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2 years ago

If a circle has circumference 100pi units, what is it’s area

Mathematics

1 answer:

const2013 [10]2 years ago

8 0

Answer:

2500pi^2 units

Step-by-step explanation:

Circumference = pi * diameter

Circumference = pi * 100

Radius = diameter/2

Radius = 50

Area = pi * radius^2

Area = pi * 50^2

Area = pi * 2500

Area = 2500pi^2 units

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Please help me solve for X

Akimi4 [234]

Step-by-step explanation:

According to the given diagram,

By exterior angle property,

x=46°+30°

x=76°

4 0

3 years ago

Solve this inequality: 3b – 7 < 32

butalik [34]

It's a lot like solving equations.

3b-7 < 32
Add 7 to each side.
3b < 39
Divide by 3 on each side.
b < 13

Hope this helps :)

6 0

3 years ago

Read 2 more answers

The following points for a function are graphed in the coordinate plane: (0, 4), (1, 5), (2, 6), and (3, 7).What function is bei

Alexxx [7]

Answer:

The correct answer is

$y=x+4$

Explanation:

We are given the points:

(0, 4)

(1, 5)

(2, 6)

(3, 7)

We can see that for each unit that x-coordinate grows, the y-coordinate also grows one.

This means that the slope of the line is m = 1

The first point given, tell us the y-intercept: (0, 4)

The slope-intercept form of a line is:

$y=mx+b$

Where m is the slope and b the y-intercept.

For the points given:

m = 1

b = 4

Thus:

$y=1\cdot x+4=x+4$

8 0

1 year ago

En un polinomio P(x,y), homogéneo y completo en "x" e "y", la suma de los grados absolutos de todos sus términos es 420. ¿Cuál e

Mandarinka [93]

Answer:

the degree of homogeneity is 20.

Step-by-step explanation:

In a polynomial P (x, y), homogeneous and complete in "x" and "y", the sum of the absolute degrees of all its terms is 420. What is its degree of homogeneity?

A homogeneous polynomial is one in which all monomials have the same degree.

This is an example of a homogeneous polynomial of degree 4 (the degree of all monomials is 4):

x ^ 4 + 3x ^ 3y + 2x ^ 2y ^ 2 + xy ^ 3 + 8y ^ 4.

As you can see, the sum of the exponents of the variables x, y in each monomial is 4.

And the number of terms is 5, that is, it is the degree of homogeneity plus 1.

In relation to the sum of the absolute degrees of all monomials or terms it will be: 4 + 4 + 4 + 4 + 4 = 4 * 5 = 20.

In general, you can say that the sum of the absolute degrees in a homogeneous polynomial will be the degree of each monomial by the number of terms = degree * (degree + 1)

Calling n, the degree of our polynomial, it must be fulfilled:

n (n + 1) = 420

=> n ^ 2 + n = 420

=> n ^ 2 + n - 420 = 0

Factoring:

(n + 21) (n - 20) = 0

=> n = -21 and n = 20.

Only the positive value makes sense, therefore n = 20.

In other words, the polynomial is of the form (excluding the coefficients):

x ^ 20 + x ^ 19 y + x ^ 18 y ^ 2 + x ^ 17 y ^ 3 + .... x ^ 3 y ^ 17 + x ^ 2y ^ 18 + xy ^ 19 + y ^ 20

That polynomial has 21 terms.

So the sum of the degrees will be 20 * 21 = 420, as required in the statement.

Therefore, the degree of homogeneity is 20.

8 0

3 years ago

Help I cannot figure this question out.

netineya [11]

Answer:

B. x = -1 ± i

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Standard Form: ax² + bx + c = 0
Factoring
Quadratic Formula: $\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Algebra II

Imaginary Numbers: √-1 = i

Step-by-step explanation:

Step 1: Define

x² + 2x = -2

Step 2: Identify Variables

Rewrite Quadratic in Standard Form [Addition Property of Equality]: x² + 2x + 2 = 0
Break up Quadratic: a = 1, b = 2, c = 2

Step 3: Solve for x

Substitute in variables [Quadratic Formula]: $\displaystyle x=\frac{-2 \pm \sqrt{2^2-4(1)(2)}}{2(1)}$
[√Radical] Evaluate exponents: $\displaystyle x=\frac{-2 \pm \sqrt{4-4(1)(2)}}{2(1)}$
Multiply: $\displaystyle x=\frac{-2 \pm \sqrt{4-8}}{2}$
[√Radical] Subtract: $\displaystyle x=\frac{-2 \pm \sqrt{-4}}{2}$
[√Radical] Factor: $\displaystyle x=\frac{-2 \pm \sqrt{-1}\sqrt{4}}{2}$
[√Radicals] Simplify: $\displaystyle x=\frac{-2 \pm 2i}{2}$
Factor: $\displaystyle x=\frac{2(-1 \pm i)}{2}$
Divide: $\displaystyle x = -1 \pm i$

3 0

3 years ago