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Vaselesa [24]
2 years ago
10

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select t

wo options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Mathematics
1 answer:
Oksanka [162]2 years ago
4 0

Equation 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p has the same soltion as the provided equation option second and third are correct.

<h3>What is an expression?</h3>

It is defined as the combination of constants and variables with mathematical operators.

We have an equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Combine like terms:

2.3p – 10.1 = 6.49p – 4

Or in the equation 2.3p – 10.1 = 6.5p – 4 – 0.01p mulitply by 100 on both sides.

We get:

230p – 1010 = 650p – 400 – p

Thus, equation 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p has the same soltion as the provided equation option second and third are correct.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ1

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by
a_sh-v [17]

Answer:

Dimension of the box is 16.1\times 7.1\times 2.45

The volume of the box is 280.05 in³.

Step-by-step explanation:          

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is L=21-2h

The width of the box is W=12-2h

The volume of the box is V=L\times W\times H

V=(21-2h)\times (12-2h)\times h

V=(21-2h)\times (12h-2h^2)

V=252h-42h^2-24h^2+4h^3

V=4h^3-66h^2+252h

To maximize the volume we find derivative of volume and put it to zero.

V'=12h^2-132h+252

0=12h^2-132h+252

Solving by quadratic formula,

h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}

h=\frac{132\pm72.99}{24}

h=2.45,8.54

Now, substitute the value of h in the volume,

V=4h^3-66h^2+252h

When, h=2.45

V=4(2.45)^3-66(2.45)^2+252(2.45)

V\approx 280.05

When, h=8.54

V=4(8.54)^3-66(8.54)^2+252(8.54)

V\approx -170.06

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is L=21-2(2.45)=16.1

The width of the box is W=12-2(2.45)=7.1

So, Dimension of the box is 16.1\times 7.1\times 2.45

6 0
4 years ago
Factor out the coefficient 1/2d+6
Ratling [72]
To factor, we always have to look for common factors in the numbers given to us. In this case, in 1/2 and 6, the common factor is 1/2. Therefore, we will have to factor like so:

1/2d + 6 = 1/2 (d + 3)

Hope this helps!
4 0
3 years ago
Read 2 more answers
Kate paid $118.65 for a jacket. the price includes a 5% sales tax. how much was the jacket before the tax?
Harman [31]

Let, the price of jacket before tax = x

it would be: x*105/100 = 118.65

x = 11865/105

x = $113

8 0
3 years ago
You buy milk in 1 gallon containers. One portion of waffles requires 0.4 ounces of milk. How many portions can be made with one
xenn [34]

320 portions of waffles can be made with one container.

Step-by-step explanation:

Given,

Milk is bought in 1 gallon container.

One portion of waffles require = 0.4 ounces of milk

We know that;

1 gallon = 128 ounces

Now;

No. of portions of waffles = \frac{Total\ ounces\ of\ milk}{Milk\ used\ per\ waffle}

No. of portions of waffles = \frac{128}{0.4}

No. of portions of waffles = 320

320 portions of waffles can be made with one container.

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Factor the expression.<br><br> 3x + 21
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Answer: 3  ( x + 7 )

Step-by-step explanation:

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