What is the distance around a triangle that has sides measuring 2 1/8, 3 1/2, and 2 1/2 feet?

Answers

Answer 1

Answer: Perimeter = 2 1/8 + 3 1/2 + 2 1/2 = 7 (1 + 4 + 4)/8 = 7 9/8 = 8 1/8

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HELLPP WORTH 20 POINTS ✨
What is the solution to the equation 9^(x - 2) = 27 ? x = 2.5/ x = 0.5/ x = -0.5 /x = 3.5

If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Answers

The correct answers are:
1) sin(x) = $( √(3) )/(2)$
2) tan(x) = $√(3)$

Explanation:
Given:
$cos(x) = (1)/(2)$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( (1)/(2) )^2 = 1 \n sin^2(x) + (1)/(4) = 1 \n sin^2(x) = (3)/(4)$

Step 3:
Take square-root on both sides:
$√(sin^2(x)) = \sqrt{(3)/(4)}$

sin(x) = $( √(3) )/(2)$

Now to find the tan(x), we would use the following formula:

tan(x) = $(sin(x))/(cos(x))$ --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $( ( √(3) )/(2) )/( (1)/(2) )$

Hence tan(x) = $√(3)$

Answer:

The value of $\sin x=(√(3))/(2)$

The value of $\tan x=√(3)$

Step-by-step explanation:

Given = $\cos x=(1)/(2)$

To find : $\sin x=?$ and $\tan x=?$

Solution:

We know that, if the cosine function of an angle is $(1)/(2)$ then the angle is equal to the 60°.

$\cos x=(1)/(2)$

x = 60°

The value of the :

$\sin x=\sin 60^o=(√(3))/(2)$

We know that ratio of sine function to the cosine function is equal tto the tangent

$\tan x=(\sin x)/(\cos x)=((√(3))/(2))/((1)/(2))=√(3)$

The value of $\sin x=(√(3))/(2)$

The value of $\tan x=√(3)$

The price of a pair of trousers was decreased by 22% to $30. What was the original price of the trousers?

Answers

Answer:

$38.46

Step-by-step explanation:

It is given that the price of a pair of trousers was decreased by 22% to $30.

Let $x be the original price of the trousers.

22% less of original price is equal to $30.

$x-(22)/(100)x=30$

$x-0.22x=30$

$0.78x=30$

Divide both sides by 0.78.

$x=(30)/(0.78)$

$x\approx 38.46$

Therefore, the original price of the trousers is $38.46.

4) A sequence is defined recursively by f(1) = 2and f(n) = 3f(n-1) + 1. Find the first three
terms of the sequence.

- How do I do this question and just Recursive Sequences in general?

Answers

$S=[2,7,22,\dots]$ .

Let me explain why.

$f(1)=2$ this is our first term.

$f(2)=3f(2-1)+1=3f(1)+1=7$ second term.

$f(3)=3f(3-1)+1=3f(2)+1=22$ third term.

...

Pretty simple huh?

Hope this helps.

Answer:

The first 3 terms are 2, 7, 22.

Step-by-step explanation:

The n is the sequence number of the term: f(1) means the first term.

The second term

f(2) = 3f(n - 1) + 1 We make n = 2:

= 3f(2-1) + 1

= 3f(1) + 1 f(1) = 2 so:

= 3*2 + 1

= 7.

3rd term f(3)

= 3f(3 - 1) + 1

= 3f(2) + 1

= 3(7) + 1

= 22.

There are 9 roses and 7 diasies. What is the ratio of roses to daisies?

Answers

$9:7$
.....................................

A van travels 220 miles on 10 gallons of gas. Find how many gallons the van needs to travel 550 miles.31 gallons of gas
121 gallons of gas
25 gallons of gas
115 gallons of gas

Answers

The van will need 25 gallons of gas for it to travel 550 miles. This is calculated by dividing 10 gallons to 220 miles to get the miles per gallons, which in this case is 22 miles per gallon. Then we have to divide 550 miles by 22 miles per gallon to get the total gas consumption, which is 25 gallons.

Answer:

Step-by-step explanation:

To calculate how many gallons the van needs to travel 550 miles you should multiply the number of miles by the relationship between the number of gallons of gas it needs to travel 220 miles, (it is important to put the quantity in miles on the denominator) as follows:

$550miles*(10gallons)/(220miles)=25$