If m< 4=2x degrees, and m< 5 = 4x degrees , what is the value of x?

First step is to remember that all three interior angles on any triangle must equal 180 degrees, okay?  

Second, you are given the measures of two angles with the third missing.  

Let's solve, okay?  

(4x + 5) + (5x -1) + x = 180   x is for the third angle which was not given.

Now simplify.  

4x + 5 + 5x -1 + x = 180  

Combine like terms.  

10x + 4 = 180 solve for x  

10x = 176

x = 17.6  

Now, plug the value of x into each of the given angle measures, okay?  

4 * 17.6 + 5 = 75.4 degrees  

5 * 17.6 - 1 = 87 degrees  

Proof your work.  

When adding the two given angles and subtracting the total you should have the original value of x = 17.6 degrees since again all three interior angles must equal 180 degrees.  

75.4 + 87 + x = 180 ...solve for x  

162.4 + x = 180subtract 162.4 from both sides of equation

x = 17.6  

It proofs. I hope this assists you and that you have a great day today. If you have any further questions, or comments, please place in the comment section below.  

PLEASE NOTE: If you plug the value of 17.6 into the above for each time an x appears in an angle it will also proof.  

Given the data you provided, this is the only possible answer and it does not fit one of the four answers you provided us. If I am still missing a piece of information, please provide so we can ensure you have the correct solution. Many thanks in advance.

Step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt