Answer:
d = 256 ft.
Step-by-step explanation:
The distance an object falls is directly proportional to the square of the time it falls.
First, we name the variables.
Let d= the distance.
t= time
Write the formula for direct variation, where y varies directly with the square of x.
y=kx2
We will use d in place of y and t in place of x.
d=kt2
Substitute the given values for the variables.
d=144whent=3144=k⋅32
Solve for the constant of variation.
144916=k⋅99=k
Write the equation that relates d and t.
d=kt2
Substitute in the constant of variation.
d=16t2
Find d when t=4.
Write the equation that relates d and t.
d=16t2
Substitute the given value for t.
d=16⋅42
Simplify.
d=256
An object will fall 256 feet in 4 seconds.
The required distance fall by fall in 4 seconds is 192 feet.
Given that,
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 is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
here,
The rate of fall of the ball = 144 / 3
= 48 feet second
Now distance fall by the ball in 4 seconds = 48 * 4 = 192 feets.
Thus, the required distance fall by fall in 4 seconds is 192 feet.
Learn more about arithmetic here:
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The equation C = 5 9 F − 160 9 gives the relation between temperature readings in Celsius and Fahrenheit.
(a) Is C a function of F? Yes, C is a function of F. No, C is a not a function of F.
(b) What is the mathematical domain of this function? (Enter your answer using interval notation. If C is not a function of F, enter DNE.)
(c) If we consider this equation as relating temperatures of water in its liquid state, what are the domain and range? (Enter your answers using interval notation. If C is not a function of F, enter DNE.) domain range
(d) What is C when F = 71°? (Round your answer to two decimal places. If C is not a function of F, enter DNE.) C(71) = °C
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]
Range and Domain of A FunctionThe 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:
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I really need help can someone please understand
sure what’s the problem
-3 = 5 - 4x in algebra tiles
c - 3/4 = 1/8
Please answer
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
Help look at the image
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!
easy question solve and get 10 points 3245=3×100__×2×__×__4×__+5
the same number goes in each of the blank space to make the number sentence correct what is the missing number
options
10
100
311
1000
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
PLEASE SOMEONE I NEED IT ASAP DUE AT 6:30!!!
Someone please....
Please define the following terms:
mercantilism, import, export, enumerated article, legislature, indentured servant, Navigation Acts, Dominion of New England, English Bill of Rights.
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
business success edge
hello again thanks for the points but why are you putting these questions because you passed the essay?
The following statements as true or false.
a. m23 + m25 = 180
b. m22 + m26 = 180
C. m28 = m_1
Which ones are true and false plzzzzz this is urgent
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)
Household incomes are normally distributed with a mean of $47,500 and a standard deviation of $12,500. What is the probability of having incomes of $60,000
or more?
a) 2.50%
O b) 5.0096
C) 15.87%
od) 7.8096
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
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (-4, -5)(−4,−5). What is the vertex of the function defined as g(x)=f(x+2)+3g(x)=f(x+2)+3?
Answer:
The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)
Step-by-step explanation:
If the graph of the function f(x) is translated h units to the left, then its image g(x) = f(x + h)If the graph of the function f(x) is translated k units up, then its image g(x) = f(x) + kLet 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)
Please find the x, thank you!
Answer:
X=8
Step-by-step explanation:
Hope this helps
what are the terms in the expression 2x-4y+8?
A.) 8
B.) 2x and 4y
C.) 2x, -4y, and 8
D.) 2, 4, and 8
P.S PLS HELP DUE TODAY!!!
Write the fraction 5/8 as a percent and as a decimal.
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
Jan ran for 1 hour and 15 minutes. If Jan can run a mile in 7.5 minutes, how many miles did she run? There are 60 minutes in an hour
Answer:
10 miles
Step-by-step
(07.03)
What is the value of y in the equation 2(4y - 1) = 6? (4 points)
0
Ob
1
Ос
6
Od
8
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
What is the length of segment DF?
B
4/28
1
68°
C
2
А A
2
3
8
4
68°
28°
F
5
Type your answer.
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
how much ₹ each will get if 242.46₹ is distributed equally among the students
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
What are the partial products that result from multiplying 17*32?
Answer:
544
Step-by-step explanation:
what is the determinant ?
PLS RESPOND IM IN DEEP NEED
=======================================================
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.
What is the greatest possible error if Irina measured the weight of her dog as 13 pounds?
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 -2e -7 = 10
e =
Solve for e
Answer:e=-10
Step-by-step explanation:
-2e-7=13
-2e=20
e=-10
Turn the sentence into an expression
5.three times the sum of two consecutive
integers
3(x+x+1)
hope this helps
Explain to me in words how you would find the slope of this line and explain your answer
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
pls help what is 1+2
what is n in a hexagon
Answer:
For a hexagon, n=6.
Step-by-step explanation:
Answer:
n = 6
Step-by-step explanation:
A hexagon has 6 sides
4.3.AP-10
Question Help
On a team, 7 girls and 5 boys scored a total of 91 points. The difference between the number of points scored by the 7 girls and the number of points scored by the
5 boys is 21. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each
boy
Answer:
u want step by step?
Step-by-step explanation:
Joan planted 150 tulip bulbs, but only 20% of them bloomed. How many tulips
bloomed?
Ben’s favorite deli says the average serving time is 12 minutes. Ben notices that the wait time at the deli varies at different times of day, before and after noon. His observations when the wait time is as advertised can be represented by the equation 2|x − 2| − 12 = 0. Solve for the times when the serving time is as advertised, relative to noon. Group of answer choices (THERES ALOT OF ANSWERS BE PREPARED) SELECT ALL THE ANSWER CHOICES.
4pm,
8pm,
9am,
3pm,
noon,
11am,
6pm,
9pm,
7am,
1pm,
2pm,
5pm,
10pm,
10am,
8am,
7pm,
6am,
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.
Sean has some candy bars that he wants to give away. He is going to give each person 1/8 of a bar, and he has 2 3/4 bars to give away
how many people will get candy?
Answer:
jdfsddudnfdhujskvbusduyhd
Step-by-step explanation:
habdaerfukhdskfsubfa