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Alla [95]
4 years ago
10

Given that DE = 75 inches what is the length of EF ?

Mathematics
1 answer:
vesna_86 [32]4 years ago
5 0

Answer:

<h2>61.19 inches</h2>

Step-by-step explanation:

Use the sine law:

\dfrac{DE}{\sin(\angle F)}=\dfrac{EF}{\sin(\angle D)}

We have:

DE=75\ in\\\\m\angle F=75^o\to\sin75^o\approx0.9659\\\\m\angle D=52^o\to\sin52^o\approx0.788

Substitute:

\dfrac{75}{0.9659}=\dfrac{EF}{0.788}          <em>cross multiply</em>

0.9659EF=(75)(0.788)

0.9659EF=59.1          <em>divide both sides by 0.9659</em>

EF\approx61.19

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Which equation represents an exponential function with the initial value of 500?
EastWind [94]

Answer:

A exponential equation is usually of the form f(x)=a (1±r)ˣ.

Our limitation: Initial Vale is 500.

Let's look at our options:

#1- Initial Value of 1000  --- WRONG!

#2- Initial Value of 1000  --- WRONG!

#3- Initial Value of 500 ---- Maybe

#4- Initial Value of 500 ---- Maybe

Let's look at 3 and 4:

#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!

#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!

Hence, #3 Is correct!

Step-by-step explanation:

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5 0
2 years ago
Can anyone help me with this math question
Lynna [10]

Answer:

89 seats are not being used

Step-by-step explanation:

You subtract the seats being used by teachers

342 - 75 =267

Change 2/3 into a percentage = 66.6%

Find 66.6% of 267= 177.8 (I rounded up to 178)

Then subtract 177.8/178 from 267 to find the amount of seats not being used.

The amount of seats not being used would come down to 89 seats.

I hope this helps!

4 0
3 years ago
Find all solutions in the interval [0, 2π). tan x + sec x = 1
svp [43]
Use the identity 
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tan x + sqrt( 1 + tan^2 x) = 1
sqrt ( 1 + tan^2 x) = 1 - tan x
1 + tan^2 x  = 1 + tan^2x - 2 tan x
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tan x = 0 

x =  0, π 
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6 0
3 years ago
Write an equation in slope intercept form for the graph below
labwork [276]

Answer:

y = 10x

Step-by-step explanation:

Finding the slope (m) of the line the following points in the line, (0, 0) and (2, 20):

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 0}{2 - 0} = \frac{20}{2} = 10

y-intercept (b) is 0. The line intercepts the y-axis at 0. Thus, b = 0.

Substitute m = 10 and b = 0 in y = mx + b

The equation in slope-intercept form for the graph would be:

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8 0
3 years ago
PLEASE HELP WILL MARK BRAINLIEST IF CORRECT
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Answer:

I think 3

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