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Annette [7]
4 years ago
14

PLZZZ ANSWER THISSSSSSSS

Mathematics
1 answer:
Diano4ka-milaya [45]4 years ago
6 0
First part:

65 cats divided by the ratio of 5 = 13.

13 x ratio of 7 dogs = 91 dogs are at the show.


Second part:

65 cats + 91 dogs = 156 pets are at the show.


Third part: I think the ratio is 7:12. I found the lowest common multiple, which is 13.

91 dogs divided by 13 is 7.

156 pets overall divided by 13 is 12.

Thus, the answer of 7:12.


Hope this helps! Make sure you show your work, for example the addition, multiplication, and division parts of it. :) It shouldn't be too hard, unless you want me to do that as well.

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3 is the answer .......
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2.) What value for c will make the expression a perfect square trinomial?
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Answer : \frac{49}{4}

Given expression is x^2 - 7x + c

To make perfect square trinominal we use completing the square method

In completing the square method we add and subtract the half of square of coefficient of middle term

Here coefficient of middle term is -7

Half of -7 is \frac{-7}{2}

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So the expression becomes x^2 - 7x +  [tex] \frac{49}{4} that gives perfect square trinomial

Hence , the value of 'c' is \frac{49}{4}


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3 years ago
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Show that the set of points that are twice as far from the origin as they are from (2, 2, 2) is a sphere. Find the center and ra
Viktor [21]

Answer:

This is a sphere with a center  (\dfrac{8}{3},\dfrac{8}{3},\dfrac{8}{3} )  and radius \dfrac{4 \sqrt{3}}{3}

Step-by-step explanation:

Given that: (x,y,z)

where;

d₁ is the distance from the origin = \sqrt{x^2+y^2+z^2}

d₂ is the distance from (2,2,2) = \sqrt{(x-2)^2+(y-2)^2+(z-2)^2}

Also;

d₁ = 2d₂

\sqrt{x^2 + y^2 +z^2 } = 2 \sqrt{(x-2)^2 +(y-z)^2+(z-2)^2}

By squaring both sides;

x^2 + y^2 +z^2 = 2^2((x-2)^2 +(y-z)^2+(z-2)^2)

x^2 + y^2 +z^2 = 4(x-2)^2 +4(y-z)^2+4(z-2)^2

x^2 + y^2 +z^2 =4(x^2 -2x -2x +4) + 4(y^2 -2y -2y +4) + 4(z^2 -2z-2z+4)

x^2 + y^2 +z^2 =4x^2 -16x +16 + 4y^2 -16y  +16 + 4z^2 -16z+16

Collect the like terms:

0 = 4x^2 -x^2 -16x +16 + 4y^2 -y^2 -16y +16 +4z^2 -z^2 -16z +16

0 = 3x^2 -16x +16 + 3y^2 -16y +16 +3z^2 -16z +16

Divide both sides by 3

\dfrac{0}{3} = \dfrac{3x^2 -16x +16}{3} + \dfrac{3y^2 -16y +16 }{3} + \dfrac{ +3z^2 -16z +16}{3}

0 = {x^2 - \dfrac{16x}{3} +\dfrac{16}{3} + {y^2 - \dfrac{16y}{3} +\dfrac{16}{3}+{z^2 - \dfrac{16z}{3} +\dfrac{16}{3}

Using the completing the square method;

3(\dfrac{160}{9}) -16 = {x^2 - \dfrac{16x}{3} +\dfrac{160}{9} + {y^2 - \dfrac{16y}{3} +\dfrac{160}{9}+{z^2 - \dfrac{16z}{3} +\dfrac{160}{9}

\dfrac{16}{3}= (x - \dfrac{8}{3})^2+ (y - \dfrac{8}{3})^2+ (z - \dfrac{8}{3})^2

∴

This is a sphere with a center  (\dfrac{8}{3},\dfrac{8}{3},\dfrac{8}{3} )  and ;

radius; \sqrt{\dfrac{16}{3}}

= \dfrac{4 \sqrt{3}}{3}

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Answer:

$27.50

Step-by-step explanation:

Hope this helps and have a great day!!!!

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