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jasenka [17]
4 years ago
11

What is the range of possible sizes for side x?

Mathematics
1 answer:
jenyasd209 [6]4 years ago
3 0

Answer:

4

Step-by-step explanation:

If a, b, c are three sides of the triangle, then

a+b>c\\ \\a+c>b\\ \\b+c>a

In your case, two sides have measures of 4 units and 8 units, then

4+8>x\\ \\4+x>8\\ \\8+x>4

Hence,

12>x\\ \\x>4\\ \\x>-4

Therefore,

4

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It is estimated that t-weeks into a semester, the average amount of sleep a college math student gets per day S(t) decreases at
goldenfox [79]

Answer:

s(15)= \frac{-3}{2} e^{15^{2} } +9.6

Step-by-step explanation:

Before to getting started ,we have to consider the function which  represents  sleep decline rate S'(t) =-3te^{t^{2} } \\

Since  this function is interpreted in this case as a rate of change, we can deduce this funcion is the first derivative of the function of  average amount of sleep (S(t)).

In order to find S(t), we will integrate S'(t)

\int\limits^ {} -3t3e^{t^{2} } \, dx \\

This case corresponds to intergration by substitution  

Substituting u=x^{2} \\

Computting the differential of u

\frac{du}{dt} =2tdt\\

Now, let's go back to our integral and write it in terms of u, using both definition of u and its defferential.

\int\limits^{}-3te^{u}  \, \frac{1}{2t}du  \\\\\int\limits^{}\frac{-3}{2} e^{u}du\\

The integral  of a exponential function is itself. So the result is:

\frac{-3}{2} e^{u} +c

Now substitute u back in:

\frac{-3}{2} e^{t^{2} } +c

This answer correspond to function of average amount of sleep.

We know that when the semester begins (t=0) , math students sleep an average of 8.1 hours per day so we will use this info in order to find the value of c.

s(0)=\frac{-3}{2} e^{0^{2} } +c=8.1\\\\\frac{-3}{2} +c=8.1

Solve this equation

c=8.1+\frac{3}{2}

c=9.6

Replacing  the value of c on S(t)

S(t)= \frac{-3}{2} e^{t^{2} } +9.6

Now, let's to find the average of amount of sleep   when 15 weeks has elapsed since the start date of the semester.

s(15)= \frac{-3}{2} e^{15^{2} } +9.6

4 0
3 years ago
Will mark brainliest for correct answer !!! <3
jarptica [38.1K]

Answer:

Sudueuiwjdsvwjd dwksnswiwk

4 0
3 years ago
Read 2 more answers
Find the percentage of data points that lie between -3.01 and 2.61?<br> z= (x-u) /o
Marat540 [252]

Answer:

To find the percetage of data points that lie between the points -3.01 and 2.61, on a normal distribution we're going to need the help of a calculator. The result is: 99.42%

Attached you will find the graph that represents the result.

6 0
3 years ago
6x-9=4x-15 fill in the blank math ? please help
Vlad [161]

Answer:

x = -3

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do t one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and equals:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction.

Isolate the x. First, add 9 and subtract 4x from both sides:

6x (-4x) - 9 (+9) = 4x (-4x) - 15 (+9)

6x - 4x = -15 + 9

Combine like terms:

6x - 4x = -15 + 9

2x = -6

Next, divide 2 from both sides of the equation:

(2x)/2 = (-6)/2

x = -6/2

x = -3

x = -3 is your answer.

~

Important things to note:

- PEMDAS is the order of operation, and equals Parenthesis, Exponents (& Roots), Multiplication, Division, Addition, Subtraction.

- If there is an equal sign and the same variable on both sides, you are trying to isolate that variable.

- Remember to follow the division rule. If you are dividing two negative numbers, your answer will be positive. If you are multiplying two negative numbers, your answer will be positive. If you are dividing or multiplying one positive and one negative number, your answer will be negative.

~

3 0
3 years ago
In a basketball game, Tamara made 16 out of 20 shots from the free throw line. What percent of her shots did she make?
Contact [7]
80% because 16/20 is equal to 80/100
4 0
3 years ago
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