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Advocard [28]
3 years ago
15

A rectangular dog cage has a length of 4 1/2 feet and a width of 3 3/7 feet. What is the area of the cage?

Mathematics
1 answer:
liberstina [14]3 years ago
3 0

Step-by-step explanation:

Area of rectangle =height×base

4 1/2×3 3/7=9/2×24/7=216/14=15 6/14=15 3/7

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Find the ordered pair that makes both the equations below true
NNADVOKAT [17]

Answer:

(3, 1)

Step-by-step explanation:

(a) Algebraic solution

(1)  y = -⅔x + 3

(2) y =   2x  - 5

Set Equation (1) equal to Equation (2)

-⅔x + 3 = 2x - 5

Multiply each side by 3

-2x + 9 = 6x - 15

Add 15 to each side

-2x + 24 = 6x

Add 2x to each side

24 = 8x

Divide each side by 3

(3) x = 3

Substitute (3) into (2)

y = 2×3 - 5 = 6 - 5 = 1

The ordered pair that makes both equations true is (3, 1).

(b) Graphical solution

In the diagram below, the red line is the graph of Equation (1). The blue line is the graph of Equation (2). The point of intersection is at (3, 1).

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3 years ago
Which of the following is the graph of f(x) = -0.5|x+3| -2?
Tcecarenko [31]

Answer:

The last graph

Step-by-step explanation:

We transform functions in the following ways:

  • multiplying the function by a number to stretch or shrink it
  • multiplying by a negative to flip the orientation of the function
  • adding/subtracting a value to the input x to shift it horizontally
  • adding/subtracting a value to the output (or outside the function operation) to shift it vertically or horizontally.

Looking at the equation we can see f(x)=-0.5\left|x+3\right|-2

  • Vertically shrunk by 0.5
  • Negative leading coefficient to flip the graph's orientation
  • Horizontal shift of the vertex of 3 units to the left from (0,-2) to (-3,-2)
  • Vertical shift of the vertex of 2 units downward (-3,0) to (-3,-2)

The last graph has vertex (-3,-2) and satisfies the the equation.

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True

Step-by-step explanation:

Some of our energy comes from electrical power plants

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Find the least common denominator for these two rational expressions.
lbvjy [14]
\frac{y}{y^{2}-1},\ \frac{y}{y^{2}-8y+7}
=\frac{y}{(y-1)(y+1)},\ \frac{y}{(y-1)(y-7)}
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So the common denominator is (y-1)(y+1)(y-7)
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