What is the exact answer to 30,321 divided by 46?

Answers

Answer 1
Answer: The exact answer is 659.1521
Answer 2
Answer: 30,321÷46=659.152173913

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Wendell’ Plumbing Supply sold metal piping at $36.50 per 15 yard length. What would75.4 meter of piping cost? 1.0 meter = 1.09 yards

Answers

The answer would be $198.93

Find the value of x.



x=

Answers

Answer:

my guess is 135 because there both the same corners

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

900-(105+150+140+135+125+135)= 110

Prove the trigonometric identity
(tan x + cot x)/(csc x * cos x) = sec^2 x​

Answers

Answer:

(\tan x + \cot x)/(\csc x \cos x)=\sec^2 x

\boxed{((\sin x)/(\cos x) + (\cos x)/(\sin x))/((1)/(\sin x) \cdot \cos x)}=\sec^2 x

\boxed{((\sin^2 x)/(\sin x\cos x) + (\cos^2 x)/(\sin x \cos x))/((\cos x)/(\sin x))}=\sec^2 x

\boxed{((\sin^2 x+\cos^2 x)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x

\boxed{((1)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x

\boxed{(1)/(\sin x\cos x) \cdot (\sin x)/(\cos x)}=\sec^2 x

(1)/(\cos^2x)=\sec^2x

\sec^2x=\sec^2x

Step-by-step explanation:

Given trigonometric identity:

(\tan x + \cot x)/(\csc x \cos x)=\sec^2 x

\textsf{Use the identities\;\;$\tan x = (\sin x)/(\cos x)$\;,\;$\cot x=(\cos x)/(\sin x)$\;\;and\;\;$\csc x=(1)/(\sin x)$}:

\boxed{((\sin x)/(\cos x) + (\cos x)/(\sin x))/((1)/(\sin x) \cdot \cos x)}=\sec^2 x

Simplify the denominator and make the fractions in the numerator like fractions:

\boxed{((\sin^2 x)/(\sin x\cos x) + (\cos^2 x)/(\sin x \cos x))/((\cos x)/(\sin x))}=\sec^2 x

\textsf{Apply\;the\;fraction\;rule\;\;$(a)/(b)+(c)/(b)=(a+c)/(b)$\;to\;the\;numerator}:

\boxed{((\sin^2 x+\cos^2 x)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x

\textsf{Use\;the\;identity\;\;$\sin^2x+\cos^2x=1$}:

\boxed{((1)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x

\textsf{Apply\;the\;fraction\;rule\;\;$(a)/((b)/(c))=a \cdot (c)/(b)$}:

\boxed{(1)/(\sin x\cos x) \cdot (\sin x)/(\cos x)}=\sec^2 x

Cancel the common factor sin x, and apply the exponent rule aa = a² to the denominator:

(1)/(\cos^2x)=\sec^2x

\textsf{Use the identity\;\;$(1)/(\cos x)=\sec x$}:

\sec^2x=\sec^2x

Answer:

The proof of the trigonometric identity:

We can start by expanding the numerator and denominator. In the numerator, we can use the trigonometric identities tan x = sin x / cos x and cot x = cos x / sin x.

In the denominator, we can use the trigonometric identity csc x = 1 / sin x. This gives us:

((tan x + cot x))/((csc x * cos x) ) = (((sin x )/( cos x)) + ((cos x )/(sin x)))/(((1)/( sin x)) * cos x)

`We can then cancel the sin x terms in the numerator and denominator. This gives us:

((tan x + cot x))/((csc x * cos x) ) = (1 + 1)/(((1 )/(sin x)) * cos x)

We can then multiply the numerator and denominator by sin x. This gives us:

((tan x + cot x))/((csc x * cos x) ) = (sin x + sin x)/((1 )/(cos x))

We can then simplify the expression. This gives us:

((tan x + cot x))/((csc x * cos x) ) = (2sin x)/((1 )/(cos x)) = (2sin x)/(cos x) = 2tan x

Finally, we can use the trigonometric identity tan^2 x = sec^2 x - 1 to get:

2tan x =( 2tan^2 x )/( (sec^2 x - 1))

This gives us the following identity:

((tan x + cot x))/((csc x * cos x) ) = sec^2 x

This completes the proof of the trigonometric identity.

A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 2200 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?

Answers

Answer:

The car that has a fuel efficiency of 40 mpg consumed 35 gallons, while the car that has a fuel efficiency of 20 mpg consumed 40 gallons.

Step-by-step explanation:

The variable a will represent the fuel consumed by the first car, and the variable b will represent the fuel consumed by the second car.

Set up the formula: a+b=75, which will represent the total gas consumption.

The formula 20a+40b=2200 will help you solve.

To solve, we will first solve for a by changing the formula from a+b=75 to b=75-a. Then you plug in the value of b to the second formula:

20a+40(75-a)=2200

20a+3000-40a=2200

3000-20a=2200

After subtracting 3000 from both sides, you are left with -20a=-800. Multiply both sides by -1 so that both sides are positive:

20a=800

a=40

Now that we know that the car with a 20 mpg fuel efficiency consumed 40 gallons that week, we can subtract 40 from 75, leaving us with 35 being the amount of gallons consumed by the car with a 40 mpg efficiency.

Rita's graduation picnic will cost $3 for every attendee. At most how many attendees can there be if Rita only budgets a total of $87 dollars for her graduation picnic?

Answers

To figure out how many attendees Rita can have at her picnic, we must divide the total amount that she has in her budget for her graduation picnic ($87) by the cost for every attendee ($3).

$87/$3 = 29

Therefore, Rita can have at most 29 attendees if Rita has the above cost parameters.

Hope this helps!

16. The original price of a tie is $12.50. The new price of the tie is now$7.50. By what percentage was the tie marked down? *

Answers

The tie was marked down by 40%