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PLS HURRY I AM GIVING BRAINLIEST!!!the Question Is In The Photo!!

Answers

Answer 1

A. The expression that represents the total amount of canned food they have collected so far is: 4x² + 2xy + 3

B. Number of canned food still remaining to be collected is: 2x² - 4xy + 5

How to Solve Polynomial Expressions?

A polynomial expression is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.

Part A: To find the expression that represents the total amount of canned food they have collected so far, add the expression for each person given together.

3x² - 2 + x² + 2xy + 5

Combine like terms:

4x² + 2xy + 3

Part B: Number of canned food still remaining to be collected is calculated below.

(6x² - 2xy + 8) - (4x² + 2xy + 3)

Open bracket:

6x² - 2xy + 8 - 4x² - 2xy - 3

Combine like terms:

2x² - 4xy + 5

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Related Questions

Rebecca used 4.25pt of milk in her baking recipe. How many cups of milk did she use?

Answers

Answer: 8.25

Step-by-step explanation:

On January 10, 2022, Cullumber Co. sold merchandise on account to Robertsen Co. for $16,600, n/30. On February 9, Robertsen Co. gave Cullumber Co. a 11% promissory note in settlement of this account.

Answers

The preparation of the journal entry to record the sale and the settlement of the account receivable is as follows:

Journal Entry:

January 10, 2022:

Debit Accounts Receivable $16,600

Credit Sales Revenue $16,600

(To record the sale of merchandise on account to Robertsen Co, n/30.)

February 9, 2022:

Debit Notes Receivable $16,600

Credit Accounts Receivable $16,600

(To record the receipt of a 11% promissory note in settlement of account receivable.)

What are journal entries?

Journal entries refer to the initial records maintained about business transactions.

Journal entries show how the transactions will be posted in the general ledger.

Transaction Analysis:

January 10, 2022: Accounts Receivable $16,600 Sales Revenue $16,600

Terms n/30

February 9, 2022: Notes Receivable $16,600 Accounts Receivable $16,600

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Question Completion:

Prepare the journal entry to record the sale and the settlement of the account receivable.

a) What information is provided by each of the graphs below? b) Explain below which of the two graphs is the best representation of the data. Support your thinking by using numbers from each graph.

Answers

The information provided by each of the graphs is Sales from July to December and graph A best represents the data

What information is provided by each of the graphs?

From the question, we have the following parameters that can be used in our computation:

The graphs

On the graphs, we have the information to be

Sales from July to December

Which of the two graphs is the best representation of the data.

The graph that is the best representation of the data is the A

This is because the scale and origin of the graph are defined

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Please help !!!!!
!!!!!

Answers

Answer: 10w + 3 + 4.5w = 90

Step-by-step explanation:

a right angle is 90 degrees, so 10w + 3 and 4.5w have to add up to 90 degrees

If 90% of a number is 110, find 9% of that number.​

Answers

We can set up the equation :

0.9x = 110 ,

where x is the unknown number. To solve for x, we can divide both sides by 0.9 :

x = 110 ÷ 0.9

x = 122.22 (rounded to two decimal places)

So the unknown number is approximately 122.22.

To find 9% of that number, we can multiply 122.22 by 0.09 :

0.09 × 122.22 = 11.00 (rounded to two decimal places)

Therefore, 9% of the number is approximately 11.

Please see the attached

Answers

Using the ratios, 1 yd/3 feet, 1 mi/5,280 feet, and 200 yards/1 feet, the number of flags required to mark the racecourse with a flag every 200 yards is 22.

What are the ratios?

Ratios are relative sizes of one quantity or value compared to another.

Ratios are depicted as fractional values using decimals, percentages, or fractions, including the standard ratio form (:).

The total distance of the racecourse = 2.5 miles

The common distance between each flag = 200 yards

1 mile = 1,760 yards

2.5 miles = 4,400 yards

1 yard = 3 feel

The number of flags required to cover the distance = 22 (4,400 ÷ 200)

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 how many kilograms are in 14500 grams

Answers

Answer: 14.5 kg

Step-by-step explanation:

Answer: 14.5 kilograms.
Explanation: 1 kilogram = 1,000 grams. If you multiply that by 14, you get 14,000 grams. Half of 1,000 is 500 grams, and 500 grams is half of one kilogram. Then, you can translate 14,500 grams in to 14.5 kilograms. Hope that helped!

Three fourths of the girls in the eighth grade have long hair. One half of the girls are wearing dresses today. What is the probability that an eighth grade girl will have long hair and be wearing a dress?

Answers

The probability that an eighth-grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To solve the problem, we need to find the intersection of the events "having long hair" and "wearing a dress" and calculate the probability of that intersection.

Let L be the event "having long hair" and D be the event "wearing a dress". Then we know:

P(L) = 3/4, since three-fourths of the girls have long hair.

P(D) = 1/2, since half of the girls are wearing dresses.

To find P(L ∩ D), we need to multiply the probabilities of the two events:

P(L ∩ D) = P(L) × P(D) = (3/4) × (1/2) = 3/8

Therefore, the probability that an eighth grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.

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What is 1 and 1/4

And 1 and 1/2

Answers

The mixed fraction 1 and 1/4 is equal to 5/4 and the mixed fraction 1 and 1/2 is equal to 3/2.

Given first number = 1 and 1/4.

1 and 1/4 is a mixed fraction so, we can write it in the form as  [tex]1\frac{1}{4}[/tex] .

To find the value of  [tex]1\frac{1}{4}[/tex]  we have to multiply 4 with 1 and add the numerator part of the fraction which is 1 and then divide it by 4 which is the denominator. So,

 [tex]1\frac{1}{4}[/tex]  = ((4x1) + 1 )/4 = 5/4.

Similary, for 1 and 1/2,

[tex]1\frac{1}{2}[/tex] = ((2x1) + 1)/2 = 3/2.

From the above analysis, we can conclude that the value of 1 and 1/4 is 5/4 and the value of 1 and 1/2 is 3/2.

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The following table shows students’ test scores on the first two tests in an introductory calculus class.

Calculus Test Scores
First test, x 64
59
45
73
73
76
40
56
68
55
78
83
Second test, y 68
63
55
74
68
75
43
64
61
64
77
84

Step 2 of 2 : If a student scored a 69
on his first test, make a prediction for his score on the second test. Assume the regression equation is appropriate for prediction. Round your answer to two decimal places, if necessary.

Answers

if a student scored a 69 on his first test, predict that his score on the second test will be approximately 64.57.

Students’ test scores on the first two tests in an introductory calculus class.

To make a prediction for the student's score on the second test based on their score of 69 on the first test, we need to find the regression equation for the data set.

The regression equation for these data is

y = 0.6443x + 19.943

Where y is the predicted score on the second test and x is the actual score on the first test.

Substituting x = 69 into this equation, we get

y = 0.6443(69) + 19.943 ≈ 64.57

Therefore, if a student scored a 69 on his first test, we predict that his score on the second test will be approximately 64.57.

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One option in a roulette game is to bet 11on red.​ (There are 18 red​ compartments, 18 black​ compartments, and two compartments that are neither red nor​ black.) If the ball lands on​ red, you get to keep the 11 you paid to play the game and you are awarded 11. If the ball lands​ elsewhere, you are awarded nothing and the 11 that you bet is collected. Complete parts​ (a) through​ (b) below.

Answers

The expected value for playing roulette if a person bet $16 on red is -$0.84.

b. The statement that best describes what this value means is option b. Over the long run, the player can expect to lose about $1.05 for each game played.

What is the expected value?

To be able to calculate the expected value, you need to multiply the probability of winning by the amount won hence it will be:

Expected value = (18/38) x  $16 - (20/38) x  $16

= -$0.84

Based on the fact that the expected value has a negative sign, it implies that, on average, the player tend to lose money over the long run.

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See full question below

one option in a roulette game is to bet $16 on red. (there are 18 red compartments, 18 compartments, and two compartments that are neither red nor black) if the ball lands on red, you get to keep the $16 you paid to play the game and you are awarded $16. If the ball lands elsewhere, you are awarded nothing and the $16 that you bet is collected.

a. what is the expected value for playing roulette if you bet $16 on red?

$__________ (round to the nearest cent)

b. chosen the statment below that best describes what this value means???

Pick One!

a. over the long run, the player can expect to win about $1.05 for each game played

b. over the long run, the player can expect to lost about $1.05 for each game player

c. over the lung run, the player can expect to break even

2. Four friends have stamps, as described below.
• Samir has 60 stamps.
•Lisa has 24 times as many stamps as Samir.
Kwame has 443 stamps.
To the nearest whole number, what is the mean of the
Jake has 159 fewer stamps than Kwame.
number of stamps for these four friends?

Answers

Answer:

All of them have a combined of 2,227 Stamps

Mean: 2014

Can you help me with this please

Answers

Answer: [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{8}{25}[/tex]

Step-by-step explanation:

We can do this by counting the boxes for both the Width and the Length.

If we look at the width of these boxes (horizontally) then we see that there are 5 boxes all together, with 2 shaded green.

this means that 2 out of 5 of the boxes are shaded for the width, giving us the fraction: [tex]\frac{2}{5}[/tex]

Then for the Length (vertically) we see that there are also 5 boxes, but this time 4 are shaded. This gives us the fraction:  [tex]\frac{4}{5}[/tex].

Then, to fill the equation in, we do: [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] , which gives us          [tex]\frac{8}{25}[/tex]

2 x 4 = 8

5 x 5 = 25

To double check this answer, we can count how many boxes are shaded green.

We see that 8 are shaded green, out of the 25 boxes that are there.

Therefore, giving us a complete answer of:  [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{8}{25}[/tex]

Car A travels 221.5 km at a given time, while car B travels 1.2 times the distance car A travels at the same time. What is the distance car B travels during that time?

Answers

Answer:

Distance that car B travels =1.2× distance that car A travels

=1.2×221.5=265.8 km

Answer:

car B travels a distance of 265.8 km during the same time.

Step-by-step explanation:

Car A travels 221.5 km at a given time.

To find the distance traveled by car B, which is 1.2 times the distance traveled by car A, we can multiply the distance of car A by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, car B travels a distance of 265.8 km during the same time.

What are the solutions to the system of equations?
y=x^2−5x−6
y=2x−6

(−1, 0) and (−6, 0)
(7, 8) and (0, −6)
(−6, 0) and (0, −1)
(−1, 0) and (0, −6)

Please answer- I will report you if you do not answer and only want the points.

Answers

The solutions  of the system of equations are (0, -6) and (7, 8)

How to find the solution of the system of equations?

Here we have the system of equations:

y=x^2−5x−6

y=2x−6

To solve this, we need to solve the equation:

x^2 - 5x - 6 = 2x - 6

x^2 - 7x = 0

x*(x - 7) = 0

We can see that the two solutions are:

x = 0

x = 7

Evaluating the line in these values we get:

y = 2*0 - 6 = -6

y = 2*7 - 6 = 8

Then the solutions are (0, -6) and (7, 8)

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Select the two values of x that are roots of this equation x^2-5x+3=0

Answers

The two roots of the quadratic equation x² - 5x + 3 = 0 are (5 + √13) / 2 and (5 - √13) / 2.

To find the roots of the quadratic equation x² - 5x + 3 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values of a, b, and c from the given equation, we have:

x = (-(-5) ± √((-5)² - 4(1)(3))) / 2(1)

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of the equation are (5 + √13) / 2 and (5 - √13) / 2.

To verify that these are indeed the roots of the equation, we can substitute each of these values for x in the original equation and check if the equation is satisfied. For example, if we substitute (5 + √13) / 2 for x, we get:

(5 + √13)² - 5(5 + √13) + 3 = 0

Simplifying this equation, we get:

13 - 5√13 + 8 + 13 - 5√13 + 3 = 0

This equation is true, which means that (5 + √13) / 2 is a root of the equation x² - 5x + 3 = 0. Similarly, we can verify that (5 - √13) / 2 is also a root of the equation.

These roots can be found using the quadratic formula, which is a useful tool for solving quadratic equations.

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A box contains 16 transistors, 3 of which are defective. If 3 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
a. The probability is.
(Type a fraction. Simplify your answer.)
***

Answers

The probability of selecting all defective transistors is 1/560.

To find the probability of the statements

The probability of selecting all defective transistors can be calculated as:

P(all defective) = (number of ways to select 3 defective transistors) / (total number of ways to select 3 transistors)

The number of ways to select 3 defective transistors is simply the number of combinations of 3 defective transistors out of the total of 3, which is 1. The total number of ways to select 3 transistors out of 16 is:

total number of ways = number of combinations of 3 transistors out of 16

= (16 choose 3)

= 560

Therefore, the probability of selecting all defective transistors is:

P(all defective) = 1 / 560

To simplify the answer, we can write it as a fraction in lowest terms:

P(all defective) = 1 / 560 = 1/ (161514/321) = 1/560

Therefore, the probability of selecting all defective transistors is 1/560.

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Find z

x+y=z
y-z=x
I will award brainlest

Answers

Answer:

To solve for z in terms of x and y using the given equations:

x + y = z ........(1)

y - z = x ........(2)

From equation (2), we get:

y - x = z (by adding z on both sides)

Substituting this value of z in equation (1), we get:

x + y = y - x

2x = 0

x = 0

Substituting x = 0 in equation (2), we get:

y - z = 0

y = z

Therefore, the solution is:

z = y

We cannot determine a specific value of z without knowing the values of x and y.

PLEASE HELP!!

A cone has a radius of 3 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 6 inches?
Enter your answer in the box.

Surface area of similar cone =
___in²

Answers

Surface area of similar cone is 44π square inches

What does a cone in maths ?

A cone is referred to as a "right cone" when its vertex is higher than the base's centre (i.e., when the angle formed by the vertex, base center, and any base radius is a right angle); otherwise, the word "oblique" is used. A cone is referred to as an elliptic cone when the base is assumed to be an ellipse rather than a circle.

The surface area of a cone is given by:

surface area = πr(r + l)

where r is the radius and l is the slant height.

surface area of original cone = π(3)(3 + 12) = 45π

slant height of similar cone = (6/3)(12) = 24 inches

surface area of similar cone = π(6)(6 + 18) = 144π

ratio of surface areas = surface area of similar cone / surface area of original cone

= (144π) / (45π)

= 3.2

Therefore, The exact surface area of the similar cone is 6 times the surface area of the original cone,

6 × 45π = 144π square inches

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I need help pleaseeee

Answers

(a) The value of the row operation of -2(row1) + row (2) is [-10     4    -12].

(b) The interchange of row 1 and row 2 is  [0     6    -3]

                                                                       [5    -2     6]

What is the row operation of the matrix?

The value of the row operation of -2(row1) + row (2) is calculated as follows;

-2 (row 1) = 2 [5   -2    6]

-2 (row 1) = [-10     4    -12]

The addition of -2(row1) to row (2) is calculated as follows;

[-10     4    -12] + [0    6    -3]

= [-10   10  - 15]

The interchange of row 1 and row 2 is calculated as follows;

R₁ ↔ R₂

= [5    -2     6]    =   [0     6    -3]

  [0     6    -3]         [5    -2     6]

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The model for radioactive decay is y=y0e^-kt. a radioactive substance has a half-life of 170 years. if 40 grams are present today. in how many years will 15 grams be present? While solving this problem, round the value of k to seven decimal places. Round your answer to two decimal places.​

Answers

It will take about 225.25 years of time for 15 grams to be present.

The half-life of a radioactive substance is the time it takes for half of the substance to decay.

For this substance with a half-life of 170 years, we can use the following formula to find the value of k:

[tex]0.5 = e^(^-^1^7^0^k^)[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.5) = -170k

Solving for k, we get:

k = ln(0.5) / (-170)

= 0.004085

Now, we can use the model [tex]y = y_0e^(^-^k^t^)[/tex] to find the time t required for the substance to decay from 40 grams to 15 grams.

We have:

[tex]15 = 40e^(^-^0^.^0^0^4^0^8^5^t^)[/tex]

Dividing both sides by 40 and taking the natural logarithm of both sides, we get:

ln(15/40) = -0.004085t

Solving for t, we get:

t = ln(15/40) / (-0.004085)

= 225.25 years

Therefore, it will take about 225.25 years for 15 grams to be present.

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Given u=12i-3j and v=-5i+11j, what is u x v?

Answers

Answer:

  117

Step-by-step explanation:

You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).

Cross product

The cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.

  u×v = (12)(11) -(-3)(-5) = 132 -15

  u×v = 117

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1. Find the zeros of the quadratic function by graphing. Round to the nearest tenth if necessary.
f(x) = -2x² + 3x + 1
A 0.8,2.1) is a zero of the quadratic function because it is the peak of the parabola.
B (0,1) is a zero of the quadratic because it is where the parabola crosses the y-axis.
C (-0,3,0) and (1.8,0) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
D (0.8,2.1) and (0,1) are zeros of the quadratic function because it is where the parabola crosses the x-axis.

Answers

The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.

The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.

plot the y-get at (0,1),

x = - b/2a

To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is

f(3/4) = 1/8.

Plot the vertex at (3/4, 1/8).

Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.

To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.

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Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200


Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
50

Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
50

What is the slope of the line that connects the 3rd and 4th point?
50

What is the slope of the line that connects the 1st and the 4th point?
150

Is the common difference (aka slope aka rate of change) constant?
Yes

Why is it or is it not constant?
It is constant because it is a linear function.

Answers

Answer:

Step-by-step explanation:

The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.

The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.

The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.

The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.

B as a % of A is equal to A as a % of (A+B). Find B as a % of A.

Answers

Option (b), 62% is correct.

How to solve

By the given condition,

B/A = A/(A + B) ..... (1)

Now to find the percentage of A = B, we consider B = Ax. From (1), we get

Ax/A = A/(A + Ax)

or, x = 1/(1 + x)

or, x² + x - 1 = 0

Using the quadratic formula, we get

x = {- 1 ± √(1 + 4)}/2

= (- 1 ± √5)/2

Since x cannot be negative, we take

x = (- 1 + √5)/2

≈ 0.62

Therefore the required percentage is

= 0.62 × 100%

= 62%


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B as a percentage ofAis equal to Aas a

percentage of(A+B). How much percent

of A is B?

(a) 60%

(b) 62%

(C) 64%

(d) 66%

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)

Answers

The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²

where k is the proportionality constant.

In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.

In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:

Strength = k * width * depth² = k * x² * (d/2 - x)²

where x is the width and depth of the beam.

In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:

Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²

where θ is the angle at which the beam is cut from the log.

In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:

w = d sinθ

d = (d/2)cosθ

Then we can express the strength of the beam as:

Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²

Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.

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Complete question is:

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)


1 Soo divides a square into sixths. She colors one of the
equal parts red. What fraction of the square is red?

Answers

The fraction of the square that is red is 1/6.

Define fraction

A fraction is a number that represents a part or parts of a whole. It consists of two numbers separated by a horizontal or diagonal line, with the number above the line (numerator) representing the part and the number below the line (denominator) representing the whole. For example, the fraction 3/4 represents three parts out of a whole that is divided into four equal parts.

A square divided into six equal parts has six equal sixths.

If Soo colors one of these equal parts red, then she has colored one-sixth of the square red.

Therefore, the fraction of the square that is red is 1/6.

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Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) - 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x - 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done.

Answers

The simplification of the function is r(x)=10x - 95.

We are given that;

s(x) = -85 and a(x) = 10(x - 1)

Now,

To create a function that combines them, you can substitute these expressions into the formula above:

r(x) = s(x) + a(x) r(x) = (-85) + 10(x - 1)

You can simplify this function by distributing the 10 and combining the constants:

r(x) = -85 + 10x - 10 r(x) = 10x - 95

Therefore, the function will be r(x)=10x - 95.

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Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
-3, √3, 13/3
The other zeros are
(Use a comma to separate answers.)

Answers

Answer:

{-3, √3, -√3, 13/3}

Step-by-step explanation:

Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.

We can write the polynomial with these zeros as:

p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)

where a is some constant coefficient. Multiplying out the factors, we get:

p(x) = a(x + 3)(x^2 - 3)(x - 13/3)

To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:

a(x + 3)(x^2 - 3)(x - 13/3) = 0

This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:

(x + 3)(x^2 - 3)(x - 13/3) = 0

Expanding the quadratic factor, we get:

(x + 3)(x - √3)(x + √3)(x - 13/3) = 0

Canceling out the (x - √3) and (x + √3) factors, we get:

(x + 3)(x - 13/3) = 0

Solving for x, we get:

x = -3 or x = 13/3

Therefore, the other zeros are -3 and 13/3.

The complete set of zeros is {-3, √3, -√3, 13/3}.

Hope it helps^^

lim h -> 0 [f(x_{0} + h) - f(x_{0})] / h

Answers

the limit expression gives the value of the derivative of a function at a specific point. where f'(x_0) denotes the derivative of f(x) at x = x_0.

what is derivative  ?

The derivative of a function is a measure of how the function changes as its input variable changes. It gives the instantaneous rate of change or slope of the tangent line of the function at a specific point.

In the given question,

The expression you provided represents the limit definition of the derivative of a function f(x) at the point x = x_0. The limit evaluates the instantaneous rate of change or slope of the tangent line of the function f(x) at the point x = x_0.

To evaluate the limit, substitute x = x_0 + h in the expression of the function f(x) and simplify:

[tex]lim h - > 0 [f(x_{0} + h) - f(x_{0})] / h = f'(x_{0})[/tex]

where f'(x_0) denotes the derivative of f(x) at x = x_0.

Therefore, the limit expression gives the value of the derivative of a function at a specific point.

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