Answer:
x = 190 and x = 126
Step-by-step explanation:
In both diagrams the indicated angles are vertical and congruent, then
= 95 ( multiply both sides by 2 )
x = 190
and
x + 21 = 147 ( subtract 21 from both sides )
x = 126
Answer:
-103/6 = 17 1/6
Step-by-step explanation:
-4 1/15 = -61/15
13 1/10=131/10
-61/15*2/2=-122/30
131/10*3/3=393/30
-122/30-393/30=-515/30=-103/6
4 cos² x - 3 = 0
4 cos² x = 3
cos² x = 3/4
cos x = ±(√3)/2
Fixing the squared cosine doesn't discriminate among quadrants. There's one in every quadrant
cos x = ± cos(π/6)
Let's do plus first. In general, cos x = cos a has solutions x = ±a + 2πk integer k
cos x = cos(π/6)
x = ±π/6 + 2πk
Minus next.
cos x = -cos(π/6)
cos x = cos(π - π/6)
cos x = cos(5π/6)
x = ±5π/6 + 2πk
We'll write all our solutions as
x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k
Answer:
-12c-5
Step-by-step explanation:
Step 1- Distribute into the parenthesis(Since there's nothing next to the parenthesis to multiply, there is a 1).
-9c-1(5-3c)
-9c-5(1)-3(1)c
Step 2- Multiply,
-9c-5-3c
Step 3- Add common variables.
(-9c-3c)-5
-12c-5
The formula for the area of a rectangle is length times width, or A=l·w
The Area A=256
The width is w
The lenght is given as 6 feet less than 4 times its width, or in math language this is l=4w-6
Let's go back to the formula
A=l·w ⇒ 256=(4w-6)·w
simplify ⇒ 256=4w²-6w
put everything on the same side and set the equation equal to zero
⇒ 4w²-6w-256=0
Solve for w using quadratic formula
You are going to get two answers after using the quadratic formula: one positive and one negative. Just remember it doesn't make sense to get a negative answer if we are talking about width, so use the positive answer only
w≈8.7851 units
