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3 years ago

The map of a mall is overlaid with a numeric

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

3 0

Answer:

$\sqrt{118}$ or 10.8627805

Step-by-step explanation:

Start by taking the difference of each value of both points

Find the difference in x values

78-2 = 76

Find the difference in y values

46-4 = 42

Add the two differences

76+42=118

Take the square root of this value

$\sqrt{118}$

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3 years ago

Devon rented a U Haul truck for $48 for 4 hours plus $13.50 per each hour you go over. At the end of the day, his total bill was

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Answer:

You need to write an equation to find the answer to this:

h = hours

48 + 13.5h = 112.50 -First you need to subtract 48 from both sides

48 - 48 + 13.5h = 112.50 - 48

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3 years ago

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3 years ago

Consider a circle whose equation is x2 + y2 + 4x – 6y – 36 = 0. Which statements are true? Check all that apply. To begin conver

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Answer:

1) False, to begin converting the equation to standard form, each side must be added by 36. 2) True, to complete the square for the x terms, add 4 to both sides, 3) True, the center of the circle is at (-2, 3), 4) False, the center of the circle is at (-2, 3), 5) False, the radius of the circle is 7 units, 6) False, the radius of the circle is 7 units.

Step-by-step explanation:

Let prove the validity of each choice:

1) To begin converting the equation to standard form, subtract 36 from both sides:

Let consider the following formula and perform the following algebraic operations:

(i) $x^{2} + y^{2} + 4\cdot x - 6\cdot y - 36 = 0$ Given

(ii) $x^{2} + 4\cdot x + y^{2} - 6\cdot y - 36 = 0$ Commutative Property

(iii) $(x^{2} + 4\cdot x + 4) - 4 + (y^{2} - 6\cdot y + 9) - 9 -36 = 0$ Modulative/Associative Property/Additive Inverse Existence

(iv) $(x+ 2)^{2} - 4 + (y - 3)^{2} - 9 - 36 = 0$ Perfect Trinomial Square

(v) $(x+2)^{2} +(y-3)^{2} = 4 + 9 + 36$ Commutative Property/Compatibility with Addition/Additive Inverse Existence/Modulative Property

(vi) $(x+2)^{2} + (y-3)^{2} = 49$ Definition of Addition/Result

False, to begin converting the equation to standard form, each side must be added by 36.

2) True, step (iii) on exercise 1) indicates that both side must be added by 4.

3) The general equation for a circle centered at (h, k) is of the form:

$(x-h)^{2}+ (y-k)^{2} = r^{2}$

Where $r$ is the radius of the circle.

By direct comparison, it is evident that circle is centered at (-2,3).

True, step (vi) on exercise 1) indicates that center of the circle is at (-2, 3).

4) False, step (vi) on exercise 1) indicates that the center of the circle is at (-2, 3), not in (4, -6).

5) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

6) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

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