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AleksandrR [38]
3 years ago
13

Write an equivalent expression for n x a using only addition

Mathematics
2 answers:
bulgar [2K]3 years ago
7 0

Answer:

Equivalent expression for n x a  = a+ a+a+a....n times

Step-by-step explanation:

Given: Expression for n x a .

To find : Write an equivalent expression for n x a using only addition.

Solution : We have given that n x a .

Here, we can say Sum of  a is n times.

We can rewrite it n x a  = a+ a+a+a....n times.

Example : 3 x 2 = 2 +2+ 2.

                   6 = 6 ( true)

Therefore , equivalent expression for n x a  = a+ a+a+a....n times.

Crazy boy [7]3 years ago
6 0
Suppose that n and a are two real and integers.
 We have then that we can rewrite an expression of the form:
 n * a

 As the sum of "a" times "n".
 For example:
 For n = 4 and a = 3 we have:
 4 * 3 = 12

 Equivalently we have:
 4 * 3 = 4 + 4 + 4 = 12
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Yuto has a bag containing 3 red marbles 5 blue marbles 2 green marbles and 8 yellow Marbles what is the total number of possible
sleet_krkn [62]

Answer:

17

Step-by-step explanation:

Mission Information :

This question is incomplete this line is missing in the question " Rin reaches into the bag, pulls out a blue marble, and puts it in her pocket. Then Misaki reaches in and pulls out a marble. What is the total number of possible outcomes for Misaki’s marble"

Now coming to the solution ,

Given :

Red marbles=3

blue marbles=5

green marbles=2

yellow Marbles=8

Total number of outcomes can be determined by

=Red marbles + blue marbles + green marbles + yellow Marbles

= 3\ +\  5+2 +8=18

As mention in the given question the Rin is pulling the 1 marble ,Now Total number of outcomes

=18-1\\=17

Therefore 17 is the correct answer

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8 0
3 years ago
4. In the adjoining figure, ABCD is a
Marizza181 [45]

The missing figure is attached

(i) m∠APB = 90° ⇒ proved

(ii) AD = DP and PB = PC = BC ⇒ proved

(iii)  DC = 2 AD ⇒ proved

Step-by-step explanation:

ABCD is a  parallelogram in which:

  • m∠A = 60°
  • The bisectors of ∠A and ∠B meet DC at P

In parallelogram ABCD:

∵ m∠A = m∠C ⇒ opposite angles

∵ m∠A = 60°

∴ m∠C = 60°

∵ m∠A + m∠B = 180 ⇒ two adjacent supplementary angles

∴ 60 + m∠B = 180 ⇒ subtract 60 from both sides

∴ m∠B = 120°

∵ m∠B = m∠D ⇒ opposite angles

∴ m∠D = 120°

∵ AP is the bisector of angle A

- That means AP divide ∠A into two equal parts

∴ m∠BAP = m∠DAP = \frac{1}{2} m∠A

∴ m∠BAP = m∠DAP = \frac{1}{2} (60°)

∴ m∠BAP = m∠DAP = 30°

∵ BP is the bisector of angle B

- That means BP divide ∠B into two equal parts

∴ m∠ABP = m∠CBP = \frac{1}{2} m∠B

∴ m∠ABP = m∠CBP = \frac{1}{2} (120°)

∴ m∠ABP = m∠CBP = 60°

(i)

In ΔAPB

∵ m∠BAP = 30° ⇒ proved

∵ m∠ABP = 60° ⇒ proved

- Sum of the measures of the interior angles in a Δ is 180°

∴ m∠APB + m∠BAP + m∠ABP = 180°

∴ m∠APB + 30 + 60 = 180

- Add like terms in the left hand side

∴ m∠APB + 90 = 180

- Subtract 90 from both sides

∴ m∠APB = 90°

(ii)

In Δ ADP:

∵ m∠D = 120° ⇒ Proved

∵ m∠DAP = 30° ⇒ proved

- Sum of the measures of the interior angles in a Δ is 180°

∴ m∠APD + m∠DAP + m∠D = 180°

∴ m∠APD + 30 + 120 = 180

- Add like terms in the left hand side

∴ m∠APD + 150 = 180

- Subtract 150 from both sides

∴ m∠APD = 30°

∵ m∠DAP = m∠APD = 30°

- If two angles in a triangle are equal in measures, then the triangle

  is isosceles

∴ Δ ADP is an isosceles triangle

∴ AD = DP

In Δ BPC:

∵ m∠PBC = 60° ⇒ proved

∵ m∠C = 60° ⇒ proved

- Sum of the measures of the interior angles in a Δ is 180°

∴ m∠BPC + m∠PBC + m∠C = 180°

∴ m∠BPC + 60 + 60 = 180

- Add like terms in the left hand side

∴ m∠BPC + 120 = 180

- Subtract 120 from both sides

∴ m∠BPC = 60°

∵ m∠PBC = m∠C = m∠BPC = 60°

- If the three angles of a triangle are equal in measure, then

  the triangle is equilateral

∴ Δ BPC is an equilateral triangle

∴ PB = PC = BC

(iii)

∵ AD = BC ⇒ opposite sides in parallelogram

∵ AD = DP ⇒ Proved

- Equate the two right hand sides of AD

∴ BC = DP

∵ BC = PC

- Equate the right hand sides of BC

∴ DP = PC

∵ DC = DP + PC

∵ DP = AD

∴ PC = AD

- Substitute DP by AD and PC by AD in CD

∴ CD = AD + AD

∴ DC = 2 AD

Learn more:

You can learn more about parallelogram in brainly.com/question/6779145

#LearnwithBrainly

6 0
4 years ago
is it always true that the y-values of a quadratic function have opposite signs on either side of a zero of the function? Explai
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Answer:

It is true both sides have opposite signs

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