MATHEMATICS HIGH SCHOOL

A small swimming pool has a circumference of 3π feet. Select the true statement about the pool.a The radius is 3 ft.

b The diameter is 3 ft.

c The diameter is 1.5 ft.

d The radius is 6 ft.

Answers

Answer 1

Answer:

Answer:

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Step-by-step explanation:

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The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic expression in this equation? givwn that the equation is : x2 + x +____ = 0

Answers

Let the numbers be x and x+1
x(x+1)=420
$x^(2) +x=420$
$x^(2) +x-420=0$
The constant is -420

Answer:

-420

Step-by-step explanation:

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.

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Write the word sentence as an inequality, a number m multiplied by 4 is greater than 12

Answers

The given word sentence is m > 3

What is inequality ?

inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

"A number m multiplied by 4 is greater than 12"

"A number m" ⇒ m

"multiplied by" ⇒ ×

"4" > 4

"is greater than"⇒ >

"12" ⇒ 12

put this together and we get

m × 4 > 12

4m > 12

it can be simplified to m > 3 if you would like.

To learn more about inequality from here

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"A number m multiplied by 4 is greater than 12"

"A number m" $\rightarrow m$
"multiplied by" $\rightarrow *$
"4" --> $4$
"is greater than" $\rightarrow >$
"12" $\rightarrow 12$

put this together and we get
$m * 4 > 12$
or
$4m > 12$

it can be simplified to $m > 3$ if you would like