Answer:
Dilations produce similar figures because the image and pre-image will have congruent corresponding angles. The corresponding side lengths of the figures will be proportional based on the scale factor. The shape is preserved and the sides are enlarged or reduced by the scale factor
Step-by-step explanation:
X²+5x+5 has zeroes given by x=(-5±√25-20)/2=(-5±√5)/2=-1.3820 and -3.6180.
In simplest radical form the zeroes are -5/2+√5/2 and -5/2-√5/2.
The given function is
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments
We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:
1. Set y = f(x)
y = 4x - 3/2
2. Exchange x and y
x = 4y - 3/2
3. Solve for y
4y = x + 3/2
y = (x +3/2)/4
4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4
5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)
Answer:
Pedro needs about 8 weeks to complete 30 assignments.
X = E/W dimension
<span>y = N/S dimension </span>
<span>4x + 4x + 2y + 2y = 64 </span>
<span>8x + 4y = 64 </span>
<span>4y = 64 - 8x </span>
<span>y = 16 - 2x </span>
<span>Area = xy = x(16 - 2x) = 16x - 2x^2 </span>
<span>Maximum of y = ax^2 + bx + c is when x = -b / 2a </span>
<span>so x = -16 / -4 = 4 </span>
Given:
Annual salary average: $22,040
Annual Social security benefit: 42% of salary average
Monthly bill: $1,375
$22,040 x 42% = $9,256.80 per annum
$9,256.80 / 12 mos = $771.40 per month
$1,375 – 771.40 = $603.60
Since, Christina only receives $771.40 per month from her Social Security benefit, she has to take $603.60 from her savings each month to help pay her monthly bill of $1,375.
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