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3 years ago

Match each equation on the left to the mathematical property it uses on the right.

Mathematics

2 answers:

erma4kov [3.2K]3 years ago

6 0

Answer:

The answer to your question is:

Step-by-step explanation:

(4 + 5) + 2 = 4 + (5 + 2) Associative property of addition

2(2x + 4) = 4x + 8 Distributive property

( 7 x ) 3 = 7 (x 3) Associative property of multiplication

( 8 x 2) = (x 8 2) Commutative property of multiplication

( 7 + 3) + 1 = 1 + (7 + 3) Commutative property of addition

Lelechka [254]3 years ago

5 0

Answer:

(4+5)+2=4+(5+2) Associative property of addition

2(2x+4)=4x+8 Distributive property

(7x) × 3 = 7(x × 3) Associative property of multiplication

(8 × x × 2) = (x × 8 × 2) Commutative property of multiplication

(7+3)+1 = 1+(7+3) Commutative property of addition

Step-by-step explanation:

Associative property of addition : It is a property when we are adding numbers then we can group the numbers in any combination.

For example : a+(b+c) = (a+b)+c

Associative property of multiplication : It is a property when we are multiplying numbers then we can group the numbers in any combination.

For example : a×(b×c) = (a×b)×c

Commutative property of addition : It is a property in which we can add numbers in any order.

For example : a+b = b+a

Commutative property of multiplication : It is a property in which we can multiply numbers in any order.

For example : a×b = b×a

Distributive property : It is a combination of addition and multiplication.

For example : a×(b+c) = (a×b) + (a×c)

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Find the side lengths of the triangle in this picture.

ozzi

Answer:

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.

Step-by-step explanation:

According to the statement, we have the following information about the lengths of the right triangle:

Hypotenuse

$3\cdot x + 14$

Long leg

$3\cdot x + 13$

Short leg

$x$

By the Pythagoric Theorem, we have the following expression:

$(3\cdot x + 14)^{2} = x^{2} + (3\cdot x + 13)^{2}$ (1)

$9\cdot x^{2}+84\cdot x + 196 = x^{2} + 9\cdot x^{2} + 78\cdot x + 169$

$9\cdot x^{2} + 84\cdot x + 196 = 10\cdot x^{2} + 78\cdot x +169$

$x^{2} -6\cdot x -27 = 0$

$(x-9)\cdot (x+3) = 0$

As length is a positive variable by nature, then the only possible solution is $x = 9$ . Lastly, the side lengths of the right triangle are:

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.

8 0

3 years ago

Which equation represents the graph?

klio [65]

The second option.

That is because
$y -3 = - \frac{1}{2}(x + 1) \\ (y -3)+3 = (- \frac{1}{2} x - \frac{1}{2}) + 3 \\ y = - \frac{1}{2}x + 2 \frac{1}{2}$

6 0

3 years ago

The owner of a miniature golf course asks you to design the shape of the green section. He has several requirements

liraira [26]

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7 0

4 years ago

The midpoint of ab is m(5-2). If the coordinates of a are (6,-5), what are the coordinates of b

Alex

The coordinate of B is (4,1)

7 0

3 years ago

Choose the solution(s) of the following system of equations x2 + y2 = 6 x2 – y = 6

ElenaW [278]

<h2>Answer</h2>

$x=\sqrt{6}, y=0\\ x=-\sqrt{6} , y=0\\x=\sqrt{5} , y=-1\\x=-\sqrt{5} , y=-1$

Or as ordered pairs: $(\sqrt{6} ,0),(-\sqrt{6} ,0),(\sqrt{5} ,-1),(-\sqrt{5} ,-1)$

<h2>Explanation</h2>

Lets solve our system of equations step by step

$x^2+y^2=6$ equation (1)

$x^2-y=6$ equation (2)

1. Solve for $x^2$ in equation (2)

$x^2-y=6$

$x^2=6+y$ equation (3)

2. Replace equation (3) in equation (1) and solve for $y$

$x^2+y^2=6$

$6+y+y^2=6$

$y^2+y=0$

$y(y+1)=0$

$y=0$ or $y=-1$

3. Replace the values of $y$ in equation (3) and solve for $x$

- For $y=0$

$x^2=6+y$

$x^2=6$

$x=\sqrt{6}$ or $x=-\sqrt{6}$

- For $y=-1$

$x^2=6+y$

$x^2=6-1$

$x^2=5$

$x=\sqrt{5}$ or $x=-\sqrt{5}$

So, the solutions of our system of equation are:

$x=\sqrt{6}, y=0\\ x=-\sqrt{6} , y=0\\x=\sqrt{5} , y=-1\\x=-\sqrt{5} , y=-1$

6 0

3 years ago

Read 2 more answers