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3 years ago

27^x −1 = 9^3x−7 what is X

Mathematics

1 answer:

tigry1 [53]3 years ago

3 0

x is $\frac{11}{3}$

Step-by-step explanation:

Let us revise some rules of exponents

$(a^{n})(a^{n})=a^{m+n}$
$\frac{a^{m}}{a^{n}}=a^{m-n}$
$(a^{m})^{n}=a^{mn}$
$a^{m}=a^{n}$ , then m = n

∵ $27^{x-1}=9^{3x-7}$

- Factorize 27 and 9

∵ 27 = 3 × 3 × 3

∴ 27 = 3³

∵ 9 = 3 × 3

∴ 9 = 3²

Substitute them in the equation

∴ $(3^{3})^{x-1}=(3^{2})^{3x-7}$

- Use the third rule to simplify each side

∴ $(3)^{3x-3}=(3)^{6x-14}$

- Use the fourth rule

∵ The bases of the two sides are equal

∴ Their exponents are equal

∴ 3x - 3 = 6x - 14

- Subtract 6x from both sides

∴ -3x - 3 = -14

- Add 3 to both sides

∴ -3x = -11

Divide both sides by -3

∴ x = $\frac{11}{3}$

x is $\frac{11}{3}$

Learn more:

You can learn more about equations in brainly.com/question/4934417

#LearnwithBrainly

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yawa3891 [41]

Answer:

$(u/v)(x)=-x^{3}+x^{2}-1$

Step-by-step explanation:

You have the following functions:

$u(x)=x^{5}-x^{4}+x^{2}\\v(x)=-x^{2}$

Therefore $(u/v)(x)$ indicates that you must divide both functions, as you can see below:

$(u/v)(x)=\frac{x^{5}-x^{4}+x^{2}}{-x^{2}}$

Simplify it. Therefore, you obtain:

$(u/v)(x)=\frac{x^{5}-x^{4}+x^{2}}{-x^{2}}\\\\(u/v)(x)=-x^{3}+x^{2}-1$

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4 years ago

Read 2 more answers

We want to determine if the probability that a student enrolled in an accelerated math pathway is independent of whether the stu

Molodets [167]

Answer:

The correct option is (c).

Step-by-step explanation:

The complete question is:

The data for the student enrollment at a college in Southern California is:

Traditional Accelerated Total

Math-pathway Math-pathway

Female 1244 116 1360

Male 1054 54 1108

Total 2298 170 2468

We want to determine if the probability that a student enrolled in an accelerated math pathway is independent of whether the student is female. Which of the following pairs of probabilities is not a useful comparison?

a. 1360/2468 and 116/170

b. 170/2468 and 116/1360

c. 1360/2468 and 170/2468

Solution:

If two events <em>A</em> and <em>B</em> are independent then:

$P(A|B)=P(A)\\\\\&\\\\P(B|A)=P(B)$

In this case we need to determine whether a student enrolled in an accelerated math pathway is independent of the student being a female.

Consider the following probabilities:

$P (F|A) = \farc{116}{170}\\\\P(A|F)=\frac{116}{1360}\\\\P(A)=\frac{170}{2468}\\\\P(F)=\frac{1360}{2468}$

If the two events are independent then:

P (F|A) = P(F)

P (A|F) = P (A)

But what would not be a valid comparison is:

P (A) = P(F)

Thus, the correct option is (c).

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3 years ago

Exponet for 13 ·13·13·13

photoshop1234 [79]

The exponent for that would be 13^3.

If the answer is incorrect, then i am sorry.

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4 years ago

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Brilliant_brown [7]

Answer:

The price of one gallon of gasoline is $3.15

Step-by-step explanation:

If the lady buys 2.4 gallons of gasoline for a total of $7.56, then as the problem suggests, one can find the unknown price of gasoline per gallon (p) by solving the equation for the unknown "p":

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then divide both sides by 2.4 to isolate the unknown "" on one side of the equal sign:

p = 7.56/2.4

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3 years ago

What is the slope of the line that goes through -3,7 & -17,3

Natalka [10]

Point 1: (-3, 7)

Point 2: (-17, 3)

To find the slope, we need to use the slope formula which is as follows: m = (y2 - y1) / (x2 - x1). We will plug in each x and y coordinate from our points above, respectively.

m = (3 - 7) / (-17 - - 3)

m = (-4) / (-14)

m = 2/7

The slope of the line that goes through (-3, 7) and (-17, 3) is 2/7.

Hope this helps!! :)

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3 years ago