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laila [671]
3 years ago
14

Prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. Steps Reasons 1.

A over b plus c over d Given 2. Ad over bd plus cb over bd Multiply to get a common denominator 3. Simplify Fill in the missing step in the proof. ad times cb all over bd ad plus cb all over bd ad minus cb all over bd ad plus cb all over two times bd
Mathematics
2 answers:
harkovskaia [24]3 years ago
6 0

Answer:

\dfrac{ad+bc}{bd}

Step-by-step explanation:

Let \frac{a}{b} and \frac{c}{d} be two rational numbers, where b and d are not zero and a, b, c and d are integers.

1. Given:

\dfrac{a}{b}+\dfrac{c}{d}

2. Multiply to get a common denominator :

\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd}+\dfrac{cb}{db}

3. Simplify:

\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd}+\dfrac{cb}{db}=\dfrac{ad+bc}{bd}

4. Since b\neq 0,\ d\neq 0, then bd\neq 0.

If a,b,c,d are integers, then bd, ad,bc, ad+bc are integers too. So the fraction

\dfrac{ad+bc}{bd}

is a rational number

LuckyWell [14K]3 years ago
3 0

Answer:

c

Step-by-step explanation:

i took the test

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Step-by-step explanation:

<h2>photosynthesis</h2>

Photosynthesis is a process by which phototrophs convert light energy into chemical energy, which is later used to fuel cellular activities. The chemical energy is stored in the form of sugars, which are created from water and carbon dioxide.

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3 years ago
Read 2 more answers
ΔMNO is shown.
JulijaS [17]

Answer:

ABC - AAS

DEF - not enough information

GHI - not enough information

JKL - SAS

Step-by-step explanation:

SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

AAS postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

HL postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

SSS postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

1. In triangles MNO and ABC, there are two congruent sides and non-included angle - AAS

2. In triangles MNO and DEF, there are two congruent sides  - there is not enough information

3. In triangles MNO and GHI, there are three congruent angles  - there is not enough information

4. In triangles MNO and JKL, there are two congruent sides and included angle - SAS

5 0
3 years ago
Explain how you know that 7/12 is greater than 1/3 but less than 2/3
PtichkaEL [24]
Or this question you should know that:
1/3 = (1*4)/(3*4) = 4/12 
and 
2/3 = (2*4)/(3*4) = 8/12 
so you can see that 7/12 is greater than 4/12 which is 1/3 and less than 8/12 which is 2/3 :))))
i hope this is helpful
have a nice day
7 0
3 years ago
Read 2 more answers
4. Which ordered pair is a solution of 3y + 2 = 2x - 5?
Lyrx [107]

Answer:

we determine that none of the ordered pair is a solution of  3y\:+\:2\:=\:2x\:-\:5  as none of the ordered pairs satisfy the equation.

Step-by-step explanation:

Considering the equation

3y\:+\:2\:=\:2x\:-\:5

  • Putting (-5,2) in the equation

3y\:+\:2\:=\:2x\:-\:5

3\left(2\right)\:+\:2\:=\:2\left(-5\right)\:-\:5

8=-15         ∵ L.H.S ≠ R.H.S

FALSE

  • Putting (0,-5) in the equation

3y\:+\:2\:=\:2x\:-\:5

3\left(-5\right)\:+\:2\:=\:2\left(0\right)\:-\:5

-13=-5       ∵ L.H.S ≠ R.H.S

FALSE

  • Putting (5,1) in the equation

3y\:+\:2\:=\:2x\:-\:5

3\left(1\right)+\:2\:=\:2\left(5\right)-\:5

5\:=-5          ∵ L.H.S ≠ R.H.S

FALSE

  • Putting (7,5) in the equation

3y\:+\:2\:=\:2x\:-\:5

3\left(5\right)+\:2\:=\:2\left(7\right)-\:5\:\:

17=9          ∵ L.H.S ≠ R.H.S

FALSE

From the above calculations, we determine that none of the ordered pair is a solution of  3y\:+\:2\:=\:2x\:-\:5  as none of the ordered pairs satisfy the equation.

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3 years ago
83 Tee (CsT Sequences and Functions
NISA [10]

Answer:

The common difference is same = d = -9

Therefore, the data represent a linear function.

Step-by-step explanation:

Given the table

x                        y

1                         4

2                        -5

3                        -14

4                        -23

5                         -32

Finding the common difference between all the adjacent terms of y-values

d = -5 - 4 = -6,

d = -14 - (-5) = -14+5 = -9

d = -23 - (-14) = -23 + 14 = -9

d = -32 - (-23) = -32 + 23 = -9

It is clear that the common difference between all the adjacent terms is same.

Thus,

d = -9

We know that when y varies directly with x, the function is a linear function.

Here, it is clear that each x value varies 1 unit, and each y value varies -9 units.

i.e. The common difference is same = d = -9

Therefore, the data represent a linear function.

3 0
2 years ago
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