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2 years ago

A right triangle has an area of 38 square units

Mathematics

1 answer:

oksian1 [2.3K]2 years ago

6 0

Answer:

1 | 38

2 | 76

3 | 114

5 | 190

1/2 | 19

2/3 | 25.33

Step-by-step explanation:

I am assuming that you need to multiply the area by the scale factors

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In 2014, Chile experienced an intense earthquake with a magnitude of 8.2 on the Richter scale. In 2010, Haiti also experienced a

serg [7]

Answer:

The intensity of the earthquake in Chile was about 16 times the intensity of the earthquake in Haiti.

Step-by-step explanation:

Given:

magnitude of earthquake in Chile = 8.2

magnitude of earthquake in Haiti = 7.0

To find:

Compare the intensities of the two earthquakes

Solution:

The magnitude R of earthquake is measured by R = log I

R is basically the magnitude on Richter scale

I is the intensity of shock wave

For Chile:

given magnitude R of earthquake in Chile = 8.2

R = log I

8.2 = log I

We know that:

$y = log a_{x}$ is equivalent to: $x = a^{y}$

$R = log I$

8.2 = log I becomes:

$I = 10^{8.2}$

So the intensity of the earthquake in Chile:

$I_{Chile} = 10^{8.2}$

For Haiti:

R = log I

7.0 = log I

We know that:

$y = log a_{x}$ is equivalent to: $x = a^{y}$

$R = log I$

7.0 = log I becomes:

$I = 10^{7.0}$

So the intensity of the earthquake in Haiti:

$I_{Haiti} = 10^{7}$

Compare the two intensities :

$\frac{I_{Chile} }{I_{Haiti} } }$

$= \frac{10^{8.2} }{10^{7} }$

= $10^{8.2-7.0}$

= $10^{1.2}$

= 15.848932

Round to the nearest whole number:

Hence former earthquake was 16 times as intense as the latter earthquake.

Another way to compare intensities:

Find the ratio of the intensities i.e. $\frac{I_{Chile} }{I_{Haiti} } }$

$log I_{Chile}$ - $log I_{Haiti}$ = 8.2 - 7.0

$log(\frac{I_{Chile} }{I_{Haiti} } })$ = 1.2

Convert this logarithmic equation to an exponential equation

$log(\frac{I_{Chile} }{I_{Haiti} } })$ = 1.2

$10^{1.2}$ = $\frac{I_{Chile} }{I_{Haiti} } }$

Hence

$\frac{I_{Chile} }{I_{Haiti} } }$ = 16

6 0

2 years ago

These two triangles are similar. What are a and b? Note: the two figures are not drawn to scale. Please help with this!

borishaifa [10]

Answer:

A.36 inches B.150 inches

Step-by-step explanation:

multaply 9×4 for A and 10×15 forB

4 0

3 years ago

Equivalent fractions of 2 6th

marta [7]

2/6 is also equal to 1/3. This is because the GCF of 2 and 6 is 2, and dividing both the numerator and denominator by 2 gets us a simplified fraction of 1/3.

:)

3 0

3 years ago

Read 2 more answers

Suppose f(x) = mx + b. What is the inverse function in terms of m and b?

katrin2010 [14]

Answer:

f^(-1)(x) = (x-b)/m or x/m - b/m

Step-by-step explanation:

f(x) = y = mx + b

To find the inverse function, interchange x and y and solve for y, i.e.

x = my + b

my = x-b

y = (x-b)/m = x/m - b/m

7 0

2 years ago

Lin runs 5 laps around a track in 6 minutes. How many minutes per lap is that? ___minutes How many laps per minute is that? ___

snow_lady [41]

Answer:

a. 1.2 minutes

b. 0.83 laps

c. 25.2 minutes

Step-by-step explanation:

Lin runs 5 laps around a track in 6 minutes.

a. How many minutes per lap is that?

5 laps = 6 minutes

1 laps = x minutes

Cross Multiply

x minute × 5 laps = 6 minutes × 1 laps

x minute = 6 minutes × 1 laps/5 laps

x laps = 1.2 minutes

Hence, it is 1.2 minutes per lap

b. How many laps per minute is that?

6 minutes = 5 laps

1 minute = x laps

Cross Multiply

6 minutes × x laps = 1 minute × 5 laps

x laps = 1 minute × 5 laps/6 minutes

x laps = 0.8333333333 laps

Hence, it is 0.83 laps per minute.

c. If Lin runs 21 laps at the same rate,

5 laps = 6 minutes

21 laps = x minutes

Cross Multiply

x minute × 5 laps = 6 minutes × 21 laps

x minute = 6 minutes × 21 laps/5 laps

x laps = 25.2 minutes

Hence, it takes her 25.2 minutes

3 0

2 years ago