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:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1