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2 years ago

For the equations given below, which statement is true?

Mathematics

1 answer:

allochka39001 [22]2 years ago

5 0

Answer: C. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

Step-by-step explanation:

You know that the first equation is:

$-3x-8=19$

And the second equation is:

$-3x-2=25$

According to the Addition property of equality:

If $a=b$ ; then $a+c=b+c$

Then, you can add 6 to both sides of the first equation to keep it balanced. Then, you get:

$-3x-8=19\\\\-3x-8+(6)=19+(6)$

$-3x-2=25$

Therefore, you can observe that the second equation can be obtained by adding 6 to both sides of the first equation, therefore, the equations have the same solution.

If you want to verify this, you can solve for "x" from both equations:

- First equation:

$-3x-8=19\\\\-3x=19+8\\\\x=\frac{27}{-3}\\\\x=-9$

- Second equation:

$-3x-2=25\\\\-3x=25+2\\\\x=\frac{27}{-3}\\\\x=-9$

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A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x3 – 4x, where

marta [7]

Answer:

$Height =3$

Step-by-step explanation:

Given

$Length = x + 2$

$Width = x - 2$

$Height = x$

$Volume = 15$

Required

Find the height

The volume is calculated as thus:

$Volume = Length * Width * Height$

This gives

$15 = (x + 2) * (x - 2) * x$

Apply difference of two squares

$15 =(x^2 - 4 ) * x$

$15 = x^3 - 4x$

Subtract 15 from both sides

$x^3 - 4x - 15 = 0$

Using a calculator to factorize, we have:

$(x-3)(x^2+3x+5) = 0$

Split

$x - 3 = 0$ or $x^2 + 3x + 5 = 0$

$x = 3$ or $x^2 + 3x + 5 = 0$

x has complex roots for $x^2 + 3x + 5 = 0$

Hence:

$x = 3$

Recall that:

$Height = x$

$Height =3$

3 0

2 years ago

Let f(x)<br> -4x - 6 and g(x) = 3x + 5. Find (fºg)(-3).

Allushta [10]

Answer:

Step-by-step explanation:

f(g(-3)

g(-3) = 3(-3) = -9 - 5 = -14

f(-14)= -4(-14) - 6 = 56 - 6 = 50

7 0

2 years ago

To transport 228 people to an island island ferry make six different trips on each trip the ferry carries the same number of peo

Tju [1.3M]

240 I calculated it your welcome :)

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3 years ago

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The paint mixer wants to mix paint that is 30% gloss with paint that is 15% gloss to make 3.75 gallons of paint that is 20% glos

Kipish [7]

The paint mixer should mix 1.238 gallon paint that is 30 % gloss and 2.512 gallon paint that is 15 % gloss to get 3.75 gallon of paint that is 20 % gloss.

In this question we must determine the correct volumes of each paint to obtain a 20 % gloss with paint by means of weighted averages:

$c_{r} = x\cdot c_{a} +(1-x)\cdot c_{b}$ (1)

Where:

$x$ - Proportion of the paint that is 30 % gloss.
$c_{a}$ - Concentration ratio of the paint that is 30 % gloss.
$c_{b}$ - Concentration ratio of the paint that is 15 % gloss.
$c_{r}$ - Resulting concentration ratio

If we know that $c_{a} = 0.3$ , $c_{b} = 0.15$ and $c_{r} = 0.2$ , then the proportion of the paint that is 30 % gloss is:

$0.2 = 0.3\cdot x +(1-x)\cdot 0.15$

$0.2 = 0.15\cdot x+0.15$

$0.15\cdot x = 0.05$

$x = 0.33$

And the quantity of gallons needed of each paint are:

Paint (30 % gloss)

$V_{a} = 0.33\cdot (3.75\,gal)$

$V_{a} = 1.238\,gal$

Paint (15 % gloss)

$V_{b} = V-V_{a}$

$V_{b} = 3.75\,gal-1.238\,gal$

$V_{b} = 2..512\,gal$

The paint mixer should mix 1.238 gallon paint that is 30 % gloss and 2.512 gallon paint that is 15 % gloss to get 3.75 gallon of paint that is 20 % gloss.

To learn more on weighted averages, we kindly invite to check this question: brainly.com/question/18554478

8 0

2 years ago

Ben and Eva place stickers of animals on a large sheet of paper. Ben places 45 stickers on the paper. This is 5 times the number

OLga [1]

Answer:

9 stickers

Step-by-step explanation:

45/5=9

we divided 45 with 9 since __*5=45 and the figure out the__ we need to do the opposite operation(division)

8 0

3 years ago

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