MATHEMATICS HIGH SCHOOL

Divide -12×8y8 by 3×⁴y²

Answers

Answer 1
Answer: -12x⁸y⁸ ÷ 3x⁴y².       

Applying laws of indices. When you divide same base, you subtract the powers.

= (-12/3)x⁸⁻⁴y⁸⁻²

= -4x⁴y⁶

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Amanda’s dad is twice as old as she is today. The sum of their ages is 66. Find the ages of Amanda and her dad.

Answers

Let amanda's age be x and her dad's age be y.

Amanda’s dad is twice as old as she,  therefore 2x=y

The sum of their ages is 66, therefore x+y=66

x+y=66

2x=y,

substitute.

2x+x=66

3x=66

Divide.

x=22.

plug it back in, 22+y=66, y=44.

Amanda's age is 22 and her dad's age is 44.

Factor the expression completely.

4x2 - 12x + 9

Answers

(2x - 3)(2x - 3)
the answer to the question

What is the domain of the relation {(2, 8), (0, 8), (–1, 5), (–1, 3), (–2, 3)}?

Answers

The domain is simply all of the x values.

We have a 2, 0, -1, -1, and -2.

Get rid of duplicates, so 2, 0, -1, and -2.

We're going to want to order those, so -2, -1, 0, and 2.

And put some fancy brackets on that. {-2, -1, 0, 2}
Domain          Range
    -1                    3
     0                    5
     2                    8
     3

The domain of the relation {(2, 8), (0, 8), (-1, 5), (-1, 3), (-2, 3)} is {-1, 0, 2, 3}.

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.

Learn more about Unit conversion click;

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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.

Learn more about Scale Factor here:

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Will give brainliest

Answers

Answer:

A' = ( 3+1,2+2) =(4,4)

B'=(4+1,5+2)=(5,7)

C'=(6+1,3+2)=(7,5)

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Find the unknown side of the right triangle. Round to the nearest thousandths. One side is 9yd, the other side is 12 yd.

Answers

You haven't told us whether 9 and 12 are the two legs of the triangle, or whether the 12yd is the longest side.

If the 9 and the 12 are the two legs, then:
C² = A² + B²
C² = 81 + 144
C² = 225
C = 15 yd

If the 12 is the longest side, then:
(12)² = (9)² + B²
B² = (12)² - (9)² = 144 - 81 = 63
B = √63 = 7.937yd  (rounded)
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