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Evaluate the given expression. Subscript 5 Baseline P Subscript 2 a. 40 c. 25 b. 32 d. 20

Leto [7]

Answer:

d. 20

Step-by-step explanation:

The given question implies 5 permutation 2, i.e $_{5}$ $P_{2}$ .

But,

$_{n}$ $P_{r}$ = $\frac{n!}{(n - r)!}$

So that for $_{5}$ $P_{2}$ , n = 5 and r = 2.

$_{5}$ $P_{2}$ = $\frac{5!}{(5 - 2)!}$

= $\frac{5!}{3!}$

= $\frac{5*4*3*2!}{3*2!}$

Cancel out 3 and 2 with respect to the numerator and denominator.

$_{5}$ $P_{2}$ = 5 * 4

= 20

Therefore,

$_{5}$ $P_{2}$ = 20

So that the correct option is D.

6 0

3 years ago

Read 2 more answers

What is the inverse of the function f(x) = x +3?

MAXImum [283]

Answer:

f⁻¹(x) = x - 3

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

Functions
Function Notation
Inverse Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x + 3

Step 2: Find

Swap: x = y + 3
[Subtraction Property of Equality] Isolate y: x - 3 = y
Rewrite: f⁻¹(x) = x - 3

6 0

3 years ago

I NEED HELP RNNNNNNNNNN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Law Incorporation [45]

The answer is the last option 32x8 hope this helps

3 0

2 years ago

Read 2 more answers

find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

Snezhnost [94]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - A trapezium ABCD with non parallel sides of measure 15 cm each ! along , the parallel sides are of measure 13 cm and 25 cm

To find - Area of trapezium

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

Construction -

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

Since we've obtained the height now , we can easily find out the area of trapezium !

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$

hope helpful :D

6 0

1 year ago

Changing Bases to Evaluate Logarithms in Exercise, use the change-of-base formula and a calculator to evaluate the logarithm. Se

son4ous [18]

Answer:

The question is incomplete, the complete question is "Changing Bases to Evaluate Logarithms in Exercise, use the change-of-base formula and a calculator to evaluate the logarithm. See Example 9. $log_{4}7$ .