Answers
On comparing the given expressions we get-
[tex]9^{-2} < (\frac{1}{9}) ^{-1}[/tex]
[tex](\frac{1}{9}) ^{-1} < (\frac{1}{9}) ^{-2}[/tex]
[tex]9^{-1} > 9^{-2}[/tex]
Here, we are given 3 pairs of expression. Let us evaluate them one by one.
[tex]9^{-2}[/tex] _ [tex](\frac{1}{9}) ^{-1}[/tex]
The negative exponent means that the base is the reciprocal raised to a positive power. Thus, [tex]9^{-2}[/tex] can be written as- [tex](\frac{1}{9}) ^{2}[/tex] = 1/81
similarly, [tex](\frac{1}{9}) ^{-1}[/tex] can be written as- [tex](9}) ^{1}[/tex] = 9
Thus, the expression becomes-
1/81 _ 9
clearly we can see that 1/81 < 9
Now, we have [tex](\frac{1}{9}) ^{-1}[/tex] _ [tex](\frac{1}{9}) ^{-2}[/tex]
As shown above, the expression can be simplified as-
[tex](9) ^{1}[/tex] _ [tex](9) ^{2}[/tex]
9 _ 81
clearly we can see that 9 < 81
Next, we have- [tex]9^{-1}[/tex] _ [tex]9^{-2}[/tex]
we can write this as-
1/9 _ 1/81
Clearly, 1/9 > 1/81
Hence, we have solved the given inequalities.
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Related Questions
1. When five is added to three more than a certain number, the result is 19.
What is the number?
Answers
Answer:
11
Step-by-step explanation:
triangle jkl is similar to Triangle jkl find the length of segment JK I'll send you the picture
Answers
Two triangles that are similar have the following characteristics:
1) The corresponding angles are congruent
2) The corresponding sides ratios have the same proportion.
So for triangles, JKL and J'K'L' the ratios of the corresponding sides are:
[tex]\frac{J^{\prime}K^{\prime}}{JK}=\frac{K^{\prime}L^{\prime}}{KL}=\frac{J^{\prime}L^{\prime}}{JL}[/tex]Given
JK=10cm
KL=30cm
K'L'=13.5cm
We can calculate the length of J'K' using the ratios:
[tex]\begin{gathered} \frac{K^{\prime}L^{\prime}}{KL}=\frac{J^{\prime}K^{\prime}}{JK} \\ \frac{13.5}{30}=\frac{x}{10} \\ (\frac{13.5}{30})\cdot10=x \\ x=4.5 \end{gathered}[/tex]Segment J'K'=4.5cm
Given rectangle ABCD with vertices A(5,-4), B(5,4), C(-5,4) and D(-5,-4), what is the length ofthe diagonal of ABCDA 12.81B 13.54C 12.57D 25.62E11.81
Answers
The rectangle ABCD has coordinates given.
The diagonal is either of AC or BD, and the lengths are the same.
The distance between point A and point C (length of the diagonal) is calculated with the formula below;
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{The coordinates are;} \\ (x_1,y_1)=(5,-4) \\ (x_{2,}y_2)=(-5,4) \\ d=\sqrt[]{(-5-5)^2+(4-\lbrack-4\rbrack)^2} \\ d=\sqrt[]{(-10)^2+(4+4)^2} \\ d=\sqrt[]{100+(8)^2} \\ d=\sqrt[]{100+64} \\ d=\sqrt[]{164} \\ d=12.8062\ldots \\ d\approx12.81 \end{gathered}[/tex]The correct answer is option A
In the following statement, express the first number as a percentage of the second number.
The 2016 revenue for Company A was $364 million, compared to $495 million for Company B.
The 2016 revenue for Company Awas% of the revenue for Company B.
(Round to the nearest tenth as needed.)
Answers
Answer:
?
Step-by-step explanation:
did you find answer?
An equation of the parabola shown in the xy-plane is y = ax² - c, where a is a constant and c is an integer. What is the value of c ?
Answers
To find c we notice that this value happens when x=0, then we have the equation:
[tex]y=-c[/tex]Now, from the graph we notice that when x=0 the value of y=-10, then we have:
[tex]\begin{gathered} -10=-c \\ c=10 \end{gathered}[/tex]Therefore the value of c is 10.
What was the amount of increase between the original $9 billion estimated costand the current $32.347 billion?
Answers
Given that:
- The original estimated cost was:
[tex]\text{ \$}9\text{ }billion[/tex]- The current estimated cost is:
[tex]\text{ \$}32.347\text{ }billion[/tex]You can determine that the amount of increase is the Difference between the estimated cost and the current estimated cost. Therefore, you need to subtract the original estimated cost from the current estimated cost to find it.
Knowing that:
[tex]1\text{ }billion=1,000,000,000[/tex]You can rewrite the amounts as follows:
[tex]\text{ \$}9,000,000,000[/tex][tex]\text{ \$}32,347,000,000[/tex]Then, you get:
[tex]\text{ \$}32,347,000,000-\text{\$}9,000,000,000=\text{\$}23,347,000,000[/tex]Hence, the answer is:
[tex]\text{\$}23,347,000,000[/tex]
The highest temperature ever recorded in Africa was 136F in Libya . The lowest temperature ever recorded in Africa was -11F in Morocco what is the difference in these temperatures extremes
Answers
The difference between these temperature extremes is 147.
We are given the highest temperature that was recorded.We are also given the lowest temperature that was recorded.We need to find the difference between these temperature values.This means we need to find the range of the temperature.The highest temperature ever recorded in Africa was 136°F in Libya.The lowest temperature ever recorded in Africa was -11°F in Morocco.The difference in the temperature values is the highest temperature value minus the lowest temperature value.The difference in the temperature values is 136 - (-11).The difference in the temperature values is 136 + 11.The difference in the temperature values is 147.To learn more about temperature, visit :
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Write the first six terms of the sequence.a₁ = 1, ª₁ = ª₁_1 – 5a₁ = ===a5a,= , a = |, a=a3wwwa6
Answers
Given,
The expression is:
[tex]a_1=1,a_n=a_{n-1}-5[/tex]Required:
The first six term of the series.
The first six term of the series is,
[tex]\begin{gathered} a_1=1 \\ a_2=a_1-5=-4 \\ a_3=a_2-5=-9 \\ a_4=a_3-5=-14 \\ a_5=a_4-5=-19 \\ a_6=a_5-5=-24 \end{gathered}[/tex]Hence, the first six term of the series is obtained.
A 6 3/4-inch candle burns down in 9 hours. How far has it burned after 6 hours? Use the dropdown menu to state your answer as a decimal, mixed number, or improper fraction.
Answers
The question can be solved using fractions, 4 and 1/2 inches of the candle will burn in 6 hours.
What is fractions?
The components of an entity or group of entities are represented as fractions. A fraction consists of two components. The numerator is the number at the top of the line (slash). It tells us how many equal portions of the whole or collection were taken. The denominator is the figure that appears below the line (slash). It displays the total number of identical objects in a collection or the total number of equal portions.
As given in the question, 6 3/4-inch (27/4) inch candle burns down in 9 hours.
We have to find the candle burnt in 6 hours.
Fraction for 9 hours = Fraction for 6 hours
So,
27/4:9 = x:6
We can also write it as,
(27/4)9 = x/6
x = 4.5 inch
It could also be written as 4 1/2 inches.
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What is the y-intercept in the following equation?
y = 2x
O
2
1
X
Answers
Answer:
2
Step-by-step explanation:
i took this test
What is the measure of angel k ? A. 180 B. 58C. 32D. 122
Answers
Given two parallel lines and a transversal
As shown the measure of the angle O = 58
The angles 58 and K are supplementary angles
So, the sum of the angles = 180
So,
[tex]\begin{gathered} m\angle K+58=180 \\ m\angle K=180-58=122 \end{gathered}[/tex]so, the answer will be option D. 122
May I please get help with this problem? For I have Ed tried many times but still could not get the right answer
Answers
Given the square root of 64
[tex]\sqrt[]{64}[/tex]As we know 64 = 8 x 8
So, the square root of 64 = 8
[tex]\sqrt[]{64}=\sqrt[=]{8\times8}=8[/tex]So, the answer will be 8
Draw a histogram with given figures (label endpoints) help please
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
is the point (20,13) in this line
Answers
So, the point (20,13) is on the same line.
Define line.A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. the trail of a moving point; a continuous length, straight or curved, without breadth or thickness. something lined up in a line, especially one that is straight; a line or sequence: a row of trees a group of people waiting in line after one another to do something or receive something.
Given Data
point (20,13) in this line
On the line y=1/2x+3, the point (20, 13) fits.
By entering the x and y values, this may be demonstrated.
13=[tex]\frac{1}{2}[/tex](20) +3
[tex]\frac{1}{2}[/tex](20)=10
13=10+3
13=13
20 and 13 fit on the line
So, the point (20,13) is on the same line.
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i need help asap please help worth alot points
Answers
There are 24 question in the picture. We have to solve the problem by multiplication and division.
Given that,
There are 24 question in the picture.
We have to find the multiplication and division for the given question.
Multiplication condition:
Plus multiply minus is equal to minus
Plus multiply plus is equal to plus
Minus multiply minus is equal to plus
Minus multiply plus is equal to minus
Division condition:
Plus divided by minus is minus
Plus divided by plus is plus
Minus divided by minus is plus
Minus divided by plus is minus
1. -2×5= -10
2. -16÷-8= 2
3. 60÷-5= -12
4. 11×-1= -11
5. 18÷-2= -9
6. 28÷-4= -7
7. 7×-8= -56
8. -8×11= -88
9. -70×-3= 210
10. -60÷-2= 30
11. 8×-90= -720
12. -80÷40= -2
13. 300÷-6= -50
14. -80×50= -4000
15. -200÷40= -5
16. -70×-60= 4200
17. -3×2= -6
18. -16÷-4= 4
19. 5×-6= -30
20. 12÷-3= -4
21. -18÷6= -3
22. 7×9= 63
23. -60÷-6= 10
24. -8×-5= 40
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The given table of values represents a linear equation. What is the slope?
X 1 2 3 4 y 5 8 11 14
Answers
The slope of the straight line is 3.
What is slope of a line?
Slope is the measure of steepness. Slope is determined by the tangent of angle a line makes with the x-axis. It is calculated as rise over run. Mathematically for the coordinates (a, b) (c, d) it can be given as [tex]\frac{d-b}{c-a}[/tex].
We are given a table which contains some coordinates of a straight line
We have to find the slope of the line
This can be done as
Slope[tex]=\frac{8-5}{2-1}[/tex]
Slope[tex]=3[/tex]
Hence the slope of the line is 3.
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please help this is for my study guide thanks! (at the end it says round to the nearest hundredth)
Answers
Given the figure of a cylinder:
As shown the radius of the cylinder = r = 11 ft
The height of the cylinder = h = 18 ft
the volume of the cylinder is given by the formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]where: π = 3.14
Substitute with the given values:
[tex]V=3.14\cdot11^2\cdot18=6838.92[/tex]so, the answer will be:
The volume = 6,838.92 ft³
how do you rewrite an expression with parenthesisthe question is 5(x+2)
Answers
We have the following:
[tex]5(x+2)=5x+10[/tex]the answer is 5x + 10
find arc fghaving trouble with this, hope you can help
Answers
Answer:
237 degrees
Explanation:
In the diagram, chord FG and tangent ED meet at F.
We use the theorem below:
Arc FG is the intercepted arc, therefore:
[tex]\begin{gathered} m\angle EFG=\frac{1}{2}m\widehat{FG} \\ \implies118.5\degree=\frac{1}{2}m\widehat{FG} \end{gathered}[/tex]Multiply both sides by 2:
[tex]\begin{gathered} 2\times118.5\degree=2\times\frac{1}{2}m\widehat{FG} \\ m\widehat{FG}=237\degree \end{gathered}[/tex]The measure of arc FG is 237 degrees.
Find the perimeter of ATUV. Round your answer to the nearest tenth if necessary.Figures are not necessarily drawn to scale.
Answers
Explanation
To solve the question, we will first apply a similar triangle theorem
Similar triangles are triangles that have the same shape, but their sizes may vary.
so, we can compare similar sides to get x before we get the perimeter
Thus
[tex]\frac{SR}{VU}=\frac{QR}{TU}[/tex]Hence
[tex]\frac{23}{x}=\frac{20}{24}[/tex]Solving for x
[tex]\begin{gathered} x=\frac{23\times24}{20} \\ x=27.6 \end{gathered}[/tex]Thus, we will have
Then the perimeter will be:
[tex]VT+VU+TU=36+24+27.6=87.6[/tex]Therefore, the perimeter of the triangle TUV is 87.6
The dial on a combination lock contains markings which represent the numbers from 0 to 39. How many 3-
number combinations are possible if the first and the second must be different odd numbers, while the third
number must not be an odd number?
a. 7600
b. 8000
c. 59280
d. 57720
e. 43520
Answers
Answer:
C
Step-by-step
c
TechWiz Electronics makes a profit of $35 for each MP3 or player sold and $18 for each DVD player sold. Last week, TechWiz sold a combined total of 118 MP3 and
DVD players.
Let x be the number of MP3 players TechWiz sold last week. Write an expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD
players last week.
Answers
Answer: 118=x+y z=35x+18y
Step-by-step explanation: x= the amount of MP3 players, and y= DVD Players. The 35 and 18 represent the profit for both of them, and in the first equation, the 118 shows the total amount sold. The z represents the profit made, because you are multiplying the amount of MP3 players and DVD players by their price, then adding them for the total amount.
Which of the graphs on the right is the graph of C?
Answers
Answer: D
Step-by-step explanation:
The cost function gives that 75 is the initial cost and adds 0.25 per copy. the only graph that has a positive slope and has a y-intercept of 75 is D.
Math Message
Mr. Pracher went fishing and did great. He and the captain pulled the
boat into the dock and prepared the bins of fish to sell. Each species of
fish is worth different amounts of money, below is a list of the species
of fish and the amount per pound they sell for. How much total money
did they earn?
• Striped bass 140 pound
• Sea bass 86 pounds
• Fluke 45 pounds
• Bluefish 93 pounds
$3.25 per pound
$2.78 per pound
$4.34 per pound
$1.09 per pound
Answers
Answer: $990.75
Step-by-step explanation:
140*3.25=455
86*2.78=239.08
45*4.34=195.30
93*1.09=101.37
adding all the results you get 990.75 dollars for 364lbs of fish
The product of two numbers is 10,000. If neither number contains a zero digit, what are the two numbers?
Answers
The two numbers are 16 and 625.
What is multiplication?
Multiplication is a basic arithmetic process in which we add a number, particular number of times.
We are given a number is 10000.
The factor of 10000 are [tex]2,2,2,2,5,5,5,5,[/tex]
Now we multiply all the 2 and all the 5 separately
Hence the factor becomes, [tex]2^{4}[/tex]·[tex]5^{4}[/tex]
i.e [tex]16[/tex]·[tex]625[/tex]
as 16 and 625 neither contains any zero and there product is 10000
Hence the two numbers are 16 and 625
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what is a reasonable minimum value for the dependent variable? explain how you arrived at your answer
Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} f(x)=-16x^2+64 \\ x\text{ is the time in seconds} \\ f(x)\text{ is the distance of the pumpkin from the ground} \\ \\ \text{ When the pumpkin is on the ground, its distance from the ground is zero. Thus,} \\ f(x)=0,\text{ when the pumpking is on the ground.} \\ \\ -16x^2+64=0 \\ \text{ Subtract 64 from both sides} \\ -16x^2=-64 \\ \text{ Divide both sides by -16} \\ x^2=-\frac{64}{-16} \\ \\ x^2=4 \\ \text{ Take the square root of both sides} \\ \\ x=\pm\sqrt{4} \\ x=+2\text{ or }-2 \\ \\ \text{ Since we cannot have negative time, } \\ x=2\text{ seconds} \end{gathered}[/tex]Final Answer
It takes 2 seconds for the pumpkin to hit the ground
Help me out with this pls
Answers
Answer:
7.5
0
5
1
3.67
Step-by-step explanation:
absolute value (the ||) means negative numbers become positive
it does not change values that are already positive
abs of 7.5 is 7.5
abs of 0 is 0
abs of -5 is 5
abs of -1 is 1
abs of -3.67 is 3.67
Factor completely 21b^4 +5b^2m^2- 4m^2
Answers
Factor completely
[tex]21b^4+5b^2m^2-4m^4[/tex]We need to split the expression into convenient groups
[tex]21b^4+5b^2m^2-4m^4=21b^4+12b^2m^2-4m^4-7b^2m^2[/tex]Factor 3b^2 from the first group and -m^2 from the second group:
[tex]21b^4+5b^2m^2-4m^4=3b^2(7b^2+4m^2)-m^2(4m^2+7b^2)[/tex]Factor out the common term 7b^2+4m^2:
[tex]21b^4+5b^2m^2-4m^4=(3b^2-m^2)(4m^2+7b^2)[/tex]This is the final factorization
Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y+1=-3(x-4)
Answers
The given equation is expressed as
y + 1 = - 3(x - 4)
The first step is to expand the bracket by multiplying each term inside the bracket by the term outside. It becomes
y + 1 = - 3x + 12
3x + y = 12 - 1
3x + y = 11
A = 3
B = 1
C = 11
Order Least to Greatest3.141592653.14444443.140000003.141414143.0000000
Answers
If we are to order from least to greatest
The first number is;
3.0000000
Then followed by;
3.14000000
Then followed by;
3.14141414
Then followed by;
3.14159265
and then;
