9 less than the square root of a number, №14501474, 07.04.2022 01:28

Mathematics

9 less than the square root of a number

Step-by-step answer

P Answered by PhD

\sqrt{x} - 9

Step-by-step explanation:

sorry if that's not what you needed

Mathematics

What is the algebraic expression for 9 less than the square root of a number?

Step-by-step answer

P Answered by Specialist

$✿\:Let\: the\:number\:be\:x$

$As\:per\: Question\:$

$\large{\color{cyan}{Expression\::}}$

$\rightarrow{\sqrt{x}\:-\:9}$

Mathematics

What is the algebraic expression for 9 less than the square root of a number?

Step-by-step answer

P Answered by Specialist

$✿\:Let\: the\:number\:be\:x$

$As\:per\: Question\:$

$\large{\color{cyan}{Expression\::}}$

$\rightarrow{\sqrt{x}\:-\:9}$

Mathematics

9 less than the square root of a number

Step-by-step answer

P Answered by PhD

\sqrt{x} - 9

Step-by-step explanation:

sorry if that's not what you needed

Mathematics

There are three questions. i ll give brainliest if you show your work for all three of them. plz and answer quickly! what square root best approximates the point on the graph? a square root of 5 a square root of 15 a square root of 28 a square root of 53 hassan used the iterative process to locate the square root of 15 on the number line. which best describes hassan’s estimation? hassan is correct because the square root of 15 is about 0.4 hassan is correct because the point is on the middle of the number line. hassan is incorrect because the square

Step-by-step answer

P Answered by PhD

99

Hello! I apologize for any wait, I was away for some time. Once again, I apologize for any inconvenience, and if you have already moved on, I'll go ahead and explain this out anyways for future reference.

1: What square root best approximates the point on the graph?
Well, here you are shown a number line. On the number line, there is a point. Guesstimating it shows it's around 5.1-5.2. It is definitely lower than 5.5, as that would be directly in the middle of 5 and 6.

Well, the answer are:
A square root of 5
A square root of 15
A square root of 28
A square root of 53

Well, this question is a little unclear to me. I am considering if the question is stating that those numbers, 5, 15, 28, and 53 are ALREADY the sqaure root of a number, or if those 4 numbers are what you are supposed to find out which square root lines up to the point on the chart.

Because it seems that none of these four numbers would work with my first theory, I'll go with the simpler of the two, the latter. Meaning those four numbers are the numbers that you have to find the square root of, and the correct one should line up with the chart.

SO, pull out your calculator kiddo. You don't want to have to calculate square root by hand, you'll run out of paper/and or pencils before you know it. It usually takes a bit of time for each one, and considering you have multiple one's to calculate. . . Yeah, go with the calculator.

So, plug in each of the numbers into a TI-84 or basically any calculator that works with square root calculations.

Square root of 5: 2.2360679775
Square root of 15: 3.87298334621
Square root of 28: 5.29150262213
Square root of 53: 7.28010988928

Alright. Well, what do we know? From our guesstimation, the point looked to be close to 5.2

None of these match that EXCEPT C: 28

Your best shot for #1 is 28

2. Hassan used the iterative process to locate the square root of 15 on the number line.

I'll be frank: I've never heard of the "iterative process" in my life, and if I have, i definitely can't recall. This is most likely a different term used for some other process that I probably DO know, but anyways, that's not quite relevant, so I'll carry on:

Looking at the graph we see H-man graphed his point on the number line at EXACTLY .45
We know this because the dot is directly in the middle of .4 and .5, and .45 is the best way to represent that (imagine .4 is .40, and .5 is .50 if this helps, the value is ultimately the same)

Now, H-man graphed this point specifically because he used his "process" to find the square root of 15.

Once again, I'm not sure what this process is, but I'll help to the best of my ability. The square root of 15 is around 3.9

I'm assuming H-man's process simply moved around the decimal place, somehow. This I am not sure on, but it's the only thing that makes somewhat sense to me.

So, if this is correct, on his terms, the graphed point should be more like: 0.39

Now, his point is considerably further than this. This would mean (don't quote me on this) that Hassan is incorrect, and I would say this because the sqare root of 15 is less than .4

Yes, this doesn't make much sense to me, but if I'm correct, then this answer should also be correct. Relatively.

3. The point plotted on the number line is the square root of x.
What is the approximate value of x?

Basically X represents the original number, and the numbers they give you are what they want you to choose the original number is. This is based on the point on the graph, which is at around 4.1, because this number is the square root of X.

To solve this, find the square roots of all 4 numbers (separately of course).

The square root of 4 is: 2
The square root of 9 is: 3
The square root of 17 is: 4.12310562562
The square root of 20 is: 4.472135955

Now, from our guess we can clearly see the point is around 4.1
The answer that nearly matches this estimate EXACTLY is C: 17

Your choice here is 17

Total:

#1=28
#2=Hassan is incorrect because the square root of 15 is less than 0.4 (guess)
#3=17

Mathematics

There are three questions. i ll give brainliest if you show your work for all three of them. plz and answer quickly! what square root best approximates the point on the graph? a square root of 5 a square root of 15 a square root of 28 a square root of 53 hassan used the iterative process to locate the square root of 15 on the number line. which best describes hassan’s estimation? hassan is correct because the square root of 15 is about 0.4 hassan is correct because the point is on the middle of the number line. hassan is incorrect because the square

Step-by-step answer

P Answered by PhD

99

Hello! I apologize for any wait, I was away for some time. Once again, I apologize for any inconvenience, and if you have already moved on, I'll go ahead and explain this out anyways for future reference.

1: What square root best approximates the point on the graph?
Well, here you are shown a number line. On the number line, there is a point. Guesstimating it shows it's around 5.1-5.2. It is definitely lower than 5.5, as that would be directly in the middle of 5 and 6.

Well, the answer are:
A square root of 5
A square root of 15
A square root of 28
A square root of 53

Well, this question is a little unclear to me. I am considering if the question is stating that those numbers, 5, 15, 28, and 53 are ALREADY the sqaure root of a number, or if those 4 numbers are what you are supposed to find out which square root lines up to the point on the chart.

Because it seems that none of these four numbers would work with my first theory, I'll go with the simpler of the two, the latter. Meaning those four numbers are the numbers that you have to find the square root of, and the correct one should line up with the chart.

SO, pull out your calculator kiddo. You don't want to have to calculate square root by hand, you'll run out of paper/and or pencils before you know it. It usually takes a bit of time for each one, and considering you have multiple one's to calculate. . . Yeah, go with the calculator.

So, plug in each of the numbers into a TI-84 or basically any calculator that works with square root calculations.

Square root of 5: 2.2360679775
Square root of 15: 3.87298334621
Square root of 28: 5.29150262213
Square root of 53: 7.28010988928

Alright. Well, what do we know? From our guesstimation, the point looked to be close to 5.2

None of these match that EXCEPT C: 28

Your best shot for #1 is 28

2. Hassan used the iterative process to locate the square root of 15 on the number line.

I'll be frank: I've never heard of the "iterative process" in my life, and if I have, i definitely can't recall. This is most likely a different term used for some other process that I probably DO know, but anyways, that's not quite relevant, so I'll carry on:

Looking at the graph we see H-man graphed his point on the number line at EXACTLY .45
We know this because the dot is directly in the middle of .4 and .5, and .45 is the best way to represent that (imagine .4 is .40, and .5 is .50 if this helps, the value is ultimately the same)

Now, H-man graphed this point specifically because he used his "process" to find the square root of 15.

Once again, I'm not sure what this process is, but I'll help to the best of my ability. The square root of 15 is around 3.9

I'm assuming H-man's process simply moved around the decimal place, somehow. This I am not sure on, but it's the only thing that makes somewhat sense to me.

So, if this is correct, on his terms, the graphed point should be more like: 0.39

Now, his point is considerably further than this. This would mean (don't quote me on this) that Hassan is incorrect, and I would say this because the sqare root of 15 is less than .4

Yes, this doesn't make much sense to me, but if I'm correct, then this answer should also be correct. Relatively.

3. The point plotted on the number line is the square root of x.
What is the approximate value of x?

Basically X represents the original number, and the numbers they give you are what they want you to choose the original number is. This is based on the point on the graph, which is at around 4.1, because this number is the square root of X.

To solve this, find the square roots of all 4 numbers (separately of course).

The square root of 4 is: 2
The square root of 9 is: 3
The square root of 17 is: 4.12310562562
The square root of 20 is: 4.472135955

Now, from our guess we can clearly see the point is around 4.1
The answer that nearly matches this estimate EXACTLY is C: 17

Your choice here is 17

Total:

#1=28
#2=Hassan is incorrect because the square root of 15 is less than 0.4 (guess)
#3=17

Mathematics

Check if my answers are correct. will mark brainliest to whoever comments first! you, and god bless. 2. how is the graph of y equals -8x^2 - 2. different from the graph of y equals negative 8x squared.? (1 point) it is shifted 2 units to the left it is shifted 2 units to the right. *** it is shifted 2 units up. it is shifted 2 units down. a model rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y equals negative 0.06 x squared plus 9.6 x plus 5.4 where x is the horizontal distance, in meters,

Step-by-step answer

P Answered by PhD

29

1. It is shifted 2 units down.

The graph of y=-8x^2 -2 is shifted 2 units down with respect to the graph of y=-8x^2 . We can prove this by taking, for instance, x=0, and calculating the value of y in the two cases. In the first function:

y=-8*0^2 -2=-2

In the second function:

y=-8*0^2 =0

So, the first graph is shifted 2 units down.

2. 160.56 m

The path of the rocket is given by:

y=-0.06 x^2 +9.6 x +5.4

The problem asks us to find how far horizontally the rocket lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

-0.06 x^2 +9.6 x+5.4 =0

Using the formula,

$x=\frac{-9.6 \pm \sqrt{(9.6)^2-4(-0.06)(5.4)}}{2(-0.06)}$

which has two solutions: x_1 = 160.56 m and x_2 = -0.56 m . The second solution is negative, so it has no physical meaning, therefore the correct answer is 160.56 m.

3. 27.43 m

The path of the rock is given by:

y=-0.02 x^2 +0.8 x +37

The problem asks us to find how far horizontally the rock lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

-0.02 x^2 +0.8 x+37 =0

Using the formula,

$x=\frac{-0.8 \pm \sqrt{(0.8)^2-4(-0.02)(37)}}{2(-0.02)}$

which has two solutions: x_1 = 67.43 m and x_2 = -27.43 m . In this case, we have to choose the second solution (27.43 m), since the rock was thrown backward from the initial height of 37 m, so the negative solution corresponds to the backward direction.

4. (-2, 16) and (1, -2)

The system is:

y=x^2 -5x +2 (1)

y=-6x+4 (2)

We can equalize the two equations:

x^2 -5x+2 = -6x +4

which becomes:

x^2 + x -2 =0

Solving it with the formula, we find two solutions: x=-2 and x=1. Substituting both into eq.(2):

x=-2 --> y=-6 (-2) +4 = 12+4 = 16

x=1 --> y=-6 (1) +4 = -6+4 =-2

So, the solutions are (-2, 16) and (1, -2).

5. (-1, 1) and (7, 33)

The system is:

y=x^2 -2x -2 (1)

y=4x+5 (2)

We can equalize the two equations:

x^2 -2x-2 = 4x +5

which becomes:

x^2 -6x -7 =0

Solving it with the formula, we find two solutions: x=7 and x=-1. Substituting both into eq.(2):

x=7 --> y=4 (7) +5 = 28+5 = 33

x=-1 --> y=4 (-1) +5 = -4+5 =1

So, the solutions are (-1, 1) and (7, 33).

6. 2.30 seconds

The height of the object is given by:

h(t)=-16 t^2 +85

The time at which the object hits the ground is the time t at which the height becomes zero: h(t)=0, therefore

-16t^2 +85 =0

By solving it,

16t^2 = 85

$t^2 = \frac{85}{16}$

$t=\sqrt{\frac{85}{16}}=2.30 s$

7. Reaches a maximum height of 19.25 feet after 0.88 seconds.

The height of the ball is given by

h(t)=-16t^2 + 28t + 7

The vertical velocity of the ball is equal to the derivative of the height:

v(t)=h'(t)=-32t+28

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

-32t + 28 =0

from which we find t=0.88 s

And by substituting these value into h(t), we find the maximum height:

h(t)=-16(0.88)^2 + 28(0.88) + 7 = 19.25 m

8. Reaches a maximum height of 372.25 feet after 4.63 seconds.

The height of the boulder is given by

h(t)=-16t^2 + 148t + 30

The vertical velocity of the boulder is equal to the derivative of the height:

v(t)=h'(t)=-32t+148

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

-32t + 148 =0

from which we find t=4.63 s

And by substituting these value into h(t), we find the maximum height:

h(t)=-16(4.63)^2 + 148(4.63) + 30 = 372.25 m

9. 12 m

Let's call x the length of the side of the original garden. The side of the new garden has length (x+3), so its area is

(x+3)^2 = 225

Solvign this equation, we find

$x+3 = \sqrt{225}=15$

x=15-3=12 m

10. 225/4

In fact, if we write $x^2 +15 x + \frac{225}{4}$ , we see this is equivalent to the perfect square:

$(x+\frac{15}{2})^2 = x^2 +15 x +\frac{225}{4}$

11. -11.56, 1.56

The equation is:

x^2 +10 x -18 =0

By using the formula:

$x=\frac{-10 \pm \sqrt{(10)^2-4(1)(-18)}}{2*1}$

which has two solutions: x=-11.56 and 1.56.

12. -10.35, 1.35

The equation is:

x^2 +9 x -14 =0

By using the formula:

$x=\frac{-9 \pm \sqrt{(9)^2-4(1)(-14)}}{2*1}$

which has two solutions: x=-10.35 and 1.35.

Mathematics

Check if my answers are correct. will mark brainliest to whoever comments first! you, and god bless. 2. how is the graph of y equals -8x^2 - 2. different from the graph of y equals negative 8x squared.? (1 point) it is shifted 2 units to the left it is shifted 2 units to the right. *** it is shifted 2 units up. it is shifted 2 units down. a model rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y equals negative 0.06 x squared plus 9.6 x plus 5.4 where x is the horizontal distance, in meters,

Step-by-step answer

P Answered by PhD

29

1. It is shifted 2 units down.

The graph of y=-8x^2 -2 is shifted 2 units down with respect to the graph of y=-8x^2 . We can prove this by taking, for instance, x=0, and calculating the value of y in the two cases. In the first function:

y=-8*0^2 -2=-2

In the second function:

y=-8*0^2 =0

So, the first graph is shifted 2 units down.

2. 160.56 m

The path of the rocket is given by:

y=-0.06 x^2 +9.6 x +5.4

The problem asks us to find how far horizontally the rocket lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

-0.06 x^2 +9.6 x+5.4 =0

Using the formula,

$x=\frac{-9.6 \pm \sqrt{(9.6)^2-4(-0.06)(5.4)}}{2(-0.06)}$

which has two solutions: x_1 = 160.56 m and x_2 = -0.56 m . The second solution is negative, so it has no physical meaning, therefore the correct answer is 160.56 m.

3. 27.43 m

The path of the rock is given by:

y=-0.02 x^2 +0.8 x +37

The problem asks us to find how far horizontally the rock lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

-0.02 x^2 +0.8 x+37 =0

Using the formula,

$x=\frac{-0.8 \pm \sqrt{(0.8)^2-4(-0.02)(37)}}{2(-0.02)}$

which has two solutions: x_1 = 67.43 m and x_2 = -27.43 m . In this case, we have to choose the second solution (27.43 m), since the rock was thrown backward from the initial height of 37 m, so the negative solution corresponds to the backward direction.

4. (-2, 16) and (1, -2)

The system is:

y=x^2 -5x +2 (1)

y=-6x+4 (2)

We can equalize the two equations:

x^2 -5x+2 = -6x +4

which becomes:

x^2 + x -2 =0

Solving it with the formula, we find two solutions: x=-2 and x=1. Substituting both into eq.(2):

x=-2 --> y=-6 (-2) +4 = 12+4 = 16

x=1 --> y=-6 (1) +4 = -6+4 =-2

So, the solutions are (-2, 16) and (1, -2).

5. (-1, 1) and (7, 33)

The system is:

y=x^2 -2x -2 (1)

y=4x+5 (2)

We can equalize the two equations:

x^2 -2x-2 = 4x +5

which becomes:

x^2 -6x -7 =0

Solving it with the formula, we find two solutions: x=7 and x=-1. Substituting both into eq.(2):

x=7 --> y=4 (7) +5 = 28+5 = 33

x=-1 --> y=4 (-1) +5 = -4+5 =1

So, the solutions are (-1, 1) and (7, 33).

6. 2.30 seconds

The height of the object is given by:

h(t)=-16 t^2 +85

The time at which the object hits the ground is the time t at which the height becomes zero: h(t)=0, therefore

-16t^2 +85 =0

By solving it,

16t^2 = 85

$t^2 = \frac{85}{16}$

$t=\sqrt{\frac{85}{16}}=2.30 s$

7. Reaches a maximum height of 19.25 feet after 0.88 seconds.

The height of the ball is given by

h(t)=-16t^2 + 28t + 7

The vertical velocity of the ball is equal to the derivative of the height:

v(t)=h'(t)=-32t+28

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

-32t + 28 =0

from which we find t=0.88 s

And by substituting these value into h(t), we find the maximum height:

h(t)=-16(0.88)^2 + 28(0.88) + 7 = 19.25 m

8. Reaches a maximum height of 372.25 feet after 4.63 seconds.

The height of the boulder is given by

h(t)=-16t^2 + 148t + 30

The vertical velocity of the boulder is equal to the derivative of the height:

v(t)=h'(t)=-32t+148

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

-32t + 148 =0

from which we find t=4.63 s

And by substituting these value into h(t), we find the maximum height:

h(t)=-16(4.63)^2 + 148(4.63) + 30 = 372.25 m

9. 12 m

Let's call x the length of the side of the original garden. The side of the new garden has length (x+3), so its area is

(x+3)^2 = 225

Solvign this equation, we find

$x+3 = \sqrt{225}=15$

x=15-3=12 m

10. 225/4

In fact, if we write $x^2 +15 x + \frac{225}{4}$ , we see this is equivalent to the perfect square:

$(x+\frac{15}{2})^2 = x^2 +15 x +\frac{225}{4}$

11. -11.56, 1.56

The equation is:

x^2 +10 x -18 =0

By using the formula:

$x=\frac{-10 \pm \sqrt{(10)^2-4(1)(-18)}}{2*1}$

which has two solutions: x=-11.56 and 1.56.

12. -10.35, 1.35

The equation is:

x^2 +9 x -14 =0

By using the formula:

$x=\frac{-9 \pm \sqrt{(9)^2-4(1)(-14)}}{2*1}$

which has two solutions: x=-10.35 and 1.35.

Computers and Technology

The mathematical constant Pi is an irrational number with value approximately 3.1415928... The precise value of this constant can be obtained from the following infinite sum: Pi^2 = 8+8/3^2+8/5^2+8/7^2+8/9^2+... (Pi is of course just the square root of this value.) Although we cannot compute the entire infinite series, we get a good approximation of the value of Pi by computing the beginning of such a sum. Write a function approxPIsquared that takes as input float error and approximates constant Pi to within error by computing the above sum, term

Step-by-step answer

P Answered by Specialist

I am writing a Python program:

def approxPIsquared(error):

previous = 8

new_sum =0

num = 3

while (True):

new_sum = (previous + (8 / (num ** 2)))

if (new_sum - previous <= error):

return new_sum

previous = new_sum

num+=2

print(approxPIsquared(0.0001))

Explanation:

I will explain the above function line by line.

def approxPIsquared(error):

This is the function definition of approxPlsSquared() method that takes error as its parameter and approximates constant Pi to within error.

previous = 8 new_sum =0 num = 3

These are variables. According to this formula:

Pi^2 = 8+8/3^2+8/5^2+8/7^2+8/9^2+...

Value of previous is set to 8 as the first value in the above formula is 8. previous holds the value of the previous sum when the sum is taken term by term. Value of new_sum is initialized to 0 because this variable holds the new value of the sum term by term. num is set to 3 to set the number in the denominator. If you see the 2nd term in above formula 8/3^2, here num = 3. At every iteration this value is incremented by 2 to add 2 to the denominator number just as the above formula has 5, 7 and 9 in denominator.

while (True): This while loop keeps repeating itself and calculates the sum of the series term by term, until the difference between the value of new_sum and the previous is less than error. (error value is specified as input).

new_sum = (previous + (8 / (num ** 2))) This statement represents the above given formula. The result of the sum is stored in new_sum at every iteration. Here ** represents num to the power 2 or you can say square of value of num.

if (new_sum - previous <= error): This if condition checks if the difference between the new and previous sum is less than error. If this condition evaluates to true then the value of new_sum is returned. Otherwise continue computing the, sum term by term.

return new_sum returns the value of new_sum when above IF condition evaluates to true

previous = new_sum This statement sets the computed value of new_sum to the previous.

For example if the value of error is 0.0001 and previous= 8 and new_sum contains the sum of a new term i.e. the sum of 8+8/3^2 = 8.88888... Then IF condition checks if the

new_sum-previous <= error

8.888888 - 8 = 0.8888888

This statement does not evaluate to true because 0.8888888... is not less than or equal to 0.0001

So return new_sum statement will not execute.

previous = new_sum statement executes and now value of precious becomes 8.888888...

Next num+=2 statement executes which adds 2 to the value of num. The value of num was 3 and now it becomes 3+2 = 5.

After this while loop execute again computing the sum of next term using new_sum = (previous + (8 / (num ** 2)))

new_sum = 8.888888.. + (8/(5**2)))

This process goes on until the difference between the new_sum and the previous is less than error.

screenshot of the program and its output is attached.

The mathematical constant Pi is an irrational number with value approximately 3.1415928... The preci

Mathematics

What is the standard deviation of company r s earnings per month for this year? (1) the standard deviation of company r s earnings per month in the first half of this year was $2.3 million. (2) the standard deviation of company r s earnings per month in the second half of this year was $3.9 million. 2. what is the standard deviation of q, a set of consecutive integers? (1) q has 21 members. (2) the median value of set q is 20. 3. lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. if

Step-by-step answer

P Answered by Master

9

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 are all factors of 2

9 less than the square root of a number

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