What is the
relationship among the unit rate, slope, and constant
rate of change of a proportional linear relationship?

Answer:

1. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  [0, ∞)

2. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  (-∞, ∞)

3. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  (-∞, ∞)

4. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  [0, ∞)

Step-by-step explanation:

Rule for end behavior of polynomials:

(a) Positive leading coefficient, even degree:  y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞

(b) Negative leading coefficient, even degree: y ⇒ -∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞  

(c) Positive leading coefficient, odd degree:  y ⇒ ∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞

(d) Negative leading coefficient, odd degree:  y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞

Domain and range for a polynomial function with an odd degree will always be all real numbers, whether or not there's a constant or not.

Domain will always be all real numbers for a polynomial function with an even, whether or not there's a constant.

For a polynomial function with an even degree, the range will extend from the y-coordinate of the vertex to ∞, if the leading coefficient is positive

For a polynomial function with an even degree, the range will extend from -∞ to the y-coordinate of the vertex if the leading coefficient is negative.

Triangle C forms a right angle triangle.

Given:

Triangle A : 8 cm , 13 cm , 5 cm

Triangle B : 14 cm , 30 cm , 17 cm

Triangle C : 26 cm , 10 cm , 24 cm

To form a right angled triangle the longest side square is equal to the sum of squares of other sides.

In triangle A :

[tex]13^{2} = 8^{2} +5^{2}[/tex]

169 = 64 + 25

169 ≠ 89.

This is not a right angle triangle.

In triangle B:

[tex]30^{2} =17^{2} +14^{2}[/tex]

900 =  289 + 196

900 ≠ 485

This is not a right angle triangle.

In triangle C:

[tex]26^{2} = 10^{2} +24^{2}[/tex]

676 = 100 + 576

676 = 676

so it is a right angle triangle.

Therefore Triangle C forms a right angle triangle.

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According to the scale factor, When the scale is changed to 20 feet to 1 unit, then the drawing would be exactly the same shape, here only each side would have half the original drawing units.

Scale factor:

The ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller) is known as scale factor.

Given,

This is a scale drawing of an apartment. The actual apartment has a perimeter of 160 ft.

Here we need to find the reason for the scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment

Here we know that the actual apartment has a perimeter of 160 ft.

And we have to draw another scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment to the drawing.

So, as per the given details, the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter, this means that each square is calculated as,

=> 160 / 16 = 10 feet on a side.

Therefore, 10 feet in real life plots to 1 unit on the drawing

Therefore, if we change the scale to 20 feet to  1 unit , then the drawing would be exactly the same shape, only each side would have half the original drawing units.

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The equation y = -|x - 3| + 2 written as a piecewise function is;

f(x) = {y = x - 1, if x < -3

        {y = -x + 1, if x ≥ -3

A function can be written as piecewise function if it changes its behavior ( increasing or decreasing ) about a point.

The function f(x) = y = |x| changes its behavior at |x| = 0 i.e , x = 0 .

y = | x | = x , if x < 0

= - x , if x > 0

| x | = a => x = ± a

• | x | ≥ a ( a ≥ 0 ) => x € ( -∞ , -a ] U [ a , ∞ )

• | x | ≤ a ( a ≥ 0 ) => x € [ -a , a ]

The given function is : y = -|x - 3| + 2

The function will change its behavior when; -| x - 3 | = 0

-x + 3 = 0

x = -3

If x < -3 , then ;

y =  -(-(x - 3)) + 2

y = x -3 + 2

y = x - 1

If x ≥ -3, then ;

y = -(x - 3) + 2

y = -x + 3 + 2

y = -x + 1

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The following equation expressed in scientific notation would be as follows:

SCIENTIFIC NOTATION FORM:

[tex]1.28*10^1^3[/tex]

Hope this helps!

The different possibilities available for selecting an executive board in Student Council in election is 990 ways

In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6

The problem is a permutation problem trying to select 3 from 11 where order matters. The order include choosing the president the ramainig position is left 2 for 10. and so on.

This is shown in permutation as follows

₁₁P₃  = 11! / (11 - 3)!

= 11! / 8!

= 990 ways

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Answer:

-3≥11.5

Step-by-step explanation:

-3≥1/2+11

-3≥11.5

The linear equation that represents the hours Yuson has left after x days is (A) y = -2x + 30

Given in question,

Hours she should complete = 30 hours

Hours she complete each day = 2 hours

Hours completed in x days = 2x

Hours left after x days = 30 -2x

Hence, the linear equation that represents the hours Yuson has left after x days is y = -2x + 30.

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The equation of line passes through the point (0, 7) will be;

⇒ y  = 1/2x + 7

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (0, 7).

And, The perpendicular line is,

⇒ y = -1/2x + 5

Now,

Since, The equation of line passes through the point (0, 7).

So, We need to find the slope of the line.

Since, The product of slope of the perpendicular lines is - 1.

Hence, Slope of the perpendicular line is,

y = -1/2x + 5

m₁ = dy/dx = - 1/2

m₁ = - 1/2

So, The slope of the line,

m₂ = - (- 1/2)

    = 1 / 2

Thus, The equation of line with slope 1/2 is,

⇒ y - 7 = 1/2 (x - 0)

⇒ y - 7 = 1/2 x

⇒ y  = 1/2x + 7

Therefore, The equation of line passes through the point (0, 7) will be;

⇒ y  = 1/2x + 7

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Answer:

Convergence

Step-by-step explanation:

Use the Squeeze Theorem,

I know that

[tex] \frac{k \sin {}^{2} (k) }{1 + k {}^{3} } [/tex]

lies between 0 and 1 so

[tex]0 \leqslant \frac{k \sin {}^{2} (k) }{1 + {k}^{3} } \leqslant \frac{k}{1 + k {}^{3} } [/tex]

The final series behaves like

[tex] \frac{1}{k {}^{2} } [/tex]

Using the p series, since p is 2, the series

[tex] \frac{k}{1 + k {}^{3} } \: converges[/tex]

Since the 0 and k/1+k^3 converges, the series converge.

Convergence

Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork

Answer:

B, C

Step-by-step explanation:

A is incorrect, it should be seventy-six hundredths.

D is incorrect, the place value for the third term is wrong - it should be 0.06.

The union of the sets P and Q does not have the integer 5 since it is neither a multiple of 3 or a multiple of 4.

P is the set of integers between 1 and 10 and multiple of 3.

∴P = {3,6,9}

Q is the set of positive integers less than 15 and multiple of 4.

∴Q = {4,8,12}

Now the union of the sets P and Q is given by :

P∪Q = {3,4,6,8,9,12}

Now the union of the sets does not contain the integer 5.

Any collection of items, including a set of raw materials, the seven days of the week, several car types, etc., can be categorized as a set.

Any set component counts as an element of the set. Curly brackets are used to write a set. A very basic set would resemble something like this:

Q = {4,8,12}.

Therefore the integer 5 does not belong to the union of P and Q .

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The length of q, to the nearest 10th of a centimeter, is 8.8 cm.

We are given the following;

In ΔQRS, s = 7.9 cm, ∠Q=125° and ∠R=23°.

The third angle can be calculated using the angle sum property:

angle Q + angle R + angle S = 180 degrees

125 degrees + 23 degrees + angle S = 180 degrees

angle S = 180 - (125 + 23) degrees

angle S = 180 - 148 degrees

angle S = 32 degrees

To find the length of q we shall apply the Sine rule.

q / Sin Q = s / Sin S

q / Sin 125 = 7.9 / Sin 32

by cross multiplication we will get;

q = (7.9 x Sin 125) / Sin 32

q = (7.9 x 0.61) / 0.55

q = 8.8 cm (approximately)

So,  the length of q is 8.8 cm.

Thus, the length of q, to the nearest 10th of a centimeter, is 8.8 cm.

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Answer:

Step-by-step explanation:

Hi, Julia,  they are trying to ask about error, or the confidence that there is not an error. It's kinda like saying,  we're 100% sure the answer is correct, mostly :DDDD   which really lowers your confidence about the 100% correct statement.   Anyway,  sooo then they give the way to show deviation,  from something.  if you've had Calculus one,  this is the same thing as the Delta , Epsilon thing, about a small distance away from the target is still with in a certain range.   I feel like if they had written the inequality like this...

( p' - E) < p < (p'+E)   it would be clearer about the inequality.  E is just a tiny distance away in the positive and negative direction.  E plays the role of epsilon.  the numbers they give are the range of the confidence. I don't think they ask a very clear question.  

0.056<p<0.112

p is kinda like our "best guess"  answer, and we're giving it this range that it's probably within,   for a certain level of confidence.   You can see, that as the confidence goes down,  that range can become bigger.  

The measure of the exterior angle is 139 degrees.

The sum of the interior angle of a triangle is 180 degree.

The sum of angles on a straight line is 180 degrees.

From the diagram;

First, we determine the third interior angle of the triangle.

Angle 1 + Angle 2 + Angle 3 = 180

64 + 75 + Angle 3 = 180

139 + Angle 3 = 180

Angle 3 = 180 - 139

Angle 3 = 41 degrees

Now, angle 3 and the exterior angle forms a angle on a straight line.

Hence;

Angle 3 + Exterior angle = 180

41 +  Exterior angle = 180

Exterior angle = 180 - 41

Exterior angle = 139 degrees.

Therefore, 139 degrees is the exterior angle.

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Each student should work for 7 hours on the project.

Given, the equation the quantity x plus 56 end quantity over 3 equals 5 times x models the workload of a class project,

where x is the number of hours each student must contribute.

Now, according to question,

56 - 3x = 5x

56 = 5x + 3x

8x = 56

x = 7

So, x = 7 hours

Hence, each student should work for 7 hours on the project.

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Answer:

4 hours

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x = 14/3

Decimal Form:

x = 4.6

Mixed Number Form:

x = 4 2/3

Therefore, 4 hours is how much the students work on the project.

Answer:

"Multiply to remove the fraction then set it equal to 0 and solve."

Exact form

x = - 39/2

Decimal Form:

x = -19.5

Mixed Number Form:
x = - 19 1/2

Hope this helped...!

Therefore , the solution of the given problem of interest comes out to be $4,088.14 is the new balance.

Divide the number by the expense of borrowing, the remaining time, and other factors to get the simple interest rate. In marketing, the straightforward return plan is principal interest payments plus hours. This technique is the simplest way to figure out interest. The most common way to determine income is as a percentage of the principal sum.

Here,

We must first figure out the interest on the present balance.

The interest rate is 27.99%/12, or 0.0233, per month.

As a result, the current balance's interest rate is:

=> 3,109.87 x 0.0233 = $72.43

When this interest is added to the outstanding amount, Kye's new balance is as follows:

=>  3,109.87 + 72.43 + 532.42 = $3,714.72

The minimum payment for the new amount must now be determined:

=>  3,714.72 x 0.02 = $74.29

Kye's minimum payment for the following month will be $159.00 because the minimum payment is the higher of $74.29 or that amount.

Kye's new balance with interest as a result of making the required minimum contribution and spending $532.42 is as follows:

=>  3,714.72 - 159.00 + 532.42 = $4,088.14.

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Answer:

percentage = 80÷4000=0.02

The correct number of servings would be = 12/25

A cooking class is defined as the class that is made up of students that are being thought how to prepare and serve different types of food.

The total amount of quarts of food made by the students = 4½.

The number of servings to friends = ⅘

The quantity of quarts in each serving = ⅗ quarts

Total number of quarts served = ⅘ × ⅗= 12/25

The correct number of servings = 12/25

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Jimmy has to write 369 words per day for the next 6 days to finish the paper.

The total number of words in the paper has to be 3000

Jimmy has already written = 786 words.

3000-786 = 2214

So, Jimmy still has to write 2214 words.

He has 6 days to write the paper and he wants to write the same number of words per day.

With this in mind to find out how many words he has to write per day we can divide 2214 by 6.

2214/6 = 369 words

So, Jimmy has to write 369 words per day for the next 6 days to finish the paper.

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Answer: 19.2, I think.

Step-by-step explanation: 10*1.2 = 12.

To keep the ratio balanced, you must also do 16*1.2, which is 19.2. Making the ratio 12 : 19.2

Answer: Symmetry Property of Equality

Answer:

Domain: [0,∞), {x|x ≥ 0}

Range: [0,∞), {y|y ≥ 0}

Step-by-step explanation:

1. Find where the FUNCTION is DEFINED.

A function is a set of ordered pairs where each first element is paired with one, and only one, second element. No element in either pair is without a partner.

2. Find the DOMAIN: The set of all x-values that a function passes through. Also, it is the left coordinate in a coordinate pair.

3. The RANGE: the set of all y-values that a function passes through. Also, it is the right coordinate in a coordinate pair.

The equation that can be used to find the length of the afternoon practice is B. 4(h + 3) = 20

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, during the summer the team practices 4 days per week and each of those days, they practice for 3 hours in the morning and practice again in the afternoon.

Let the afternoon practice be h.

Therefore, the equation will be:

4(h + 3) = 20

In conclusion, the correct option is B.

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Answer:

The third option, as x approaches infinity y approaches infinity and as x approaches negative infinity y approaches negative infinity.

Step-by-step explanation:

The expression will be i.e., 2(8 + 7).

The correct option is (D)

Given,

In the question:

Joan has a vegetable garden in her backyard that measures 8 feet 7 feet.

To find the which expression would not calculate the garden's perimeter?

Now, According to the question;

Based on the given conditions:

Formulate:

Measurement of garden is :

Length and breadth is 7 ft. and 8 ft.

Calculate:

2 x (7 + 8)

= 30

Hence, The expression will be i.e., 2(8 + 7).

The correct option is (D)

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Answer: I don't know

Step-by-step explanation:

I have no idea