ANSWER
EXPLANATION
According to the power property of logarithms:
The given logarithm is
When we apply the power property to this logarithm, we get,
Answer:
1. B) 5.7
2. A) 12
3. A) 11.4
4. A) 5.7
5. A) 16.2
6. A) 11.2
7. No, they do not form a right triangle
8. Yes, they do form a right triangle
Step-by-step explanation:
Extra tip: The hypotenuse has to be less than both sides added together, but cannot be more than either of the sides alone.
1.
16² + b² = 17²
256 + b² = 289
256 - 256 + b² = 289 - 256
b² = 33
√b² = √33
b = 5.74 or 5.7
2.
16² + b² = 20²
256 + b² = 400
256 - 256 + b² = 400 - 256
b² = 144
√b² = √144
b = 12
3.
7² + 9² = c²
49 + 81 = c²
130 = c²
√130 = √c²
11.40 or 11.4 = c
4.
7² + b² = 9²
49 + b² = 81
49 - 49 + b² = 81 - 49
b² = 32
√b² = √32
b = 5.65 or 5.7
5.
a² + 5² = 17²
a² + 25 = 289
a² + 25 - 25 = 289 - 25
a² = 264
√a² = √264
a = 16.24 or 16.2
6.
10² + b² = 15²
100 + b² = 225
100 - 100 + b² = 225 - 100
b² = 125
√b² = √125
b = 11.18 or 11.2
7.
15² + 8² = 16²
225 + 64 = 256
289 ≠ 256
8.
5² + 12² = 13²
25 + 144 = 169
169 = 169
Looking at the graph closely we can see that the heart rate increases from 0 to 6 min then became steady from 6 to 25 min then finally decreases from 25 to 30 min. Therefore the correct answer is:
“The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.”
In real life cardiac exercises, we can interpret that the period from 0 to 6 min is the period where the person is still warming up thus leading to an increase in heart rate. At 6 min, the person is fully warmed up hence reaching a stable heart rate. Then at 25 min, the person starts cooling down which means that the exercise is ending soon.
You can use either of these, depending on your teacher.
2.e+14
2.0*10^14
Answer:
y = 
x + 
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = 
with (x₁, y₁ ) = (- 2, 1 ) and (x₂, y₂ ) = (6, 3 )
m = 
= 
= 
= , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 3 ) , then
3 = + c ⇒ c = 3 - =
y = x + ← equation of line
