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3 years ago

Identify the property used in the first four steps to solve the equation 4(x-7)=2x-6

Mathematics

1 answer:

myrzilka [38]3 years ago

4 0

Answer:

x = 11

distributive law

additive law

multiplication property

Step-by-step explanation:

Given in the question an equation

4(x-7) = 2x-6

Distributive law

a(b+c) = ab +ac

4x - 4(7) = 2x - 6

4x -28 = 2x - 6

Use the addition property of equality to reduce the 2x on the right.

4x - 2x - 28 = 2x - 2x -6

4x -2x -28 = -6

Use the addition property of equality to reduce -28 to zero on the left.

4x - 2x- 28 + 28 = -6 + 28

2x = 22

Use the multiplication property of equality to reduce 2x to just x

2x2 = 22/22

x = 22/2

x = 11

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hoa [83]

Given:

The expressions are:

$2x(x^2-6x+3)$

$2a^2(5b^2+3ab+6a+1)$

To find:

The product of each expression.

Solution:

According to the distributive property of multiplication over addition, we get

$a(b+c)=ab+ac$

The first expression is:

$2x(x^2-6x+3)$

Using distributive property of multiplication over addition, we get

$2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)$

$2x(x^2-6x+3)=2x^3-12x^2+6x$

Therefore, the product of $2x(x^2-6x+3)$ is $2x^3-12x^2+6x$ .

The second expression is:

$2a^2(5b^2+3ab+6a+1)$

Using distributive property of multiplication over addition, we get

$2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)$

$2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2$

Therefore, the product of $2a^2(5b^2+3ab+6a+1)$ is $10a^2b^2+6a^3b+12a^3+2a^2$ .

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3 years ago

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frutty [35]

Answer:

$\boxed{\boxed{\sf x>-7}}$

Step-by-step explanation:

$\sf -5x-7$

Add 7 to both sides:

$\sf -5x-7+7$

$\sf -5x$

Multiply both sides by -1:

$\sf \left(-5x\right)\left(-1\right)>35\left(-1\right)$

$\sf 5x>-35$

Divide both sides by 5:

$\sf \cfrac{5x}{5}>\cfrac{-35}{5}$

$\sf x>-7$

_________________________________

3 0

3 years ago

Find the measures of two complementary angles, ÐA and ÐB, if mÐA = (7x + 4)° and mÐB = (4x + 9)°. Measure of angle A = ... Measu

Westkost [7]

Answer:

The measure of angle A is 53 degrees

The measure of angle B is 37 degrees

Step-by-step explanation:

Here in this question, we are interested in calculating the measure of the two angle.

When how angles are complementary, it means the sum of both equals 90 degrees

mathematically ;

(7x + 4) + (4x + 9) = 90

7x + 4x + 4 + 9 = 90

11x + 13 = 90

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11x = 77

x = 77/11 = 7

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4 years ago

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Dominik [7]

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$x_1,\ x_2,\ldots,x_n$

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$p(x)=(x-x_1)(x-x_2)\cdots(x-x_n)$

So, in this case, we're looking for the solutions of

$3x^2-25=0 \iff 3x^2=25 \iff x^2 = \dfrac{25}{3} \iff x=\pm\sqrt{\dfrac{25}{3}}=\pm\dfrac{5}{\sqrt{3}}$

So, the polynomial can be written as

$3x^2-25 = \left(x-\dfrac{5}{\sqrt{3}}\right)\left(x+\dfrac{5}{\sqrt{3}}\right)$

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4 years ago