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Elden [556K]
2 years ago
5

Nigel makes the claim that x=6 is the solution to the equation 4(5x−12)−7x=5x. His work to support his claim follows. Given: 4(5

x−12)−7x=5x Step 1: 20x−48−7x=5x Step 2: 20x−7x−48=5x Step 3: 13x−48=5x Step 4: 13x−13x−48=5x−13x Step 5: 0−48=−8x Step 6: 6=x Which of the following justifications can be used to justify and support Nigel's work? Select all justifications that are correct.
Step 1 is justified by the Distributive Property. , Step 1 is justified by the Distributive Property. , ,

Step 4 is justified by the Symmetric Property. , Step 4 is justified by the Symmetric Property. , ,

Step 5 is justified by the Property of Additive Inverses. , Step 5 is justified by the Property of Additive Inverses. , ,

Step 2 is justified by the Commutative Property. , Step 2 is justified by the Commutative Property. , ,

Step 6 is justified by the Associative Property.
Mathematics
1 answer:
RSB [31]2 years ago
5 0

Answer:

Step 1 is justified by the Distributive Property.

Step 4 is justified by the Symmetric Property

Step-by-step explanation:

Given the equation solved by Nigel expressed as

4(5x−12)−7x=5x.

First, we need to expand the bracket using the distributive property

4(5x−12)−7x=5x.

4(5x)-4(12) -7x = 5x

20x - 48 - 7x = 5x

Hence Step 1 is justified by the Distributive Property.

Next is to collect the like terms;

20x - 7x - 48 = 5x

Take the difference

13x - 48 = 5x

Next is to subtract 13x from both sides according to the symmetric property

13x - 48 - 13x = 5x - 13x

Hence Step 4 is justified by the Symmetric Property

The resulting equation will be

0-48 = -8x

Divide both sides by -8

-48/-8 = -8x/-8

6 = x

Hence the correct justifications are Step 1 is justified by the Distributive Property AND Step 4 is justified by the Symmetric Property

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irina1246 [14]

Hello!

This question is about which values you are changing when you are transforming an equation.

Let's go through the parent function for an absolute value equation and its various transformations.

y=a|b(x-c)|+d

Since we are only looking at horizontal and vertical transformations, we only need to worry about the c and d values.

The c value of a function determines a function's horizontal position, and the d value of a function determines a function's vertical position.

One thing to note here is that the c value is being subtracted from the x value, meaning that if the function is being transformed to the right, you would actually be subtracting that value, while the d value behaves like a normal value, if it is being added, the function is transformed up, and vice versa.

Now that we know this, let's write each expression.

a) y=|x+2|+1

b) y=|x+2|-1

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Hope this helps!

6 0
3 years ago
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sdas [7]
Use the Sum of Angles In a Triangle therom.
8 0
3 years ago
to find the area of a trapezoid dylan uses the formula A=1/2 (B1+B2)h the bases have lengths of 3.6 cm and 12 1/3 cm. the height
Artemon [7]

Answer:

It is irrational because it can not be represented as a fraction of two integers

Step-by-step explanation:

Given

B_1 = 3.6

B_2 = 12\frac{1}{3}

H = \sqrt[3]5

Required

Why is the area irrational?

First, we need to calculate the area

Area = \frac{1}{2}(B_1 + B_2) * H

Area = \frac{1}{2}(3.6 + 12\frac{1}{3}) * \sqrt[3]5

Area = \frac{1}{2}(3.6 + \frac{37}{3}) * 17100

Area = \frac{1}{2}(\frac{10.8+37}{3}) * 1.710

Area = \frac{1}{2}(\frac{47.8}{3}) * 1.7100

Area = \frac{47.8}{6} * 1.7100

Area = \frac{47.8* 1.7100}{6}

Area = \frac{81.738}{6}

Area = 13.623

<em>It is irrational because it can not be represented as a fraction of two integers</em>

5 0
2 years ago
The following lines are ______ <br><br> 4x + 2y = 10 y = -2x + 15
zmey [24]

Answer:

Parallel

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + 2y = 10 ( subtract 4x from both sides )

2y = - 4x + 10 ( divide through by 2 )

y = - 2x + 5 ← in slope- intercept form

with slope m = - 2

and

y = - 2x + 15 ← is in slope- intercept form

with slope m = - 2

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then the 2 lines are parallel

4 0
1 year ago
Read 2 more answers
The function f is linear. If f(2) = 2 and f(-6)=6 find f(6)
lina2011 [118]
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therefore:f(x)=-\frac{1}{2}x+3\Rightarrow f(6)=-\frac{1}{2}\cdot6+3=-3+3=0\\\\Answer:\boxed{f(6)=0}
5 0
3 years ago
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