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3 years ago

Quadrilateral RAPS is located at the vertices

Mathematics

1 answer:

blondinia [14]3 years ago

3 0

Answer:

R''(-1, 4), A''(-4, 3), P''(-5, 0), S''(-1, 1)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new position. Types of transformation include dilation, reflection, translation and rotation.

If a point A(x, y) is reflected over the line y = x, the new point is at A'(y, x)

If a point A(x, y) is rotated 180° clockwise about the origin, the new location is at A'(-x, -y)

Since Quadrilateral RAPS is located at the vertices R(-4,1), A(-3, 4), P(0,5), S(-1,1), After been reflected across the line y = x, the new locations are at:

R'(1, -4), A'(4, -3), P'(5, 0), S'(1, -1)

Then the rotation of the points R'(1, -4), A'(4, -3), P'(5, 0), S'(1, -1) 180° about the origin gives:

R''(-1, 4), A''(-4, 3), P''(-5, 0), S''(-1, 1)

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Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x

Sati [7]

Answer:

$x = 2-t$ and $y = -5\cdot t +21$

Step-by-step explanation:

Given that $y = 5\cdot x + 11$ and $t = 2-x$ , the parametric equations are obtained by algebraic means:

1) $t = 2-x$ Given

2) $y = 5\cdot x +11$ Given

3) $y = 5\cdot (x\cdot 1)+11$ Associative and modulative properties

4) $y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11$ Existence of multiplicative inverse/Commutative property

5) $y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11$ Associative property

6) $y = -5\cdot (-x)+11$ $\frac{a}{-b} = -\frac{a}{b}$ / $(-1)\cdot a = -a$

7) $y = -5\cdot (-x+0)+11$ Modulative property

8) $y = -5\cdot [-x + 2 + (-2)]+11$ Existence of additive inverse

9) $y = -5 \cdot [(2-x)+(-2)]+11$ Associative and commutative properties

10) $y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11$ Distributive property

11) $y = (-5)\cdot (2-x) +21$ $(-a)\cdot (-b) = a\cdot b$

12) $y = (-5)\cdot t +21$ By 1)

13) $y = -5\cdot t +21$ $(-a)\cdot b = -a \cdot b$ /Result

14) $t+x = (2-x)+x$ Compatibility with addition

15) $t +(-t) +x = (2-x)+x +(-t)$ Compatibility with addition

16) $[t+(-t)]+x= 2 + [x+(-x)]+(-t)$ Associative property

17) $0+x = (2 + 0) +(-t)$ Associative property

18) $x = 2-t$ Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is $x = 2-t$ and $y = -5\cdot t +21$ .

5 0

3 years ago

A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these

Vinvika [58]

Answer:

133 fishes

Step-by-step explanation:

Units of food A = 400 units

Units of food B = 400 units

Fish Bass required 2 units of A and 4 units of B.

Fish Trout requires 5 units of A and 2 units of B.

i. For food A,

total units of food A required = 2 + 5

= 7 units

number of bass and trout that would consume food A = 2 x $\frac{400}{7}$

= 114.3

number of bass and trout that would consume food A = 114

ii. For food B,

total units of food B required = 4 + 2

= 6 units

number of bass and trout that would consume food B = 2 x $\frac{400}{6}$

= 133.3

number of bass and trout that would consume food B = 133

Thus, the maximum number of fish that the lake can support is 133.

4 0

3 years ago

6/(v+4) + 2/(v-6)<br> What is the answer?

laiz [17]

Answer:

8v-28/v^2-2v-24

Step-by-step explanation:

1. Find common denominator

2. Combine fractions with common denominator

3. Re-order terms so constants are on the left

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2 years ago

Translate the statements into a confidence interval for p. Approximate the level of confidence. In a survey of 8451 U.S. adults,

Sedaia [141]

Answer:

The confidence interval is $0.304 < p < 0.324$

Step-by-step explanation:

From the question we are told

The sample proportion $\r p = 0.314$

The margin of error is $E = 0.01$

The confidence interval for p is mathematically represented as

$\r p - E < p < \r p + E$

=> $0.314 - 0.01 < p < 0.314 + 0.01$

=> $0.304 < p < 0.324$

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3 years ago

Factor this polynomial expression.<br> x2 – 16x+64

Sladkaya [172]

x^2-16x+64

(x-8)(x-8)

x(x)*(x)(-8)*(-8)(x)(-8)(-8)

x^2-8x-8x+64

x^2-16x+64

Answer: (x-8)^2 or (x-8)(x-8)

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3 years ago