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solniwko [45]
3 years ago
10

B. 2(3x - 5) = 2x + 6

Mathematics
2 answers:
Leto [7]3 years ago
8 0

Answer:

x = 4

Step-by-step explanation:

Given

2(3x - 5) = 2x + 6 ( divide both sides by 2 )

3x - 5 = x + 3 ( subtract x from both sides )

2x - 5 = 3 ( add 5 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

gogolik [260]3 years ago
6 0

Answer:

x = 4

Step-by-step explanation:

2(3x - 5) = 2x + 6

expand- 2(3x-5):6x+10

6x-10= 2x+6

Add 10 to both sides

6x-10+10=2x+6+10

simplify

6x=2x+16

subtract 2x from both sides

6x-2x=2x+16-2x

simplify

4x=16

divide  both sides by 4

4x/4=16/4

x=4

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Kelly has a rectangular fish aquarium that measures 18 inches long, 8 inches wide, and 12 inches tall.
BigorU [14]

Answer:

a) The maximum amount of water the aquarium can hold is 1728 in³.

b) The cover has to be 624 in² big.

Step-by-step explanation:

a) The maximum volume of water that the aquarium can have is the same as the volume of the aquarium:

V=L×W×H=18 in × 8 in × 12 in= 1728 in³

b) The protective covering is used on the four walls of the aquarium. We have to find the areas of the four walls:

One of them is given by the multiplication of the width and the height:

A₁= W×H= 8 in × 12 in=96 in²

The other area is given by the multiplication of the length and the height:

A₂= L×H= 18 in × 12 in= 216 in²

As the fish aquarium is rectangular the area of the walls is given by:

A_T=2A_1+2A_2=2×96 in²+2×216 in²=624 in²

8 0
2 years ago
4. If DF = 9x - 39, find EF.<br><br> Help I’m so confused!!!!
topjm [15]

Answer:

EF =58

Step-by-step explanation:

from the illustration,

EF =DF - DE

<em>give</em><em>n</em><em> </em><em>that</em><em> </em><em>DF</em><em> </em><em>=</em><em>9</em><em>x</em><em>-</em><em>3</em><em>9</em><em> </em><em>,</em><em> </em><em>DE</em><em> </em><em>=</em><em>4</em><em>7</em><em> </em><em>EF</em><em>=</em><em>3</em><em>x</em><em> </em><em>+</em><em>1</em><em>0</em>

<em>sub</em><em>stitute</em><em> </em><em>them</em><em> </em><em>into</em><em> </em><em>the</em><em> </em><em>formu</em><em>la</em><em>,</em>

<em> </em><em> </em>

<em>3</em><em>x</em><em> </em><em>+</em><em>1</em><em>0</em><em>=</em><em>9</em><em>x</em><em>-</em><em>3</em><em>9</em><em> </em><em>-</em><em> </em><em>4</em><em>7</em>

<em>sol</em><em>ving</em><em> </em><em>for</em><em> </em><em>x</em>

<em>3</em><em>x</em><em> </em><em>+</em><em>1</em><em>0</em><em> </em><em>=</em><em>9</em><em>x</em><em> </em><em>-</em><em>8</em><em>6</em>

<em>grou</em><em>ping</em><em> like</em><em> </em><em>ter</em><em>ms</em>

<em>3</em><em>x</em><em> </em><em>-</em><em> </em><em>9x</em><em> </em><em>=</em><em>-</em><em>8</em><em>6</em><em> </em><em>-</em><em>1</em><em>0</em>

<em>-6x</em><em>=</em><em>-</em><em>9</em><em>6</em>

<em>div</em><em>iding</em><em> </em><em>throu</em><em>gh</em><em> </em><em>by</em><em> </em><em>-</em><em>6</em>

<em>\frac{ - 6x}{ - 6}  =  \frac{ - 96}{ - 6}</em>

<em>x  =  \frac{96}{6}</em>

<em>x = 16</em>

<em>but</em><em> </em><em>EF</em><em>=</em><em>3</em><em>x</em><em>+</em><em>1</em><em>0</em>

substitute x=16 into it to get the EF

EF= 3(16)+10

EF=48+10

EF=58

6 0
3 years ago
Read 2 more answers
Rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$
solniwko [45]

Rewrite the expression  6j^2 - 4j + 12$ in the form $c(j + p)^2 + q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$

The ratio of \frac{q}{p}  = - 34

How to solve such questions?

Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.

Completing the square is a method that is used for converting a quadratic expression of the form ax^{2} + bx + c to the vertex form

a(x - h)^{2} + k. The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^{2} + n, such that the left side is a perfect square trinomial

$6j^2 - 4j +12$

=  $6(j^2 - \frac{2}{3} j )+12$

= $6(j^2 - \frac{2}{3} j  +  \frac{1}{9}  )+\frac{102}{9}                   (Completing Square method)

=6( j- \frac{1}{3} )^{2}  +  \frac{34}{3}

On comparing with the given equation we get

p = - \frac{1}{3}     and q = \frac{34}{3}

∴ \frac{q}{p} = \frac{\frac{34}{3} }{\frac{-1}{3} }

= - 34

Learn more about completing the square method here :

brainly.com/question/26107616

#SPJ4

7 0
2 years ago
Eloise's rabbit cage is shape like a rectangular prism. The cage has a height of 28 inches and a volume of 8,680 cubic inches. E
Tems11 [23]

Answer:

310 inches²

Step-by-step explanation:

Given: A rectangular prism cage has a height of 28 inches.

           Volume of prism is 8680 cubic inches.

           

We know the area of base of rectangular prism is equal to the area of rectangle.

∴ Lets find out the lenght and width of rectangular prism.

Volume of rectangular prism= w\times l\times h

Where, w is width

             l is length

             h is height.

Now, putting the value in the formula of volume.

⇒ 8,680= w\times l\times 28

cross multiplying

⇒ wl= \frac{8680}{28}

∴ wl= 310 inches²

As we need to find the area of the plastic mat on the bottom of the cage, which is rectangle in shape.

Area of rectangle= wl

∴ Area of rectangle= 310 inches²

Hence,  310 inches² is the area of the plastic mat on the bottom of the cage.

4 0
3 years ago
!!!!!!!!!HELP ASAP!!!!!!! WORTH 20 POINTS
Juliette [100K]
F(x)=∛x

The domain will be all real numbers.

Answer: A) all real numbers.

Ej: if x=-8 ⇒∛-8=-2

8 0
3 years ago
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