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3 years ago

Which property was applied to create this equivalent expression? 7x+(5+6×)--->(7x+5)+6x

Mathematics

2 answers:

liraira [26]3 years ago

5 0

Answer:

Associative property is applied

Step-by-step explanation:

7x+(5+6×)--->(7x+5)+6x

In the given expression , the terms are grouped in different order

In associative property, we can group the numbers in any order

(a+b)+c -------> a+(b+c)

first two terms are grouped on the left side

last two terms are grouped on the right side

7x+(5+6×)--->(7x+5)+6x

In the given expression, the terms are grouped in different order

So Associative property is applied

Leto [7]3 years ago

4 0

Answer:

Associative property of Addition.

Step-by-step explanation:

We are given the following information in the question:

We are given the expression:

$7x + (5+6x) = (7x+5)+6x$

We have used the associative property of addition.

Associative property of addition:

The associative property states that we can add regardless of how the numbers are grouped.
By grouped it is meant how you use parenthesis are used.
In other words, if we are adding, it does not matter where you put the parenthesis.
Whatever may be the order of addends, the sum will always be same.

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Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (w.y) be the unknown

Reil [10]

Answer:

Step-by-step explanation:

Given two coordinates (x₁,x₂) and (y₁,y₂), their midpoint (w,y) is expressed as:

M(X,Y) = $(\dfrac{x_1+w}{2}, \dfrac{y_1+y}{2})$

From the question, we are given the midpoint (X,Y) to be (2,2) and one endpoint as (1, -2) and we are to find the other end point expressed as (w,y). From the coordinates given, i can be seen that X = 2, Y =2, x₁ = 1 and y₁ = -2

Substituting the given end points into the given formula to get the other end points, we will have;

$X = \dfrac{x_1+w}{2} \\2 = \dfrac{1+w}{2} \\cross\ multiply\\4 = 1+w\\w = 4-1\\w = 3$

Similarly;

$Y = \dfrac{y_1+y}{2} \\2 = \dfrac{-2+y}{2} \\cross\ multiply\\4 = -2+y\\y = 4+2\\y = 6$

<em>Hence the other endpoint (w, y) is (3,6)</em>

8 0

3 years ago

The length and width of a rectangular frame is 15 inches and 8 inches.What is the length of the diagonal of this frame

anastassius [24]

Answer:

The length of the diagonal of the frame equal 17 inches

Step-by-step explanation:

The diagonal dividing the rectangle as made the rectangle 2 triangles

So according to Pythagoras Theorem,

Hypothenus² = opposite² + adjacent²

The diagonal lent is the Hypothenus.

so the two other sides are taking as opposite and adjacent respectively

so taking h as hypothenus,

h² = 15² + 8²

h² = 225 + 64

h² = 289

h = √289

h = 17

4 0

2 years ago

The hare challenged the tortoise to a race from the water fountain to the park bench. In order to ensure a fair race, the tortoi

BabaBlast [244]

A. I believe the hare never catches up to the tortoise
B. The hare waited 50 minutes before walking
C. The tortoise won the race

5 0

2 years ago

a parking garage has 6 levels. Each level has 15 row. Each row has the same number of parking spaces. there are 2,250 parking sp

Mandarinka [93]

To start with, we know there’s a definite amount of parking spaces in all(2,250) and we also know each level(6 in all) had 15 rows of parking spaces.

Equation

A = Parking spots per row

A = 2,250 Divided by(6 levels times 15 rows)

A= 2,250 Divided by 90

A = 25

The correct answer is 25 parking spots per row

To check this answer we can do

25 spots per row, Times 15 rows per level, Times the total amount of levels (6)

= the total amount of parking spots

25*15*6= 2,250

True

This confirms this answer as correct. Hope this helps.

6 0

2 years ago

HELPPPP!!!

Hatshy [7]

Answer:

(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

(x - h)²/a² - (y - k)²/b² = 1 where a > b

- So lets collect x in a bracket and make it a completing square and

also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x + 16y - 31 = 0

∴ (x² - 2x) + (-4y² + 16y) - 31 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y² - 4y) - 31 = 0

∴ (x² - 2x) - 4(y² - 4y) - 31 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵ (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1

- We will do the same withe bracket of y

- Lets make 4(y² - 4y) completing square

∵ √y² = y

∴ The 1st term in the bracket is x

∵ 4y ÷ 2 = 2y

∴ The product of the 1st term and the 2nd term is 2y

∵ The 1st term is y

∴ the second term = 2y ÷ y = 2

∴ The bracket is 4(y - 2)²

∵ 4(y - 2)² = 4(y² - 4y + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out

the bracket to keep the equation as it

∴ 4[y² - 4y + 4) - 4]

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify

∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms

∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides

∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - (y - 2)²/4 = 1

∵ 16 = (4)² and 4 = (2)²

∴ The standard form of the equation of the hyperbola is

(x - 1)²/4² - (y - 2)²/2² = 1

4 0

3 years ago