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GalinKa [24]
3 years ago
13

a code is made up of 1 letter, out of a possible 26, in the first position. one digit, 0–9, occupies each of the second and thir

d positions. the digit cannot be repeated. how many possible outcomes exist?
Mathematics
1 answer:
drek231 [11]3 years ago
3 0
I believe it would be 26x10x9 which would equal 2340
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LOTS OF POINTS GIVING BRAINLIEST I NEED HELP PLEASEE
Sidana [21]

Answer:

Segment EF: y = -x + 8

Segment BC: y = -x + 2

Step-by-step explanation:

Given the two similar right triangles, ΔABC and ΔDEF, for which we must determine the slope-intercept form of the side of ΔDEF that is parallel to segment BC.

Upon observing the given diagram, we can infer the following corresponding sides:

\displaystyle\mathsf{\overline{BC}\:\: and\:\:\overline{EF}}

\displaystyle\mathsf{\overline{BA}\:\: and\:\:\overline{ED}}

\displaystyle\mathsf{\overline{AC}\:\: and\:\:\overline{DF}}

We must determine the slope of segment BC from ΔABC, which corresponds to segment EF from ΔDEF.

<h2>Slope of Segment BC:</h2>

In order to solve for the slope of segment BC, we can use the following slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}  }

Use the following coordinates from the given diagram:

Point B:  (x₁, y₁) =  (-2, 4)

Point C:  (x₂, y₂) = ( 1,  1 )

Substitute these values into the slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{1\:-\:4}{1\:-\:(-2)}\:=\:\frac{-3}{1\:+\:2}\:=\:\frac{-3}{3}\:=\:-1}

<h2>Slope of Segment EF:</h2>

Similar to how we determined the slope of segment BC, we will use the coordinates of points E and F from ΔDEF to find its slope:

Point E:  (x₁, y₁) =  (4, 4)

Point F:  (x₂, y₂) = (6, 2)

Substitute these values into the slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{2\:-\:4}{6\:-\:4}\:=\:\frac{-2}{2}\:=\:-1}

Our calculations show that segment BC and EF have the same slope of -1.  In geometry, we know that two nonvertical lines are <u>parallel</u> if and only if they have the same slope.  

Since segments BC and EF have the same slope, then it means that  \displaystyle\mathsf{\overline{BC}\:\: | |\:\:\overline{EF}}.

<h2>Slope-intercept form:</h2><h3><u>Segment BC:</u></h3>

The <u>y-intercept</u> is the point on the graph where it crosses the y-axis. Thus, it is the value of "y" when x = 0.

Using the slope of segment BC, m = -1, and the coordinates of point C, (1,  1), substitute these values into the <u>slope-intercept form</u> (y = mx + b) to solve for the y-intercept, <em>b. </em>

y = mx + b

1 = -1( 1 ) + b

1 = -1 + b

Add 1 to both sides to isolate b:

1 + 1 = -1 + 1 + b

2 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 2.

Therefore, the linear equation in <u>slope-intercept form of segment BC</u> is:

⇒  y = -x + 2.

<h3><u /></h3><h3><u>Segment EF:</u></h3>

Using the slope of segment EF, <em>m</em> = -1, and the coordinates of point E, (4, 4), substitute these values into the <u>slope-intercept form</u> to solve for the y-intercept, <em>b. </em>

y = mx + b

4 = -1( 4 ) + b

4 = -4 + b

Add 4 to both sides to isolate b:

4 + 4 = -4 + 4 + b

8 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 8.

Therefore, the linear equation in <u>slope-intercept form of segment EF</u> is:

⇒  y = -x + 8.

8 0
2 years ago
How many ways could you draw a single card from a 52 card deck and get either a heart or a king?
alekssr [168]
25 is the correct answer
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3 years ago
at a party at the middle school over on third avenue next to the bank, $60\%$ of the students are seventh graders. these student
Vaselesa [24]

There are 600 students including the seventh and eighth graders at the party.

This problem uses the concept of percentages to define the conditions that are laid in front of us.

Let the original  number of students be S , and the number of seventh graders be   = 0.60S

We know that percent is used to convey the mathematical term of a fraction multiplied by 100.

Total students  after 20 eighth graders arrive = S + 20

And we have that

Number of seventh graders / total number of students  =  58%

.60S  / [ S + 20 ]  =   .58    we multiply both sides by  S +  20

0.60S  =0 .58 [ S + 20]

.60S  = .58S + 11.6   we subtract  0.58S from  both the sides

0.02S = 11.6  we divide both the sides  by .02

S  = 11/6 / 0.02 =    580

So the total number of students = 580 + 20  = 600 .

Hence there are 600 students at the party at that time.

To learn more about students visit:

brainly.com/question/17332524

#SPJ1

5 0
1 year ago
N to the second power - 5 in - 1 in equals 6​
Wittaler [7]

Answer:

the question is incorrect.

4 0
3 years ago
Venla is 5 years older than her cousin Kora. Write an equation for the age of Venla, v, when Kora is k years old
Maksim231197 [3]
V=k+5

Here you go, hope this helps
6 0
3 years ago
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