Simplify the following expression. Leave your answer in the form a^b.3^19/3^13= ___
Answers
Given the expression:
[tex]\frac{3^{19}}{3^{13}}[/tex]To simplify the expression, we will use the following rule of the exponents:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]The answer will be:
[tex]\begin{gathered} \frac{3^{19}}{3^{13}}=3^{19-13}^{} \\ \\ =3^6 \end{gathered}[/tex]you will write the answer as 3^6
Related Questions
Solve for r and s. 2r + 6s =6 and 6r +2s =2 what kid of line are they
Answers
r = 0, s = 1
The lines are neither parallel nor perpendicular
Explanation:The given equations are:
2r + 6s = 6........(1)
6r + 2s = 2........(2)
Multiply equation (1) by 3
6r + 18s = 18........(3)
Subtract equation (2) from equation (3)
16s = 16
s = 16/16
s = 1
Substitute s = 1 into equation (2)
6r + 2(1) = 2
6r + 2 = 2
6r = 2 - 2
6r = 0
r = 0/6
r = 0
Make r the subject of the formula in equation (1)
2r = -6s + 6
r = -3s + 6
The slope of the line represented by equation (1) = -3
Make r the subject of the formula in equation (2)
6r = -2s + 2
r = (-2/6)s + (2/6)
r = (-1/3)s + 1/3
The slope of the line represented by equation (2) = -1/3
As seen above, the slope are not equal and are not negative inverses of each other. therefore, the lines are neither parallel nor perpendicular
-121+17:[(93:3+3):2]x50=? 1) 2) 3) 4) 5) 6)
Answers
Hope this helped
Thank you
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced. Assume that you take out a $3000 loan for 30 months at 9% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)
Answers
Given parameters:
[tex]\begin{gathered} P=Loan\text{ amount=\$3000} \\ r=rate\text{ intersest per period=9\%=}\frac{9}{100\times12}=\frac{0.09}{12}=0.0075 \\ n=n\nu mber\text{ of payments=30 months} \\ \end{gathered}[/tex]We can now apply the formula below to calculate the payment amount per period
[tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex][tex]\begin{gathered} A=3000\times\frac{0.0075(1+0.0075)^{30}}{(1+0.0075)^{30}-1} \\ \\ A=3000\times\frac{0.0075(1.25127)}{(1.25127)-1}=\frac{28.1536}{0.25127}=112.05 \end{gathered}[/tex]Thus his monthly payment will be $112.05
But since we have to get the interest on the first month's pay,
The interest is
[tex]r\times P=0.0075\times3000=\text{ \$22.5}[/tex]Thus, $22.50 is the interest on the first month's payment
Write the standard form of the equation of the circle with the given center and radius.Center (−2,−5), r=6
Answers
Given, center of the circle (-2,-5)
The radius is r=6
Now the form of the equation of circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Thus,
[tex]\begin{gathered} (x-(-2))^2+(y-(-5))^2=6^2 \\ \Rightarrow(x+2)^2+(y+5)^2=36 \\ \Rightarrow x^2+4+4x+y^2+25+10y=36 \\ \Rightarrow x^2+y^2+4x+10y+29=36 \\ \Rightarrow x^2+y^2+4x+10y-7=0 \end{gathered}[/tex]The answer is
[tex]x^2+y^2+4x+10y-7=0[/tex]I need help with this I was absent in school and the teacher won’t help me
Answers
Step-by-step explanation:
Given the equation
-45n + 45 = 90
Step 1: Isolate n
We can isolate n by subtracting 45 from both sides
-45n + 45 - 45 = 90 - 45
-45n + 0 = 45
-45n = 45
Divide through by -45
-45n/-45 = 45/-45
n = -1
Hence, the value of n is -1
Please help me with a question Rewrite the polar equation r=3sin(0) as a Cartesian equation.
Answers
Given,
The expression is,
[tex]r=3sin\theta[/tex]Required
The cartesian form of the given expression.
The cartesian form of the expression is,
A small town has two local high schools. High School A currently has 900 students and is projected to grow by 50 students each year. High School B currently has 500 students and is projected to grow by 100 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Graph each function and determine which high school is projected to have more students in 4 years.
Answers
ANSWER
Red line: function A(t)
Blue line: function B(t)
High school A is projected to have more students in 4 years.
EXPLANATION
We have,
• A: number of students in school A after t years
,• B: number of students in school B after t years
School A is projected to have 50 more students each year, while school B is projected to have 100 more students each year. Thus, both functions are linear.
High school A starts with 900 students and each year it will have 50 more,
[tex]A(t)=900+50t[/tex]On the other hand, high school B starts with 500 students and each year will have 100 more,
[tex]B(t)=500+100t[/tex]In 4 years each school will have,
[tex]A(4)=900+50\cdot4=900+200=1100[/tex][tex]B(4)=500+100\cdot4=500+400=900[/tex]The graphs of each function are lines. The graph of A is a line passing through points (0, 900) - which is the y-intercept, and (4, 1100).
The graph of B is a line passing through points (0, 500) and (4, 900).
From these calculations and from the graph, we can see that function A has a higher value than function B at t = 4. Hence High School A is projected to have more students in 4 years.
use the diagrams to answer the following questions Number 7
Answers
To solve this we going to need the Tangent-Secant Interior Angle Theorem
Works in the following way
Using that formula we get
[tex]\begin{gathered} \beta=\frac{x}{2} \\ \\ 2\beta=x \\ \\ x=2*35\degree \\ x=70\degree \end{gathered}[/tex]Answer: x=70°
2) Write an equation of a line that is parallel to the line whose equation is 3y = x + 6 and that passes through the point (-3,4). Y-Y=m(x-x) y = mx + b ino
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Write an equation of a line that is parallel to the line whose equation is
[tex]\text{3 y = x + 6}[/tex]and that passes through the point (-3,4)
Step 2:
From the question, we can see that the given equation is given as:
[tex]\begin{gathered} 3\text{ y = x + 6} \\ \text{Divide both sides by 3, we have that:} \\ y\text{ = }\frac{1}{3}x\text{ + 2} \end{gathered}[/tex]Comparing this, with the equation of a line, we have that:
[tex]\begin{gathered} y\text{ = mx + c} \\ \text{Then, the gradient of line, m = }\frac{1}{3} \end{gathered}[/tex]Step 3:
Now, using the equation of a line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where (x }_1,y_1)\text{ = ( -3 , 4 )} \\ m\text{ = }\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} y\text{ - }4\text{ = }\frac{1}{3}(\text{ x -- 3)} \\ y\text{ - 4 =}\frac{1}{3}(\text{ x+ 3)} \end{gathered}[/tex]Multiply through by 3, we have that:
[tex]\begin{gathered} \text{3 ( y - 4 ) = ( x + 3)} \\ 3y\text{ - 12 = x + 3} \\ \text{Hence, we have that:} \\ 3y\text{ = x + 3 +1 2} \\ 3\text{ y = x + 15} \end{gathered}[/tex]CONCLUSION:
The equation of the line that is parallel to the given line is:
[tex]3y\text{ = x + 15}[/tex]
What is the slope of (17, 11) (5, 0)
Answers
Solution
- The formula for the slope is given below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ (x_1,y_2)\text{ and (}x_2,y_2)\text{ are the coordinates of the points given} \end{gathered}[/tex]- We have been given the points (17, 11) and (5, 0).
- Thus, we can proceed to find the slope as follows:
[tex]\begin{gathered} x_1=17,y_1=11 \\ x_2=5,y_2=0 \\ \\ \therefore m=\frac{0-11}{5-17}=-\frac{11}{-12} \\ \\ \therefore m=\frac{11}{12} \end{gathered}[/tex]Final Answer
The value for the slope is
[tex]\therefore m=\frac{11}{12}[/tex]Yurly and his brother Anduray are each mailing a birthday gift to a friend. Yuriy's package weighs one lesspound than three times the weight of Anduray's package. The combined weight of both packages is 7pounds.Part 3: Yuriy and Anduray each graph the system that represents this situation. Who is correct? Explain why.
Answers
Yuriy
Explanations:[tex]\begin{gathered} \text{Let the weight of Yuriy's package be w}_y \\ \text{Let the weight of Anduray's package be w}_a \end{gathered}[/tex]Yuriy's package weighs one less pound than three times the weight of Anduray's package.
[tex]w_y=3w_a-1[/tex]The combined weight of both packages is 7 pounds
[tex]w_y+\text{ }w_a=\text{ 7}[/tex]The graph representing the two equations is:
The population of a village increases by 25% every year. The District Assemblygrants the village GH¢ 150.00 per head at the beginning of every year. If thepopulation of the village was 5.000 in the year 2005, calculate the Assembly'stotal grant from 2005 to 2010.
Answers
Explanation
We are given the following information:
• The population of a village increases by 25% every year.
,• The District Assembly grants the village GH¢ 150.00 per head at the beginning of every year.
,• The population of the village at the beginning of the year 2005 is 5,000.
We are required to determine the total grant from 2005 to 2010.
This is achieved th
the Venn diagram below models the possibility of three events a b and c the probabilities for each event or given by the ratio of the area of the event to the total area of 72 for example event C is read-only so for the probability that event C,you haveP(C)=area Red/total area =18/12×6=18/72=1/4=0.25are A&B dependent or independent events use conditional probability to support your conclusion
Answers
The events A and B are dependent events. This is because unlike the red area, event A means green given that blue has already occured. Event A includes blue and green and then event B includes green and yellow. Therefore event B cannot take place unless event A (which includes green area) has already taken place. Same goes for event A, it cannot take place unless event B has occured because the green area occurs in event B. Both events are dependent events. The result of one will influence the result of the other on.
**Event C is the only independent event**
Consider the function f(x) = 22 - 102 – 24. Given that one of the solutions of thefunction is r = -2 , what is the other solution of the function?
Answers
The initial function is:
[tex]f(x)=x^2-10x-24[/tex]And we know that one solution is r=-2
Write the equation to solve and then find the measure of each acute angle(3x + 8° (2x + 12)°
Answers
We have here a right triangle, and that is why we have two acute angles (that is, the measure of each of them is less than 90 degrees).
We also know that the sum of the inner angles of a triangle is 180 degrees.
Having this information at hand, we can proceed as follows:
[tex](3x+8)+(2x+12)+90=180[/tex]This is the equation. Now, we need to solve this equation to find x, and then we need to use the algebraical equations to find each of the acute angles.
Solving the equation
1. Sum the like terms (like terms have the same variable or they are constants.)
[tex]3x+2x+8+12+90=180[/tex]Then, we have:
[tex]5x+110=180\Rightarrow5x=180-110\Rightarrow5x=70[/tex]2. We need to divide each side of the equation by 5 to isolate x:
[tex]\frac{5x}{5}=\frac{70}{5}\Rightarrow x=14[/tex]Now, we have x = 14. Therefore, the values for each of the acute angles are (we need to substitute the value of x in each equation):
a. 3x + 8 ---> 3 * (14) +8 = 42 + 8 =50. Hence, one acute angle measures 50 degrees.
b. 2x + 12 ---> 2 * (14) + 12 = 28 + 12 = 40 degrees. Therefore, the other acute angle measures 40 degrees.
In summary, the equation to solve is:
[tex](3x+8)+(2x+12)+90=180[/tex]And the values for each of the acute angles are 50 and 40 degrees.
Write an expression to represent the perimeter of the figure below: p=
Answers
Answer:
[tex]P=6x-8[/tex]
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
[tex]P=2(x+4+2x-8) \\ \\ =2(3x-4) \\ \\ =6x-8[/tex]
Sophie is going to drive from her house to City A without stopping. Let D represent Sophie's distance from City A t hours after leaving her house. The table below has select values showing the linear relationship between t and D. Determine the average speed that Sophie travels, in miles per hour.
Answers
Answer:
55 miles per hour.
Explanation:
To determine the average speed traveled by Sophie, we find the slope of the function given from the linear table.
[tex]\begin{gathered} \text{Slope}=\frac{82.5-165}{2.5-1} \\ =-\frac{82.5}{1.5} \\ =-55 \end{gathered}[/tex]What this means is that Sophie's distance from City A is reducing at a rate of 55 miles per hour.
Thus, the average speed that Sophie travels, is 55 miles per hour.
Find the volume of a road construction marker, a cone with height 2 ft and base radius 1/5 ft. Use 3.14 as an approximation for π.The volume of the cone is __. (ft^2, ft^3, ft)(Simplify your answer. Type an integer or decimal rounded go the nearest hundredth as needed.)
Answers
Remember that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
r=1/5 ft
pi=3.14
h=2 ft
substitute given values
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot(\frac{1}{5})^2\cdot2 \\ V=0.08\text{ ft3} \end{gathered}[/tex]the answer is 0.08 ft^3What is the value of x if the acute angles of a right triangle measure 8xº and12xº? Remember the interior angles of a triangle measures 18. degrees. *4.59.527
Answers
We have a right triangle (one of its angle is a 90 degrees angle).
We know that
What is the measure in degrees of an angle that is
54/ 360
of a turn through a circle?
Answers
The measure of the angle through a circle will be 54°.
We are given that:
The measure in degrees of an angle = 54 / 360 of a turn through a circle.
This means that:
An arc should be proportional to the angle.
The circle have the angle as 360 degrees.
So, the angle will become:
54 / 360 × 360° = 54°
Therefore, we get that, the measure of the angle through a circle will be 54°.
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the line on the coordinate plane makes an angle of depression 32 degrees
Answers
From the given figure
The angle is in the third quadrant
This means we must add 180 degrees to the given angle to get the true angle
Since 32 + 180 = 212,
Then look at the third row on the table to find the sine of the angle
sine the true angle is the number in the 3rd-row 1st column is -0.5299
The answer is B
b.
The slope of the line is
[tex]\begin{gathered} m=\tan (212) \\ m=0.6249 \end{gathered}[/tex]The slope of the line is 0.6249
Please provide the slope and the work showing how you got the slope for each equation please!
Answers
Slope for (16, -10) and (16, 15) is undefined, slope for (-19, -6) and (15, 16) is 11/17, slope for (19, -2) and (-11, 10) is -2/5, and slope for (12, -18) and (-15, 18) is -4/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
For (16, -10) and (16, 15)
m=15-(-10)/16-16=15+10/0=25/0=undefined
For (-19, -6) and (15, 16)
m=16-(-6)/15-(-19)
=22/34=11/17
For (19, -2) and (-11, 10)
m=10-(-2)/-11-19
=10+2/-30
=-12/30=-2/5
For (12, -18) and (-15, 18)
m=18-(-18)/-15-12
=36/-27
=-12/9
=-4/3
Hence slope for (16, -10) and (16, 15) is undefined, slope for (-19, -6) and (15, 16) is 11/17, slope for (19, -2) and (-11, 10) is -2/5, and slope for (12, -18) and (-15, 18) is -4/3.
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A coordinate map of the local grocery store is shown below. ice cream is located at the point (-8,0) sprinkles. are located at the point (-8,6)
Answers
The points (-8,0) & (-8,6)
To find the distance between then
Apply the distance formulae for coordinates:
[tex]\text{ Distance=}\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Substitute the coordinates:
[tex]\begin{gathered} \text{ Distance=}\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{ Distance=}\sqrt[]{(6-0)^2+(-8-(-8))^2} \\ \text{ Distance=}\sqrt[]{6^2+0} \\ \text{Distance =6 units} \end{gathered}[/tex]So, Icecream is 6 units away from the sprinkles
Answer : 6 unit
Use the protractor to find the measure of ABC. Then classify the angle.
Answers
We are asked to find the measure of angle ABC and classify the angle.
As you can see from the figure, vertex A is at 30° and vertex C is at 155°
So, the angle ABC is
[tex]\angle ABC=155\degree-30\degree=125\degree[/tex]So, the angle ABC is 125°
Now recall that an obtuse angle is greater than 90° and less than 180°
Since 125° is between 90° and 180°, therefore, the angle ABC is an obtuse angle.
[tex]m\angle ABC=125\degree,\quad obtuse[/tex]2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations
Answers
right
[tex]\begin{gathered} AI)\text{ 400 ft} \\ MI)412.31\text{ f} \\ \text{angle = 76} \end{gathered}[/tex]Explanation
Step 1
AI?
we have a rigth triangle
then
let
[tex]\begin{gathered} AB=side1 \\ AI=side\text{ 2} \\ IB=\text{ hypotenuse} \end{gathered}[/tex]we can use the pythagorean Thoerem to find the missing vale
so
[tex]\begin{gathered} (AB)^2+(AI)^2=(BI)^2 \\ \text{replace} \\ 300^2+(AI)^2=500^2 \\ so \\ (AI)^2=500^2-300^2 \\ AI=\sqrt[]{500^2-300^2}=\sqrt[]{160000}=400 \\ AI=400 \end{gathered}[/tex]Step 2
MI?
let
[tex]\begin{gathered} \text{angle}=x \\ \text{opposite side=100 m} \\ \text{adjacent side=400 m} \end{gathered}[/tex]so, we need a function that relates those 3 values
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]replace
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan x=\frac{400}{100} \\ \tan x=4 \\ \text{hence} \\ x=\tan ^{-1}(4) \\ x=75.96 \\ \text{rounded} \\ x=76\text{ \degree} \end{gathered}[/tex]As 76 is greater than 68, the zipline cable compliance with these regulations.
Also, the hypotenuse (zipline ) is
[tex]\begin{gathered} (MI)^2=(AI)^2+(AM)^2 \\ \text{replace} \\ (MI)^2=(400)^2+(100)^2 \\ (MI)^2=170000 \\ MI=\sqrt[]{17000} \\ MI=412.31\text{ ft} \end{gathered}[/tex]I hope this helps you
The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.
Answers
The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.
In this problem we have that
UV+VW+WX=UX -----> by addition segment postulate
we have
UX=8 units
so
UV+VW+WX=8 -------> equation A
UV/VW=1/3 ------> equation B
UV/WX=1/4 -----> equation C
Solve the system of equations
In equation B isolate the variable VW
so
3UV=VW
VW=3UV -------> equation D
In equation C isolate the variable WX
4UV=WX
WX=4UV ------> equation E
Substitute equation D and equation E in equation A
UV+(3UV)+(4UV)=8
solve for UV
8UV=8
UV=1
Find VW
VW=3UV
VW=3(1)=3 units
FInd WX
WX=4UV
WX=4(1)=4 units
Find out the value of VX
we have that
VX=VW+WX
substitute
VX=3+4=7 units
therefore
VX=7
Cindy read a total of 8 books over 2 months. If Cindy has read 20 books so far, how many
months has she been with her book club? Solve using unit rates.
months
Submit
3
Answers
3a) Find length between A(-3,8) and B(5,-4) in simplest radical form:
Answers
Find length between A(-3,8) and B(5,-4) in simplest radical form:
we know that
The distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2\text{ +(x2-x1)\textasciicircum{}2}}[/tex]we have
(x1,y1)=A(-3,8)
(x2,y2)=B(5,-4)
substitute in the formula
|||RATIOS, PROPORTIONS, AND PERCENTSFinding the original amount given the result of a percentage...Va o- httpemployeesA company has been forced to reduce its number of employees. Today the company has 28% fewer employees than it did a year ago. If there are currently306 employees, how many employees did the company have a year ago?I need help with this math problem
Answers
The amount of employees on the previous year represents 100%. If today the company has 28% fewer employees, then the current amount of employees represents:
[tex]100\%-28\%=72\%[/tex]72% of the amount of employees of the previous year. Rewritting this percentage as a decimal, we have:
[tex]72\%=\frac{72}{100}=0.72[/tex]If we divide the current amount of employees by 0.72, we're going to find the original amount.
[tex]\frac{306}{0.72}=425[/tex]The company had 425 employees on the previous year.
Write a rule for the nth term of the geometric sequence given a_7=58, a_11=94
Answers
We are told the sequence is arithmetic. This means that the difference between one therm and the next is a constant.
We are also given two terms of the sequence. Let's see what their difference is
[tex]a_{11}-a_7=94-58=36[/tex]This means that, in general
[tex]a_{k+4}-a_k=36[/tex]With this, we can deduce that the difference between any two cnsecutive terms will be 9, for example
[tex]a_7=58,a_6=49,a_5=40,a_4=31,a_3=22[/tex]Indeed,
[tex]a_7-a_3=58-22=36[/tex]Now we should find the first term of the sequence, a₀, in order to find the rule for the nth term.
[tex]a_2=13,a_1=4,a_0=-5[/tex]In general, the rule for the nth term of an arithmetic sequence is given by
[tex]a_n=a_0+d(n)[/tex]where d is the difference between two consecutive term. In this case we have
[tex]a_n=-5+9\cdot n[/tex]with n=0,1,2,....