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pentagon [3]
3 years ago
14

(01.07, 02.01 MC) Brian solved the following equation: 6(3x – 5) = 4(4x + 2) Step Work Justification 1 18x – 30 = 16x + 8 2 2x –

30 = 8 3 2x = 38 4 x = 19 Which of the following has all correct justifications Brian used to solve this equation? 1. Associative property of addition. 2. Subtraction property of equality. 3. Addition property of equality. 4. Multiplicative inverse. 1. Associative property of addition. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality. 1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality. 1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Multiplicative property of equality.
Mathematics
1 answer:
HACTEHA [7]3 years ago
4 0

6(3x - 5) = 4(4x + 2)    Given

(6)(3x) + (6)(-5) = (4)(4x) + (4)(2)    Distributive property

18x - 30 = 16x + 8

18x - 16x - 30 = 16x - 16x + 8     Subtraction property of equality

2x - 30 = 8

2x - 30 + 30 = 8 + 30     Addition property of equality

2x = 38

2x : 2 = 38 : 2     Division property of equality

x = 19


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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
If someone can pls give the answer with steps that would be greatly appreciated :)
AleksAgata [21]

Answer:

Step-by-step explanation:

Let C be the number of correct answers

Let B be the number of questions not answered

Let W be the wrong answers

Total = 2*C + B -  W

It's a trinomial. There are three unrelated terms.

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Amount =$48003.20

Step-by-step explanation:

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Interest earned after the period= $48003.20-$37500 =$10503.20

Learn More

Compound Interest formula application: brainly.com/question/7014337

Keywords: inherit, sum, money, interest

#LearnwithBrainly

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Answer:

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