Answer:
<h3>#1</h3>
- x² - 9 = 0
- x² = 9
- x = ± √9
- x = ± 3
Yes, -3 and 3 are zeroes of this polynomial
<h3>#2</h3>
<em>See attached graphs</em>
Zero's of a polynomial are the intersection of the graph with the x-axis.
They include coordinates as (x, 0), so the x-coordinates are zero's.
The attached shows the zero's.
<h3>#3</h3>
<em>See attached graphs</em>
Zero's of each polynomial are reflected in the graphs.
- () y = x² - x - 6 has zeros x = -2 and x = 3
- (ii) y = 6 - x - x² has zero's x = -3, x = 2
Answer:
2.25 + 1 1/3=3.5833333 combined number of pounds of mulch and gravel sold.
2.25/3.583333 X 172=108 pounds of mulch that the supplier sells
(1 1/3) / 3.583333 X 172=64 pounds of gravel that the supplier sells.
Step-by-step explanation:
Let 'x' = pounds of gravel The ratio of mulch to gravel is given 2 1/4 / 1 1/3 Which equals 9/4 / 4/3 = 27/16
So the total gravel and much is equal to x + 27/16x = 172
Solving for 'x'
43/16 x = 172
x = 172 (16/43) = 64 pounds of gravel Mulch = 27/16x = 64 (27/16)= 108 pounds
Answer:
9:40 am
Step-by-step explanation:
Let time taken from when Smith left compound to when Garcia overtakes Smith's car be represented by y
After y hours, Smith has covered 48*y=48y miles
Similarly, due to a difference of 20 minutes which is 20/60=1/3 hours, Garcia moves a distance of
60(y-1/3)
Equating both distances to be the same
60y-20=48y
12y=20
y=20/12=5/3 hours
Converted to minutes
5/3*60=100 minutes= 1 hr 40 mins
Therefore, adding 100 minutes to to starting time of Smith
8:00+1:40=9:40 am
The time that Garcia overtakes Smith is 9:40am
Answer:
x = 3
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
10x + 2 is an exterior angle of the triangle, thus
10x + 2 = 2x + 1 + 25
10x + 2 = 2x + 26 ( subtract 2x from both sides )
8x + 2 = 26 ( subtract 2 from both sides )
8x = 24 ( divide both sides by 8 )
x = 3
We know that the right triangle has one 90 degree angle and two acute (< 90 degree) angles. Since the sum of the angles of a triangle is always 180 degrees.
<u>To find x:</u>
(10x - 20) + (6x + 8) = 180
16x - 12 = 180
+12 +12
16x = 192
----- -----
16 16
x = 12
<u>Check:</u>
(10(12) - 20) + (6(12) + 8) = 180
(120 - 20) + (72 + 8) = 180
100 + 80 = 180
180 = 180
<u>Angle (10x - 20):</u>
(10(12) - 20)
(120 - 20)
100
<u>Angle (6x + 8):</u>
(6(12) + 8)
(72 + 8)
80
