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
Answer:
f(n) = -n^2 -3n +5
Step-by-step explanation:
Suppose the formula is ...
f(n) = an^2 +bn +c
Then we have ...
f(1) = 1 = a(1^2) +b(1) +c
f(2) = -5 = a(2^2) +b(2) +c
f(3) = -13 = a(3^2) +b(3) +c
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Here's a way to solve these equations.
Subtract the first equation from the second:
-6 = 3a +b . . . . . 4th equation
Subtract the second equation from the third:
-8 = 5a +b . . . . . 5th equation
Subtract the fourth equation from the fifth:
-2 = 2a
a = -1
Then substituting into the 4th equation to find b, we have ...
-6 = 3(-1) +b
-3 = b
and ...
1 = -1 +(-3) +c . . . . . substituting "a" and "b" into the first equation
5 = c
The formula is ...
f(n) = -n^2 -3n +5
Answer:
I think a but I am not 100 percent sure
Step-by-step explanation:
Answer:
Jason has $58.20 and Jeff has $13.80.
Step-by-step explanation:
Let x represent the amount of money Jason has, and y represent the amount of money Jeff has.
We know that together they have $72. So, we can write the following equation:
We know that Jason has three <em>more</em> than four <em>times</em> the amount of money Jeff has. So:
This is a system of equations. We can solve it by using substitution. Let's substitute the second equation into the first. This yields:
Combine like terms:
Subtract 3 from both sides:
Divide both sides by 5:
So, Jeff has $13.80
We know that Jason has three more than four times the amount of money Jeff has.
Therefore, Jason has:
Multiply and add:
So, Jason has $58.20 and Jeff has $13.80.
And we're done!
Answer:
Sin0= y/r
X= -4 and r= 9 (radius is also the hypotenuse)
In quadrant II y is positive
X^2 +y^2 = r^2
-4^2 + y^2 = 9^2
16 + y^2 = 81
Y^2 = 81-16
Y^2 = 65
Y= sqrt65
Sin0= sqrt65/9
Step-by-step explanation:
