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irga5000 [103]
3 years ago
8

Which of the expressions can you use to find the number of 3-digit passwords you can make using the digits 5, 6, and 7, if you d

o not repeat any of the digits?
3 x 2 x 1
3 + 2 + 1
5 x 6 x 7
5 + 6 + 7
Mathematics
1 answer:
allochka39001 [22]3 years ago
5 0
Hello,

Codes are :
5_6_7, 5_7_6

6_5_7,6_7_5

7_5_6,7_6_5

Choising the first (3 possibilities)
next choising the second (2 possibilities)
chosing the last  (1 possibility)

So 3*2*1=6

Answer A

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To determine the fraction of her classmates with dogs as pets, we simply multiply the two given fractions based from the survey. 

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3 years ago
The product of five and a number plus 10 is at least thirty
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Step-by-step explanation:

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3 years ago
At what point on the parabola y = 3x^2 + 2x is the tangent line parallel to the line<br> y = 10x −2?
oksian1 [2.3K]

Answer:

( \frac{4}{3} , 8 )

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 10x - 2 ← is in slope- intercept form

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then the tangent to the parabola with a slope of 10 is required.

the slope of the tangent at any point on the parabola is \frac{dy}{dx}

differentiate each term using the power rule

\frac{d}{dx} (ax^{n} ) = nax^{n-1} , then

\frac{dy}{dx} = 6x + 2

equating this to 10 gives

6x + 2 = 10 ( subtract 2 from both sides )

6x = 8 ( divide both sides by 6 )

x = \frac{8}{6} = \frac{4}{3}

substitute this value into the equation of the parabola for corresponding y- coordinate.

y = 3(\frac{4}{3} )² + 2

   = (3 × \frac{16}{9} ) + 2

   = \frac{16}{3} + \frac{8}{3}

   = \frac{24}{3}

   = 8

the point on the parabola with tangent parallel to y = 10x - 2 is ( \frac{4}{3} , 8 )

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