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3 years ago

The circumference of a circle is approximately 39.25 mm. What is the length of the diameter?

Mathematics

1 answer:

melomori [17]3 years ago

6 0

Answer:

<h2>12.5 millimeters (mm).</h2>

Step-by-step explanation:

Explain/define:

CIRCUMFERENCE: THE DISTANCE AROUND A CIRCLE.

DIAMETER: THE LENGTH OF A STRAIGHT LINE THROUGH THE CENTER OF A CIRCLE.

Mathematics: Formula

$d=c/3.14$

$d-diameter$

$c-circumference$

Mathematics: Solve

To find the length of the diameter from the circumference, divide the circumference by pi. The quotient is the diameter.

3.14 is often used for pi.

$39.25/3.14=12.5.$

Conclude:

Therefore, the length of the diameter of the circle is 12.5 millimeters (mm).

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Create a system of linear equations that when solved algebraically, prove to have no solution.

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The answer is y=3x+7 and y=3x+4

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2 years ago

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timofeeve [1]

The question above was not written properly

Complete Question

Lacey and Haley are rewriting expressions in an equivalent, simpler form.

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

Answer:

a) Haley is correct, Lacey simplified wrongly.

b) Haley is incorrect

Step-by-step explanation:

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

For Question a, when it comes to simplifying algebraic expression that has to do with powers, there are certain rules that should be followed.

For example

x^a × x^b = x^(a + b)

For Haley, she simplified x³⋅ x² and got

x⁵

She is correct because this follows the product rule of powers or exponents above

= x³⋅ x² = x³+² = x⁵

For Lacey she is wrong because:

x³ + x² ≠ x⁵

x³ + x² when simplified as quadratic equation = x²(x + 1)

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

For question b, when we have two distinct or different numbers with the same power(exponents) the rule states that:

x^a × y^a = (x × y)^a = (xy)^a

Haley is simplified wrongly. She did not apply the rule above

Haley simplified 3⁵⋅ 4⁵ = (3 × 4) ⁵+⁵

= 12^10, this is wrong.

The correct answer according to the rule =

3⁵⋅ 4⁵ = (3 × 4) ⁵ = 12⁵

Therefore,

3⁵⋅ 4⁵ ≠ 12^10

3⁵⋅ 4⁵ = 12⁵

Haley is wrong.

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3 years ago

Factor completely. x^3 + 2x^2 + x + 2

slega [8]

$x^3 + 2x^2 + x + 2=\\
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(x^2+1)(x+2)$

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3 years ago

Simplify by dividing (3/5) divided by -4/9

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3 years ago

A movie theater sends out a coupon for 85% off the price of a ticket. Write an equation for the situation, where y is the pri

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Answer:

$y=0.15x$

Step-by-step explanation:

Given:

Original price of the ticket is $x$

Price after using the coupon is $y$

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Therefore, the price after applying coupon is given as the difference of the original price and the coupon discount. That is,

$y=x-0.85x=x(1-0.85)=0.15x\\\therefore y=0.15x$

The graph is shown below. The graph passes through the origin as the above relationship is a proportional relationship.

The line $y=0.15x$ strictly remains in the first quadrant as both $x$ and $y$ can't be negative as they represent price of tickets and price can never have negative values. Hence, only the first quadrant has both the values of $x$ and $y$ positive.

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