George is solving the equation below by finding successive approximations. He started from a graph where he found the solution to be between 5 and 6. Using the lower and upper bounds from the graph, George did the following work for the first iteration. Step 1 Rewrite the equation so that it equals zero. Step 2 Evaluate the rewritten equation at the lower and upper bounds. Since the solution to the original equation is represented by a zero, one of the bounds should yield a negative difference and the other should yield a positive difference. Step 3 Take the average of the lower and upper bounds from the graph. Step 4 Evaluate the rewritten equation at . Step 5 Since this value of x yields a negative difference, use it to replace the previous upper bound that yielded a negative difference, . So, the bounds are now and . In what step, if any, did George make his first mistake? A. In step 1, George should have subtracted in the opposite order to set the equation equal to 0. B. In step 5, George should have used as the new lower bound. C. George made no mistakes, and his work is correct. D. In step 3, George should have averaged the two differences instead of the two bounds.

Answer: [tex]D. 6\sqrt{x} 2[/tex] is the answer

Step-by-step explanation:

Answer:

(8w + 7)(7w + 9)

Step-by-step explanation:

56w² + 121w + 63

consider the factors of the product of the coefficient of the w² term and the constant term which sum to give the coefficient of the w- term

product = 56 × 63 = 3528 and sum = 121

After much trial and error the factors are + 49 and + 72

use these factors to split the w- term

56w² + 49w + 72w + 63 ( factor first/second and third/fourth terms )

= 7w(8w + 7) + 9(8w + 7) ← factor out (8w + 7) from each term

= (8w + 7)(7w + 9) ← in factored form

Answer:

decimal point is moved one digit towards the left when divided by 10.

for example:

50.1 ÷ 10 = 5.01

hope that helps you...

[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]

Answer:X is equal to -4 twice

Step-by-step explanation:

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the equation 2x² + 8x = x² - 16, we first simplify it by moving all the terms to one side:

2x² + 8x - x² + 16 = 0

Simplifying further, we get:

x² + 8x + 16 = 0

This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 8, and c = 16.

We can solve this equation by factoring it:

(x + 4)(x + 4) = 0

This gives us two solutions:

x + 4 = 0 or x + 4 = 0

x = -4 or x = -4

Therefore,

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

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The number of trucks needed to deliver the rock in one trip will be 6.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

V =  a x b x c

A transport company needs to deliver 500,000 pounds of rocks to a construction site.

The company owns a set of dump trucks- each with a container in the shape of a rectangular prism (figure A).

If each pound of rock has a volume of 0.01 cubic feet.

Then the total volume of rock that the transport company is responsible for.

Volume of rocks = 0.01 x 500,000

Volume of rocks = 5,000 ft³

Then the maximum volume of each dump truck will be

Volume of truck = 12 x 9 x 8

Volume of truck = 864 ft³

Then the number of the trucks are needed to deliver the rock in one trip will be

Number of trucks = 5000 / 864

Number of trucks = 5.787

Number of trucks ≅ 6

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Answer:

[tex]f(-3) = -3 + 8 \\= 5\\f(0) = 0 + 8 \\= 8\\f(5) = 5 + 8 \\= 13[/tex]

Step-by-step explanation:

All we need to do is plug in the x-values.

if

[tex]f(x) = x + 8[/tex]

then

[tex]f(-3) = -3 + 8 \\= 5\\f(0) = 0 + 8 \\= 8\\f(5) = 5 + 8 \\= 13[/tex]

hope this helped!!

Answer:

^2x2√3+2x√2-^2x2√3-2x√2

Step-by-step explanation:

Answer:

Mean:  The sum of all data values divided by the total number of data values.

Median: The middle value when all data values are placed in order of size.  If there is an even number of data values, the median is the mean of the middle two values.

Mode: The most frequently occurring data value.

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Question 3

[tex]\textsf{Mean}=\dfrac{69 + 70 + 71 + 73 + 74 + 75 + 76 + 76 + 76 + 86}{10}=74.6[/tex]

Ordered data values:  69, 70, 71, 73, 74, 75, 76, 76, 76, 86

Median = (74 + 75) / 2 = 74.5

Mode = 76

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Question 4

[tex]\textsf{Mean}=\dfrac{3 + 5 + 5 + 5 + 6 + 6 + 7 + 8 + 8}{9}=5.9\: \sf (nearest \:tenth)[/tex]

Ordered data values:  3, 5, 5, 5, 6, 6, 7, 8, 8

Median = 6

Mode = 5

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Question 5

[tex]\begin{aligned}\textsf{Mean} & =\dfrac{11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 16 + 16 + 17 + 18 + 19 + 20 + 23}{15}\\ & =15.5 \: \sf (nearest\:tenth)\end{aligned}[/tex]

Ordered data values:  11, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 18, 19, 20, 23

Median = 15

Mode = 12, 13, 14, 16

Answer:

see explanation

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

the median is the middle value of a set of data. If there is no exact middle value then it is the average of the values on either side of the middle.

the mode is the value that occurs most often in the data set

A data set can have more than 1 mode

------------------------------------------------------------------------

(3)

(a)

mean = [tex]\frac{74+73+75+76+71+69+70+76+76+86}{10}[/tex] = [tex]\frac{746}{10}[/tex] = 74.6

(b)

Arrange the data in ascending order

 69  70  71  73  74  75  76  76  76  86

                              ↑ middle

median = (74 + 75) ÷ 2 = 149 ÷ 2 = 74.5

(c)

mode = 76

(4)

(a)

mean = [tex]\frac{6+8+8+5+6+7+5+3+5}{9}[/tex] = [tex]\frac{53}{9}[/tex] ≈ 5.9 ( to 1 dec. place )

(b)

3  5  5  5  6  6  7  8  8

                 ↑ middle

median = 6

(c)

mode = 5

(5)

(a)

mean = [tex]\frac{12+13+18+23+14+17+14+16+13+16+15+19+11+20+12}{15}[/tex] = [tex]\frac{233}{15}[/tex]  ≈ 15.5 ( to 1 dp )

(b)

11  12  12 13  13  14  14  15  16  16  17  18  19  20  23

                                      ↑ middle

median = 15

(c)

the mode is multimodal

modes are 12, 13, 14, 16

Answer:

x= 3

x= -2

Step-by-step explanation:

x^2-x=6

x^2-x-6=0

find which 2 numbers when multiplied give -6 and

when added give -1

they are -3 and 2

(x-3)(x+2)

x= 3

x= -2

Answer:

The way the problem is written: y = 8x/3 - 20/3

If the two numbers are the same: the number is 4.

Step-by-step explanation:

She thought of 2 numbers.

The first number is x.

The second number is y.

8(x - 5/2) = 3y

We have one equation with two variables, so we do not have enough information to find the two numbers.

We can just express one number in terms of the other number.

8x - 20 = 3y

3y = 8x - 20

y = 8x/3 - 20/3

If the problem were:

"Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?",

then there is only one variable, and we can find the number.

8(x - 5/2) = 3x

8x - 20 = 3x

5x = 20

x = 4

The number is 4.

Answer:

1 is d

the square root of 36 = 6 which is the only equation with 36

2 is d

Answer:

Step-by-step explanation:

2.2:

[tex]3^2(6)(3.14) = 169.56 in^3[/tex]

3.3

[tex]9^2(5)(3.14) = 1287.4 un^3[/tex]

The Probability of that more than 7 of them germinate is 0.2948.

We are to determine the probability that more than 7 of 10 seeds (i.e. 8, 0r 9 0r 10) germinate.

The probability that all 10 seeds germinate is equal 0.80¹⁰= 0.1073 = 10.73%.

The probability that only the first (only the second, etc ) seed does not germinate is equal 0.20 X 0.80⁹= 0.0268 = 2.68%.

The probability that 6 seeds germinate is the sum of the probabilities that only the first seed does not germinate, only the second one does not germinate, etc, and equals to 10 X 0.0268  = 0.268 = 26.8%.

The total probability that more than 7 of 10 seeds germinate is the sum of the probabilities that 10 seeds germinate and that 7 seeds germinate, i.e. 2.68 % + 26.8 % = 29.48 %.

Thus, The Probability of that more than 7 of them germinate is 0.2948.

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Answer:

approximately 4.23 cm

Answer:

please explain the question better so sorry

Step-by-step explanation:

I can't understand the question please explain it and I'll help the best I can

Answer:

Solution: (-1, 1) and (10/3, 16/3) are Intercepts.

Step-by-step explanation:

Set the equations equal to themselves and solve for x and y.

Hope this helps! :)

The expected value of the net gain from selling the stock in 2 years is $-3.

The net gain is the total profit from selling the stock less the total cost of buying the stock

Total cost of buying the stock = 10 x $10 = $-100

Expected selling price = (0.3 x $100 x 3) + (0.7 x$100 x 1/10) += $97

Net gain = $97 - $100= $-3

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Answer:

n = 7.

Step-by-step explanation:

Sum S of an AP = (n/2)[2a + d(n - 1)]

112 = (n/2)[2*25 - 3(n -1)]

n/2 (53 - 3n) = 112

n(53 - 3n) = 224

-3n^2 + 53n - 224 = 0

3n^2 - 53n + 224 = 0

(3n - 32 )(n  - 7 ) = 0

n = 7, 32/3

So n must be 7 as its a whole number.

The solution to the given quadratic expression using the completing the square is  x = ±√10 +8

This is a method of factoring quadratic expression. Given the quadratic function.

x^2 − 16x + 54 = 0

Subtract 54 from both sides

x^2 − 16x = -54

Complete the square

x^2 -16x +8^2 = -54 + 64

(x-8)² = 10
x - 8 = ±√10
x = ±√10 +8

Hence the solution to the given quadratic expression using the completing the square is  x = ±√10 +8

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The mean of the age data of the players is 20 and on average the age of each player is 1 far from mean.

The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.

The data of the age of the player is,

18,19,20,21,21,21

The number of player are 6. Thus, the mean of the data is,

Mean=(18+19+20+21+21+21)/6

Mean=20

The distance form mean 20 of each player age is, 2,1,0,1,1,1. The mean deviation is,

Mean Deviation= (2+1+0+1+1+1)/6

Mean Deviation=1

Thus, the mean of the age data of the players is 20 and on average the age of each player is 1 far from mean.

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Answer:

  8 feet

Step-by-step explanation:

The length can be found using the volume formula with the known values. The resulting equation can be solved for the unknown value.

__

  V = LWH . . . . . volume of a prism is the product of its dimensions

  108 ft³ = l×(3 ft)×(4.5 ft) . . . . . known values filled in

  l = 108 ft³/(13.5 ft²) = 8 ft . . . . . . divide by the coefficient of length

The length of the prism is 8 feet.

Answer:

8ft

Step-by-step explanation:

Answer:

18 . 75

Step-by-step explanation:

1.50's half is 0.75 , Then multiply £1.50 × £25

Answer:

one book=1.50

the other half priced book=0.75

so 0.75+1.50=2.25

25/2.25

=11.111

so eleven books

Answer:

The lateral area is 439.82  I don't know the single base one and The surface area is 747.7

Step-by-step explanation:

Answer:

you will subtract 6 from 5 then your answer will be  g ≥ -1

Step-by-step explanation:

hope this helps

Answer: I will give you a answer for both of them.

Step-by-step explanation:

First equation: x+y=20

1. Subtract y from both sides.

x=20−y

Second equation: 2x+y=25

1. Subtract y from both sides.

2x=25−y

2. Divide both sides by 2.

[tex]X[/tex][tex]=[/tex][tex]\frac{25-y}{2}[/tex]

Answer:

Step-by-step explanation:

Area Formula

Given

Solving

Dimensions

Now

Take it positive

Answer: Please see the analysis