/tex]
Answer:
2x^3 (C on edge)
Step-by-step explanation: