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3 years ago

which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x?

1 answer:

7 0

First, take a look at 3 less than twice x. Twice x would be 2x and 3 less than it would become 2x-3.

Next, 2 more than the quantity 3 times x. The quantity of 3 times x is 3x and 2 more than that would be 3x+2.

Now that we have our two equations, we need to multiply them together, which can be shown as (2x-3)(3x+2).

Then, multiply the two equations together using FOIL (multiply the first two terms, then the outside terms, then inside, and lastly, the last two terms): 2x times 3x, 2x times 2, -3x times 3x, and 2 times -3, which equates to 6x^2+4x-9x-6.

Your final answer is 6x^2-5x-6.

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Which logarithmic equation is equivalent to the exponential equation below?

aleksandr82 [10.1K]

Option B: $\ln 6=5 x$ is the correct answer.

Explanation:

The exponential equation is $e^{5 x}=6$

If $f(x)=g(x)$ , then $\ln (f(x))=\ln (g(x))$

Thus, the equation becomes

$\ln \left(e^{5 x}\right)=\ln (6)$

Applying log rule, $\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)$ and thus the equation becomes

$5 x \ln (e)=\ln (6)$

Since, we know that, $\ln (e)=1$ , using this we get,

$5 x=\ln (6)$

Hence, the logarithmic equation which is equivalent to the exponential equation $e^{5 x}=6$ is $\ln 6=5 x$

Thus, Option B is the correct answer.

7 0

3 years ago

Matt Bonner has 8 dimes, 9 pennies, and 4 quarters in his pocket. If each coin is equally likely to be pulled out of his pocket

Lesechka [4]

Answer:

B. 0.602%

Step-by-step explanation:

Probability is essentially (# times specific event will occur) / (# times general event will occur). Here, we have a few specific events: draw a quarter, draw a second quarter, draw a penny, and draw another penny. The general event will just be the number of coins there are to choose from.

The probability that the first draw is a quarter will be 4 / (4 + 8 + 9) = 4/21.

Since we've drawn one now, there's only 21 - 1 = 20 total coins left. The probability of drawing a second quarter is: (4 - 1) / (21 - 1) = 3/20.

The probability of drawing a penny is: 9 / (20 - 1) = 9/19.

The probability of drawing a second penny is: (9 - 1) / (19 - 1) = 8/18.

Multiply these four probabilities together:

(4/21) * (3/20) * (9/19) * (8/18) = 864 / 143640 ≈ 0.602%

The answer is B.

8 0

3 years ago

Read 2 more answers

Simplify.<br> X+1<br> - 1 - 4.2

Hoochie [10]

Answer:

X − 4.2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

ernie thinks he is being stalked by his own shadow. if the ratio of ernie's height to his shadow's height is 1.5 to 1, and ernie

Anna71 [15]

The height of Ernies shadow is 4 feet when his height is 6 feet.

<h3>equation</h3>

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the length of his shadow. Given that the ratio of ernie's height to his shadow's height is 1.5 to 1. Hence:

(1.5/2.5) * y = 6
y = 10 feet

(1/2.5) * 10 = x

x = 4 feet

The height of Ernies shadow is 4 feet when his height is 6 feet.

Find out more on equation at: brainly.com/question/13763238

7 0

2 years ago

Can someone figure out b please

labwork [276]

Scaled by 2, side lengths are 3, 4 and 5

3 0

3 years ago