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3 years ago

Which number is the inequality m>7\12

Mathematics

2 answers:

fiasKO [112]3 years ago

4 0

7....................................................

Leokris [45]3 years ago

4 0

Answer:

The answer is the option A $1$

Step-by-step explanation:

The options of the question are

A. 1

B. -1

C. -9

D. -5

we have

$m>\frac{7}{12}$

The solution of this inequality is the interval------> $(\frac{7}{12}, infinite)$

All real numbers greater than $\frac{7}{12}$

Remember that

$\frac{7}{12}=0.58$ ------> using a calculator

$m>0.58$

we know that

If a number is a solution of the inequality

then

the number must satisfy the inequality

Verify each case

case A) $m=1$

substitute the value of m in the inequality and compare

$1>0.58$ ------> is true

therefore

the number $m=1$ is a solution

case B) $m=-1$

substitute the value of m in the inequality and compare

$-1>0.58$ ------> is not true

therefore

the number $m=-1$ is not a solution

case C) $m=-9$

substitute the value of m in the inequality and compare

$-9>0.58$ ------> is not true

therefore

the number $m=-9$ is not a solution

case D) $m=-5$

substitute the value of m in the inequality and compare

$-5>0.58$ ------> is not true

therefore

the number $m=-5$ is not a solution

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Which shows the dimensions of two rectangular prisms that have volumes of 240 ft3 but different surface areas?

bulgar [2K]

Calculate the volume and surface areas of both rectangular prisms for each option.

A:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(8)(5)(6)=240~ft^3$

$\sf A=2((8)(5)+(6)(5)+(6)(8))$
$\sf A=236~ft^2$

Rectangular Prism #2
$\sf V=lwh$
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$\sf A=236~ft^2$

This is incorrect, they have the same volume of 240 cubic feet and the same surface areas.

B:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(8)(5)(6)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((8)(5)+(6)(5)+(6)(8))$
$\sf A=236~ft^2$

Rectangular Prism #2
$\sf V=lwh$
$\sf V=(10)(8)(3)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((10)(8)+(3)(8)+(3)(10))$
$\sf A=268~ft^2$

$\boxed{\sf Correct~Answer}$ : Both have the same volume of 240 cubic feet, but different surface areas.

C:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(15)(8)(2)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((15)(8)+(2)(8)+(2)(15))$
$\sf A=332~ft^2$

Rectangular Prism #2
$\sf V=lwh$
$\sf V=(6)(4)(15)=360~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((6)(4)+(15)(4)+(15)(6))$
$\sf A=348~ft^2$

This is incorrect, they have different surface areas, but only Rectangle #1 has a volume of 240 cubic feet.

D:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(12)(6)(5)=360~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((12)(6)+(5)(6)+(5)(12))$
$\sf A=324~ft^2$

Rectangular Prism #2
$\sf V=lwh$
$\sf V=(8)(10)(3)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((8)(10)+(3)(10)+(3)(8))$
$\sf A=268~ft^2$

This is incorrect, they both have different surface areas but only Rectangle #2 has a volume of 240 cubic feet.

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Step-by-step explanation:

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