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3 years ago

11

Rina’s recipe uses 2 cups of sugar to make 2 ½ dozen cookies. Jonah’s recipe uses 2 ¼ cups of sugar to make 3 dozen cookies. Whi

ch recipe uses more sugar for a dozen cookies? Why?

1 answer:

WITCHER [35]3 years ago

8 0

Answer:

Let's calculate the "cups of sugar per dozen cookies" ratio:

2 cups

---------- = 0.8 (Rina)

2.5

2.25 cups

------------- = 0.75 (Jonah)

3

Rina uses more sugar for a dozen cookies.

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Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t

Marat540 [252]

Answer:

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

$x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$A$ , $B$ , $C$ - Circunference constants.

Given the number of variable, we need the location of three distinct points:

$(x_{1},y_{1}) = (6,0)$

$36 +6\cdot A + C = 0$

$(x_{2},y_{2}) = (8,4)$

$80 + 8\cdot A + 4\cdot B + C = 0$

$(x_{3},y_{3}) = (3,9)$

$90 + 3\cdot A + 9\cdot B + C = 0$

Then, we have the following system of linear equations:

$6\cdot A + C = -36$ (2)

$8\cdot A +4\cdot B + C = -80$ (3)

$3\cdot A + 9\cdot B + C = -90$ (4)

The solution of this system is:

$A = -6$ , $B = -8$ , $C = 0$

By comparing the general form with the standard form of the equation of the circunference is:

$A = -2\cdot h$ (5)

$B = -2\cdot k$ (6)

$C = h^{2}+k^{2}-r^{2}$ (7)

Where:

$h$ , $k$ - Coordinates of the center of the circle.

$r$ - Radius of the circle.

If we know that $A = -6$ , $B = -8$ and $C = 0$ , then coordinates of the center of the circle and its radius are, respectively:

$h = -\frac{A}{2}$

$k = -\frac{B}{2}$

$r = \sqrt{h^{2}+k^{2}-C}$

$h = 3$ , $k = 4$ , $r = 5$

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

3 0

2 years ago

Elsa's magic wand can cast 53 spells. Her wand can cast 17fewer spells than her sister Anna's wand, which is a little bigger and

Mademuasel [1]

Answer:

<em> Anna's wand can cast 70 spells</em>

<em></em>

Step-by-step explanation:

Elsa's wand can cast 53 spells

her wand casts 17 fewer cells than her sister Anna's

Amount of spells cast by Anna's wand = ?

We write the question down in the form of an equation

$x - 17 = 53$

where $x$ is the amount of spells Anna's wand can cast.

we then proceed to solve by collecting like terms to different sides of the equation. We'll have

$x = 53 + 17$

which leaves us with

$x = 70$

This means that<em> Anna's wand can cast 70 spells.</em>

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3 years ago

A high school basketball player attempted 42 free throws in a season. An analyst determined that the player successfully made 5

patriot [66]

The answer is 35 free throws

5 0

4 years ago

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Aquarius is an underwater ocean laboratory located in the Florida keys national marine sanctuary. Solve the equation 31/25x = -6

serg [7]

Answer:

x=-50

Step-by-step explanation:

31/25x=-62

x=-62/(31/25)

x=(-62/1)(25/31)

x=--1550/31

x=-50

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3 years ago

Three bus tickets cost $5.<br><br> How many bus tickets can you buy with $15?

Pavel [41]

Answer: 9 tickets

Step-by-step explanation:

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3 years ago