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3 years ago

Write an exponential function y=ab^x whose graph passes through (1,6) and (3,54)

1 answer:

7 0

$y=ab^x\\\\(1;\ 6)\to x=1;\ y=6\\(3;\ 54)\to x=3;\ y=54\\\\\text{substitute the values of x and y to the equation}\\\\ \left\{\begin{array}{ccc}6=ab^1&\to&a=\dfrac{6}{b}^{(*)}\\54=ab^3\end{array}\right\\\\\text{substitute (*) to the second equation}\\\\54=\dfrac{6}{b}\cdot b^3\\\\54=6\cdot b^2\ \ \ \ |:6\\\\b=9\to b=\sqrt9\to b=3 \\\\\text{substitute the value of b to the (*)}\\\\a=\dfrac{6}{3}=2\\\\\text{Answer:}\ y=2\cdot3^x$

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Mr. Tolin purchased a used car for $2,816, which was 12% off the asking price. What was the asking price of the used car?

Nina [5.8K]

Answer:

Original price= $3,200

Step-by-step explanation:

Giving the following information:

Purchase price= $2,816

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Original price= purchase price / (1 - discount rate)

Original price= 2,816 / 0.88

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3 years ago

A college basketball coach has 12 players on his team. eight players are receiving scholarships, and four are not. the coach dec

EleoNora [17]

Solution: The given problem is a binomial distribution.

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Therefore, the given problem follows binomial with n = 5 and p = 0.6667

Now the probability that 4 of 5 players selected are on scholarship is:

$P(x=4) = \binom{5}{4} \times 0.6667^{4} (1-0.6667)^{5-4}$

$=5 \times 0.1976 \times 0.3333$

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3 years ago

Ten times the difference of a number x and 8

AleksAgata [21]

Answer:

Expression will be 10(x - 6).

Step-by-step explanation:

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(x - 6)

Then ten times the difference of this number and 6 will be represented by

10(x - 6)

Therefore, the statement " ten times the difference of a number and six " will be represented by the expression 10(x - 6)

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3 years ago

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Alja [10]

Answer:

Step-by-step explanation:

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2 years ago

Read 2 more answers

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GrogVix [38]

Answer:

a. y = -1/2x - 2

Step-by-step explanation:

The correct answer choice can be determined by finding the slope of the line. The slope is the ratio of rise to run.

<h3>slope</h3>

The x-intercept is 4 units left of the y-axis. As the line "runs" those 4 units, it "rises" -2 units to intercept the y-axis at -2. The slope of the line is ...

m = rise/run = -2/4 = -1/2

In the slope-intercept form of the equation of a line, the slope is the coefficient of x. This information is sufficient to let us choose the first answer choice.

<h3>equation</h3>

The slope-intercept equation is ...

y = mx +b . . . . . . . slope m, y-intercept b

We know the slope is -1/2, and the y-intercept is where x=0, at y=-2. Then the equation is ...

y = -1/2x -2 . . . . . matches choice A

_____

<em>Additional comment</em>

When answering multiple-choice questions, you only need to do enough work to tell which answers are <em>not</em> viable.

When we plot the points, we see that the line has negative slope. (eliminates choice C). The slope is shallow, rather than steep (the x-intercept is farther from the origin than the y-intercept), so the magnitude of the slope is less than 1 and choices B and D are eliminated.

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2 years ago