1. According to the plots, the curves intersect when
and
.
We can confirm this algebraically.





(where
is an integer)


We get the two solutions we found in the interval [0°, 360°] with
in the first case, and
in the second case.
2. We have
when
. For the given plot domain [0°, 360°], this happens when
.
3. The domain for both equations is all real numbers in general, but considering the given plot, you could argue the domains would be [0°, 360°].
is bounded between -1 and 1, so
is bounded between -1 + 2 = 1 and 1 + 2 = 3, and its range is [1, 3].
Likewise,
is bounded between -1 and 1, so that
is bounded between -1 + 3 = 2 and 1 + 3 = 4, so its range would be [2, 4].
Answer:
f(g(4)) = 213
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
- Composite Functions
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = 8x + 5
g(x) = 7x - 2
<u>Step 2: Find f(g(4))</u>
- Substitute in <em>x</em> [Function g(x)]: g(4) = 7(4) - 2
- Multiply: g(4) = 28 - 2
- Subtract: g(4) = 26
- Substitute in function value [Function f(x)]: f(g(4)) = 8(26) + 5
- Multiply: f(g(4)) = 208 + 5
- Add: f(g(4)) = 213
Answer:
Total area = 31.5 unit²
Step-by-step explanation:
Assume 1 block = 1 unit²
Divide diagram into 3 part
1. 5 by 5 block square
2. 2 by 2 block triangle(1)
2. 3 by 3 block triangle(2)
Area of square = side × side
Area of square = 5 × 5
Area of square = 25 unit²
Area of triangle(1) = [1/2][base][height]
Area of triangle(1) = [1/2][2][2]
Area of triangle(1) = 2 unit²
Area of triangle(2) = [1/2][base][height]
Area of triangle(2) = [1/2][3][3]
Area of triangle(2) = 4.5 unit²
Total area = Area of square + Area of triangle(1) +Area of triangle(2)
Total area = 25 unit² + 2 unit² + 4.5 unit²
Total area = 31.5 unit²
Answer:
The number of pages that Polina read was 90 and the number of pages that Marcus read was 18
Step-by-step explanation:
Let
x -----> number of pages that Polina read
y ----> number of pages that Marcus read
we know that
x+y=108 ----> equation A
x=5y -----> equation B
substitute equation B in equation A and solve for y

Find the value of x

therefore
The number of pages that Polina read was 90 and the number of pages that Marcus read was 18
Y = -3/2x + 4
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