Figure b is a scale image of Figure A, as shown. Figure a is an Rectangle with 9 on left side and 12 on bottom of rectangle. and
1 answer:
The scale factor that was applied to figure A to produce figure B is: 11/3 = 3.67.
<h3>How to Find the Scale Factor of a Dilation?</h3>The ratio of the corresponding dimensions of the image to the preimage gives the scale factor of any dilation.
That is:
Scale factor = dimension of image (new figure) / corresponding dimension of pre-image (original figure).
The scale factor that was applied to figure A to produce figure B = dimension of figure B / corresponding dimension of figure A.
A dimension of figure B = 33
Corresponding dimension of figure A = 9
Therefore, we would find the scale factor as shown below:
The scale factor that was applied to figure A to produce figure B = 33/9
= 11/3 = 3.67
Therefore, the scale factor that was applied to figure A to produce figure B is: 11/3 = 3.67.
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Answer:
12. Range = -∞ < x <+∞; Domain = y > 0
13. Range = -∞ < x <+∞; Domain = y > 3
Step-by-step explanation:
12. f(x) = ½(6)^x
(a) Create a table containing a few values of x and y
x y
-2 ½(6)⁻² = ½(⅙)² = ½ × ¹/₃₆ = ¹/₇₂ = 0.01
-1 ½(6)⁻¹ = ½(⅙) = ½ × ¹/₁₂ = ¹/₂₄ = 0.08
0 ½(6)⁰ = ½ × 0 = ½ = 0.5
1 ½(6)¹ = ½ × 6 = 3
2 ½(6)² = ½ × 36 = 18
(b) Draw your axes
Let the x-axis run from -5 to +5 and the y-axis from 0 to 20
(c) Plot your points
They should look like Fig. 1 below.
(d) Draw the graph
Draw a smooth line through the points.
Extend the line in both directions to the edges of the graph.
Your graph should look like Fig. 2.
(e) Identify the domain and range of the function
The <em>domain</em> is the set of all possible x-values that will give real values for y.
It looks like x can vary from -∞ to +∞ and give a real value for y.
The <em>domain is -∞ < x <+∞</em>.
The <em>range</em> of a function is the spread of all possible y-values.
It looks like y ⟶ ∞ as x ⟶ ∞, but y ⟶ 0 as x ⟶ -∞.
The x-axis is an <em>asymptote</em>. The function can get as close as possible to the x-axis, but it can never be zero or negative.
The range is y > 0.
12. f(x) = 2^x +3
(a) Create a table containing a few values of x and y
<u> x </u> <u> y </u>
-4 2⁻⁴ + 3 = (½)⁴ + 3 = ¹/₁₆ + 3 = 3¹/₁₆ = 3.1
-2 2⁻² + 3 = (½)² + 3 = ¼ + 3 = 3¼ = 3.2
0 2⁰ + 3 = 1 + 3 = 4
2 2² + 3 = 4 + 3 = 7
4 2⁴ + 3 = 16 + 3 = 19
(b) Draw your axes
(c) Plot your points
(d) Draw the graph
Your graph should look like Fig. 3.
(e) Identify the domain and range of the function
The domain is -∞ < x <+∞.
It looks like y ⟶ ∞ as x ⟶ ∞, but y ⟶ 3 as x ⟶ -∞. The line y = 3 is an asymptote.
The range is y > 3.
Answer:
see explanation
Step-by-step explanation:
multiply both sides by 2 to eliminate the fraction
2d = 2 t + a
, that is
a + 2
t= 2d ( subtract 2
t from both sides )
at² = 2d - 2 t= 2(d -
t)
divide both sides by t²
a = 2(d - t) / t²