Consider the inequity

(a) Function formula of f(t) in terms of t is,  f(t)=17-1.3t

(b) The domain of the function is 0 to 13.076.

(c) The range is 0 to 17

(d) 9.38 is the value exist for f(t)=4.8

(e) The correct option of this sub part is How many hours since the candle was lit when it is 4.8 inches long.

An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Also, the input and output are somehow connected.

The initial length of the candle is 17 inch. It also given that, it burns with a constant rate of 1.3 inches per hour.

After one hour since the candle was lit, the length of the candle will be (17 – 1.3) = 15.7 inch.

After two hour, since the candle was lit, the length of the candle will be (15.7-1.3) = 14.4 inch.17 - 2(1.3) can be used to represent the candle's length after two hours.

Hence, the length of the candle after t hours when it was lit can be represented by the function, f(t)=17-1.3t

Putting f(t)=0 in the equation, we get

0=17-1.3t

-17=-1.3t

t=13.076

Hence, The domain of the function is 0 to 13.076

Putting t=0 in the equation, we get

f(t)=17-1.3t

f(t)=17-1.3×0

f(t)=17

Hence, The range is 0 to 17.

putting f(t)=4.8 in the equation we get

4.8=17-1.3t

4.8-17=-1.3t

t=9.38

Hence, the value of t for f(t) =4.8 is 9.38.

When the candle was 4.8 inches long, then time taken to lit from the equation is 9.38 hours.

Hence, The correct option of this sub question is  How many hours since the candle was lit when it is 4.8 inches long.

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A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!

Answer:

24 bows

Step-by-step explanation:

In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.

Proportion shows the relative number of objects or people in the whole.

Proportions are ratios equated to each other.

They are expressed as fractional values, in decimals, percentages, and fractions.

The percentage of Boomers who want to shop in-store = 84%

The sample size of the Boomer Generation = 75

The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)

Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.

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The Reflexive Property is a property of equality that states that anything is equal to itself. This property is true for numbers, shapes, angles, and more.

In the context of geometry, the Reflexive Property of Congruence states that any geometric figure is congruent to itself. This includes angles, segments, triangles, and other polygons.

So, when you see "<J ≅ <J", it's saying that angle J is congruent to angle J, which is an application of the Reflexive Property. In other words, any angle is congruent (equal in measure) to itself.

The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.

In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.

The next choice shows the triangle's side length:

The point is,

The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.

Using Pythagoras' Theorem.

Use the formula:

a² + b² = c²

For 4, 8, 11

4, 8, 11

4² + 8² = 16 + 64 = 80

11² = 121

80 is not equal to 121 it cann ot form a right triangle

For 6, 8, 13

6² + 8² = 36 + 64 = 100

13² = 169

100 is equal to 169 - 69 can form a right triangle

For √3, √5, 8

(√3)² + (√5)² = 3 + 5 = 8

8² = 64

8 is equal to 64 cannot form a right triangle

For √3, √13, 4

(√3)² + (√13)² = 3 + 13 = 16

4² = 16

16 is equal to 16 can form a right triangle

In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.

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Answer:

Option (3)

Step-by-step explanation:

\(\text{tan}(\frac{\theta}{2})=\text{sin}\theta\)

\(\text{tan}(\frac{\theta}{2})=2\text{sin}{\frac{\theta}{2}} \text{cos}(\frac{\theta}{2})\)

\(\frac{\text{sin}\frac{\theta}{2}}{\text{cos}\frac{\theta}{2}} =2\text{sin}{\frac{\theta}{2}}\text{cos}(\frac{\theta}{2})\)

\(\text{sin\frac{\theta}{2}}=2\text{sin}{\frac{\theta}{2}}\text{cos}^2(\frac{\theta}{2})\)\(\text{sin\frac{\theta}{2}}=2\text{sin}{\frac{\theta}{2}}\text{cos}^2(\frac{\theta}{2})\)\(\text{sin}\frac{\theta}{2}=2\text{sin}{(\frac{\theta}{2})}\text{cos}^2(\frac{\theta}{2})\)

\(\text{sin}\frac{\theta}{2}-2\text{sin}{(\frac{\theta}{2})}\text{cos}^2(\frac{\theta}{2})=0\)

\(\text{sin}\frac{\theta}{2}[1-2\text{cos}^2(\frac{\theta}{2})]=0\)

\(\text{sin}\frac{\theta}{2}=0\) ⇒ \(\theta=0\)

\(1-2\text{cos}^2(\frac{\theta}{2})=0\)

\(\text{cos}(\frac{\theta}{2})=\frac{1}{\sqrt{2}}\)

\(\frac{\theta}{2}=\frac{\pi}{4}\)

\(\theta=\frac{\pi}{2}\)

Therefore, θ = 0 and \(\frac{\pi}{2}\) are the solutions.

Option (3) will be the answer.

Answer:

105.12

Step-by-step explanation:

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Answer:

The vertex is (-5, -2)

Step-by-step explanation:

y = 2(x + 5)^2 - 2

The vertex form of a parabola is

y =a(x-h)^2 +k  where (h,k) is the vertex

y = 2(x  -  -5)^2 - 2

The vertex is (-5, -2)

Answer:A temperature that is below zero is negative. Integers are positive and negative whole numbers.

Step-by-step explanation:

Give me 5 star please

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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\(-3x = -5y -8~~~....(i) \\\\6x -3y = -5 ~~......(ii)\\\\\text{Multiply equation (i) by 2 and do (i) + (ii):}\\\\2 \cdot (-3x) + 6x -3y = 2(-5y-8) + (-5)\\\\\implies -6x +6x -3y = -10y -16 -5 \\\\\implies -3y = -10y -21\\\\\implies -3y +10y =-21\\\\\implies 7y = -21 \\\\\implies y = -\dfrac{21} 7 = -3\\\\\text{Substitute}~y =-3~ \text{in equation (ii):} \\\\6x - 3(-3) = -5\\\\\implies 6x +9 = -5\\\\\implies 6x = -5 -9 = -14\\\\\implies x = -\dfrac{14}6 = - \dfrac{7}3\\\)

\(\text{Hence}~ (x,y) = \left(-\dfrac 73, -3 \right)\)

The domain of the function f(t) is best described as 608 ≤ t ≤ 620

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

Rate = 2.5 kilograms per hour

Mass of the car (including the fuel) = 1550 kg

Mass of the car (not including the fuel) = 1520 kg

Calculate the times using the rate and the masses above

So, we have the following representations

Time 1 = 1550/2.5

Time 1 = 620

Time 2 = 1520/2.5

Time 2 = 608

Express as an interval

608 ≤ t ≤ 620

Hence, the domain is 608 ≤ t ≤ 620

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Answer/Step-by-step explanation:

The length of the boxes and whiskers of a box plot tells us more about the spread the data being represented is and as well as the shape of the spread.

Invariably, if the length of the left box and left whiskers is of the same length as the right box and right whiskers, this implies that the distribution of the data point is close to being symmetric, or approximately symmetrical.

Answer:

£50-£y or 50-y

Step-by-step explanation:

remaining = initial - taken

remaining = 50 - y

Answer:

1 is the answer

Step-by-step explanation:

a-b+c       Substitute values into the equation

4-2+(-1)

2+(-1)

2-1

1 Answer

The value of: 1) a - b + c is, 1 is the solution.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

a=4 b=2 and C=-1

now,

a-b+c      

Substitute values into the equation

we get,

4-2+(-1)

=2+(-1)

=2-1

=1  (Answer)

Hence, The value of: 1) a - b + c is, 1 is the solution.

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Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

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Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer: I believe that by helping or answering others you can get get questions, but I do know there is a limited amount of questions being able to ask before paying monthly. Hope this helps

Answer:

What you have to do is answer peoples question to gain more

Step-by-step explanation:

Answer: 1200= 4s+h

Step-by-step explanation: solve! I don’t know how many equations

Answer:

Answer:

There would be 2 sliders and 8 hotdogs.

Step-by-step explanation:

1 slider= 200 cal

2 sliders= 400 cal

2x4= 8

1 mini hotdog= 100 cal

8 mini hotdogs= 800 cal

800 cal + 400 cal = 1200 cal

Answer:

just 1

Step-by-step explanation:

there can be only one

The person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

To determine how high up the person was shot, we can use the principles of projectile motion and the dimensions of the blood drop. Since we have the horizontal distance and the dimensions of the blood drop, we can assume that the drop followed a parabolic trajectory.

First, let's convert the distance from feet to meters for consistency. 5.1 feet is approximately 1.554 meters. Now, we need to calculate the time of flight. Since there is no information about the drop's initial velocity or angle, we cannot calculate the exact time. However, we can estimate it by assuming a reasonable range of velocities.

Let's assume the drop was traveling between 5 and 20 meters per second. With a distance of 1.554 meters, the estimated time of flight would be between 0.0777 and 0.311 seconds.

Next, we need to calculate the vertical displacement. We have the dimensions of the blood drop, with a width of 0.8 mm and a length of 2.1 mm. Assuming the drop maintained a spherical shape while in motion, we can take the average of the width and length to find the diameter. So, the diameter is approximately 1.45 mm, which is 0.00145 meters.

Using the estimated time of flight, we can calculate the vertical displacement using the formula:

Vertical displacement = (1/2) * g * t^2

where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the estimated values, the vertical displacement ranges from 0.0038 to 0.0301 meters (3.8 to 30.1 mm).

Therefore, based on the given information, the person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

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Answer:

(0, 2)

Step-by-step explanation:

Answer:

The last one:

30(0.5b + 3.75)