Answer:
12∠x∠16
Step-by-step explanation:
For the triangle to be acute,a²+b²+c²,
Where c is the largest side of the triangle.
Hence, we must say x²+(x+4)²≥20²,
or after simplifying, x²+4x-192≥0 or (x+16)(x-12)≥0
Since x must have positive values only, x≥12
Therefore, for the triangle to be acute,we must have 12≤x≤16.
Answer:
31 / 12
Step-by-step explanation:
To get the perimeter, just add up all the sides of the parallelogram, so 5/8 + 5/8 + 2/3 + 2/3 = 31/12
The terminal point represented by P(x,y), is the coordinate where a certain point lies. Given is 5pi/4 radians - this will be our angle.
Evaluate the values of x and y using sin θ and cos θ
x = cos (5pi/4)
x = -√2/2
y = sin (5pi/4)
y = -√2/2
Therefore, (x,y) is (-√2/2, -√2/2)
If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
Answer:
54 three- point field goals
Step-by-step explanation:
184 points = <em>x </em>free throws and 3<em>y </em> three-point field goals
x= 22 free throws, each one is 1 point
184 - 22 = 162
162 ÷ 3 = 54
54=y
54 three point field goals
