Answer:
Step-by-step explanation:
Given equation is,
x² + (p + 1)x = 5 - 2p
x² + (p + 1)x - (5 - 2p) = 0
x² + (p + 1)x + (2p - 5) = 0
Properties for the roots of a quadratic equation,
1). Quadratic equation will have two real roots, discriminant will be greater than zero. [(b² - 4ac) > 0]
2). If the equation has exactly one root, discriminant will be zero [(b² - 4ac) = 0]
3). If equation has imaginary roots, discriminant will be less than zero [(b² - 4ac) < 0].
Discriminant of the given equation = 
For real roots,
p² + 2p + 1 - 8p + 20 > 0
p² - 6p + 21 > 0
For all real values of 'p', given equation will be greater than zero.
Answer:
Rotate 90 degrees clockwise around the origin and then translate down. Reflect across the x-axis and then reflect across the y-axis.
Step-by-step explanation:
Reflection across the y-axis. 90o counter clockwise rotation. 2. Multiple-choice. 1 minute. Q. Identify the transformation from ABC to A'B'C'. Draw the final image created by reflecting triangle RST in the x-axis and then rotating the image 90° counterclockwise about the origin. BER goo Clockwise 90c ...C-level G2-1 Reflections and Rotations ... X-axis. 00. G2-2 Rotations. 4. Rotate the figure 90° clockwise around the origin. ... Rotation 90° counter.
Answer:
3/2
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
2 × 1 = 2
Step 2
Add the answer from Step 1 to the numerator
2 + 1 = 3
Step 3
Write answer from Step 2 over the denominator
3/2
Dup= 72 miles
<span>ddown= 120 miles </span>
<span>v= riverspeed </span>
<span>rup= 32mph - v </span>
<span>rdown= 32mph + v </span>
<span>t both ways= t </span>
<span>d=r*t </span>
<span>d/r=t </span>
<span>t=ddown/rdown </span>
<span>t=dup/rup </span>
<span>dup/rup = ddown/rdown </span>
<span>(72)/(32-v)=(120)/(32+v) </span>
<span>3840-120v=2304+72v </span>
<span>1536=192v </span>
<span>v=8</span>
9514 1404 393
Answer:
- (2x-10) +x +(x+10) = 180
- x = 45
- (2x-10)° = 80°
- (x+10)° = 55°
- x° = 45°
Step-by-step explanation:
The equation is an expression of the fact that <em>the sum of the angles in a triangle is 180°.</em>
(2x -10)° +x° +(x +10)° = 180°
For the purposes of the answer box, I'd leave off the degree symbol:
(2x -10) +x +(x +10) = 180
__
This simplifies to ...
4x = 180
x = 45
Then the angles (CW from top) are ...
(2·45 -10) = 80°
(45 +10)° = 55°
(45)° = 45°
