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likoan [24]
2 years ago
10

PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPP
SHOW YOUR WORKKKKKKKKKKKKKKKKKK




1) Evaluate the following expression. Show your work and EXPLAIN each step needed to determine the value.

Mathematics
1 answer:
castortr0y [4]2 years ago
4 0

Answer:

1/2 x -5/2 = -5/4

-1 1/4 + -1/4

-1 2/4

- 1 1/2

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Could you please help me for this question?
Olin [163]

Answer:

  See attached for graphs

  g(x) -- domain: -∞ < x < ∞; range: 0 < y < ∞

  g^-1(x) -- domain: 0 < x < ∞; range: -∞ < y < ∞

Step-by-step explanation:

g(x) is an exponential decay function. Its base is 1/3, so each increase of 1 unit in x will multiply the y-value by a factor of 1/3. The graph will rapidly approach its horizontal asymptote of y=0 as x gets large. The y-intercept is (0, 1). Just as y gets smaller as x increases, so it gets larger as x decreases. Each decrease of x by 1 unit causes the y-value to be multiplied by 3.

__

The graph of g^-1(x) is the graph of g(x) reflected across the line y=x. That is, each coordinate pair (x, y) on the graph of g(x) becomes a point (y, x) on the graph of the inverse function. In order to graph g^-1(x), you don't need to write down the function, you only need to know the relationship between the graphs.

Just as x- and y- are interchanged on the graph, so the domain, range, and intercepts are interchanged. g^-1(x) will have a vertical asymptote of x=0, and an x-intercept of (1, 0). The domain of g^-1(x) is the range of g(x): 0 < x < ∞; and the range of g^-1(x) is the domain of g(x): -∞ < y < ∞.

__

The attached graph shows g(x) in red and g^-1(x) in blue. As you can see, we created the graph simply by interchanging x and y. The line y=x is shown for reference, so you can see that each curve is a reflection of the other across that line.

_____

<em>Additional comment</em>

The explicit expression for g^-1(x) can be found by solving for y:

  x = g(y)

  x=\left(\dfrac{1}{3}\right)^y=\dfrac{1}{3^y}=3^{-y}\\\\ \log(x)=-y\cdot\log(3)\qquad\text{take logarithms}\\\\y=-\dfrac{\log{x}}{\log{3}}=-\log_3{x}\qquad\text{use the change of base relation}\\\\\boxed{g^{-1}(x)=-\log_3{x}}

If you're familiar with the log function, you know it has an x-intercept of 1 and a vertical asymptote at x=0. The base of the log function is simply a vertical scale factor. The minus sign reflects it across the x-axis.

6 0
2 years ago
A G.P has its 3rd term and 7th term as 45 and 3645 respectively. what is the product of its 2nd and 4th
Ede4ka [16]

Answer:

2,025

Step-by-step explanation:

Given:

Third term ar² = 45

Seventh term ar⁶ = 3,645

Find:

ar x ar³

Computation:

From 7th term / 3rd term

ar⁶ / ar² = 3,645 / 45

r⁴ = 81

r = 3

So,

ar² = 45

a(3)² = 45

a = 5

So,

ar x ar³

(5)(3) x (5)(3)³

2,025

3 0
3 years ago
An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest cir
rjkz [21]

Answer:

The artist used 8.6 inches more of silver wire

Step-by-step explanation:

Perimeter of the square

P = 4*a

P = 4*a = 40 in

a = 10 in

Each side of the square has a length of 10 in

The diameter of the circle is equal to the length of the side of  the square

Diameter = 10 in

Perimeter of the circle

P_c = 2*π*radius  = π*diameter

P_c = (3.14)*10 in = 31.4 in

Inches of silver wire (square)   =  40 in

Inches of copper wire (circle)   =  31.4 in

40- 31.4  in  = 8.6 in

3 0
2 years ago
Find the perimeter of the polygon.
Semmy [17]

9514 1404 393

Answer:

  30 in

Step-by-step explanation:

The enclosing rectangle is 4 by 10, so has a perimeter of ...

  P = 2(L+W) = 2(10+4) = 28

The notch adds 2 inches to the perimeter, so the total of all side lengths is ...

  28 +2 = 30 . . . inches

5 0
2 years ago
Read 2 more answers
During a baseball season, team a scores 9 runs for every 7 runs that team b scores. The total number of runs scored by both team
mrs_skeptik [129]

Answer:

∴ Team b scores is 630

And team a scores is 810

Step-by-step explanation:

Given;

Team a scores 9 runs for every  7 runs that team b scores.

Lets,

Think b is scores  x runs;

Then a is scores x+(2\times\frac{x}{7} );

Because every 7 runs of b , a is scores more 2 runs.

Total number of runs scored by both teams is 1440

Runs score by team a + Runs score by team b=1440

x+(2\times\frac{x}{7} )+  x =1440

2\times x+ \frac{2\times x}{7}=1440

\frac{(14\times x)+(2\times x)}{7} =1440

\frac{16\times x}{7} =1440

16\times x=1440\times 7

x=\frac{10080}{16}

x=630

∴ Team b scores is 630

And team a scores is 630+(2\times \frac{630}{7} )=810

5 0
3 years ago
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