The distance an object falls is directly proportional to the square of the time it falls. A ball falls 144 feet in 3 seconds. How far will an object fall in 4 seconds?

Step-by-step explanation:

The question is wrong. The correct equation is :

[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex]

We know that the equation gives the relation  between temperature readings in Celsius and Fahrenheit.

Therefore, giving that we know the value in Fahrenheit ''F'' we can find the reading in Celsius ''C''. This define a function C(F) that depends of the variable ''F''.

So for the incise (a) we answer Yes, C is a function of F.

For (b) we need to find the mathematical domain of this function. Giving that we haven't got any mathematical restriction, the mathematical domain of the function are all real numbers.

Dom (C) = ( - ∞ , + ∞)

For (c) we know that the water in liquid state and at normal atmospheric pressure exists between 0 and 100 Celsius.

Therefore the range will be

Rang (C) = (0,100)

Now, we need to find the domain for this range. We do this by equaliting and finding the value for the variable ''F'' :

For C = 0 :

[tex]0=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒ [tex]F=32[/tex]

And for C = 100 :

[tex]100=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒ [tex]F=212[/tex]

Therefore, the domain as relating temperatures of water in its liquid state is

Dom (C) = (32,212)

For (d) we only need to replace in the equation by [tex]F=71[/tex] and find the value of C ⇒

[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒

[tex]C=(\frac{5}{9})(71)-\frac{160}{9}[/tex]

[tex]C=\frac{65}{3}[/tex] ≅ 21.67

C(71) = 21.67 °C

a. Yes, C is a function of F.

b. Domain of the function is: ( - ∞ , + ∞)

c. Range of function C is: (0, 100)

the domain of function C is: (32, 212).

d. [tex]\mathbf{C(71) = 21.67^{\circ}C}[/tex]

The domain of a function is the input value, while the range is the corresponding output value.

a. Given the equation of the function as, [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex], this means that, the value of C is dependent on the value of F, therefore, the answer is, Yes, C is a function of F.

b. Since no mathematical restriction was stated, therefore:

Domain of the function is: ( - ∞ , + ∞)

c. Temperature of water in its liquid state ranges between 0 and 100°C, therefore:

Range of function C is: (0, 100)

To find the domain, substitute C = 0 and C = 100, respectively, into  [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex].

Thus:

[tex]0 = \frac{5}{9}(F) - \frac{160}{9}\\\\F = 32[/tex]

[tex]100 = \frac{5}{9}(F) - \frac{160}{9}\\\\F = 212[/tex]

Therefore, the domain of function C is: (32, 212).

d. To find C when F = 71°, substitute F = 71° into  [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex].

Thus:

[tex]C(71) = \frac{5}{9}(71) - \frac{160}{9}\\\\C(71) = \frac{65}{3} \\\\\mathbf{C(71) = 21.67^{\circ}C}[/tex]

Learn more about domain and range of function on:

https://brainly.com/question/10197594

Answer:e=-10

Step-by-step explanation:

-2e-7=13

-2e=20

e=-10

Answer:

The missing numbers are (1000, 100, 10) 3 x 1000 + 2 x 100 + 4 x 10 + 5

Step-by-step explanation:

3 x 1000 = 3000

2 x 100 = 200

4 x 10 = 40

0 + 5 = 5

3000 + 200 + 40 + 5 = 3245

Answer:

jdfsddudnfdhujskvbusduyhd

Step-by-step explanation:

habdaerfukhdskfsubfa

Answer:

For a hexagon, n=6.

Step-by-step explanation:

Answer:

n = 6

Step-by-step explanation:

A hexagon has 6 sides

hello again thanks for the points but why are you putting these questions because you passed the essay?

Answer:

Option C: 15.87 is the correct answer

Step-by-step explanation:

Given

Mean = $47500

SD = $12500

We have to find the probability of having $60000 or more

So,

x = $60000

The z-score will be:

[tex]z-score = z = \frac{x-mean}{SD}\\z = \frac{60000-47500}{12500}\\= \frac{12500}{12500}\\= 1[/tex]

Looking in the z-score table, we get

P(Z<60000) = 0.8413

In order to find the probability P(Z>60000) => 1-P(Z<60000)

= 1-0.8413

=0.1587

Converting into percentage: 0.1587*100 = 15.87%

Hence,

Option C: 15.87 is the correct answer

=======================================================

Explanation:

Check out the diagrams below. I posted two of them. Start with figure 1.

Notice how I've copied the first two columns and placed them on the right side of the matrix.

After that, I've highlighted the diagonals. The numbers in each diagonal grouping multiply together. I've used color coding to show this.

Once you find all those products, you add up the values. Figure 1 shows a result of 42. This isn't the final answer, but it helps us get there.

Figure 2 is a similar idea, but we're doing the off diagonals instead of the main diagonals. The result here is 15.

The last step is to subtract the results found in figures 1 and 2. We get 42-15 = 27 as the final answer.

You could use co-factor expansion as an alternative method. For me, I prefer this method of multiplying diagonals. Unfortunately the method only works for 3x3 matrices.

Answer:

The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)

Step-by-step explanation:

Let us use these facts above to solve the question

∵ The quadratic function f(x) = y has a vertex point (-4, -5)

∵ g(x) = f(x + 2) + 3

→ By using the two facts above

∴ f(x) is translated 2 units to the left

∴ f(x) is translated 3 units up

→ That means the vertex point must move 2 units left and 3 units up

∵ The rule of translation is T (x, y) → (x - 2, y + 3)

∵ The coordinates of the vertex point of f(x) are (-4, -5)

∴ Its image is (-4 - 2, -5 + 3)

∴ Its image is (-6, -2)

∴ The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)

Answer:

u want step by step?

Step-by-step explanation:

Answer: m=7/3

Step-by-step explanation:

the point were at (4,3)(1,-4)

m=y2-y1/ x2-x1

m= -4-3/ 1-4

m= -7/-3

m=7/3

Answer:

0.5

Step-by-step explanation:

Given that:

Irina measured the weight of her dog to be 13 pounds.

The greatest possible error that could have to occur will be the maximum error.

Let assume that the 13th value obtained was rounded between the range of 12.5 → 13.49 to 13 pounds

Then;

The greatest possible error that could have to occur = 13.0 - 12.5 pounds

The greatest possible error that could have to occur = 0.5 pounds

Answer:

0.5

Step-by-step explanation:

EDGE 2020 Unit Test

3(x+x+1)

hope this helps

Answer:

Mercantilism - trading or selling various of goods or products for commission

import - to bring goods in form another source/place

export - send goods to another coutry for money or other items

enumerated article - english colonies could export only to England in the 17th century were sugar, tobacco, cotton and indigo (types of goods)

Navigation Acts - An act that allowed ONLY english ships to bring goods into England, and let north American export their items to England

Dominion of New England - A bunch of England colonies made by king James II of England in 1686 used to tighten British administration of their colonies.

English Bill of Rights - A act that was signed by the law used to ultimately give the parliament power over the monarchy  

Answer:

0.625

62.5%

Step-by-step explanation:

5/8 is 0.625 as a decimal and

0.625*100 is 62.5 as a percent

Answer:

10 miles

Step-by-step

Answer:

There. I looked at the image.

The thing is right because they are all the same.

Step-by-step explanation:

Plz mark as Brainliest!

Answer:the answer is 1

Step-by-step explanation:

2(4y-1)=6

Divid by 2 on both sides

4y-1=3

Add 1 to both sides

4y=4

Divid both sides by 4

Y=0

Complete Question:

How much ₹ will each get if 242.46₹ is distributed equally among the 6 students​

Answer:

Each of the 6 students will get ₹40.41

Step-by-step explanation:

Given

[tex]Amount = 242.46[/tex]

[tex]Students = 6[/tex]

Required

Determine how much each student gets

To do this, we simply divide the total amount by the number of students

i.e.

[tex]Each\ Students = \frac{Amount}{Number\ Students}[/tex]

[tex]Each\ Students = \frac{242.46}{6}[/tex]

[tex]Each\ Student = 40.41[/tex]

Hence, each of the 6 students will get ₹40.41

Answer:

X=8

Step-by-step explanation:

Hope this helps

Answer:

8 pm and 8 am

Step-by-step explanation:

Let us solve the equation

[tex]2|(x-2)|-12=0[/tex]

There is a modulus in the equation this means that one value of the modulus will be positive and the other will be negative

Let us solve for the positive first

[tex]2(x-2)-12=0\\\Rightarrow 2x-4-12=0\\\Rightarrow x=\dfrac{16}{2}\\\Rightarrow x=8[/tex]

Now we add this value with 12 noon

So

[tex]12+8=8\ \text{pm}[/tex]

Let us solve for the negative

[tex]2(-(x-2))-12=0\\\Rightarrow 2(2-x)-12=0\\\Rightarrow 4-2x-12=0\\\Rightarrow x=-\dfrac{8}{2}\\\Rightarrow x=-4[/tex]

So

[tex]12-4=8\ \text{am}[/tex]

The times when the serving time is as advertised is 8 pm and 8 am.

Answer:

True

False

True

Step-by-step explanation:

Interior angles are supplementary

Corresponding angles makes mangle2 and mangle6 the same deg

mangle1 = mangle5 (corresponding angles)

mangle5 = mangle8 (vertically opposite angles)

Answer:

544

Step-by-step explanation:

sure what’s the problem

Answer:

The answer is 7/8.

Step-by-step explanation:

to get the answer you must use inverse operation so 3/4 + 1/8 = 0.875 or 7/8.

If this helped I would appreciate it if you marked me Brainliest. thank you and have a nice day!

Answer:

c = 7/8

Step-by-step explanation:

c - 3/4 = 1/8

First I will make sure that they all have the same denominator.

[tex]\frac{3}{4} * 2= \frac{6}{8}[/tex]

Our new equation will look like:

c - 6/8 = 1/8

Now we will add 6/8 to both sides.

c = 1/8 + 6/8

c = 7/8

Our final answer is:

c = 7/8

Answer:

DF = 17.12

Step-by-step explanation:

From the picture attached,

From ΔABC and ΔEFD,

m∠ABC = m∠EFD = 28°

m∠BAC = m∠EDF = 68°

By AA property of similarity, ΔABC and ΔEFD will be similar.

And their corresponding sides will be proportional.

[tex]\frac{AB}{EF}=\frac{BC}{DF}=\frac{AC}{ED}[/tex]

[tex]\frac{4}{EF}=\frac{BC}{DF}=\frac{2}{8}[/tex]

[tex]\frac{4}{EF}=\frac{1}{4}[/tex]

EF = 16

Now by applying cosine rule in ΔDEF,

DF² = ED² + EF² - 2(ED)(EF)cos(E)

DF² = 8² + (16)² - 2(8)(16)cos(84)°

DF² = 320 - 26.76

DF = √(293.24)

DF = 17.12