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iren [92.7K]
2 years ago
8

3x + 2 = 2x + 7 Solve x

Mathematics
1 answer:
Doss [256]2 years ago
7 0

3x + 2 = 2x + 7

Subtract 2 from both sides:

3x = 2x +5

Subtract 2x from both sides:

x = 5

Answer: x = 5

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A radio station signal covers a circular area out from the signal tower. It gets weaker the farther away your are. The local sta
valentinak56 [21]

Answer:

1. We would hear better at Dunkin's since its distance from the radio station is the shortest.

2. McDonald's is out of range of the radio station since its distance is greater than the range of the radio station.

Step-by-step explanation:

1) Will we hear it better at Zaxby's (2,-4), McDonalds (4, -4), or Dunkin' (-3,3). Show work to support your decision and explain your reasoning.

We need to find the distance of each point from the tower.

The shorter the distance from the radio station the better the signal.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

<u>Since Dunkin's distance, d₃ = 4.24 is the least distance from the radio station and is within range of 5 miles, we would hear better at Dunkin's.</u>

2) Are any of these location outside the range of the radio station? If so, which one(s). Defend your decision mathematically.

The radio station is outside of range if its distance is greater than 5 miles. That is, d > 5 miles.

So, we calculate the distance of each point from the radio station.

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

<u>So, for each of the distances calculated above, only McDonald's distance, d₂ = 5.66 miles > 5 miles. </u>

<u>So, McDonald's is out of range of the radio station.</u>

5 0
3 years ago
0 What is A U B?<br> Set A = 1, 2, 3, 4<br> Set B = 2, 3, 6, 10, 11
Oxana [17]

Answer:

A U B= 1,2,3,4,6,10,11

Step-by-step explanation:

because A union B is all number from set A and set B together without repeating

4 0
3 years ago
Brian is driving 168km to visit some friends . He wants to get there in 6 hours . How many kilometers does he need to drive each
Tasya [4]

Answer:

28 km per hour

Step-by-step explanation:

Kilometres Brian needs to drive in an hour = total kilometres / total hours

168 km / 6 hours = 28 km per hour

5 0
2 years ago
Given f(x)=5x+7 and g(x)=x-9;what is f(x)•g(x)?
inysia [295]
Give me the brainliest if u like the answer

f(x)•g(x) = (5x+7)×(x-9)
now multiply 5x with both terms and 7 with both terms

5 {x}^{2} - 45x + 7x - 63 \\ 5 {x}^{2} - 38x - 63
7 0
3 years ago
Find the third term of the geometric sequence when a1=1/4 and r=−2
Jobisdone [24]

Answer:

1 is the third term.

Step-by-step explanation:

Geometric sequences have a common ratio.  This means a term divided by previous term is the same no matter the choosing of term.

So for example:

\frac{a_{n}}{a_{n-1}}=\frac{a_{n-1}}{a_{n-2}}=\cdots=\frac{a_4}{a_3}=\frac{a_3}{a_2}=\frac{a_2}{a_1}

So anyways geometric sequences means you are just multiply the common ratio over and over to generate the next term.

So, the first term is 1/4.

The second term is (-2)(1/4)=-1/2.

The third term is (-2)(-1/2)=1.

7 0
3 years ago
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