Is 42,260 irrational or rational

Find the area of the triangle. 3 m 6 m

belka [17]

Answer:

18m

Step-by-step explanation:

3m and 6m.

3mX6m

equals to 12m

3 0

3 years ago

Read 2 more answers

Find the area of the region enclosed by the graphs of the functions

Vaselesa [24]

Answer:

$\displaystyle A = \frac{8}{21}$

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

Terms/Coefficients
Functions
Function Notation
Graphing
Solving systems of equations

Calculus

Area - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

*Note:

Remember that for the Area of a Region, it is top function minus bottom function.

Step 1: Define

f(x) = x²

g(x) = x⁶

Bounded (Partitioned) by x-axis

Step 2: Identify Bounds of Integration

Find where the functions intersect (x-values) to determine the bounds of integration.

Simply graph the functions to see where the functions intersect (See Graph Attachment).

Interval: [-1, 1]

Lower bound: -1

Upper Bound: 1

Step 3: Find Area of Region

Integration

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx$
[Area] Rewrite [Integration Property - Subtraction]: $\displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx$
[Area] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}$
[Area] Evaluate [Integration Rule - FTC 1]: $\displaystyle A = \frac{2}{3} - \frac{2}{7}$
[Area] Subtract: $\displaystyle A = \frac{8}{21}$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Area Under the Curve - Area of a Region (Integration)

Book: College Calculus 10e

6 0

3 years ago

A box contains 12 chocolates, 3 of which are white chocolate, 4 milk chocolate, and 5 dark chocolate. I am sharing the box with

Kay [80]

Answer:

Step-by-step explanation:

Given that a box contains 12 chocolates, 3 of which are white chocolate, 4 milk chocolate, and 5 dark chocolate.

a) the chance that I draw a dark chocolate

b) Given that none of my friends draws a dark chocolate, the chance that I draw a dark chocolate is

$\frac{5}{9}$ since now all 5 dark chocolates would be there and total changed to 9 because 3 friends took 1 each.

c) All four drawn milk chocolates would be

$\frac{4C4}{12C4} \\=\frac{1}{495}$

d) the chance that the friend who gets to select first draws a dark chocolate and I draw a dark chocolate too

=P(first friend draws a dark chocolate) * P(I draw a dark chocolate)

When it comes to me chances are either there are 4 dark, or 3 dark, or 1 dark depending upon the other two friends drew black or not

= $\frac{5}{12} *\frac{7}{11} *\frac{6}{11} +2(\frac{5}{12} *\frac{4}{11} *\frac{7}{11} ) +\frac{5}{12} *\frac{4}{11} *\frac{4}{11} \\= \frac{140+280+80}{1452} \\=\frac{500}{1452} \\=\frac{125}{363}$

4 0

3 years ago

Which postulate can be used to prove the triangles shown are congruent ?

gogolik [260]

As we see from the diagram, in order:- side - angle - side are equal

So its SAS

4 0

3 years ago

What is the down payment of the sale price

amm1812

Answer:

The down payment is the lower of sale price and appraised value less the loan amount. It is not the same as the borrower's cash outlay if some of that outlay is used for settlement costs. Financing settlement costs does not affect the down payment.

8 0

3 years ago