Answer:
x = 15.65 and y = 5√2
Step-by-step explanation:
To get x and y we will use the Pythagoras theorem as shown
hyp^2 = adj^2 + opp^2
x^2 = 14^2+7^2
x^2 = 196 + 49
x^2 = 245
x = √245
x = 15.65
Similarly for y;
y2 = 5^2 + 5^2
y^2 = 25 + 25
y^2 = 50
y = √2*25
y = 5√2
Hence x = 15.65 and y = 5√2
Answer:
0.336
Step-by-step explanation:
Use binomial probability:
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
Here, n = 8, r = 7, p = 0.8, and q = 0.2.
P = ₈C₇ (0.8)⁷ (0.2)⁸⁻⁷
P = 0.336
Answer:
Choice A)
.
Step-by-step explanation:
What are the changes that would bring
to
?
- Translate
to the left by
unit, and - Stretch
vertically (by a factor greater than
.)
. The choices of
listed here are related to
:
- Choice A)
; - Choice B)
; - Choice C)
; - Choice D)
.
The expression in the braces (for example
as in
) is the independent variable.
To shift a function on a cartesian plane to the left by
units, add
to its independent variable. Think about how
, which is to the left of
, will yield the same function value.
Conversely, to shift a function on a cartesian plane to the right by
units, subtract
from its independent variable.
For example,
is
unit to the left of
. Conversely,
is
unit to the right of
. The new function is to the left of
. Meaning that
should should add
to (rather than subtract
from) the independent variable of
. That rules out choice B) and D).
- Multiplying a function by a number that is greater than one will stretch its graph vertically.
- Multiplying a function by a number that is between zero and one will compress its graph vertically.
- Multiplying a function by a number that is between
and zero will flip its graph about the
-axis. Doing so will also compress the graph vertically. - Multiplying a function by a number that is less than
will flip its graph about the
-axis. Doing so will also stretch the graph vertically.
The graph of
is stretched vertically. However, similarly to the graph of this graph
, the graph of
increases as
increases. In other words, the graph of
isn't flipped about the
-axis.
should have been multiplied by a number that is greater than one. That rules out choice C) and D).
Overall, only choice A) meets the requirements.
Since the plot in the question also came with a couple of gridlines, see if the points
's that are on the graph of
fit into the expression
.
Answer: a^2x^2+9x^2+13x+6a
Step-by-step explanation:
(a^2+9) x^2+ 13x +6a
x^2(a^2+9)+13x+6a
Expand:x^2(a^2+9): a^2 x^2+9^2
x^2 a^2 +x^2*9
a^2 x^2+9x^2
a^2 x^2+9x^2+13x+6a