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3 years ago

Solving Exponential Equations (lacking a common base) 4^x-5=8

Mathematics

2 answers:

avanturin [10]3 years ago

8 0

Answer:

x= 6 1/2 or 6.5

Step-by-step explanation:

4^x-5 =8

2^2(x-5) =2^3

since the base is equal, the powers are equal

2(x-5) = 3

2x - 10 = 3

2x = 3 + 10

2x = 13

2x/2 = 13/2

x = 6 1/2 or 6.5

Tju [1.3M]3 years ago

6 0

Answer:

6.5

Step-by-step explanation:

4^(x-5) = 8

2^[2(x-5)] = 2³

Equating powers:

2(x-5) = 3

x-5 = 3/2

x = 13/2 or 6½

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1. A store manager marked up the price of a $12 clock by 20%. What is the new price of the clock?

Anon25 [30]

Answer:

1) new price of the clock is $14.4

2) Kyra scored 70% marks

3) 43.75% students are not eighth graders

Step-by-step explanation:

1. A store manager marked up the price of a $12 clock by 20%. What is the new price of the clock?

Price of Clock = $12

Mark up = 20%

We need to find new price of clock.

The price of clock can be found by finding 20% of 12 and then adding that amount in original price.

So, finding 20% of 12

$20\% of 12 \\=\frac{20}{100}\times 12\\=2.4$

So 20% of 12 is 2.4

Now finding new price:

New Price = Actual Price + Mark up

New Price = 12 + 2.4

New Price = 14.4

So, new price of the clock is $14.4

2. On a math quiz, Kyra answered 7 of 10 questions correctly. Express her quiz score as a percent.

Total questions = 10

Correct answers = 7

We need to express her quiz score as percent

It can be found using formula: $Percent Score = \frac{Obtained\:Marks}{Total\:Marks}\times 100\%\\$

Putting values and finding percentage

$Percentage = \frac{Obtained\:Marks}{Total\:Marks}\times 100\%\\\\Percentage = \frac{7}{10}\times 100\%\\Percentage = 70\%$

So, Kyra scored 70% marks

3. 96 students are enrolled in the Dance Program at Castillero. Of those students, 54 are eighth-graders. The remaining students are 6th or 7th graders. What percentage of the students are not eighth graders?

Total Students = 96

Number of eighth-graders students = 54

Remaining students = 96 - 54 = 42

So, 42 students are 6th or 7th graders

We need to find percentage of the students are not eighth graders.

$\frac{42}{96}\times 100\%\\=43.75\%$

So, 43.75% students are not eighth graders

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3 years ago

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2 years ago

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Roman55 [17]

Answer:

Step-by-step explanation:

We are given the function f(x) = -3/4(x) +6.

We know that the slope intercept form of a line is y = mx + b

Here, the slope m = -3/4.

The y-coordinate of the y intercept is b = 6 so the y-intercept is at the point (0,6) [x is always 0 at the y-intercept]

If you have to points you can graph the line, we only have the point (0,6).

To find the second point we use the slope.

We add the bottom point of the slope to the x coordinate of the y-intercept and we add the top part of the slope to the y coordinate of the y-intercept, so our second point is (0 + 4, 6 +(-3)) = (4, 3).

You then plot the points we have: (0,6) and (4,3) and draw the line through them.

Download pdf

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