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tangare [24]
3 years ago
15

A team of storm enthusiasts collected data to show the relationship between the time between seeing lightning and then hearing t

hunder, and how far away you are from the lightning. The results are in the graph below.
What is the constant of proportionality expressed as miles per second?
Answer: The constant of proportionality is _____________miles per second.

Mathematics
1 answer:
never [62]3 years ago
3 0

Answer:

Proportionality constant = \frac{1}{5}

Step-by-step explanation:

From the graph attached,

Data set representing the relation between seeing lightning and the hearing thunder is,

{(15, 3), (25, 5), (35, 7), (45, 9)}

Since, Distance from lightening (d) ∝ Time between lightening and thunder (t)

d = kt

Here k = proportionality constant

k = \frac{d}{t}

From the data set one point is (15, 3).

k = \frac{3}{15}

k = \frac{1}{5} miles per second

Therefore, proportionality constant is \frac{1}{5} miles per second.

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What are the potential solutions of log4x+log4(x+6)=2?
lions [1.4K]

The potential solutions of log_4x+log_4(x+6)=2 are 2 and -8.

<h3>Properties of Logarithms</h3>

From the properties of logarithms, you can rewrite logarithmic expressions.

The main properties are:

  • Product Rule for Logarithms - log_{b}(a*c)=log_{b}a+log_{b}c
  • Quotient Rule for Logarithms - log_{b}(\frac{a}{c} )=log_{b}a-log_{b}c
  • Power Rule for Logarithms - log_{b}(a^c)=c*log_{b}a

The exercise asks the potential solutions for  log_4x+log_4(x+6)=2. In this expression you can apply the Product Rule for Logarithms.

                                  log_4x+log_4(x+6)=2\\ \\ x*(x+6)=4^2\\ \\ x^2+6x=16\\ \\ x^2+6x-16=0

Now you should solve the quadratic equation.

 

 Δ=b^2-4ac=36-4*1*(-16)=36+64=100. Thus, x will be x_{1,\:2}=\frac{-6\pm \:\sqrt{100} }{2\cdot \:1}=\frac{-6\pm \:10}{2}. Then:

x_1=\frac{-6+10}{2}=\frac{4}{2} =2\\ \\ \:x_2=\frac{-6-10}{2}=\frac{-16}{2} =-8

The potential solutions  are 2 and -8.

Read more about the properties of logarithms here:

brainly.com/question/14868849

4 0
2 years ago
4. Order the set of numbers from least to greatest: 164.8. 814 7 (5 points) 2 o 15 V64 88.14 V64.8 81 2 3. 814 64 o V64 . 3. 814
kirza4 [7]

Answer:

For the answer to the question above,

the Order the set of numbers from least to greatest: square root 64, 8 and 1 over 7, 8.14 repeating 14, 15 over 2

15 over 2, square root 64, 8 1 over 7, 8.14 repeating 14.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the probability that a randomly drawn marble from bag is green. Given that it is not red?
tatiyna

Answer:

The probability is 0.2, or 20%.

Step-by-step explanation:

A probability is the ratio of the number of relevant outcomes and the number of all possible outcomes. If we know that the marble drawn is not red, the number of possible outcomes N is

N = (number of blue marbles) + (number of green marbles) = 25

and the number of relevant outcomes (marble being green) is n:

n = (number of green marbles) = 5

So, the probability is

P = n / N = 5 / 25 = 1 / 5 or 0.2, or 20%

6 0
3 years ago
What is the value of x?<br><br> a. 71°<br> b. 142°<br> c. 152°<br> d. 76°
alexgriva [62]
The sum of the measures of the angles of a triangle is 180 degrees.
An isosceles triangle has two congruent sides.
The angles opposite the congruent sides are congruent.
Just like the bottom left angle measures x, the bottom right angle also measures x.

x + x + 38 = 180

2x + 38 = 180

2x = 142

x = 71
3 0
3 years ago
Read 2 more answers
A log splitter can split 6/5 cords of wood in 4/5 of an hour. Complete the unit rate by setting up a complex fraction and simpli
Digiron [165]

Answer:

1½ cords per hour

Step-by-step explanation:

A log splitter can split 6/5 cords of wood in 4/5 of an hour.

To find a unit rate, we divide the quantity of cords of wood by the time.

This gives us the complex fraction.

\frac{ \frac{6}{5} }{ \frac{4}{5} }

This is the same as

\frac{6}{5}  \div  \frac{4}{5}

To divide two fractions, we multiply by the reciprocal of the second fraction.

\frac{6}{5}   \times   \frac{5}{4}

\frac{3}{1}   \times   \frac{1}{2}

This simplifies to:

\frac{3}{2}  = 1 \frac{1}{2}

The unit rate is 1.5 cords per hour

3 0
2 years ago
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