Answer:
1) 4
2) y <= 9
3) NO SOLUTION
4) 24
5) 5 cards
Step-by-step explanation:
1st pic) 2x + 7 = 15
2x + 7 = 15
<u> -7 -7</u>
2x = 8
divide by 2 to isolate x
<u>x = 4</u>
2nd pic) y - 3 <= 6
y - 3 <= 6
<u> +3 +3</u>
<u>y <= 9</u>
<u />
3rd pic) x + 0.5 = x + 6
x + 0.5 = x + 6
<u> -0.5 -0.5</u>
x = x + 5.5
NO SOLUTION
4th pic) 5m + 10 <= 130
5m + 10 <= 130
<u> -10 -10</u>
5m <= 120
divide by 5 to isolate the m
<u>m <= 24</u>
5th pic) 2c - 8 > 0
2c - 8 > 0
<u> +8 +8</u>
2c > 8
divide by 2 to isolate the c
<u>c > 4</u>
Answer:
(a) AD=6 cm
(b) 66 cm²
(c) 38 cm
Step-by-step explanation:
(a) To get the length of AD, we can use pythagoras on the triangle part. Let's say the dotted line intersects DC at E. Then since AB and DC are parallel, AD is equal to BE. EC = 8 cm simply by subtracting AB from DC (15-7=8).
Then pythagoras says that 8²+BC²=10². So BC = √(100-64) = 6. And since BC=AD, AD is also 6.
(b) Area of the rectangle DEBA is 7*6 = 42. Area of triangle ECB is base times half height: 8*3 = 24. Sum is 42+24 = 66 cm²
(c) Perimeter is 7+10+15+6 = 38 cm. Add all the side lengths.
Answer:
[0,2]
Step-by-step explanation:
local maximum is a maximum within some region of x values
Answer:
(x - 7)^2 + (y - 2)^2 = 5^2
Step-by-step explanation:
Center at (7, 2); radius 5
Adapt (x - h)^2 + (y - k)^2 = r^2 to this situation. Replace h by 7, k by 2 and r by 5:
(x - 7)^2 + (y - 2)^2 = 5^2
Answer:
10 units
Step-by-step explanation:
Given that:
Cos a = 3 /5
From trigonometry ;
Cos θ = Adjacent / hypotenus
Side Adjacent angle a = 3 = FD
Hypotenus = 5 = DE
3 / 5 = FD / DE
FD = 6 units
3/5 = 6/DE
DE * 3/5 = 6
DE = 6 ÷ 3/5
DE = 6 * 5 /3
DE = 30 /3
DE = 10 units
