Answer:
The answer is below
Step-by-step explanation:
a) Triangle A is attached in the image below.
The base of triangle A is 3 units and its height is 3 units. The area of a triangle is given as:
Area = (1/2) × base × height
Area of triangle A = (1/2) × base × height = (1/2) × 3 × 3 = 4.5 unit²
Area of the scaled copy = 72 unit²
Ratio of area = Area of the scaled copy / Area of triangle A = 72 unit² / 4.5 unit² = 16
Hence the scaled copy area is 16 times larger than that of triangle A.
b) For the scaled copy:
Area of the scaled copy = (1/2) × base × height = 72 unit²
base × height = 144
Since the base and height are equal
base² = 144
base = 12, also height = 12
Base of scaled copy = 12 = 4 × base of triangle A
Therefore the scale factor used is 4
Hello,
I note (a,b,c) the result of a quarters, b dimes and c pennies:
2 solutions:
106=( 3, 3, 1)=( 1, 8, 1)
106=( 0, 0, 106) but : 100= 0*25+ 0*10+ 100
106=( 0, 1, 96) but : 100= 0*25+ 1*10+ 90
106=( 0, 2, 86) but : 100= 0*25+ 2*10+ 80
106=( 0, 3, 76) but : 100= 0*25+ 3*10+ 70
106=( 0, 4, 66) but : 100= 0*25+ 4*10+ 60
106=( 0, 5, 56) but : 100= 0*25+ 5*10+ 50
106=( 0, 6, 46) but : 100= 0*25+ 6*10+ 40
106=( 0, 7, 36) but : 100= 0*25+ 7*10+ 30
106=( 0, 8, 26) but : 100= 0*25+ 8*10+ 20
106=( 0, 9, 16) but : 100= 0*25+ 9*10+ 10
106=( 0, 10, 6) but : 100= 0*25+ 10*10+ 0
106=( 1, 0, 81) but : 100= 1*25+ 0*10+ 75
106=( 1, 1, 71) but : 100= 1*25+ 1*10+ 65
106=( 1, 2, 61) but : 100= 1*25+ 2*10+ 55
106=( 1, 3, 51) but : 100= 1*25+ 3*10+ 45
106=( 1, 4, 41) but : 100= 1*25+ 4*10+ 35
106=( 1, 5, 31) but : 100= 1*25+ 5*10+ 25
106=( 1, 6, 21) but : 100= 1*25+ 6*10+ 15
106=( 1, 7, 11) but : 100= 1*25+ 7*10+ 5
106=( 1, 8, 1) is good
106=( 2, 0, 56) but : 100= 2*25+ 0*10+ 50
106=( 2, 1, 46) but : 100= 2*25+ 1*10+ 40
106=( 2, 2, 36) but : 100= 2*25+ 2*10+ 30
106=( 2, 3, 26) but : 100= 2*25+ 3*10+ 20
106=( 2, 4, 16) but : 100= 2*25+ 4*10+ 10
106=( 2, 5, 6) but : 100= 2*25+ 5*10+ 0
106=( 3, 0, 31) but : 100= 3*25+ 0*10+ 25
106=( 3, 1, 21) but : 100= 3*25+ 1*10+ 15
106=( 3, 2, 11) but : 100= 3*25+ 2*10+ 5
106=( 3, 3, 1) is good
106=( 4, 0, 6) but : 100= 4*25+ 0*10+ 0
If RS is the hypotenuse of the triangle RST and point T is in Quadrant 3, then point T must be the intersection of the lines: x = - 4 and y = - 5.
Therefore, the coordinates of point T are ( x, y ) = ( - 4, - 5 )
Answer:
T ( - 4, - 5 )
Answer:
- x-intercept: (-0.1, 0)
- Horizontal Asymptote: y = -3
- Exponential <u>growth</u>
(First answer option)
Step-by-step explanation:
<u>General form of an exponential function</u>
where:
- a is the initial value (y-intercept).
- b is the base (growth/decay factor) in decimal form:
If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function. - y=c is the horizontal asymptote.
- x is the independent variable.
- y is the dependent variable.
Given <u>exponential function</u>:
<h3><u>x-intercept</u></h3>
The x-intercept is the point at which the curve crosses the x-axis, so when y = 0. To find the x-intercept, substitute y = 0 into the given equation and solve for x:
Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.
<h3><u>Asymptote</u></h3>
An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.
The <u>parent function</u> of an <u>exponential function</u> is:
As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.
Therefore, there is a horizontal asymptote at y = 0.
This means that a function in the form 
always has a horizontal asymptote at y = c.
Therefore, the horizontal asymptote of the given function is y = -3.
<h3><u>Exponential Growth and Decay</u></h3>
A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.
A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.
The part of an exponential function that shows the growth/decay factor is the base (b).
- If b > 1 then it is an increasing function.
- If 0 < b < 1 then it is a decreasing function.
The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.
Learn more about exponential functions here:
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brainly.com/question/27955470
