Determine the measure of angle ABC to the nearest degree

mABC = 59°

Step-by-step explanation:

To find the value of x, we can call the height BD by 'h' and then use the Pythagoras' theorem in the triangles ABD and BCD:

triangle ABD:

(3x + 1)^2 = (x + 1)^2 + h2

9x2 + 6x + 1 = x2 + 2x + 1 + h2

h2 = 8x2 + 4x

triangle BCD:

(4x - 1)^2 = (2x + 1)^2 + h2

16x2 - 8x + 1 = 4x2 + 4x + 1 + 8x2 + 4x

4x2 - 16x = 0

x2 - 4x = 0

x - 4 = 0

x = 4 units

Now we can find the angles mABD and mBDC using the sine relation:

sin(mABD) = (x + 1) / (3x + 1) = 5 / 13

mABD = 22.62°

sin(mBDC) = (2x + 1) / (4x - 1) = 9 / 15

mBDC = 36.87°

So we have that:

mABC = mABD + mBDC = 22.62° + 36.87° = 59.49°

Rounding to the nearest degree, we have mABC = 59°

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

answer: 1,380

step-by-step explanation:

1: you turn %15 into a decimal by moving the decimal point two places to the left.

2: and then you multiply .15 by 1,200 , which will get you 180.00

3: from there you will add 180 to 1,200

4: which will get you 1,380

hope it *im kind of slow so idk if my answer is right*