If a> 1 then prove that a^2>1

Answers

Answer 1

Step-by-step explanation:

a² = a × a

a > 1

a² = (1+d) × (1+d) = 1² + 2d + d²

with d > 0

since d > 0, then so is 2d and also d².

so, a² is the sum of 1² = 1 and something greater than 0.

so, a² > 1


Related Questions

A construction crew has just finished building a road. The road is 8 kilometers long. If the crew worked for 3 1/3 days, how many kilometers of road did they build each day? ( Assume they built the same amount each day.) write your answer as a mixed number in simplest form.

Answers

Answer:

They built 2.4 kilometers each day

Step-by-step explanation:

8 divided by 3 1/2

Mathematics need help with this paper

Answers

Answer:

5. x = 39°

6. x = 46°

7. x = 24°

8. x = 19°

Step-by-step explanation:

5.

Base angles are the same due to it being an isosceles triangle

Sum of angles in triangle = 180°

2x + 2x + (x - 15) = 1804x + x - 15 = 1805x - 15 = 1805x = 195x = 39

6.

Angle VZW and XZW are supplementary, meaning that they add up to 180°

3x + 17 + (x - 9) = 1803x + 17 + x - 9 = 1804x + 8 = 1804x = 184x = 46°

7.

Sum of angles in a straight line add up to 180°

(2x - 4) + (3x + 5) + (2x + 11) = 1802x - 4 + 3x + 5 + 2x + 11 = 1807x + 12 = 1807x = 168x = 24

8.

All angles add up to 90°

x + (x + 4) + (3x - 9) = 90x + x + 4 + 3x - 9 = 905x - 5 = 905x = 95x = 19

-Chetan K

0.45 as fraction in simplified form

Answers

Answer:

9/2

Step-by-step explanation:

0.45 = 45/100 = 9/20.

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

Convert to fraction:

[tex]0.45[/tex]

Convert decimal to fraction:

[tex]\frac{45}{100}[/tex]

Reduce the fraction:

[tex]\frac{9}{20}[/tex]

Please help, thanks in advance

Answers

Answer:

D. [tex]\frac{45a^{16}c^{34}}{b^{27}}[/tex]

Step-by-step explanation:

Here you are...

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

Can someone please help me find out the answer to this question?

Answers

Answer:

A

Step-by-step explanation:

Hello!

The answer is attached with explanation. Please note me if you have any more questions.

Answer:

Letter A.

[tex] {f}^{ - 1} (x) = \frac{ x + 8}{9} [/tex]

For homework Sarah had 45 English problems for spring break homework. If she can finish nine problems in an hour, how long will it take her to finish all the problems?

Answers

Answer:

5 hours

Step-by-step explanation:

assuming she works consecutively on these problems. if it takes 9 problems for 1 hour, and there are 45 problems, all that's needed to be done is 45/9, which is 5

Carmen is a professor at a local university. In collecting data on her Introduction to Business course for a year, she wants to calculate the z-score for a student who scores a 92 on the final exam. The mean and the standard deviation scores on the exam are 76 and 6, respectively. Calculate the z-score.

Answers

The z score of a student who scores a 92 on the final exam is 2.67.

Z score

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where x is the raw score, μ is the mean and σ is the standard deviation

Given that σ = 6, μ = 76. For a raw score of 92:

z = (92 - 76) / 6 = 2.67

The z score of a student who scores a 92 on the final exam is 2.67.

Find out more on Z score at: https://brainly.com/question/25638875

Hi help me please if you can

Answers

Answer:

277/8  =34.625

Step-by-step explanation:

Given the lengths of two sides of a triangle, write an inequality to indicate between which two numbers the length of the third side must fall. 8 and 13

Answers

Answer:

13-8<3rd<13+8 so

5<3rd<21

Step-by-step explanation:

The theorem of Angles-Sides Inequalities.

I got this question too in RSM

Answer: 5 and 21

Step-by-step explanation: look below

Please help me I will give you brainliest!

Answers

Answer:

data set 1 - y=x*3.5 data set 2 - y=x*3

Step-by-step explanation:

=======

Slope is 3.5 for first one second one is slope of 3

What's the answer for 6m^2+18m+17=-3m^2+9

Answers

Answer:

m=−2/3 or m=−4/3

Step-by-step explanation:

Step 1: Subtract -3m^2+9 from both sides.

6m^2+18m+17−(−3m^2+9)=−3m^2+9−(−3m^2+9)

9m^2+18m+8=0

Step 2: Factor left side of the equation.

(3m+2)(3m+4)=0

Step 3: Set factors equal to 0.

3m+2=0 or 3m+4=0

m=−2/3 or m=−4/3

Please help me with this !!!

Answers

Step-by-step explanation:

sorry bro, ìdk dis answer

G.O.O.G.L.E IT....MAYBE YOU WILL FIND THE ANSWER...

Fraction………………..::::::

Answers

Answer:

0.45

Step-by-step explanation:

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathsf{\dfrac{12}{25}\times\dfrac{15}{16}}[/tex]

[tex]\mathsf{= \dfrac{12\times15}{25\times16}}[/tex]

[tex]\mathsf{= \dfrac{180}{400}}[/tex]

[tex]\mathsf{= \dfrac{180\div5}{400\div5}}[/tex]

[tex]\mathsf{= \dfrac{36}{80}}[/tex]

[tex]\mathsf{= \dfrac{36\div4}{80\div4}}[/tex]

[tex]\mathsf{= \dfrac{9}{20}}[/tex]

[tex]\huge\textbf{Therefore, your answer is: \boxed{\mathsf{\dfrac{9}{20}}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Simplify the expression.

5(10 + g) + 14g + 4
A.
19g + 54
B.
9g + 44
C.
14g + 50
D.
15g + 15

Answers

Answer:

A. 19g+54

let me know if this helps :3

Step-by-step explanation:

6.82×105 minus 3.11×104

Answers

Answer:

Simplify the expression.

answer :

392.66

Step-by-step explanation:

Answer:

392.66

Step-by-step explanation:

Our equation at first is (6.82x105) - (3.11x104)

We first multiply 6.82 and 105 and we get 716.1

Now our equation is 716.1 - (3.11x104)

Now we multiply 3.11 and 104 and we get 323.44

We now subtract 716.1-323.44 and we get our final answer of…

392.66!

Please award brainliest if possible!

please helpppppppppppp

Answers

Answer:

[tex] \frac{x - 3}{x} [/tex]

Step-by-step explanation:

[tex]f(x) = \frac{1}{x} \: \: g(x) = x - 3 \\ \\ \implies \: (f•g)(x) = \frac{1}{x} (x - 3) \\ \\ = \frac{x - 3}{x} [/tex]

Evaluate 7 1/6- 3 5/8

Answers

Answer:

3 13/24

Step-by-step explanation:

hope this helps you!

let's firstly convert the mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{7\frac{1}{6}}\implies \cfrac{7\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{43}{6}} ~\hfill \stackrel{mixed}{3\frac{5}{8}}\implies \cfrac{3\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{29}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{43}{6}~~ - ~~\cfrac{29}{8}\implies \cfrac{(4)43~~ - ~~(3)29}{\underset{\textit{using this LCD}}{24}}\implies \cfrac{172~~ - ~~87}{24}\implies \cfrac{85}{24}\implies 3\frac{13}{24}[/tex]

The citizens of a city were asked to choose their favorite pet. The circle graph shows how the citizens answered. If 65,000
citizens answered the question, how many chose Dogs or Snakes?

Answers

Answer:

Dogs: 14,300 people

Snakes: 3,900 people

Lincoln High School has 84 teachers. 12 of the teachers teach math. Of the 32 females teachers, 6 teach math.

What is the probability that a teacher is a woman or teaches math? Express your answer as both a fraction and a percetage.

Answers

Probabilities are used to determine the chances of events

The probability that a teacher is a woman or teaches math is 45.24%

How to determine the probability

The given parameters are:

Teachers = 84

Math teachers = 12

Female teachers = 32

Female math teachers = 6

The number of female or math teachers is:

Female or math = Math + Female - Female math

So, we have:

Female or math = 12 + 32 - 6

Female or math = 38

The probability that a teacher is a woman or teaches math is:

[tex]Pr = \frac{38}{84}[/tex]

Simplify

[tex]Pr = \frac{19}{42}[/tex]

Express as percentage

[tex]Pr = 45.24\%[/tex]

Hence, the probability that a teacher is a woman or teaches math is 45.24%

Read more about probability at:

https://brainly.com/question/25870256

*PLEASE HELP* *IRRELEVANT ANSWERS WILL BE REPORTED AS SPAM*

A plane left Chicago at 8:00 A.M. At 1:00 P.M., the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip? (include units)

Find slope:
Then find the average speed of the plane for the trip

Answers

Time taken=13:00-8:00=5hDistance=1500mi

[tex]\\ \rm\hookrightarrow Avg\: Speed=\dfrac{Total\: distance}{Time}[/tex]

[tex]\\ \rm\hookrightarrow Avg\:Speed=\dfrac{1500}{5}[/tex]

[tex]\\ \rm\hookrightarrow Avg\:Speed=500mph[/tex]

Step-by-step explanation:

150/50=50

So 50mph is average speed

Formula Used :-

Speed=Distance/Time

#14-#19

help would rlly be great! i'm struggling rlly hard

Answers

Answer:

  14. ∠UVS = 63.6°

  15. ∠TWU = 90°

  16. ∠TUV = 116.4°

  17. UW = √111 ≈ 10.5

  18. SU = 2√111 ≈ 21.1

  19. VT = 34

Step-by-step explanation:

The relevant relations for a rhombus are ...

diagonals bisect each other at right angles, dividing the figure into 4 congruent right trianglesthe diagonals bisect the vertex anglesadjacent vertex angles are supplementary

__

14.

Angle UVS is double the measure of angle UVW. 2×31.8° = 63.6°.

  angle UVS = 63.6°

__

15.

As we said above, the angles where the diagonals cross are right angles.

  angle TWU = 90°

__

16.

Angle TUV is supplementary to angle UVS. 180° -63.6° = 116.4°

  angle TUV = 116.4°

__

17.

UW is found using the Pythagorean theorem.

  UW² +TW² = TU²

  UW² = TU² -TW² = 20² -17² = 111

  UW = √111 ≈ 10.536

__

18.

The whole diagonal is twice the measure of half of it. SU = 2×UW

  SU = 2√111 ≈ 20.071

__

19.

The whole diagonal is twice the measure of half of it. 2×17 = 34

  VT = 34


Please answer this question thank you

Answers

Answer:

74

Step-by-step explanation:

What I'm getting at, is that you need to add all the hour sold cups up, and then double it because she expects to sell twice as much. 15 + 11 +5 +6 = 37, and 37 doubled is 74

Answer:

74 cups

Step-by-step explanation:

Total for today: 37

6 + 5 + 11 + 15 = 37

Tomorrow is twice of today

2(37) = 74

I hope this helps!

Chase and Sara went to the candy store. Chase bought {6}6 pieces of fudge and {3}3 pieces of bubble gum for a total of ${18.00}18.00. Write an equation using {f}f for cost of fudge and {g}g for cost of gum. (No spaces, just numbers and symbols.)

Answers

6f+3g=18

Hopefully this helps you

PLEASE HELP ASP!!!!!!!!!!!A birch tree that is 4 ft tall grows at a rate of 1 ft per year. A larch tree that is 6 ft tall grows at a rate of 0.5 ft per year.

Let the variable t represent time in years and let the variable h represent height in feet.

In how many years will the trees be the same height?

Which system of equations can be used to solve this problem?




{h=1+4th=0.5+6t

{h=4+th=6+0.5t

{h=5th=6.5t

{h=4−th=6−0.5t

Answers

Answer:

4 Years

Step-by-step explanation:

1:0.5 = 2:1

So, every two years, the birch tree grows 1 foot more than the larch tree

Currently, they are 2 feet apart, so in 4 years, they will be the same height

A woman is 69 1/2 inches tall and her son is 66 2/9 inches tall. How much taller is the woman?

Answers

Answer:

Find The InterestRs1000 rateRs10%isRs1200

6) Suppose you put $200 in a savings account. The account earns simple interest at an
annual rate of 10%. You earned $100 in interest. How many years did you keep the
money in your savings account?

Answers

Answer:  5 years

====================================================

Work Shown:

i = P*r*t

100 = 200*0.10*t

100 = 20t

20t = 100

t = 100/20

t = 5

Brent and his family spent $21 for admission to the country fair. They bought two adult passes for six dollars each and three children passes for three dollars each. How much more money did Brents family spend on adults passes then children's passes?

Answers

They spent $3 more on adult passes. 6+6=12 3+3+3=9 12-9=3

Urgent, please reply as soon as possible! 30 points on brainly!
The above graph shows the acceleration of an object. use the information from the graph to answer the following question. During which section of the graph is there no acceleration? Explain why or why not.

Answers

Answer:

during section b

Step-by-step explanation:

the line is flat

Answer:

Yes beavause the graph goes up and then straight down

Step-by-step explanation:

can you answer my question?

You just bought a new laptop and paid an initial payment of $150.00. You will make 12 payments of $69.50. How much will the computer cost if your state charges 6% sales tax on the total sale.

Answers

The computer will cost $924.96 after 6% tax.

Total cost of laptop

The initial payment of the laptop made = $150.00

The remaining balance that would be made = 12 × 69.50

=$834

Therefore total cost of laptop before tax = 834 + 150

= $984

But tax is 6% of total cost =

[tex] \frac{6}{100} \times 984[/tex]

[tex] \frac{5904}{100} [/tex]

= $59.04

Therefore, total cost of laptop after tax = 984 - 59.04

= $924.96

Learn more about costs of products here:

https://brainly.com/question/24494976

8≥−6x−x^2
find Inequality for X

Answers

Inequality for X.......:)

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