Answer:
The resulting graph is 
.
Step-by-step explanation:
The resulting function is of the form:
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Amplitude, dimensionless.
- Midpoint value, dimensionless.
The sine function is bounded, between -1 and 1, and must be multiplied by a stretch factor. That is: 
. According to the graph, the function is bounded between 5 (
) and -5 (
), and the midpoint value () is 0. The amplitude is determined by the following calculation:
If 
and 
, then:
The resulting graph is .
Hey there!
In order for two figures to be congruent, each named angle must correspond and be congruent to ONE other angle. If you have ZYV and XWV, Z must be congruent to X as they both show up first in the ordering.
This means...
∠Z≅∠X
∠Y≅∠W
∠V≅∠V
Our first answer option has to do with parallelism, which does not influence if certain angles are congruent or not.
For the second answer option, ∠Z is congruent to ∠X, not ∠Y, so it is incorrect.
For the third answer option, it shows that ∠Z would correspond to ∠V, but it does not, so it is also incorrect.
For D, ∠Z IS congruent to ∠X, and ∠W IS congruent to ∠Y
Therefore, our answer is D) ∠Z≅∠X and ∠W ≅ ∠Y.
I hope this helps!
Answer:
A) The equation for circumference is C=2piR. So Filling in for circle A we have 28.26=2*pi*4.5 so we want to isolate pi which I'm gonna call x for it's easier for me xD. So we're gonna start by dividing 4.5 from each side which is gonna leave us with 6.28=2*x which gives you x(pi)= 3.14. For circle B we have 15.70=2*x*2.5 isolate x by first dividing 2.5 which leaves us again with 6.28=2x and x= 3.14.
B) The equation for area is A=piR^2. So again for circle A we have 63.585=x9^2. This one is harder but also are you sure that the area is 63.585 it's supposed to be 254.469 (We'll come back to this)
C) The observation you can make about the value of pi for circles A and B is that it stays consistent at 3.14
hoped i helped : )
Answer:
20 ft long; 12 ft wide
Step-by-step explanation:
Let w = the width of the garden
Then l = w + 8
A = lw
A = (w + 8)w
=====
The sidewalk is 4 ft wide, so, for the big rectangle consisting of garden plus sidewalk:
Width = w +8
Length = w + 16
Area = (w + 8)(w + 16)
=====
The <em>difference</em> between the two areas is the area of the sidewalk (320 ft²).
(w + 8)(w + 16) - (w + 8)w = 320 Factor out w + 8
(w+ 8)(w + 16 – w) = 320 Combine like terms
(w+ 8) × 16 = 320 Divide each side by 16
w + 8 = 20 Subtract 8 from each side
w = 12 ft
l = 12 + 8
l = 20 ft
The garden is 20 ft long by 12 ft wide.
