Arc PQR has the central angle (360 - [150+73]), or 223. The circumference of this circle is C = pi*2*r, or C = pi*2(6.48 in) = 40.72 in. The arc length in question is a fraction of that, namely:
223
----- * 40.72 in = 25.22 in (answer)
360
We know, 1 year = 12 month.
So, 3 month = 3/12 = 0.25 year.
Now, principle amount, P = $400 .
Rate is, r = 8% = 0.08
Time period, t = 0.25 year.
Now, Interest is given by :
I = P × r × t
I = $( 400 × 0.08 × 0.25 )
I = $8
Therefore, she will pay $8 interest in total.
Answer:
f(x) = 2(x –3)²
Step-by-step explanation:
f(x) = 2x² – 12x + 18
The vertex form of the above expression can be obtained as follow:
f(x) = 2x² – 12x + 18
Factorise
f(x) = 2(x² – 6x + 9)
Next, we shall simplify x² – 6x + 9 by factorisation method.
This is illustrated below:
x² – 6x + 9
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, find two factors of 9x² such that their sum will result to the 2nd term i.e –6x in the expression above.
The factors are –3x and –3x
Next, replace –6x with –3x and –3x in the equation above as shown below:
x² – 6x + 9
x² – 3x –3x + 9
Factorise
x(x – 3) –3(x –3)
(x –3)(x –3)
(x –3)²
f(x) = 2x² – 12x + 18
f(x) = 2(x² – 6x + 9)
f(x) = 2(x –3)²
Therefore, the vertex form of the function f(x) = 2x² – 12x + 18 is
f(x) = 2(x –3)²
Answer: 25
Step-by-step explanation: The absolute value is the distance between a number and zero. The distance between −
25 and 0 is 25
Answer:the greatest number of pieces that can be cut is 2
Step-by-step explanation:
The total length of ribbon available is 3/4 meter. Sunday needs pieces measuring 1/3 meter for their project. This means that each length needed would be exactly 1/3 meter.
The number of pieces measuring 1/3 meter that can be cut from the ribbon would be
(3/4)/(1/3) = 3/4×3/1 = 9/4 = 2.25
Since the length needed is exactly 1/3 meter, the greatest number of pieces that can be cut will be 2
