What is a reciprocal?

2 answers:

6 0

The reciprocal is the fraction flipped. so the reciprocal of 1/2 is 2/1. It's used when dividing fractions to make it multiplication, so you use the reciprocal for the second fraction.

Jlenok [28]3 years ago

5 0

A number which when multiplied by x yields the multiplicative identity 1.

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If a+b=1, find N=a^3+b^3+3ab

mart [117]

Answer: 1

Step-by-step explanation:

a + b = 1

a³ + b³ = (a + b)(a² - ab + b²) formula for a perfect cube

a³ + b³ + 3ab = (a + b)(a² - ab + b²) + 3ab

↓

= 1 (a² - ab + b²) + 3ab

= a² - ab + b² + 3ab

= a² + 2ab + b² this is a perfect square

= (a + b)(a + b)

↓ ↓

= (1) (1)

= 1

4 0

3 years ago

Read 2 more answers

Given: 2x + 11 = 15 Prove: x = 2 Statements Reason 1. 2x + 11 = 15 1. Given 2. 2x = 4 2. 3. X = 2 3. Division Property of Equali

wariber [46]

Answer:

Statements Reasons

1. 2x + 11 = 15 1. Given

2. 2x = 4 2. Subtraction Property of Equality

3. X = 2 3. Division Property of Equality

Step-by-step explanation:

An equation can be solved and its solution proven using algebraic theorems and properties. To create a proof, form two columns. Label one side Statements and the other Reasons.

Begin your proof listing the any information given to you. List as the reason - Given.

Then list the next step which here would be to subtract by 11 on both side. The reason is Subtraction Property of Equality. Subtraction is the inverse of addition. Inverse axiom is another acceptable reason.

Then divide both sides by 2. The reason is Division Property of Equality or Inverse axiom once again. See the proof below.

Statements Reasons

1. 2x + 11 = 15 1. Given

2. 2x = 4 2. Subtraction Property of Equality

3. X = 2 3. Division Property of Equality

6 0

3 years ago

Read 2 more answers

if cot theta = -24/7 and cos theta < 0, name the quad in which theta lies, then find the exact value of csc theta

NemiM [27]

Cot θ = -24/7 and cos θ < 0

"cos θ < 0" means cosine is negative

Remember osmething like "ALL students Take Calculus"?

all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4

since cot(angent) is the reciprocal of tangent, tangent must also be negative.

tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III

therefore, θ must lie in quadrant II.

remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle

then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.

csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine

the hypotenuse can be found w/ pythagorean theorem

hypotenuse = √[(-24)² + 7²] = 25

therefore,
cot θ = 25/7