Maude's living room is in the shape of a rectangle. Its dimensions are 21 feet by 14 feet. Find the length of the diagonal of the living room. Round your answer to the nearest tenth if necessary.

Answers

Answer 1

Answer:

The length of the diagonal of the living room is 25.23 feet.

What is the Pythagorean theorem?

Pythagoreantheorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Maude's living room:

Length = 21 feet

Width = 14 feet

Now,

The diagonal of the living room.

Using the Pythagorean theorem.

Diagonal² = 21² + 14²

Diagonal = √(441 + 196)

Diagonal = √(637)

Diagonal = 25.24 feet

Thus,

The length of the diagonal is 25.23 feet.

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Answer 2

Answer: Use the pythagorean theorem A²+B²=C²

Use 21ft for A
Use 14ft for B
Then solve for C (the diagonal)

21²+14²=C²

441+196=C²

673=C²

√673 = √C²

C≈25.24 or if you leave in radical form it is the square root of 637

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Donnie is solving the equation 2x2 = 27 + 3x with the quadratic formula.What values should he use for a, b, and c

Answers

$2x^2 = 27 + 3x \n \n2x2 -3x-27=0 \n \n a=2 , \ b = -3 , \ c=-27 \n \n\Delta = b^(2)-4ac = (-3)^(2)-4*2*(-27)= 9+216 =225\n \nx_(1)=(-b-√(\Delta ))/(2a) =(3-√(225))/(2*2)=(3-15)/(4) =(-12)/(4)= -3\n \nx_(2)=(-b+√(\Delta ))/(2a) = (3+√(225))/(2*2)=(3+15)/(4) =(18)/(4)= (9)/(2)=4.5$

Which expression is a difference of cubes?
X^6-6
X^6-8
x^8-6
X^8-8

Answers

Answer: The correct expression is, $x^6-8$

Step-by-step explanation:

$x^6$ is represented in cube form as, $(x^2)^3$

'8' is represented in cube form as, $2^3$

$x^8$ and '6' will not show cube form of integer power.

The expanded form of the given expression, $x^6-8$ is represented as,

$x^6-8=(x^2)^3-2^3$

This expression will showing the difference of cubes.

And the other options, $x^6-6,x^8-6,x^8-8$ will not show the difference of cubes.

Therefore, the correct answer is, $x^6-8$

The expression $\boxed{{x^6} - 8}$ is a difference of cubes. Option (b) is correct.

Further Explanation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

Given:

The options are as follows,

(a). ${x^6} - 6$

(b). ${x^6} - 8$

(c). ${x^8} - 6$

(d). ${x^8} - 8$

Calculation:

8 is a cube of 2 and can be written as follows,

$8 = {2^3}$

${x^6}$ can be written as a cube of ${x^2}.$

${x^6} = {\left( {{x^2}} \right)^3}$

Use the identity ${a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)$ in above expression.

$\begin{aligned}{x^6} - 8&= {\left( {{x^2}} \right)^3}- {\left( 2 \right)^3} \n&= \left( {{x^2} - 2} \right)\left( {{x^4} + 2{x^2} + 4} \right)\n\end{aligned}$

The expression $\boxed{{x^6} - 8}$ is a difference of cubes. Option (b) is correct.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, $x^12y^18+1$ , exponents, power, equation, power rule, exponent rule.

Pierce works at a tutoring center on the weekends. At the center, they have a large calculator to use for demonstration purposes that is a scale model of calculators available for the students to use. Each key on the student calculators is 14 millimeters wide, and each key on the demonstration calculator is 2.8 centimeters wide. If the student calculators are 252 millimeters tall, how tall is the demonstration calculator?

Answers

The height of the demonstration calculator is 504 millimeters.

To find the height of the demonstration calculator, we can use the ratio of the key widths between the student calculators and the demonstration calculator.

Let's first convert all measurements to the same unit for consistency. Since we need to find the height of the demonstration calculator, let's convert the width of the keys on the demonstration calculator to millimeters, which is the unit used for the height of the student calculator.

1 centimeter (cm) = 10 millimeters (mm)

Width of the key on the demonstration calculator =

= 2.8 cm x 10 mm/cm

= 28 mm

Now, we know the width of each key on the demonstration calculator is 28 millimeters.

We can use this information to find the height of the demonstration calculator.

The ratio of the width of the keys on the demonstration calculator to the width of the keys on the student calculator is:

= 28 mm (demonstration calculator) / 14 mm (student calculator)

Now, let's set up a proportion to find the height of the demonstration calculator (Hd):

Hd (demonstration calculator) / 252 mm (student calculator)

= 28 mm (demonstration calculator) / 14 mm (student calculator)

Hd / 252 = 28 / 14

Hd / 252 = 2

Hd = 2 x 252

Hd = 504 millimeters

So, the height of the demonstration calculator is 504 millimeters.

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Final answer:

The height of the large demonstration calculator is 50.4 cm, determined by converting measurements to the same units and using the scale factor between the student and demonstration calculators.

Explanation:

The question involves scale factor and unit conversion in mathematics. The scale factor between the student calculator buttons and the large demonstration calculator buttons is 2.8 cm (button size of large calculator) divided by 1.4 cm (button size of student calculator, which equates to 14 mm). Therefore, the scale factor is 2.

To find the height of the large calculator, we multiple the height of the student's calculator (252 mm or 25.2 cm) by the scale factor 2. Therefore, the height of the large demonstration calculator is 50.4 cm.