Write a linear function f with the values f(0) =10 and f(6) =34.

The absolute value equation modelling this situation is presented as follows:

|x - 58.2| = 6.4.

The function giving the absolute value of another function is defined by the piece-wise rule presented as follows:

The result is never negative, as the function gives the distance of the function f(x) from the origin, which is the point in which f(x) = 0.

The difference between both the fastest and the slowest time from the average time of 58.2 seconds is of 6.4 seconds, hence the absolute value equation is given as follows:

|x - 58.2| = 6.4.

Which can be solved applying these following rules:

To find the fastest and slowest times, respectively.

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Answer: 5

Step-by-step explanation: First we do (-4-(-7))^2 which is 9 and then

(8-4)^2 which is 16 so 9+16=25 and √25 = 5.

The equivalent linear equation in standard form is 4x + 3y = 5

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

Points = (-7, 11) and (8, –9)

Point-slope form is y - 11 = -4/3(x + 7).

Recall that the point-slope form is y - 11 = -4/3(x + 7).

So, we have

y - 11 = -4/3(x + 7).

Multiply through both sides by 3

This gives

3y - 33 = -4(x + 7).

Open the brackets

3y - 33 = -4x - 28

Evaluate the like terms

3y = -4x +  5

Add 4x to both sides

4x + 3y = 5

Hence, the equation is 4x + 3y = 5

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Answer:

burgers

Step-by-step explanation:

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The technological innovation could help solve an environmental issue that is likely to threaten Australia in the future is D. Using electric cars could help lessen droughts.

Streamflows decrease, water levels in lakes and reservoirs fall, and the depth to water in wells increases when rainfall is less than normal for a period of weeks to years. If the dry weather continues and water supply issues arise, the dry period may turn into a drought.

For the first time since 2017, Australia ended 2021 in an unusual climatic state, with no region in this famously vast, mostly brown land officially declared to be in drought. It should be noted that the country has drought challenges and electric cars could help reduce the water used.

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The length of the garden is:  l ≥ 6225ft.

Area = L multiplied by W. Since you measure the area in square feet, your final number should reflect that.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Let l serve as a symbol for the garden's length.

Let w be the symbol for the garden's width.

The perimeter is 540 feet.

The rectangle's circumference is equal to

2(l + w)2(l + w) = 540 l + w = 270.      (1)

The rectangle's area is equal to its length times its width, which equals 12000.            (2)

Make the variable w the subject of the following equation:

w = 270 - l.   (3)

Substitute equation (3) into equation (2)

(270 - l)(l)   ≤    12000

270l  -  l²  ≤   12000

0   ≤  l²  -  270l +  12000

l²  -  270l  +  1200  ≥  0

Solving the quadratic inequality above:

l  ≥  6225

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(98 × 100) ÷ 70

= 140%

or

[(98 - 70) × 100] ÷ 70

2800 ÷ 70

40%

basically, 40% increase

B) The missing angle at the intersection point of both triangles is; x = 15°

C) The missing angle is gotten as; x = 61°

B) In the second image given, we can see two angles;

Now, we know that sum of angles in a triangle is 180 degrees. Thus, for the interior angles, we have;

90 + 5x - 14 + y = 180

where y is the third interior angle

Now, we know that sum of angles on a straight line is equal to 180 degrees. Thus;

y = 180 - (9x + 16)

Put 180 - (9x + 16) for y into the first equation to get;

90 + 5x - 14 + 180 - (9x + 16) = 180

180 will cancel out to get;

90 + 5x - 14 - (9x + 16) = 0

4x = 90 - 14 - 16

4x = 60

x = 60/4

x = 15°

C) The missing angle of the triangle with side of 12y + 3 is an alternate angle to get;

Missing angle = 63°

Sum of angles in a triangle is 180 degrees. Thus;

56 + 63 + 3rd angle = 180

3rd angle = 180 - (56 + 63)

3rd angle = 61°

Thus, x = 61° because they are opposite angles

Also, the two given sides are equal to each other as shown. Thus;

51 = 12y + 3

12y = 51 - 3

12y = 48

y = 48/12

y = 4

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The remainder is 360.

When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).

Given a cubic polynomial, x³+8x²+11x-20

The zero of the linear polynomial.

Substitute it in the given polynomial.

As a result, we get the remainder.

x - 5 = 0

x = 5

Substitute 5 to x³ + 8x² + 11x - 20:

5³ + 8×5² + 11×5 - 20 = 125 + 8×25 + 55 - 20 = 160 + 200 = 360

Hence, The remainder is 360.

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Answer:

calculate the difference ere

(3-22)+5

remove unnecessary parentheses

-19+5

calculate the sum

= -14

Answer:

A. Subtract the distance between each point and the x-axis.

Step-by-step explanation:

As the two points have the same x-coordinate, x = 6, it means they lie on the vertical line x = 6.

Therefore, the distance between the points can be found by subtracting the distance between each point and the x-axis.

In the given example, the points are C(6, -4) and D(6, -8).

To find the distance between a point and the x-axis, we simply take the absolute value of the y-coordinate of the point:

Distance between point C and the x-axis = |-4| = 4

Distance between point D and the x-axis = |-8| = 8

Subtracting the distances, we get:

Distance = 8 - 4

Distance = 4

Therefore, the distance between points C and D is 4 units.

Farmer A planted a greater ratio of green beans to corn

Ratio is defined as the comparison of two quantities (a and b) of the same units which indicates how much of one quantity is present in the other quantity. They are written a / b, where b does not equal 0

Given that:  Farmer A planted green beans and corn at a ratio of 5:3 and farmer B planted green beans and corn at a ratio of 3:2

To find the greater ratio treat the ratio as a fraction:

Farmer A => 5:3  and Farmer B => 3:2

5/3  and  3/2      (LCM of 2 and 3 is 6)

10/6 and 9/6

10:6 and 9:6

Since 10:6 is greater than 9:6. Therefore, Farmer A planted a greater ratio of green beans to corn

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The polynomial function which has a leading coefficient 1 is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Given that a polynomial function has leading coefficient 1 and roots (7+i) and (5-i) with multiplicity 1.

We want to find the polynomial function.

As we know that the complex conjugate properties of the roots of a polynomial states that if a+bi is a root of a polynomial then their complex conjugate a-bi is also a root.

So, according to this property (7-i) and (5+i) with multiplicity 1 is also a root of polynomial.

Thus, all the roots are x=7+i, x=7-i, x=5+i and x=5-i

So, the polynomial is f(x)=(x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Hence, the polynomial function which has a leading coefficient 1 and roots (7+i) and (5-i) is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i)).

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The relationship has a constant of proportionality of 37

From the graph, we have the following points

x = 1 and y = 37

These points can be represented:

x = 1

y = 37

The above parameters can be represented as the following points

(x, y) = (1, 37)

The constant of proportionality of the points is then calculated as

k = y/x

Substitute the known values in the above equation

So, we have the following equation

k = 37/1

Evaluate the quotient

So, we have

k = 37

Hence, the constant of proportionality is 37

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With the help of equations we can say that function has a f(x) = x,straight line.

What is an equation?

acc to our question-

f(x) = Ixl

f(x) = x

f(x)=x²

Hence, function f(x) = x is a line.

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Solution

From given equation

Slope = -2

and y-intercept is (0,0)

Therefore,

if we put x= 0

then y = -2*0 = 0

if we put x = 1

then y = -2*1 = -2

for graph plotting, see the attachment.

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Solution

From given equation

Slope = -2

and y-intercept is (0,0)

Therefore,

if we put x= 0

then y = -2*0 = 0

if we put x = 1

then y = -2*1 = -2

for graph plotting, see the attachment.

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the given expressions solved by using factorization.

What is factorization of the expression ?

  To factorize an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse.

Here

4) [tex]x^4-36[/tex]

=> [tex](x^2)^2 -6^2[/tex]

=> [tex](x^2-6)(x^2+6)[/tex]

5)64[tex]c^3+1[/tex]

=> [tex](4c)^3+1^3[/tex]

=> (4c+1)([tex](16c^2+4c+1)[/tex]

6)[tex]k^3-27[/tex]

=> [tex]k^3-3^3[/tex]

=>(k-3)([tex]k^2+3k+9[/tex])

7)[tex]54x^3+250y^3[/tex]

=> 2([tex]27x^3+125y^3[/tex])

=> 2([tex](3x)^3+(5y)^3[/tex])

=> 2 ( 3x+5y)([tex]9x^2+15xy+25y^2[/tex])

8)[tex]3m^4-48n^2[/tex]

=> 3([tex](m^2)^2-(4n)^2[/tex])

=> 3[tex](m^2-4n)(m^2+4n)[/tex]

9)[tex]a^7b^2-ab^2[/tex]

=> [tex]ab^2(a^6-1)\\[/tex]

=>[tex]ab^2(a^3-1)(a^3+1)[/tex]

=> [tex]ab^2(a+1)(a-1)(a^2-a+1)(a^2+a+1)[/tex]

10)[tex]x^3y^2-343y^5[/tex]

=> [tex]y^2(x^3-(7y)^3)[/tex]

=>[tex]y^2(x-7y)(x^2-7xy+49y^2)[/tex]

11)[tex]9y^7-144y[/tex]

[tex]= > 9y(y^6-16)\\= > 9y((y^3)^2-4^2)\\= > 9y(y^3+4)(y^3-4)[/tex]

Hence we can solve by using factorization formula.

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Using the concept of application of derivative it is concluded that the rate of change in the area of square tile is 94.25 cm²/hour.

The area of the square is defined as the square of its sides.

Let the side of the square is a then its area will be a².

Area of square figure = Side².

Let the side of the square is x= 29cm.

It is given that the side 29 cm tile is growing by 1.625 cm per hour on heating.

And the rate of change in side of square dx/dt = 1.625 cm/hour

We have to calculate the rate of change in an area of the square (A).

hen, area A = x²

On differentiating A with respect to time(t) we get a rate of change in area

dA/dt = d(x²)/dt

= 2x dx/dt

= 2×29×1.625

= 94.25 cm²/hour

Hence, the rate of change in the area of the square tile is 94.25 cm²/hour.

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With the help of standard deviation we can conclude our answer.

acc to our question-

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19.50 cost of pizza

Step-by-step explanation:

$8.00-$1.50 = $6.50 × 3 =19.50

Answer:

ask this braslate which matirias

An equation that represents a vertical shrinkage of the graph of g(x)=1/3|x|-1 by a factor of three.

Given,

f(x) = |x|-3;

vertical shrink by a factor of = 1/3

Therefore,

g(x)=1/3|x|-1

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Using the concepts of straight line, we got 7 movies did marc watch between the beginning of week 1 and the beginning of week 5.

From the diagram given, we got that during the week 1 number of movies watch by marc is 2,while at the beginning of the week 5 the number of movies watch by marc is 9.

So, we need total  number of movies watched by marc in between week 1 and week 9 which is given by-

Number of movies watch at the beginning of week 5-Number of movies watch at the beginning of week 1

Number of movies=9-2

=>Number of movies watched by marc=7.

Hence, the number of movies marc watch between the beginning of week 1 and the beginning of week 5 is 7.

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(Complete question)

Marc is keeping track of the total number of movies he has watched over time. The line graph below actually shows the data where the number of movies corresponds to  number of movies that had been watched at the beginning of  week shown on the horizontal axis.

How many movies did Marc watch between  beginning of week 1 and the beginning of week 5? Do not include the unit in your answer.

a. The relationship between time and distance is not an arithmetic sequence, as the rate of change is not constant.

b. The distance is given by: d(n) = 5n².

An arithmetic sequence happens when the change in the output is always the same when the input changes by one, that is, the rate of change is constant.

From the table, the increases when the input(time) increases by one are given as follows:

15, 15, 35, 45.

The increases are not constant, hence the relationship between time and distance is not an arithmetic sequence.

The equation for the distance is given as follows:

d(t) = 0.5gt².

The constant is:

g = 10.

Hence:

d(t) = 5t².

At a time of n seconds, the distance is found replacing the lone instance of t by n, hence:

d(n) = 5n².

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By identifying the vertex of the function, we conclude that it is increasing for:

x > -1

Here we have an absolute value function:

f(x) = |x + 1| - 3

This absolute value function has a positive coefficient, which means that the function opens upwards, so it looks like a regular "V" letter.

The function is increasing when, reading from left to right, we see that the line goes upwards. And for functions like this, this happens for values of x larger than the vertex x-value.

For:

f(x) = |x + 1| - 3

The vertex is at (-1, -3)

Then the function is increasing for x > -1

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Answer:

Round to the nearest tenth.

a. 0.54 + 0.278 = 0.5 +0.3 = 0.8

b. 2.65 + 28. 17= 2.70 + 28.20 = 30.9

c. 3.09 + 2.41 + 9.86 = 3.10+ 2.40 + 9.90= 15.4

d. 15.234 + 1.37 + 0.76 = 15.20 + 1.3 + 0.8 = 17.30

e. 39.18 + 2.48+ 0.84 = 39.20 + 2.5 + 0.8 = 42.5

Round to the nearest whole number.

f. 4.112 + 3.89 = 4 + 4 = 8

g. 23.14 + 7.6 + 3.67 = 23 + 8 + 4= 35

h. 53.2 + 3.08 + 27.51 = 53 + 3+ 28 = 84

i. 11.08 + 17.28 + 92.6 = 11 + 17 + 93 = 121

j. 24.08+ 7.9 + 3.06 = 24 + 8 + 3 = 35

Step-by-step explanation:

Hopefully it's right!!!

The unit rate for 96 kilometers in 3 hours  is 32 kilometer per hour.

What is unit rate?

A unit is one of a particular object. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Given in the question,

96 kilometer in 3 hours,

In order to find unit rate we have to change given values in kilometers per hour.

Do, 96 kilometer = 3 hours

96/3 kilometer = 1 hour

Therefore, unit rate is 32 kilometer per hour.

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For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June

Mean = sum of data / Number of data

The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,

Only the top 200200200 longest streaks worldwide in June will win.

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Answer:

Point-slope: y-5=x-6

Slope intercept: y=x-1

Step-by-step explanation:

y-y1=m(x-x1) Point slope form

y-5=1(x-6)

y-5=x-6

y=x-1