Simplify. Write the expression using only positive exponents. n8.58 The simplified expression is
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Given the expression:
\(\frac{r^8\cdot r^{-8}}{4}\)to simplify, first we must use the following rule for exponents:
\(a^n\cdot a^m=a^{n+m}\)then, in this case we have the following:
\(\frac{r^8\cdot r^{-8}}{4}=\frac{r^{8+(-8)}}{4}=\frac{r^{8-8}}{4}=\frac{r^0}{4}\)now, remember that any number with an exponent 0 is the unit, this means that a^0=1, then:
\(\frac{r^0}{4}=\frac{1}{4}\)therefore, the simplified expression is 1/4
Related Questions
Find the next 2 terms in the geometric sequence: 4, 12, 36,
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Slove each system by graphing
16-+4y+5x=0
-48-12y=-9x
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The system of equations 16 + 4 y + 5 x = 0 and - 48 - 12 y = - 9 x will have the solution as x = 0 and y = - 4.
We are given a system of equations as:
16 + 4 y + 5 x = 0 … (1)
- 48 - 12 y = - 9 x
- 16 - 4 y = - 9 x
9 x - 16 = 4 y … (2)
Substitute the equation (2) in the equation (1), we get that:
16 + 9 x - 16 + 5 x = 0
14 x = 0
x = 0
4 y = 9 ( 0 ) - 16
4 y = - 16
y = - 16 / 4
y = - 4
Therefore, we get that, the system of equations 16 + 4 y + 5 x = 0 and - 48 - 12 y = - 9 x will have the solution as x = 0 and y = - 4.
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Shown below is a regular pentagon inscribed in a circle. Calculate the area of the shaded region. Round your answer to the nearest tenth.
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Answer:
S(a) = 27,5036 squared units
Step-by-step explanation:
Shaded area is :
S(a) = Area of the circle - area of the regular pentagon (1)
A(c) = area of the circle
A(c) = π*(r)² ⇒ A(c) = π*(6)² ⇒ A(c) = 36*π ⇒ A(c) = 113,0976 squared units
Area of a regular pentagon:
a) If we draw a straight line between the center and each vertex we get 5 triangles, and if we draw the apothem for each side, we get 10 triangles. We will calculate the area of one of these triangles
The first 5 triangles has a central angle equal to 72⁰ according to:
360/5 = 72
When we divide these triangles in two triangles by means of the apothem, each central angle will be of 36⁰, then
sin 36⁰ = 0,58778 and cos 36⁰ = 0,809017 and sin 36⁰ = x/6 here x is half of the side of the regular pentagon. Then
0,58778 = x/6
x = 6*0,58778
x = 3,52668 units of length
and cos 36⁰ = a/6 where a is the apothem, then
0,809017 = a / 6 ⇒ a = 6*0,809017
a = 4,8541 units of length
Now we are in conditon to calculate area of the triangles as:
A(t) = (1/2)*b*h
A(t) = (1/2)*x*a ⇒ A(t) = 0,5* 3,52668*4,8541
A(t) = 8,5594 squared units
Finally we have 10 of these triangles, then
Area of regular pentagon is : 10*A(t) squared units
A(p) = 85,594 squared units
Now plugging these values in equation (1) we get the shaded area
S(a) = 113,0976 - 85,594
S(a) = 27,5036 squared units
Please help!!!!!!!!!!!!!!
Answers
Answer:
312.29 square feet
Step-by-step explanation:
\(w = \sqrt{ {d}^{2} - {l}^{2} } = \sqrt{ {25}^{2} - {18}^{2} } \\ \)
w = 17.35
A= l × w
= 18 × 17.35
= 312.29 square feet
The subtotal on a restaurant bill was $45.00. The customer paid $47.81 after taxes, not including a tip. What was the tax rate? Round your answer off to the nearest tenths place.
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Answer:
6.2 percent
Step-by-step explanation:
47.81 - 45 = 2.81
2.81/45
The tax applied on the bill is given as 6.2%.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The amount of bill is given as $45.
And, the final amount after tax is $47.81.
The tax rate can be obtained as follows,
Difference of bill amount before and after tax ÷ Original amount × 100.
⇒ (47.81 - 45) ÷ 45 × 100
⇒ 6.24%
Which is approximately 6.2%.
Hence, the tax rate can be obtained as 6.2%.
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A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
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Step-by-step explanation:
To eliminate x in the system of equations:
1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:
Equation 1: 36x -54y = 90
Equation 2: -36x - 8y = -28
2. Add the two equations together to eliminate x:
(36x - 54y) + (-36x - 8y) = 90 - 28
Simplifying, we get:
-62y = 62
3. Solve for y:
y = -1
4. Substitute y = -1 into one of the original equations, say Equation 1:
4x - 6(-1) = 10
Simplifying, we get:
4x + 6 = 10
5. Solve for x:
4x = 4
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.
A science class has 5 girls and 7 boys in the seventh grade and 5 girls and 5 boys in the eighth grade. The teacher randomly selects a seventh grader and an
eighth grader from the class for a competition. What is the probability that the students she selects are both boys?
Write your answer as a fraction in simplest form.
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We have a total of 10 boys & 8 Girls, then the sample space consist of 18 elements.
P(selecting 1 boy) = (total number of boys/by 18) = P(boy)=10/18=5/9
True or False?
The following relation represent a function.
Question 4 options:
True
False
Answers
Q - Determinate the value of the following expression:
\(\frac{\sqrt{36} - \sqrt[3]{8} - \sqrt{144}}{\sqrt[3]{-64} + \sqrt[3]{125} } -1\)
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The value of the given expression is - 9.
The square root of a number:
The square root of a number is a value that, when multiplied by itself, gives the original number.
For example, the square root of 25 is 5, because 5 x 5 = 25.
The symbol used to denote the square root of a number is √, and it is placed in front of the number.
For example, the square root of 25 can be written as √25.
Here we have
\(\frac{ \sqrt{36} - \sqrt[3]{8} - \sqrt{144} }{\sqrt[3]{-64} \sqrt[3]{125}} - 1\)
As w know,
36 = 6 × 6 = 6²
8 = 2 × 2 × 2 = 2³
144 = 12 × 12 = 12²
-64 = - 4 × -4 × -4 = (-4)³
125 = 5 × 5 × 5 = 5³
Hence, the above expression can rewrite as follows
\(\frac{ \sqrt{36} - \sqrt[3]{8} - \sqrt{144} }{\sqrt[3]{-64}+ \sqrt[3]{125}} - 1 = \frac{ \sqrt{ 6^{2} } - \sqrt[3]{ 2^{3} } - \sqrt{12^{2} } }{\sqrt[3]{ (-4)^{2} }+ \sqrt[3]{5^{3} }} - 1\)
= \(\frac{ 6 - 2 - 12 }{ -4 + 5} - 1\)
= \(\frac{ -8 }{ 1} - 1\)
= -9
Therefore,
The value of the given expression is - 9.
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Nolan drew a pre-image of a trapezoid using a dashed line. Which shows an isometric transformation of his pre-
image??
Answers
Answer:
C
Step-by-step explanation:
i just guessed but it was correct
1
4
(
8
−
6
x
+
12
)
?
1
4
(
8
−
6
x
+
12
)
?
A.
7
2
x
7
2
x
B.
−
13
2
x
−
13
2
x
C.
−
6
x
+
14
−
6
x
+
14
D.
−
3
2
x
+
5
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The equivalent expression is 5 - 3x/2. Option D
What are algebraic expressions?Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.
these algebraic expressions are also composed of mathematical operations. These operations includes;
BracketParenthesesSubtractionMultiplicationDivisionAdditionFrom the information given, we have that;
1/ 4(8 - 6x + 12)
expand the bracket, we have;
Add the like terms
1/4(20 - 6x)
now, multiply the values, we have;
20 - 6x/4
Divide by the denominator
5 - 3x/2
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The complete question:
Simply the expression:
1/ 4(8 - 6x + 12)
If two rays share an endpoint,then they are opposite rays
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convert 657 as binary form in computer language
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Answer:
1010010001
Step-by-step explanation:
Keep dividing 657 by 2, and record the quotient and remainder
657
328,1
164,0
82,0
41,0
20,1
10,0
5,0
2,1
1,0
So chain the remainders from bottom up to get the binary number:
1010010001
Check:
1+16+128+512=657 checks.
Find the amount of an annuity that consists of 25 quarterly payments of $800 each into an account that pays 8% interest per year, compounded quarterly. (Round your answer to the nearest cent.)
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Answer: 400
25 x 800 = 20,000 x 8% = 1,600 / 4 = 400
Simplify the expression .
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\(10xy^2(3x^3-5x)-2x^2y(6y^3+3y)=\\\\=30x^4y^2-50x^2y^2-12x^3y^4-6x^2y^2=\\\\=\boxed{30x^4y^2-12x^3y^4-56x^2y^2}\)
Given the following, determine the set (B n C)'.
U= {x|x EN and x < 10}
B = {x|x EN and x is even and x< 10}
C = {x|x E N and x < 10}
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Answer:
Step-by-step explanation:
U={x|x∈N and x<10}
or U={1,2,3,4,5,6,7,8,9}
B={x|x∈N and x is even and x<10}
or
B={2,4,6,8}
C={x|x∈N and x<10}
or
C={1,2,3,4,5,6,7,8,9}
(B∩C)={2,4,6,8}
(B∩C)'={1,3,5,7,9}
PLS HELP I WILL GIVE BRAINLYEST
Answers
Answer:
hey
Step-by-step explanation:
pls help me then i help u
Write an algebraic expression for the phrase 6 times Z
Answers
Answer:
6z
Step-by-step explanation:
After she pays her bills each month, Lana has $300 left. Based on the graph below, which is the best estimate of how much she will spend on movies and eating out? $180 $75 $160 $200 $90 Discretionary Spending 16- to 22-Year-Olds Shopping for Pleasure 34% Hobbies 12% Eating Out 30% Movies 24%.
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The best estimate of how much she will spend on movies and eating out is given as follows:
$162.
How to obtain the best estimate?The best estimate of how much she will spend on movies and eating out is obtained applying the proportions in the context of the problem.
The percentages associated with movies and eating out are given as follows:
Eating out: 30%.Movies: 24%.The amount that she has left is given as follows:
$300.
Hence the best estimate of how much she will spend on movies and eating out is obtained as follows:
(0.3 + 0.24) x 300 = 0.54 x 300 = $162.
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Eddie plotted his house on a coordinate plane, along with a few landmarks from his neighborhood.
Which of the following is located 4 blocks east and 5 blocks south of Eddie’s house? A. baseball field B. fountain
6 x 2 x 3 = 36
C. library D. school
Answers
Answer:
library
Step-by-step explanation:
Answer:
library
Step-by-step explanation:
Larry starts at the bottom of a long staircase. He climbs exactly of the stairs. Then, he goes back down exactly 2/3 of the way to the bottom. From that spot, he climbs exactly of the way to the top. Finally, from there he 1/2 2/3 climbs 6 stairs to reach the top. How many stairs are in the staircase?
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There are a total of 27 steps on the staircase.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Let x be the total number of steps in the staircase.
Larry climbs exactly 2/3 of the stairs.
Number of steps Larry climbed = 2x/3
She goes back exactly 1/2 of the way to the bottom.
Number of steps returned = (2x/3) (1/2) = 2x/6 = x/3
She is at x/3 steps from the bottom.
From that spot, she climbs exactly 2/3 of the way to the top.
Remaining steps to the top = x - x/3 = 2x/3
Number of steps Larry climbed = 2/3 of the way to the top = (2/3)(2x/3) = 4x/9
So we get,
x/3 + 4x/9 + 6 = x
x - x/3 - 4x/9 = 6
x - 7x/9 = 6
2x/9 = 6
2x = 54
x = 27
Hence there are 27 steps in the staircase.
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The complete question is as follows :
Lara starts at the bottom of a long staircase. She climbs exactly 2/3 of the stairs. Then, she goes back down exactly 1/2 of the way to the bottom. From that spot, she climbs exactly 2/3 of the way to the top. Finally from there, she climbs 6 stairs to reach the top. How many stairs are in the staircase?
Which event has theoretical probability of exactly 1/5 select three options
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The spinner is divided into 10 equal sections.
Which event has theoretical probability of exactly 1/5? Select three options.
A) spinning a number less than 3
B) spinning a 4 or 5
C) spinning an odd number
D) spinning a number greater than 8
E) spinning a number less than 8
Answer:
Options A, B & D are correct
Step-by-step explanation:
From the image attached, we can see that the total number on the spinner is 10.
Now, we want to find which event has theoretical probability of exactly 1/5
Option A: spinning a number less than 3 means we get 1 or 2 which is 2 numbers.
Thus; probability = 2/10 = 1/5.
This option is true
Option B: spinning a 4 or 5 means 2 numbers.
Thus; probability = 2/10 = 1/5.
This option is true
Option C: Odd numbers in the spin are 1,3,5,7,9. This is a total of 5 numbers.
Thus, probability = 5/10 = 1/2
This option is wrong.
Option D: Numbers greater that 8 are 9 & 10. That's 2 numbers.
Thus, probability = 2/10 = 1/5
This option is correct
Option E: numbers less than 8 are;
1,2,3,4,5,6,7. That's a total of 7 numbers.
Probability = 7/10
Thus, this option is wrong.
Answer: A, B, D
Step-by-step explanation:
The following data was collected from a simple random sample from a process (infinite population).
13 15 14 16 12
I've already determined that the point estimate of the population mean is 14 and the point estimate of the population std. deviation is 1.581.
What is the Mean of the Population?
A. 14
B. 15
C. 15.1581
D. Could be any Value.
Answers
The mean of the population is 14, which is the point estimate of the population mean that was determined from the simple random sample.
The mean of the population is a measure of the central tendency of the population. It is calculated by taking the sum of all the values in the population and dividing by the total number of values. In this case, the mean of the population would be calculated by adding the values of the sample (13, 15, 14, 16, 12) and dividing by the total number of values (5). The mean of the population is then 14 (13 + 15 + 14 + 16 + 12 / 5 = 14).
To calculate the mean of the population, we first need to calculate the sum of all the values in the population. This is done by adding the values of the sample together (13 + 15 + 14 + 16 + 12 = 70). We then divide the sum of the values by the total number of values in the population (70 / 5 = 14). This gives us the mean of the population, which is 14.
The mean of the population is a measure of the central tendency of the population, and it is calculated by taking the sum of all the values in the population and dividing by the total number of values. In this case, the mean of the population was 14, which is the point estimate of the population mean that was determined from the simple random sample.
The mean of the population is 14, which is the point estimate of the population mean that was determined from the simple random sample.
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In ΔEFG, e = 34 inches, f = 73 inches and g=89 inches. Find the area of ΔEFG to the nearest square inch.
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Step-by-step explanation:
Heron's formula when all 3 sides (a, b, c) are given :
s = (a + b + c)/2
A = sqrt(s(s-a)(s-b)(s-c))
in our case
s = (34+73+89)/2 = 98
A = sqrt(98(98-34)(98-73)(98-89)) =
= sqrt(98×64×25×9) = sqrt(98)×8×5×3 =
= sqrt(2×49)×120 = sqrt(2)×7×120 =
= sqrt(2)×840 = 1,187.939392... ≈ 1,188 in²
please answer asap!!
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Answer:
16
Step-by-step explanation:
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Mark this and return
Answers
Answer:
(b) 3 units
Step-by-step explanation:
You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.
DilationThe dilation factor multiplies every length.
If OB is 3/4, then OB' is 4(3/4) = 3.
The length of OB' is 3 units.
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How much would you have to deposit today to accumulate the SAME AMOUNT OF MONEY that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn?
Answers
Answer:
7606.62
Step-by-step explanation:
Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.
\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)
Now just equate this to a time 0 payment at the same rate
\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)
As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.
When 3.9 is added to 6 times a number, the result is 57.3. Find the number
Answers
Answer: 8.9
Step-by-step explanation:
Let x = the number you are finding
SOLVE:
3.9+6x=57.3 ⇔ Given
6x=53.4 ⇔ subtract 3.9 on both sides
x=8.9 ⇔ Divide 6 on both sides
ANSWER:
The number is 8.9
please help what is 4/8 divided by 4/20
Answers
Hope this helps!!!!
Answer:
The correct answer is 2 and 1/2 or 5/2
Mathematics question. Please help
Answers
Step-by-step explanation:
Look at the table in picture above the result of table is true for all values so it is called tautology.
And there is a mistake in row 1.
Note:if you need to ask any question please let me know.
