The sum of two consecutive numbers is 77. The difference of half of the smaller number and one-third of the larger number is 6. If x is the smaller number and y is the larger number, which two equations represent the sum and difference of the numbers? x - y = 6 and 1/2 x + 1/3 y = 77 x + y = 77 and 1/2 x - 1/3 y = 6 x - y = 77 and 1/2 x + 1/3 y = 6

Answer:

D.  120°

Step-by-step explanation:

Interior angles of a rhombus always add up to 360 degrees. Thus we can set up an equation:

g+g+2g+2g=360

Now let's combine all the like terms (g's).

6g=360

Now we divide both sides by six to isolate g.

g=60

We can now substitute g into angle B, to find its value.  

2g

2(60)

120

Thus, the measure of angle B is 120, or option D.

Answer:

3 is the coefficient

Step-by-step explanation:

please find the attached file for more details please

- the coefficient is always the number before a variable.

m + 3n + 5

coefficient: 3

Answer:

8

Step-by-step explanation:

To solve this, you can add 2/5 b to both sides of the equation. You now have 3 + 5/5 (or 1) b = 11. => 3 + b = 11 => Now, subtract 3 from both sides, and you have b = 11 - 3, and then b = 8.

Step-by-step explanation:

3 + 2/5 b =11 - 2/5 b (this is the given question is it?)

2/5 b + 2/5 b= 11 - 3 (like terms together, you transpose -2/5b to the other side as shown.)

2b+2b = 8 ( at that stage you would find t

5 hat 5 is the common value to go into 5 itself, as shown.

4b = 8 ( you just add 2b + 2b to have 4b)

5

4b = 8 ( at that point you cross multiply

5 1 as shown)

4b = 8 × 5 ( simple math as shown)

4b = 40 ( you multiply 8 × 5 to obtain 40)

b =10 you can prove that. Thank you.

Irene's list of factors for the number 88 is almost correct, but she forgot to include the number 1.

Irene wants to list the factors for 88 and she writes 2, 4, 8, 11, 22, 44, and 88. To verify if Irene is correct, we need to identify all of the numbers that can evenly divide 88 without leaving a remainder. Starting with the number 1, which is a factor of every number:

1 x 88 = 88, so 1 and 88 are factors.

2 x 44 = 88, so 2 and 44 are factors.

4 x 22 = 88, so 4 and 22 are factors.

8 x 11 = 88, so 8 and 11 are factors.

Since there are no other numbers between 1 and 88 that can multiply together to equal 88, the list that Irene wrote appears to be missing the number 1.

Therefore, Irene's list is almost correct, but for it to be complete, it should include the number 1. The full list of factors for the number 88 should be 1, 2, 4, 8, 11, 22, 44, 88.

Answer:

The volume of sphere is 1436.03 inches³.

Step-by-step explanation:

Given:

The radius of sphere = 7 inches.

Now, to find the volume.

So, to get the volume we put the formula:

[tex]Volume=\frac{4}{3} \pi r^3[/tex]

Taking the value of π = 3.14

[tex]Volume=\frac{4}{3}\times 3.14\times {7}^3[/tex]

[tex]Volume=\frac{4}{3}\times 3.14\times 343[/tex]

[tex]Volume=\frac{4}{3}\times 1077.02[/tex]

[tex]Volume=\frac{4308.08}{3}[/tex]

[tex]Volume=1436.03\ inches^3[/tex]

Therefore, the volume of sphere is 1436.03 inches³.

Step-by-step explanation: To find the volume of the sphere, start with the formula for the volume of a sphere.

Volume = [tex]\frac{4}{3} \pi r^{3}[/tex]

Notice that our sphere has a radius of 7 inches so plugging into the formula, we have [tex](\frac{4}{3})(\pi)(7 in.)^{3}[/tex].

Start by simplifying the exponent. (7 in.)³ is equal to 7 inches x 7 inches x 7 inches or 343 in³ so we have [tex](\frac{4}{3}) (343 in.^{3})(\pi)[/tex].

Next, 4 x 343 is 1,372 which gives us [tex]\frac{1,372\pi }{3}[/tex]. Notice that 1,372 doesn't divide by 3 so this is our final answer for the volume of the sphere.

c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat

Given that a boat rental charges $7.50 for the first hour and $2 for each additional hour.

To find: Rule that gives the cost for x hours of renting a boat

Let "x" be the total hours of renting a boat

[tex]c = f + (v \times x - 1)[/tex]

"c" is the total cost for the boat rent

"f" is the fixed cost for boat rent for first hour

"v"  is the cost for each additional hours of rent

"x" is the total hours of renting a boat

In the expression we have used "x - 1" to represent the additional hour of boat rent after first hour

Here f = $ 7.50

v = $ 2

[tex]c = 7.50 + 2 \times x - 1\\\\c = 7.50 + 2(x - 1)[/tex]

Thus c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat

The cost for renting a boat for x hours can be found using the formula y = 7.50 + 2(x - 1), where y is the total cost and x is the number of hours.

Based on the given information, the boat rental company charges $7.50 for the first hour and then an additional $2 for each subsequent hour. Therefore, if x is the number of hours you rent the boat, the total cost would be calculated using the formula y = 7.50 + 2(x - 1). Here, y represents the total cost of renting the boat for x hours. The formula subtracts the one-hour charge included in the initial payment.

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Answer:

[tex]m=-\frac{4}{3}[/tex]

Step-by-step explanation:

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

the point (13,-4) and (1,12)

substitute the values in the formula

[tex]m=\frac{12+4}{1-13}[/tex]

[tex]m=\frac{16}{-12}[/tex]

[tex]m=-\frac{16}{12}[/tex]

simplify

[tex]m=-\frac{4}{3}[/tex]

Answer:

-4/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(12-(-4))/(1-13)

m=(12+4)/-12

m=16/-12

simplify

m=-4/3

Answer:1st is 5 2nd is 15 last is 30

Step-by-step explanation:

1st = 5

2nd = 3 x 5 = 15

3rd = 15 x 2 = 30

5 + 15 + 30 = 50

The three numbers in question are 5, 15, and 30. This has been achieved by setting up and solving algebraic equations based on the given conditions.

To solve this problem, we should set up equations based on the information given. Let's define:
First number = x
Second number = 3x (since it is three times the first number)
Third number = 2 * 3x = 6x (since it is twice the second number)

According to the problem, the sum of these three numbers is 50. Therefore, we can write the equation as:
x + 3x + 6x = 50

Solve for x:
10x = 50
x = 50 / 10 = 5

So, the three numbers are:
First number = x = 5
Second number = 3x = 3 * 5 = 15
Third number = 6x = 6 * 5 = 30

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You paid 22% gratuity at the restaurant.

Step-by-step explanation:

Given,

Amount of bill = $59

Amount paid = $72

Gratuity = Amount paid - Amount of bill

Gratuity = 72 - 59 = $13

Gratuity percentage = [tex]\frac{Gratuity}{Amount\ of\ bill}*100[/tex]

Gratuity percentage = [tex]\frac{13}{59}*100=\frac{1300}{59}[/tex]

Gratuity percentage = 22.03%

Rounding off to whole percent

Gratuity percentage = 22%

You paid 22% gratuity at the restaurant.

Keywords: percentage, subtraction

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The percentage did you pay is 22.03%

Given that,

Based on the above information, the calculation is as follows:

[tex]= (\$72 - \$59) \div (\$59)\\\\= \$13 \div \$59[/tex]

= 22.03%

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Answer:

(B) 2(x+5)(x−5)

Explanation:

Factor 2x²−50

2(x+5)(x−5)

Answer:

b) 2(x - 5)(x + 5)

Step-by-step explanation:

2x² - 50

2(x² - 25)

(x² - 25) is a difference of squares and it equals (x - 5)(x + 5)

So the answer is;

2(x - 5)(x + 5)

Answer:

It is because a triangle has a total angle sum of 180 degrees.

Step-by-step explanation:

90+90=180

But that was only 2 corners so the last corner has to be 0 degrees which is impossible.

Answer: A triangle does not contain two right angles.

.

Step-by-step explanation:

A) k=2 is the right answer

Step-by-step explanation:

The downward funtion transformation is defined as:

f(x) => f(x)-b where b is an integer.

Given

[tex]f(x) = (0.5)^x[/tex]

And

[tex]g(x) = (0.5)^x-k[/tex]

It is also given that g(x)  is obtained by shifting function f 2 units downward

We will apply the transformation to function f to find the value of k.

So,

Shifting f(x) 2 units downward

we will get

[tex]g(x) = (0.5)^x-2[/tex]

comparing with [tex]g(x) = (0.5)^x-k[/tex] we get that

k = 2

So,

A) k=2 is the right answer

Keywords: Functions, shifting

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Answer:

ok k does = 2 i got it right on the test

Step-by-step explanation:

:3

Answer:

-19

Step-by-step explanation:

4x-8(2-x)

4x-16+8x

12x-16

12(-1/4)-16

-12/4-16

-3-16

-19

Answer:

-19 I think lemme know if im right

Step-by-step explanation:

For 5 games, the cost will be equal for each option.

Step-by-step explanation:

Given,

Lane rental of offer A = $20

Per game charges = $3

Let,

x be the number of games.

A(x) = 3x + 20

Lane rental is $35 for maximum 10 games.

B(x) = 35

For the cost to be same;

A(x) = B(x)

[tex]3x+20=35\\3x=35-20\\3x=15[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{15}{3}\\x=5[/tex]

For 5 games, the cost will be equal for each option.

Keywords: function, division

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Answer:

Out of every 5 trials, the desired outcome will occur approximately 2 times

Step-by-step explanation:

The first statements states that it will happen exactly two times, but probability never guarantee the outcome

The third and fourth statement states out of 7 which cannot be true as 2-5 basically means out of 5

Answer:

B: Out of every 5 trials, the desired outcome will occur approximately 2 times.

Step-by-step explanation:

Answer:

x = - 4, x = 6

Step-by-step explanation:

Given

f(x) = x² - 2x + 3 and f(x) = 27, then equating the 2 gives

x² - 2x + 3 = 27 ( subtract 27 from both sides )

x² - 2x - 24 = 0 ← in standard form

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)

The factors are - 6 and + 4, since

- 6 × 4 = - 24 and - 6 + 4 = - 2, thus

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4

f(x)= 27

x^2 -2x+3=27

×^-2x+3-27=0

x^2x-24=0

(x-6)(x-4)=0

x-6=0 or ×-4=0

×=6or ×=4

Answer:

2

Step-by-step explanation:

Find the value of c where p = 0.

0 = c² + 2c − 5

6 = c² + 2c + 1

6 = (c + 1)²

±√6 = c + 1

c = -1 ± √6

c must be positive, so c = -1 + √6 ≈ 1.45.  So John must sell at least 2 candy bars to make a profit.

We can also show this using trial and error.

If c = 0, then p = -5

If c = 1, then p = -2

If c = 2, then p = 3

Answer:

1

Step-by-step explanation:

The product of a nonzero number and its reciprocal is 1

Answer:

Step-by-step explanation:

The product will always equal 1.  This is one of the methods we use to solve equations.  If our nonzero real number is 3, for example, the reciprocal of 3 is 1/3 and

3 × [tex]\frac{1}{3}[/tex] can be written as

[tex]\frac{3}{1}[/tex] × [tex]\frac{1}{3}[/tex] which is 3/3 which = 1.

Answer:

Step-by-step explanation:

                                        Solving equation A: y = x

Let us consider the given equation A:

                                                      y = x

y = x

y = 1    ∵ x = 1

Hence, (1, 1) is the ordered pair of  y = x

y = x

y = 2    ∵ x = 2

Hence, (2, 2) is the ordered pair of  y = x

y = x

y = 3    ∵ x = 3

Hence, (3, 3) is the ordered pair of  y = x

y = x

y = 4    ∵ x = 4

Hence, (4, 4) is the ordered pair of  y = x

y = x

y = 5    ∵ x = 5

Hence, (5, 5) is the ordered pair of y = x

Lets us consider all the ordered pairs i.e. (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) to make a table for y = x.

y                 x

1                  1

2                 2

3                 3

4                 4

5                 5

As from the table, lets take the ratio of every point i.e. y/x

Hence, the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship. Please also check the graph in attached figure a.

                                          Solving equation A: y = x +2

Let us consider the given equation A:

                                                         y = x + 2    

y = x + 2

y = 1 + 2 ⇒ 3  ∵ x = 1

Hence, (1, 3) is the ordered pair of y = x + 2

y = x + 2

y = 2 +2 ⇒ 4   ∵ x = 2

Hence, (2, 4) is the ordered pair of y = x + 2

y = x + 2

y = 3 + 2 ⇒ 5    ∵ x = 3

Hence, (3, 5) is the ordered pair of  y = x + 2

y = x + 2  

y = 4 + 2 ⇒ 6   ∵ x = 4

Hence, (4, 6) is the ordered pair of  y = x + 2

y = x + 2

y = 5 +2 ⇒ 7    ∵ x = 5

Hence, (5, 7) is the ordered pair of y = x + 2

Lets us consider all the ordered pairs i.e. (1, 3), (2, 4), (3, 5), (4, 6) and (5, 7) to make a table for y = x + 2.

y                 x + 2

1                  3

2                 4

3                 5

4                 6

5                 7

As from the table, lets take the ratio of every point i.e. y/x

Hence, the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship. Please also check the graph in attached figure a.

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The total distance covered by the bicycle is calculated using the circumference of the wheel and the number of revolutions made. With a wheel diameter of 70 cm, the total distance comes to approximately 55.0 meters after 25 revolutions.

The question involves calculating the distance covered by a bicycle wheel making a certain number of revolutions. Given that the diameter of the wheel is 70 cm, we can find the circumference, which is the distance the wheel covers per revolution. The circumference is equal to \\(\pi\cdot d\\), where \\(d\\) is the diameter. Substituting the given diameter:

Since the wheel makes 25 revolutions, the total distance covered (\\em{D}}) can be found by multiplying the circumference by the number of revolutions:

Thus, the bicycle covers a distance of \\(25 \times \pi \times 70 \\text{cm}\\), or \\(25 \times \pi \times 0.7 \\text{m}\\), since 100 cm equals 1 meter.

To find the exact value, you would calculate:

Answer:

121/250

Step-by-step explanation:

Look at the picture

The decimal equivalent of 48.4% is 0.484 and the simplified fraction equivalent is 242/500.

To convert 48.4% to a decimal, you simply divide the percentage by 100. Therefore, 48.4% as a decimal would be 0.484.

To write 48.4% as a simplified fraction, we start with the fraction that percentage represents, which is 48.4 / 100. However, both these numbers are divisible by 2 which simplifies it to 242 / 500. That is the simplest form of the fraction represented by 48.4%.

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The equation of the line which is perpendicular to the line 4x + 3y = 9 and passes through the point (-2,3) is y = 3/4x + 4.5.

The original equation is 4x + 3y = 9. To start off, rewrite this equation in slope-intercept form (y = mx + b) to help find the slope. After isolating y, the equation turns into y = -4/3x + 3. So, the slope of the original line is -4/3.

Perpendicular lines have slopes which are negative reciprocals of each other, thus the slope of the line perpendicular to the given line is the negative reciprocal of -4/3, which is 3/4 (m = 3/4 for the second line)

We are also given that the line we are looking for passes through the point (-2,3). Use the point-slope form of a line, given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point. Substituting in the values, you get:

y - 3 = 3/4(x - -2).

Simplifying the equation, we find that the line perpendicular to 4x + 3y = 9 and passing through (-2, 3) is y = 3/4x + 4.5

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Answer:

.19 cent per egg

Step-by-step explanation:

15*12=180

34.20/180= .19

The unit cost per egg is $0.60 when a case of eggs costs $34.20.

The unit cost per egg is $0.60.

To find the cost per egg when a case contains 15 dozen eggs costing $34.20, you first calculate the cost per dozen by dividing the total cost by the number of dozens (15). Then, you divide the cost per dozen by 12 to find the cost per egg. In this case, $34.20 divided by 15 gives $2.28 cost per dozen. Finally, $2.28 divided by 12 equals $0.60, so each egg costs $0.60.

Answer:

-37

Step-by-step explanation:

-4(5)-17=-20-17=-37

Answer: r = 3

1st Step: Plug x in for 5

4(5)-17

Second Step: Multiply 4 and 5

20-17

Third Step: 20-17

20-17=3

So, the answer is 3 when r(5)

Hope this helps!

Answer:getting rid of the constant

Step-by-step explanation:

Answer: simplify x + 7 = 2x + 5 - 4x by combining like terms so x+7= 5-2x

Step-by-step explanation:

Answer:

33.38 km

Step-by-step explanation:

Kim drove from Math Town at (-2, 5) to Geometry Ville at (3, -1) to Algebra Springs at (-6, -5), and then back to Math town.

Now, the distance from (-2,5) point to (3,-1) point will be  

[tex]\sqrt{(- 2 - 3)^{2} + (5 - (-1))^{2}} = \sqrt{61}[/tex] km.

Again, the distance from point (3,-1) and (-6,-5) point will be  

[tex]\sqrt{(3 - (- 5))^{2} + (- 1 - (- 5))^{2}} = \sqrt{80}[/tex] km.

Therefore, the total distance Kim traveled will be = [tex]2(\sqrt{61} + \sqrt{80}) = 33.38[/tex] Km. (Answer)

The distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] on the coordinate plane is given by  

[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]  

Answer:

Step-by-step explanation:

Let x represent the number of days , then

(1) The exponential function to represent the spread of Ben's social media spread implies :

f(x) = 2([tex]3^{x}[/tex])

(2) The exponential function that represent carter;s social media spread implies

f(x) = 10([tex]2^{3}[/tex]

(3) the graph of the three functions is attached below

color red graph represents  Ben's social media spread , the graph with color blue represents Carter;s social media spread and the graph with green color represents Amber's social media spread

(4) on the 3rd day

Amber will receive 192 shares .

The equation for the spread of his shares is

f(x) = 3([tex]4^{x}[/tex]

where x is the number of days , so we have

3([tex]4^{3}[/tex])

= 3 ( 64)

= 192 shares

Ben's shares on the 3rd day will be

f(x) = 2([tex]3^{x}[/tex] )

= 2([tex]3^{3}[/tex])

= 2 ( 27)

= 54

Therefore , Ben will have 54 shares on the third day

Carter's share on the third day

f(x) = 10 ( [tex]2^{x}[/tex] )

= 10 ([tex]2^{3}[/tex] )

= 10 (8)

= 80

Therefore , Carter will receive 80 shares on the 3rd day

Option B is correct. The required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction

Composite functions are functions written inside another function e.g f(g(x))

Given the expressions

f(x) = 2/x

g(x) = 2/x

We are to find the composite function f(g(x))

f(g(x)) = f(2/x)

f(2/x) =  (2/(2/x))

f(2/x)  = 2 * x/2

f(2/x) = x

Hence the required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction

[tex]1. \( (f \circ g)(x) = \frac{1}{x^2} \)\\2. \( (f \circ g)(x) = x \)\\3. \( (f \circ g)(x) = -x \)\\4. \( (f \circ g)(x) = \frac{1}{4}x - 1 \)[/tex]

let's break down each pair of functions and find their composition:

1. For [tex]\( f(x) = x^2 \) and \( g(x) = \frac{1}{x} \):[/tex]

  To find [tex]\( (f \circ g)(x) \)[/tex], we substitute [tex]\( g(x) \) into \( f(x) \):[/tex]

  [tex]\[ (f \circ g)(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2} \][/tex]

  So, [tex]\( (f \circ g)(x) = \frac{1}{x^2} \).[/tex]

2. For [tex]\( f(x) = \frac{2}{x} \) and \( g(x) = \frac{2}{x} \):[/tex]

  Here, [tex]\( (f \circ g)(x) = f(g(x)) = f\left(\frac{2}{x}\right) \).[/tex]

  When you substitute [tex]\( \frac{2}{x} \) into \( f(x) \),[/tex]  you get:

 [tex]\[ (f \circ g)(x) = f\left(\frac{2}{x}\right) = \frac{2}{\frac{2}{x}} = x \][/tex]

  So, [tex]\( (f \circ g)(x) = x \).[/tex]

3. For [tex]\( f(x) = \frac{x-2}{3} \) and \( g(x) = 2 - 3x \):[/tex]

 [tex]\( (f \circ g)(x) = f(g(x)) = f(2 - 3x) \).[/tex]

  Substituting  [tex]\( 2 - 3x \) into \( f(x) \),[/tex]we get:

 [tex]\[ (f \circ g)(x) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x \][/tex]

  So, [tex]\( (f \circ g)(x) = -x \).[/tex]

4. For [tex]\( f(x) = \frac{1}{2}x - 2 \) and \( g(x) = \frac{1}{2}x + 2 \):[/tex]

  Here, [tex]\( (f \circ g)(x) = f(g(x)) = f\left(\frac{1}{2}x + 2\right) \).[/tex]

  When you substitute [tex]\( \frac{1}{2}x + 2 \) into \( f(x) \),[/tex] you get:

 [tex]\[ (f \circ g)(x) = f\left(\frac{1}{2}x + 2\right) = \frac{1}{2}\left(\frac{1}{2}x + 2\right) - 2 = \frac{1}{4}x + 1 - 2 = \frac{1}{4}x - 1 \][/tex]

  So, [tex]\( (f \circ g)(x) = \frac{1}{4}x - 1 \).[/tex]

So, summarizing:

1. For [tex]\( f(x) = x^2 \) and \( g(x) = \frac{1}{x} \), \( (f \circ g)(x) = \frac{1}{x^2} \).[/tex]

2. For [tex]\( f(x) = \frac{2}{x} \) and \( g(x) = \frac{2}{x} \), \( (f \circ g)(x) = x \).[/tex]

3. For [tex]\( f(x) = \frac{x-2}{3} \) and \( g(x) = 2 - 3x \), \( (f \circ g)(x) = -x \).[/tex]

4. For [tex]\( f(x) = \frac{1}{2}x - 2 \) and \( g(x) = \frac{1}{2}x + 2 \), \( (f \circ g)(x) = \frac{1}{4}x - 1 \).[/tex]

Final answer:

To find the total weight in Robbie's backpack, the weights of the history textbook (2 5/6 pounds) and lunch (1 2/3 pounds) are added, resulting in a total of 4 1/2 pounds.

Explanation:

The question involves finding the total weight of items in Robbie's backpack: a history textbook and his lunch. The history textbook weighs 2 5/6 pounds and his lunch weighs 1 2/3 pounds.

To find the total weight, we first convert the mixed numbers into improper fractions for easier addition. The history textbook's weight as an improper fraction is (2×6)+5 = 17/6 pounds. The lunch's weight is (1×3)+2 = 5/3 pounds.

Adding these two fractions gives us:

   17/6 + 5/3 = 17/6 + 10/6 = 27/6 pounds

Since 27/6 simplifies to 4 1/2 pounds, the total weight in Robbie's backpack is 4 1/2 pounds.