Question 5 (05.05)Based on the graph, what is the initial value of the linear relationship?

As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,

(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.

(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.

As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.

We  are required to determine the correct time domains for four different situations, by observing the plotted graph.

Part (A) is to determine the correct time domain where the water balloon's height remains the same.

From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

Part (B) is to determine the correct time domain where the height of the water balloon is increasing.

From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.

Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.

From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.

Since, [(30/1) > (10/0.5) > (30/3)],

Or, [30 > 20 > 10],

Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).

Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.

Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.

Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.

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Answer: 90 degree

Step-by-step explanation: the diameter of a circle compounds to an inscribed angle of  90 degree

On Solving inequality  40 + 12.5 v ≥ 225, we get solution v ≥ 14.8. It means Autumn can earn movie ticket from 15 visits.

An inequality is a statement that compares two expressions using ≤, ≥, <, > .

We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.

When we multiply both sides of the inequality with a positive number then the sign of the inequality does not change, but when we multiply both sides by an negative number then the sign of inequality reverses.

Given that Autumn receives 40 points for signing up and 12.5 points for each visit to the theatre.

Let the number of visits to the theatre be v

Then points earned by v visits = v × 12.5 = 12.5 v

Total points earned = signing up points + points of v visits

⇒ Total points earned  = 40 + 12.5 v

For earning a free movie tickets the total points must be at least 225 or greater than or equal to 225

Then the inequality becomes:

40 + 12.5 v ≥ 225

Subtracting 40 from both sides

⇒ 12.5v ≥ 225-40

⇒12.5v ≥185

Multiplying both sides by 1/12.5

⇒ v ≥ 185/12.5

⇒ v ≥ 14.8

∴ The number of visits must be greater than or equal to 14.8 or nearest integer 15

∴After 15 visits, Autumn will earn a free  movie ticket

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Answer:

+11y³ +y² -5x²

Step-by-step explanation:

-3y³-5y²+7x³+y²-5x²+7y³+5y²

= +11y³ +y² -5x²

Using the uniform distribution:

a) The height of the density function which is f(x) is [tex]\frac{1}{12}[/tex]

We know that for a uniform distribution we have two bounds, namely a and b. The probability or likelihood of finding a value of at lower than x is given by the following formula:

P (X < [tex]x[/tex]) = [tex]\frac{x-a}{b-a}[/tex]

Now where we have been mentioned that the two bounds are as follows:

a = - 5 (lower bound)

b = 7 (upper bound)

a) To find the height (h) of the density function we use the below given formula:

h = [tex]\frac{1}{b-a}[/tex]

Putting here the values of a and b we get the height as,

∴ h = [tex]\frac{1}{7-(-5)}[/tex]

⇒ h = [tex]\frac{1}{7+5}[/tex]

⇒ h = [tex]\frac{1}{12}[/tex]

Hence, the height of the density function f(x) is [tex]\frac{1}{12}[/tex]

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Answer: 0.01 more

Step-by-step explanation:

60% sure!

Answer:

-2

Step-by-step explanation:

5-7 where be -2 because 7 is More powerful than 5 so 7 push 5 all the way back to -2

The correct answer to the question would be:

D. The manufacturer tests every 500th smartphone off the production line.

Answer:

y=3/5x-7

Step-by-step explanation:

when lines are parallel they have the same slope and the slope of the first line was 3/5

Hello!

Let's consider the equation given:

 ⇒the coefficient before the x is the slope

When lines are parallel:

 ⇒the slopes are equal

Since the line given has a slope of 3/5

 ⇒ the line parallel is [tex]y = \dfrac{3}{5} x - 7[/tex]    <==Answer

Hope that helps!

Answer:

u = -40

Step-by-step explanation:

20 = -u/2

multiply both sides by 2:

2(20) = 2(-u/2)

-u = 40

divide both sides by -1:

-u/-1 = 40/-1

u = -40

Answer:

Step-by-step explanation:

u will have 1 niche of water in 2 hours

The following equations can be changed so that the subject is seen as x through the equational changes and basic mathematical concepts.

An equation that is said as a mathematical statement and the one that is that is made up of two expressions connected by an equal sign.

In its simplest form as per algebra, the definition of a provided equation is a mathematical statement that is thus showing that two mathematical expressions are seen to be equal.

There are a total of three major forms of linear equations that can be said as point-slope form, standard form, and slope-intercept form.

In this question,

1) y = kx + m

x = (y-m) / k

2) y = x/k + m

x = (y-m) k

3) y = tx + mn

x = (y - mn) / t

4)n = r(x+t)

x = (n/r) - t

5) (x + t)/h = b

x = bh - t

6) h(x + n) = a

x = a/h - n

7) b(x-d) = q

x = bq +d

8) tx-n =a

x = (a+n) / t

A mathematical equation which represents the relationship of two expressions on either side of the sign. It mostly has one variable and equal to symbol.

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Answer:

[tex]M (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

1. distribute through the parentheses

8x-6=2

2. Combine like terms

8x=8

3. Divide by 8

x=1

Hello!

Let's solve:

  [tex]\text{Copy down the equation}\\2(4x-3)=2\\\\\text{Multiply 2 into the equation in the parentheses}\\8x - 6 = 2\\\\\text{Add 6 to both sides of the equation}\\8x-6+6=2+6\\8x=8\\\\\text{Divide by 8 on both sides}\\\dfrac{8x}{8} =\dfrac{8}{8} \\\\x=1[/tex]

Answer: x = 1

Hope that helps!

The second letter is B, the eighth letter is H and the third letter is C

When we start to count from left to right starting from letter A,

               1st letter is  A

                2nd letter is B

                3rd  letter is C

                4th letter is  D

                5th letter is  E

                6th letter is F

                7th  letter is G

                8th  letter is H

                9th letter is  I

               10th letter is J

               11th  letter is K

               12th letter is L

               13th letter is M

               14th letter is N

               15th letter is  O

               16th letter is  P

               17th letter is Q

               18th  letter is R

               19th  letter is S

               20th letter is  T

               21st  letter is U

Thus,

         Second letter is  B

         Eighth letter is    H

         Third letter is      C

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The equation of the line that passes through (0, -3) and parallel to a line with slope 2 is y = 2x - 3

From the question, we are to determine the equation of the line.

From the given information, the line passes through (0, -3) and is parallel to a line with slope 2.

NOTE: If two line are parallel, then their slopes are equal

Thus,

The slope of the line is 2

Using the point-slope form of the equation of a line,

y - y₁ = m(x - x₁)

Where m is the slope

Then,

y - -3 = 2(x - 0)

y + 3 = 2x

y = 2x - 3

Therefore,

The equation is y = 2x - 3

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The interest rate for the loan is 20%.

The interest rate represents the percentage or the proportion of the interest over the total loan.

The interest is the finance charge for the credit extended by the pay lender.

The interest rate, R = Interest x 100/Principal x Time, where the simple interest equals principal x rate x time.

The total amount borrowed = $500

The total finance charge = $100

The period of the loan = 1 year

The interest rate

= $100 x 100/$500 x 1

= 20%

Thus, the pay lender is charging an interest rate of 20% per annum.

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What is the interest rate?

By performing a change of units, we will see that the distance from Los Angeles to Honolulu is 2,238 mi, so the correct option is D.

We know that the distance from Los Angeles to Honolulu is 1,946 nautical miles long.

And we know the relation:

1 nautical mile ≈ 1.15 miles

So we just ant to perform a change of units, to do so we can write:

1,946 nautical miles long = 1,946*(1.15 miles) = 2,238 mi

So the distance from Los Angeles to Honolulu is 2,238 miles.

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Answer: 11/3

Step-by-step explanation:

1. Distribute the 8: 16x + 24x + 16 = 4x + 148

2. Combine like terms: 40x + 16 = 4x + 148

3. Get the x by itself: 36x = 132

4. Divide by 36: x = 11/3

I have no : idea

Step-by-step explanation: WHat grade is this for I might be able to help you.

Option D is correct.

Extraneous information means irrelevant or unrelated to the problem or issue.

In this question, Samuel's Age is not a matter of concern and totally unrelated to the money he earns by mowing the lawn and cleaning the room

Charlie paid $13.2 for the shorts after discount

The regular price of pair of shorts = $24

Discount during the sale on shorts = 45%

Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the rebate is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price reduction, is known as the List price or Marked Price.

Amount of discount = 45% of 24

= 45/100*24

= 10.8

Amount of shorts after discount = Regular price of shorts - Discount on shorts

= 24 - 10.8

Amount after discount = $13.2

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The value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function is:

f(x) = 3(1 - x - 2x²)/2

It is required to find the value of f(-2)

Plug x = -2

f(-2) = 3(1 - (-2) - 2(-2)²)/2

f(-2) = 3(1 + 2 - 8)/2

f(-2) = 3(-5)/2

f(-2) = -15/2

Thus, the value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.

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The ratio of the blue fish in the small tank to red fish in the large tank is 10 to 69.

Ratio is the relationship between two quantities.

Let x : y = ratio of the blue fish in the small tank to red fish in the large tank

Hence, there are x blue fish in the small tank for every y red fish in the large tank.

If in each tank, the ratio of red fish to blue fish is 3 to 4, then in each tank, in terms of x and y, the ratio is:

small tank :

red : blue = 3 : 4 = (3/4)x : x

large tank :

red : blue = 3 : 4 = y : (4/3)y

If the ratio of fish in the large tank to fish in the small tank is 46 to 5, then

(y + (4/3)y) : ((3/4)x + x) = 46 : 5

Simplifying the proportion,

(y + (4/3)y) : ((3/4)x + x) = 46 : 5

(7/3)y : (7/4)x = 46 : 5

(161/2)x = (35/3)y

x/y = (35/3) / (161/2)

x/y = x : y = 10 : 69

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The domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation for the function is:

f(x) = 3x⁵

The domain of the function: D = all real number

The range of the function: R = all real number

x-intercept = 0

y-intercept = 0

Increasing interval: x ∈ [0, ∞)

Decreaing interval: x ∈ (-∞, 0]

Symmetry = The function is not symmetric

End behavior:

x → ∞, y →∞

x → -∞, y → -∞

Thus, the domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

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The length of the minor axis of the ellipse described by the equation in the task content is; 6.

It follows from the task content that the length of the minor axis of the ellipse is to be determined.

Since the equation given in the task content is;

x² + 4y² = 36.

By dividing both sides by 36; we have;

(x²/36) + (y²/9) = 1

By expressing the denominators as squares; we have;

x²/6² + y²/3² = 1

By comparison of the equation above with the standard equation of an ellipse; x²/a² + y²/b² = 1 where; a = major axis and b = minor axis.

a = 6 and b = 3.

Ultimately, the length of the minor axis is given by; 2b = 2 × 3 = 6.

The length of the minor axis is therefore; 6.

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The value of a machine at the end of t years with a rate of depreciation, r is given by the function:

It is required to find the age of a machine that originally costs $13,500, but is now valued at $10,419 and has a rate of depreciation of 0.12.

To do this, substitute C=13500, V=10419, and r=0.12 into the function:

Solve the resulting equation for t:

Take the Logarithm of both sides:

Hence, the machine is about 2.03 years.

The machine is about 2.03 years.

Paloma's median practice time would be = 26.5

Median is defined as the middle of a set of data which will be selected after the data has been grouped in an ascending or descending order.

The list to track the number of minutes Paloma spent practicing piano in ascending order include the following:

18, 23, 24, 24, 25, |25, 28,| 28, 30, 32, 32, 35

The middle figures are 25 and 28 which should be added and divided into two.

That is;

25 + 28 = 53/2

= 26.5

Therefore, the median practice time for Paloma = 26.5

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Answer:

3

Step-by-step explanation:

Since the graphs aren't parallel due to not having the same slope we can assume they will intercept once