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Nataliya [291]
2 years ago
5

Solve using logs 5^(3x-6)=125

Mathematics
1 answer:
Hitman42 [59]2 years ago
3 0
5 ^{3x-6} =125 \\ \\ 5 ^{3x-6} =5^3 \\ \\3x-6 =3 \ \ |+6 \\ \\3x=3+9 \\ \\3x=12 \ \ /:3 \\ \\x=\frac{12}{3} \\ \\x= 3
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Find the slope of the line on the graph.
Annette [7]

Answer:

3

Step-by-step explanation:

By going up 3 and right 1 you get 3/1, aka 3

The line of the equation is y=3x+2

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If the image above is rotated about the y-axis, which of the following images best represents the result?
swat32

Answer:

the answer would be x because it has a larger width than y

6 0
2 years ago
6 4/5+5 3/10 adding and subtracting mixed number
lawyer [7]

Too add mixed numbers, first convert them to improper fractions:

34/5 + 53/10

Next, find a common denominator, which in this case is 10.

Convert 34/5 so that it has a denominator of 10 by multiplying the ENTIRE fraction by 2: 68/10

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4 0
2 years ago
A tourist purchases a car in england and ships it home to the united states. the car sticker advertised that the car's fuel cons
Valentin [98]

<u>Solution-</u>

Fuel consumption rate = 40 miles per UK gallon (As the car is manufactured in UK)

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1 US gallon = 3.7853060 lit

\therefore \frac{1 \ UK \ gallon}{1 \ US \ gallon} = \frac{4.5459631}{3.7853060} = 1.2009499

\Rightarrow 1 \ UK \ gallon = 1.2009499 \ US \ gallon

As the fuel consumption rate = 40 miles per gallon

⇒ You need 1 UK gallon of fuel to go 40 miles

⇒ You need 1.2009499 US gallon of fuel to go 40 miles

Or you can say that, to go 40 miles you need 1.2009499 US gallon of fuel

⇒ To go 1 mile you will need  \frac{1.2009499}{40} = 0.0300237

⇒ To go 738 miles you will need 0.0300237×738 = 22.1574906 US gallon of fuel

∴ 22.1574906 gallon of fuel is actually required.

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6 0
2 years ago
Celeste is making fruit baskets for a local hospital. The directions say to use 5 apples for every 6 oranges. Celeste is filling
MariettaO [177]

Answer:

A. Equivalent ratios of 5:6

We multiply both the numerator and the denominator by the same number, this way:

<u>10:12 , 15:18, 20:24, 25:30</u>

B. Equivalent ratios of 2:3

We multiply both the numerator and the denominator by the same number, this way:

<u>4:6 , 6:9, 8:12, 10:15, 12:18</u>

C. We have the same number of oranges at:

<u>10:12 and 8:12</u>

<u>15:18 and 12:18</u>

<u>Like Celeste decided not to follow the directions, she's actually using less apples than expected to fill the baskets.</u>

Step-by-step explanation:

1. Let's check all the information provided to answer the question correctly:

Ratio that the local hospital say to Celeste to use : 5 apples for every 6 oranges

Ratio that Celeste is actually using: 2 apples for every 3 oranges

2.  Complete the tables to find equivalent ratios.

A. Equivalent ratios of 5:6

We multiply both the numerator and the denominator by the same number, this way:

10:12 , 15:18, 20:24, 25:30

B. Equivalent ratios of 2:3

We multiply both the numerator and the denominator by the same number, this way:

4:6 , 6:9, 8:12, 10:15, 12:18

3. Circle two columns, one in each table, in which the number of oranges is the same.

We have the same number of oranges at:

10:12 and 8:12

15:18 and 12:18

Like Celeste decided not to follow the directions, she's actually using less apples than expected to fill the baskets.

8 0
3 years ago
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