Answer:
C.) x≥
-2/3
Step-by-step explanation:
Answer:
The speed of the current is 3 miles per hour
Step-by-step explanation:
The equations for rate (r), distance (d), and time (t) are ⇒ d = rt, r = d/t, = t = d/r
Let x = speed in still water
Let c = speed of the current
The main difference with these problems is rate needs to be expressed using two variables because moving upstream the current is against you and downstream it moves with you.
Distance Rate Time
Upstream x − c
Downstream x + c
The distance column with the numbers from the problem and the value for speed in still water for x.
Distance Rate Time
Upstream 4 5 − c
Downstream 16 5 + c
The column for time using the other two columns knowing that rate, distance ⇒ time = Distance Rate Time
Upstream 4 5 − c
5 − c
4
Downstream 16 5 + c
5 + c
16
“It takes as long …” from the problem means that the two times are equal to each other. So, the equation can be written as:
4/5− c = 16/5 + c ⇒ Solve by cross-multiplying ⇒ 5(4 + c) = 16 5( − c) ⇒ c = 3
Answer:
70 and 110
Step-by-step explanation:
The two angles add to 180 degrees since they form a straight line
2x+10 +3x+20 =180
5x+30 = 180
Subtract 30 from each side
5x+30-30 =180-30
5x = 150
Divide by 5
5x/5 =180/5
x = 30
The left angle is 2x+10 = 2*30+10 = 60+10 =70
The right angle is 3x+20 = 3*30 +20 = 90+20 = 110
Answer:
i. ans in picture
ii. ans in picture
iii. ans in picture
iv. 19
v. 38
Step-by-step explanation:
i. working in picture
ii. working in picture
iii. working in picture
iv.
180-90=90
90=2x+7+45=2x+52
2x=90-52=38
x=19
v.
angle COD=3x+10
180-3x+10-2x
180+10=2x+3x
190=5x
x=38
Answer:
Step-by-step explanation:
-16x^2 + 24x + 16 = 0.
A. Divide by 8:
-2x^2 + 3x + 2 = 0, A*C = -2*2 = -4 = -1 * 4. Sum = -1 + 4 = 3 = B, -2x^2 + (-x+4x) + 2 = 0,
(-2x^2-x) + (4x+2) = 0,
-x(2x+1) + 2(2x+1) = 0,
(2x+1)(-x+2) = 0, 2x+1 = 0, X = -1/2. -x+2 = 0, X = 2.
X-intercepts: (-1/2,0), (2,0).
B. Since the coefficient of x^2 is negative, the parabola opens downward. Therefore, the vertex is a maximum.
Locate the vertex: h = Xv = -B/2A = -24/-32 = 3/4, Plug 3/4 into the given Eq to find k(Yv). K = -16(3/4)^2 + 16(3/4) + 16 = 19. V(h,k) = V(3/4,19).
C. Choose 3 points above and below the vertex for graphing. Include the points calculated in part A which shows where the graph crosses the x-axis.
