the statement 2n^2+5n-25=0 opens up because

Answers

Answer 1

The graph of 2n^2 +5n -25 opens up because the coefficient of n^2 is positive.

____
The statement 2n^2 +5n -25 = 0 defines two values of n.

Related Questions

The office of student services at a large western state university maintains information on the study habits of its full-time students. their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. the hours studied follows the normal distribution with a standard deviation of six hours. suppose we select a random sample of 144 current students. what is the probability that the mean of this sample is less than 19.25 hours?

Answers

Answer: 45.03%

To find the answer for this problem, you first need to find the z-score for a value of 19.25.

The z-score is the number of standard deviations from the mean.

Here is the work for our z-score:

19.25 - 20 = -0.75 / 6 = -0.125

Now, you just have to use a standard normal distribution table and look up the probability for a z-score of -0.125. I used the average of the probability for z-scores of -0.12 and -0.13 to get 45.03%.

Final answer:

There is a 22.66% probability that the mean study time of a random sample of 144 students at the large western state university will be less than 19.25 hours.

Explanation:

To solve this problem, we need to use the formula for the z-score, which is (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

Here, n=144, μ=20, σ=6 and X=19.25. Substituting these values into the formula, we get z = (19.25 - 20) / (6/√144) = -0.75.

The z-score tells us how many standard deviations the value is away from the mean. A negative z-score indicates that the data point is less than the mean.

To find the probability, we need to look up this z-score in the z-table, which gives the area to the left of the z-score on a standard normal distribution. The value associated with z=-0.75 on the table is approximately 0.2266, or 22.66%.

So, there is a 22.66% probability that the mean study time of a random sample of 144 students will be less than 19.25 hours.

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Please help asap. Super appreciated! <3

Answers

A will be your answer!

Solve for x: x^19 − 2x^18 + 7x^17 − 12x^6 + 6x^15 = 0

A) 0,1, +/-6i

B) -1,0, +/-√6i

C)-1, 0, +/-6i

D) 0,1, +/-√6i

Answers

It looks like you intend
x¹⁹ -2x¹⁸ +7x¹⁷ -12x¹⁶ +6x¹⁵ = 0
x¹⁵(x -1)²(x² +6) = 0

x = 0, 1, ±(√6)i . . . . . . . selection D is appropriate

Last month, the seventh grade and eighth grade math classes at Moore Middle School collected canned goods for the local food shelter. The dot plots below show the number of canned goods collected by the classes.

The mean absolute deviation for each grade level is 1.6. The difference between the mean number of canned goods collected by each grade level is how many times the mean absolute deviation?
A. 5
B. 4
C. 3
D. 6

Answers

To answer this question you will need to find the mean of each class and then subtract them. You will then compare this difference to the MAD of 1.6.

Mean of 7th grade class is:
420/20=21

Mean of 8th grade class:
325/25=13

21-13=8

To find how many times , divide 8 by 1.6.

8/1.6= 5 times

The difference of the means is 5 times the MAD (mean absolute deviation).

What is the y-intercept of the line perpendicular to y= -5/2x + 4/5 including point (-3,-1) ?

Answers

Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.

On this case they give you the equation of a line and a point, and is asked to find the y-intercept of the line that is perpendicular to the given one, and that passes through the given point.

The slope of the given line is -5/2, which means that the slope of a line perpendicular to this one, needs to be 2/5. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.

y=mx+b Substitute the values of the given point and the slope
-1=-3(2/5)+b Combine like terms
-1=-6/5+b Add 6/5 in both sides to isolate b
1/5=b
The equation of the line perpendicular to y=-5/2x+4/5 and that passes through the point (-3,-1) is y=2/5x+1/5, and the y-intercept is 1/5 or 0.2.

Roger and Sulee each decomposed 1 1/6.Roger wrote 1/6+1/6+2/6+3/6.Sulee wrote 3/6+4/6. who is correct? Explain

Answers

The correct answer is Roger

Help a fella out. Explain this to me.

Answers

HELLO

add x with exponent 2 to 5x then you get 6x with exponent 2
(if there one x with out a number it = 1x)
change the exponent like time it by its base so its 6*6=36
answer 36x +6 I think the answer is b or c I'm not very sure

have a wonderful Wednesday
can I get brainlest plz

1. What is the vertex of the parabola?
A. (-1,0) B. (0, -3) C. (1, -4) D. (3, 0)

2. Which of the following has a graph that is wider than the graph of y=3x^2+2?
A. Y=3X^2+3
B. Y=0.5X^2+1
C. Y=-4X^2-1
D.Y=4X^2+1

3. Which graph represents the unction y=-2x^2-5?

4. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2

A. f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
B. f(x)-2x^2, f(x)=-10x^2, f(x)=0.5x^2
C. f(x)=0.5x^2, f(x)=2x^2, f(x)=-10x^2
D. f(x)=0.5X62, f(x)=-10x^2, f(x)=2x^2

Answers

Answer: Without the pictures, the only questions we can answer are #2 and #4.

#2
Choice B is wider than the graph of y = 3x^2 + 2. In a quadratic function like this, the value in front of the x^2 controls the width. Any positive number smaller than 3 would be wider.

#4
Choice A has the correct order. Again, the value in front of the x^2 controls how wide or narrow the graph is. First, take the absolute value of each value. Then, place them in order from greatest to least. The greater the number the narrower the graph.

Answer:

1. what is the vertex of the parabola?

C : ( 1, -4 )

2. Which of the following has a graph that is wider than the graph of y=3x^2+2?

B : Y=0.5X^2+1

3. Which graph represents the unction y=-2x^2-5?

D : choose the graph that has the smaller curve and arrows facing down

4. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2

A : f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2

Step-by-step explanation:

these are the correct answers for 2022

i finished the quick check UwU

A dress normally sells for $45.95. How much does the dress cost after a 20% discount?

Answers

the dress would cost $36.76 after a 20% discount

$36.76

45.95 x .20 =9.19
45.95 - 9.19 =36.76

Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection y=x+2 y=−12x+5

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The decimal values correspond to (x, y) = (3/13, 2 3/13).

Rob and john share money in a ratio of 9:4. How much of the £39000 does john get ?

Answers

[tex]\bf \cfrac{Rob}{John}\qquad 9:4\qquad \cfrac{9}{4}\qquad \cfrac{9\cdot \frac{39000}{9+4}}{4\cdot \frac{39000}{9+4}}\implies \cfrac{9\cdot 3000}{4\cdot 3000}[/tex]

I Really Need Help With This Problem, Please

Listed in the Item Bank are key terms and expressions, each of which is associated with one of the columns. Some terms may display additional information when you click on them. Drag and drop each item into the correct column. The order does not matter.

Answers

1 and 5 are corresponding
1 and 8 are alternate exterior
2 and 6 are corresponding
2 and 7 are alternate exterior
3 and 5 are alternate interior
3 and 6 are consecutive interior
3 and 8 are corresponding
4 and 5 are consecutive interior
4 and 6 are alternate interior
4 and 7 are corresponding

Answer:

Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .

Alternate interior angles : 4 & 6 , 3 & 5

Alternate exterior angles : 1 &8 , 2 & 7

Consecutive interior angles : 4 & 5, 3 & 6

Step-by-step explanation:The corresponding angles are the angles that are in the same position made by a line cutting through two or more other lines.The alternate interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. The alternate exterior angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal. The consecutive interior angles are the pair of angles which are formed on one side of the transversal when two lines are intersected by transversal line .

By using the above definitions,

Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .

Alternate interior angles : 4 & 6 , 3 & 5

Alternate exterior angles : 1 &8 , 2 & 7

Consecutive interior angles : 4 & 5, 3 & 6

What is the value of x in the diagram below?

Answers

Hi,
The answer will be [tex] \frac{ 18\sqrt{2} }{ \sqrt{3} } [/tex] .

Now how is that, there is a rule for the right angled triangle which says:

cosθ = [tex] \frac{adjacent side}{hypotenuse} [/tex] so, if we applied this rule on the lower triangle we can say: cos30°= [tex] \frac{9}{hypotenuse} [/tex] and therefore the hypotenuse = [tex] \frac{9}{cos30} [/tex] = [tex] \frac{18}{ \sqrt{3} } [/tex] .

now in the upper triangle we will apply the same rule so,
cos45°=[tex] \frac{adjacent side}{hypotenuse} [/tex]
and the adjacent side in the upper triangle is [tex] \frac{18}{ \sqrt{3} } [/tex] and the hypotenuse is x.
so cos45°=[tex] \frac{( \frac{18}{ \sqrt{3} } )}{x} [/tex] and then we can say
x=[tex] \frac{ \frac{18}{ \sqrt{3} } }{cos45} [/tex] = [tex] \frac{ 18\sqrt{2} }{ \sqrt{3} } [/tex] .

Answer: B

Step-by-step explanation: EDGE 2022

Reflection across the y -axis

Answers

The reflection across the y -axis is that it would be the x -axis. Your welcome!

Answer:

G (-6,-8) H(-2,-2) F(0,-4)

Step-by-step explanation:

So really you add an negitive symbol to each number then its reflected acroos the x axis

BRAINLIESTTT ASAP!! :)

How do you know if a parabola has a maximum or a minimum?

Answers

The the parabola opens upward it has a minimum and if it opens downward then it has a maximum :)

look at the officiant of the terms, is a >0 then the parabola opens up upward and the graph has has a minimum at its vertex.

simplest form of the expression
3sqrt750+3sqrt2058-3sqrt48
can someone explain

Answers

First, you have to decompose the numbers under the square root:
750 = 2·3·5²
2058 = 2·3·7³
48 = 2⁴·3

Then, enlight all the exponents multiple of 2 (which is the index of the root):
3·√(2·3·5²) + 3·√(2·3·7²·7) + 3·√(2⁴·3)

At this point, you can take outside the square root everything that has an even number, and doing so you have to halve the exponent; you'll get:
3·5·√(2·3) + 3·7·√(2·3·7) + 3·2²·√3

You can now multiply:
15√6 + 21√42 + 12√3
which is the simplest form of your expression.

MEDAL!!!@#$%
7. According to the plate tectonics model, what layer from Earth's rigid, mobile plates?
A. inner and outer core
B. upper and lower mantle
C. crust only
D. crust and upper mantle <---
i think D is the answer,

Answers

The earth's outermost, rigid layer, the lithosphere, is fragmented into a dozen or more irregularly shaped plates that are riding atop a hotter, more mobile material, the asthenospehere. The tectonic plates are made up of Earth's crust and the upper part of the mantle. The plates fit together like a jigsaw puzzle. The lithospere is subdivided into tectonic plates.

Suppose the test scores of students in a class are normally distributed with a mean of 92 and a standard deviation of 3.

What is the z-score for a student who scored 86 on a test?

−6

−2

2

6

Answers

-2 since 86-92/3 = -6/3 which is -2

Find the number of moles in 508 g of ethanol (C2H5OH).

Answers

To find the number of moles we start by calculating the molar mass:
M(C2H5OH) = 2*M(C) + 6*M(H) + M(O)
M(C2H5OH) = 2* 12.01 + 6* 1.008 + 16
M(C2H5OH) = 46.068g

This is mass of one mole of ethanol. Total mass of ethanol can be calculated by using formula:
m = N * M
Where:
m = total mass
N = number of moles
M = molar mass

We rearrange formula for N:
N = m / M
N = 508 / 46.068
N = 11.03

508g of ethanol contains 11.03 moles.

32 = 4m + 8 solve each equation

Answers

Hey there! :D

32= 4m+8

Subtract 8 on both sides.

24=4m

Divide 4 on both sides.

m=6

I hope this helps!
~kaikers

4m + 8 = 32.

Subtract 8 from each side.

4m + 8 (-8) = 32 - 8.

Solve.
4m = 24.

Divide each side by 4.
m = 6.

Hope it helps! :)

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality 7.2b + 6.5 > 4.8b – 8.1. Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1. Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1. Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6. Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b. Which student’s first step was incorrect, and why? Amelia’s, because the variable term must be isolated on the left side Luis’s, because he flipped the inequality sign when he subtracted Shauna’s, because she did not apply the subtraction property of equality properly Clarence’s, because the terms he added together were not like terms

Answers

Luis is the one that performed an incorrect first step. When you add or subtract from either side, this does not affect the inequality symbol.

What will affect the symbol is when you divide or multiply by a negative because this means the opposite.

Answer:

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

got it right on Edge

please mark as Brainliest

(P.S. Luis is my first name)

Find the equation of line passing through (-7,-9) and parallel to the 8x-9y+2=0

Answers

Lets get started :)

8x - 9y + 2 = 0
9y = 8x + 2
y = [tex] \frac{8}{9}x + \frac{2}{9} [/tex]

Since the equation of this line is parallel to the one to be found, both have the same slopes: [tex] \frac{8}{9} [/tex]

Coordinates : ( - 7 , - 9 )

y - ( -9 ) = [tex] \frac{8}{9} [/tex] ( x - ( -7 ) )
y + 9 = [tex] \frac{8}{9}x + \frac{56}{9} [/tex]
y = [tex] \frac{8}{9}x + \frac{56}{9} - 9 [/tex]

y = [tex] \frac{8}{9}x - \frac{25}{9} [/tex]

The function rule for this graph is y =__ x +__

Answers

It is -1/2x + 2...she just didnt add the negative sign

The equation of line will be -

y = [tex]-\frac{1}{2} x[/tex] + 2

We have a graph as shown in the figure.

We have to find out the equation of this straight line in the graph.

What is the general form of the equation of a Straight line?

The general form of a equation of a straight line is -

y = mx + c

where -

m - slope of line

c - the y - intercept

We have -

The y intercept of the straight line as = (0, 2)

The x intercept of the straight line as = (4, 0)

The slope of the line will be m = [tex]\frac{2 - 0}{0 - 4}[/tex] = - [tex]\frac{1}{2}[/tex]

The y-intercept is at (0, 2) , therefore the value of c = 2.

Substituting the values in the general equation of line we get -

y = mx + c

y = [tex]-\frac{1}{2} x[/tex] + 2

Hence, the equation of line will be -

y = [tex]-\frac{1}{2} x[/tex] + 2

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This figure is made up of a triangle and a semicircle. What is the area of this figure? Use 3.14 for pi. Round only your final answer to the nearest tenth. Enter your answer, as a decimal, in the box. units²
https://static.k12.com/nextgen_media/assets/8124428-GA_GMT_IT_03_DP100_885_008.png

Answers

Finding the lengths of the legs of the right triangle, we have 6 and 3. (6*3)/2 = 9. Finding the area of the semi-circle we obtain [tex]\frac{1.5^2\pi}{2} [/tex] which rounding to 3.14 as pi, we obtain 3.5325. Adding up the area of the triangle and the semi-circle and the triangle we get 9+3.5325 which equals 12.5325

The area of the figure that is made up of a triangle and a semicircle is 23.137 units².

What is the area of a triangle?

The area of a triangle is half the product of its base and its height.

[tex]Area \triangle = \dfrac{1}{2}\times base \times height[/tex]

In order to solve the problem, we will divide the given figure into two parts such that the first one will be a right-angled triangle while the second one is a semi-circle as shown below.

As we can see in the ΔABC, the height of the triangle is 3 units, while the length of the base of the triangle is 6 units. therefore, the area of the triangle can be written as,

[tex]\begin{aligned}\triangle ABC &= \dfrac{1}{2} \times height \times base\\\\&= \dfrac{1}{2} \times BC \times AB\\\\& = 0.5 \times 3 \times 6\\\\& = 9\rm\ unit^2 \end{aligned}[/tex]

Now, if we look at the semi-circle we will find that the diameter(BC) of the semi-circle is 3 units, therefore, the area of the semi-circle can be written as,

[tex]\begin{aligned}\text{Area of Semi-circle} &= \dfrac{\pi}{2}d^2\\\\ &= \dfrac{\pi}{2}(3)^2\\\\&= 14.137\rm\ units^2 \end{aligned}[/tex]

Further, in order to get the total area of the figure, simply add the two areas, therefore,

The area of the figure = Area of triangle + Area of the semi-circle

= 9 + 14.137

= 23.137 units²

Hence, the area of the figure that is made up of a triangle and a semicircle is 23.137 units².

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Complete the two- column proof
Given: 11x - 6y = -1; x = 8
Prove: 98/6 = y
11x - 6y = -1; x = 8
88 - 6y = -1
-6y = -89
y = 89/6
89/6 = y
a. Given: b. Symmetric Property of Equality; c. Subtraction Property of Equality; d. Division Property of Equality; e. Reflexive Property of Equality
a. Given; b. Substitution Property; c. Subtraction Property of Equality; d. Division Property of Equality; e. Symmetric Property of Equality
a. Given; b. Substitution Property; c. Subtraction Property of Equality; d. Division Property of Equality; e. Reflexive Property of Equality
cant put it all in h

Answers

The correct answers are a) given; b) substitution property; c) subtraction property of equality; d) division property of equality; and e) reflexive property of equality.

Explanation:
The first line of your proof just restates what was given to us; therefore the reason is "given."

Between the first step and the second step, 11x was changed to 88; this is because x=8, and we substitute that in for x. That would give us 11*8=88, with the justification being substitution.

Between the second line and third line, 88 is cancelled from the left side and the -1 becomes -89; this happens because in order to cancel a positive 88, you must subtract it from both sides. This is the subtraction property of equality.

Between the third line and fourth line, -6 is cancelled from the left side and on the right side, -89 is changed to 89/6. This happens because in order to cancel the -6 that is beside the y (which means multiplication), we must divide both sides; this is the division property of equality.

The last step is to rewrite the equation with y on the left and the answer on the right; the reflexive property allows us to do that.

Final answer:

The correct properties of equality used to solve the equation given x = 8 are Given, Substitution Property, Subtraction Property of Equality, Division Property of Equality, and Symmetric Property of Equality.

Explanation:

The student has shared the steps of solving an equation and is asking for the correct sequence of properties used to solve it:

Given: 11x - 6y = -1; x = 8Substitute x: 88 - 6y = -1Subtract 88 from both sides: -6y = -89Divide by -6: y = 89/6State that 89/6 = y

The correct properties of equality should be applied as follows:

Given: Both the equation and x = 8 are provided information.Substitution Property: x = 8 is substituted into the equation for x.Subtraction Property of Equality: 88 is subtracted from both sides of the equation.Division Property of Equality: Both sides of the equation are divided by -6 to solve for y.Symmetric Property of Equality: Rearranges the equation to y = 89/6 for clarity.

Determine the measures of the angles of triangle DEF if the measures are in the ratio 1:1:16

Answers

the sum of all interior angles in a triangle is 180°, now, if we split that in (1+1+16) even pieces, that'd be 180 ÷ 18.

and then we give the ratio of 1, one of those pieces, the other ratio of 1, the same, and the ratio of 16, sixteen of those pieces.

[tex]\bf 1:1:16\qquad \cfrac{180}{1+1+16}\implies \cfrac{180}{18}\implies 10\quad \qquad \stackrel{1}{10}~:~\stackrel{1}{10}~:~\stackrel{16}{160}[/tex]

Final answer:

The angles of triangle DEF with the ratio 1:1:16 are 10 degrees, 10 degrees, and 160 degrees, using the property that the sum of interior angles in a triangle is 180 degrees.

Explanation:

To determine the measures of the angles of triangle DEF with the ratio 1:1:16, we utilize the property that the sum of the interior angles of any triangle is always 180 degrees. We can represent the measures of the angles as follows: let the first angle be x, the second angle be x, and the third angle be 16x. Since the sum of angles in a triangle is 180 degrees, we can write the equation:

x + x + 16x = 180

Simplifying the left side of the equation, we get:

18x = 180

Dividing both sides by 18 gives us:

x = 10

Therefore, the measures of the angles are 10 degrees, 10 degrees, and 160 degrees.

Corollary: At least two angles of a triangle are acute. In this case, the two angles with the ratio 1:1 are both acute since they measure 10 degrees each, which is less than 90 degrees.

The expression square root of 576/64 in simplest form is

Answers

The calculation is: [tex] \sqrt{ \frac{576}{64} } = \sqrt{9} = 3[/tex]

I see you have doubts, so I will explain each step.

Step 1: simpliy 576 / 64. In this case when you divide 576 by 64 you get 9 that is a whole number, so that is its simplest form.

Step 2: Calculate the square root of 9, which is 3.

If you use a simple calculator you will obtain that, but the square root of 9 is a calculation that you should know by yourself.

Remember that the square root a number N is the number that multiplied by itself results in the number N. For example the squere root of 4 is 2, because 2 times 2 is 4. So, the square root of 9 is 3 because 3 times 3 is 9.

It will be very helpful for you to learn the 12 first squares because with that you will be able to tell the square roots of the most elemental numbers:

1^2 = 1 => √1 = 1

2^2 = 4 => √4 = 2

3^2 = 9 => √9 = 3

4^2 = 16 => √16 = 4

5^2 = 25 => 25 = 5

6^2 = 36 => √36 = 6

7^2 = 49 => √49 = 7

8^2 = 64 => √64 = 8

9^2 = 81 => √81 = 9

10^2 = 100 => √100 = 10

11^2 = 121 => √121 = 11

12^2 = 144 => √144 = 12

Answer:

Just did it

The answer is 3

Step-by-step explanation:

Suppose a sheet of 100 stamps is 0.77 millimeters thick. If a stack of sheets contains 100,000 stamps, how many millimeters thick is the stack? Write the answer in scientific notation.
7.7 × 104 mm
0.77 × 103 mm
7.7 × 102 mm
77.0 × 101 mm

Answers

Final answer:

To find the thickness of the stack, multiply the thickness of a single sheet by the number of sheets. So, 0.77 mm times 1,000 equals 770 mm. In scientific notation, this is 7.7 × 10² mm.

Explanation:

To find out how many millimeters thick the stack is, you need to multiply the thickness of a single sheet of stamps by the number of sheets in the stack. In this case, the thickness of a single sheet is 0.77 millimeters, and there are 1,000 sheets in the stack (since 100,000 stamps divided by 100 stamps per sheet is 1,000).

To represent the thickness of the stack in scientific notation, you would multiply the thickness of a single sheet (0.77) by the number of sheets in the stack (1,000). Multiplying 0.77 by 1,000 gives you 770. To represent this in scientific notation, you would break it down into a number between 1 and 10 multiplied by a power of 10. So, the thickness of the stack is 7.7 × 10² mm.

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The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of . In order to determine , let G1 = 2, a number whose square is close to 5. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary. Average 2.25 and G2 to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.

Answers

... find the approximate value of √5. In order to determine √5, let ...

5 ÷ G1 = 2.5
5 ÷ G2 = 2.222
5 ÷ G3 = 2.236

That means √5 is approximately 2.236.

Using the Babylonian method, [tex]\( \sqrt{5} = 2.236}[/tex]. This method involves iteratively averaging and recalculating until the calculated value stabilizes to the desired accuracy.

To demonstrate the Babylonian method for finding the approximate value of [tex]$ \sqrt{5} $[/tex]

A. In order to determine [tex]$ \sqrt{5} $[/tex], let [tex]$ G_1 = 2 $[/tex], a number whose square is close to [tex]5.[/tex]

B. Calculate [tex]$ \frac{5}{G_1} = \frac{5}{2} = 2.5 $[/tex], which is not equal to [tex]$ G_1 $[/tex], so further action is necessary. Average [tex]$ 2 $[/tex] and [tex]$ G_1 $[/tex] to find [tex]$ G_2 = \frac{2 + 2}{2} = 2.25 $. $ \frac{5}{G_2} = \frac{5}{2.25} = 2.222 $[/tex], which is not equal to [tex]$ G_2 $[/tex], so further action is necessary.

C. Average [tex]$ 2.25 $[/tex] and [tex]$ G_2 $[/tex] to find [tex]$ G_3 = \frac{2.25 + 2.222}{2} = 2.236 $. $ \frac{5}{G_3} = \frac{5}{2.236} = 2.237 $[/tex], which is equal to [tex]$ G_3 $[/tex]. That means [tex]$ \sqrt{5} $[/tex] is approximately [tex]$ 2.236 $.[/tex]

The complete Question is

The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of .

A. In order to determine , let G1 = 2, a number whose square is close to 5.

B. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary.

C. Average 2.25 and G2 to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.

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Answers

Only constraint 2 would be met if 9 vanilla cups and 18 chocolate cups were purchased

Only constraint 1 would be met if 6 vanilla cups and 18 chocolate cups were purchased

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