Have you ever been on or seen a ride like this at a fair or amusement park? Imagine being strapped into your seat at the bottom of this 350-foot tower, with your feet dangling just above the ground. You make the trip up the tower at a steady rate of 20 feet per second, stop at the top of the tower to hang for a few seconds, then suddenly drop in a free fall for 288 feet!

The trip up the tower is a linear relationship. The height of the riders, h, is equal to the constant rate multiplied by the time, t, since they began the trip up.

The free fall down the tower is a quadratic relationship. The distance from the top to the bottom of the free fall, d, is modeled by this equation, where t is the time since the free fall began and is the initial distance above the bottom of the free fall.
Write an equation representing each relationship.

Enter the correct answer in the box.

The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;

The transformation are a rotation and a translation

A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.

The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units

The correct option is the second option; The transformation are a rotation and a translation

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The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.

In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:

Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)

Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)

Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8

Total sugar consumed = 22/8 + 1/4

Total sugar consumed = (22 + 2)/8

Total sugar consumed = 24/8

Total sugar consumed = 3 units of sugar.

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Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.

To find out how many months it takes to pay off the credit card and the total amount paid including interest, we can use the following steps:

Step 1: Calculate the monthly interest rate

Divide the annual percentage rate (APR) by 12 to get the monthly interest rate.

Monthly interest rate = 14.5% / 12 = 0.145 / 12 = 0.01208 (rounded to 5 decimal places)

Step 2: Set up the equation for the number of months

Let's denote the number of months it takes to pay off the card as 'n'. The monthly payment is $1,200.00, and the initial balance is $3,287.90. The monthly interest rate is 0.01208. The equation for the number of months can be written as:

(1) $3,287.90 ×\((1 + 0.01208)^n\) - $1,200.00 ×\([(1 + 0.01208)^n\) - 1] = 0

Step 3: Solve the equation

To find the value of 'n', we need to solve equation (1). However, solving it algebraically can be complex. Instead, we can use numerical methods like trial and error, or we can use a spreadsheet or a calculator to find the solution.

Using a spreadsheet or a calculator, we can input the values and increment 'n' until we find the point where the equation equals zero.

After performing the calculations, it is determined that it takes approximately 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.

Therefore, the answer to the original question is that it takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.

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Answer:

63diveded by 6

63/6

twenty one divided two is correct ans

21/2

From the word problem and the table, we know that:

Then, we can write and solve the following equation:

Therefore, the unit rate is 64 miles per gallon.

Answer:

\(a=4.1\)

Step-by-step explanation:

The Law of Cosines is given as:

\(a^2=c^2+b^2-2cb\cos A\).

Plugging in given values, we get:

\(a^2=4^2+2^2-2\cdot 4 \cdot 2\cos 78^{\circ},\\a^2=16+4-16\cos 78^{\circ},\\a^2\approx \sqrt{16.673},\\a\approx \fbox{$4.1$}\).

Answer:

The answer for Acellus people is a=4.1

Step-by-step explanation:

Answer:

Step-by-step explanation:

15% of 20 is 3

Answer:

Its the first graph ok kid

Step-by-step explanation:

The equation of the straight line with a slope of 1/2 and a y-intercept of -5 is y = (1/2)x - 5

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) between two expressions.

For example, the equation 2 + 3 = 5 shows that the expression 2 + 3 is equal to the expression 5. In this equation, the expressions on both sides of the equals sign have the same value.

The equation of a straight line can be written in slope-intercept form as:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Given that the slope is 1/2 and the y-intercept is -5, we can substitute these values into the equation above to get:

Therefore,  the equation of the straight line with a slope of 1/2 and a y-intercept of -5 is y = (1/2)x - 5

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\(3(x - 8) - 13x(x - 8) + 3 = 0 \\ 3x - 24 - 13 {x}^{2} + 104x + 3 = 0 \\ - 13 {x}^{2} + 107x - 21 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a } \\ a = - 13 \\ b = 107 \\ c = - 21 \\ x = \frac{ - 107 + - \sqrt{ {107}^{2} - 4(13)( - 21)} }{2( - 13)} \\ x1 = \frac{107 - \sqrt{10357} }{26} \\ x2 = \frac{107 + \sqrt{10357} }{26} \)

Hope it helps

Please give brainliest

Answer:

x = 8

Step-by-step explanation:

If segment BD bisects segment AC, then segment BD divides segment AC into two equal parts.  Therefore, AD = DC.  

According to the given triangle, AD = 8.  

As CD is the same length as AD then DC = 8, so x = 8.

Answer:

8

Step-by-step explanation:

According to question, it the given that segment BD bisects segment into AD and DC .

This means that BD divides AC into two equal parts i.e. AD and DC .

And it is given that , AD = 8 and DC = x .

Since AD and DC are equal, therefore;

x = 8

and we are done!

Answer:

The answer is 1/2. You are correct the slope is 1/2

Step-by-step explanation:

Answer:

h = 2

Step-by-step explanation:

\(-\frac{6}{h}=-3\\\\(-\frac{6}{h})h=-3h\\\\-6=-3h\\\\\frac{-6=-3h}{-3}\\\\\boxed{2=h}\)

Hope this helps.

Answer:

Kindly check explanation

Step-by-step explanation:

Using Pythagoras :

BA = hypotenus

BA = sqrt(2² + 3²)

BA = 3.6

SinA = opposite /hypotenus = 2 / 3.6

CosA = Adjacent / hypotenus = 3 / 3.6

Tan A = opposite / Adjacent = 2 /3

SinB = opposite /hypotenus = 3 / 3.6

CosB = Adjacent / hypotenus = 2 / 3.6

Tan B = opposite / Adjacent = 3 /2

Step-by-step explanation:

Here we have ,

> Hypontenuse ² = 2² + 3² = 4 + 9

> Hypontenuse = √13

> Hypontenuse = 3.6 .

Therefore ,

> SinA = perp /hypotenuse = 2 / 3.6

> CosA = b/h = 3 / 3.6

> Tan A = p / b = 2 /3

> SinB = 3 / 3.6

> CosB = 2 / 3.6

> Tan B = 3 /2

Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.

Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.

What is an Angle?

An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths

To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:

Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.

Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees

Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees

Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

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Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.

Given data ,

a)

Using cost-plus pricing, the selling price is set 20% above the costs.

Selling price=Costs+(Costs x Markup)

Selling price=$100 + ($100x0.20)

Selling price=$100+$20

On simplifying the equation , we get

Selling price=$120

The price charged for the All-Body swimsuit would be$120.

Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.

(b)

Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Price charged to retailer=Target selling price - Desired profit per unit

Price charged to retailer=$100-$20

On simplifying the equation , we get

Price charged to retailer=$80

The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.

(c)

To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Highest acceptable manufacturing cost=Target selling price-Desired profit per unit

Highest acceptable manufacturing cost=$100-$20

Highest acceptable manufacturing cost=$80

Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.

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Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

The comparison of the connection here between variable and its value is a compound inequality. In a compound inequality, a variable is compared across two ranges which may provide the variable's range by satisfying either one or both of the limitations .

The given absolute value inequalities :

|(x+1)/2 - x/2| < 1/2

Removing the modulus sign will for 2 equations:

(x+1)/2 - x/2 < 1/2  and  (x+1)/2 - x/2 < - 1/2

Simplifying each:

(x+1)/2 - x/2 < 1/2  

x/2 + 1/2 - x/2 < 1/2

Both values will get cancelled:

0 < 0

But 0 = 0

and  (x+1)/2 - x/2 > - 1/2

x/2 + 1/2 - x/2 > -1/2

0 > -1 (correct)

here also the terms are getting completely cancelled to

Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

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Complete question:

Find the set of the solutions of the following absolute value inequalities.

|(x+1)/2 - x/2| < 1/2

Answer:

we need a picture of the problem

Step-by-step explanation:

Answer: 3050

formula: \(a_{n} =a_{1}+(n-1)*d\)

80+99*30=3050

Answer:

(2,3 is dilated to 8,12 by a scale factor of 4)

Step-by-step explanation:

multiply 2,3 by numbers until it gets to 8,12, once you multiply by 4 you get 8,12 which means the answer is a scale factor of 4

Answer:

2.200 = 2.2 = 2.20 = 2.2000 = 2.20000...I could go on...

Step-by-step explanation:

Given:

Felix's total credit card balance is described by the following function

\(f(p)=p(1.30)\)

To find:

The total bill plus interest if Felix owes 2500.

Solution:

We have,

\(f(p)=p(1.30)\)

Where \(p\) is the amount Felix owes.

Putting \(p=2500\) in the given function, we get

\(f(2500)=2500(1.30)\)

\(f(2500)=3250\)

Therefore, the total bill plus interest is 3250.

Just flip the signs of co-ordinates by using formula y=>-y

\(\\ \ast\bull\rm\longmapsto Z(-5,-4)\implies Z'=(-5,-(-4))\implies Z'=(-5,4)\)

\(\\ \ast\bull\rm\longmapsto Y(-3,-4)\implies Y'=(-3,-(-4))\implies Y'=(-3,4)\)

\(\\ \ast\bull\rm\longmapsto X(-5,-1)\implies X'=(-5,-(-1))\implies X'=(-5,1)\)

Answer:

• Reflection about the x-axis, consider a point A

\({ \tt{A(x,y) \: \dashrightarrow \:A {}^{i} ( - x, \: y) }}\)

• Therefire, coordinates of X'

\( \dashrightarrow \: { \boxed{ \tt{X( - 5, \: - 1) = X'(5, \: - 1)}}}\)

Answer:

The median is usually preferred in these situations because the value of the mean can be distorted by the outliers.

Step-by-step explanation:

Answer:

If there is an outlier you should report the median. This is because the value of a mean can be distorted by the outliers. So, you can use the median when the distribution is not symmetrical.  

Step-by-step explanation:

Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

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