Select three ratios that are equivalent to 5:2.

The students in a college marching band are arranged in rows. The recursive rule f(n) = f(n − 1) + 8 and f(1) = 13 gives the num

anzhelika [568]

Answer:

There are 24 more trumpet players than clarinet players

Step-by-step explanation:

The given information are;

The recursive rule or the number of band members in a row is f(n) = f(n - 1) + 8

Where f(1) = 13

The members of the band players in row 1 = The clarinet players

The members of the band players in row 4 = The trumpet players

Therefore, the number of clarinet players = f(1) = 13

The number of band members in row 2, f(2) = f(1) + 8 = 13 + 8 = 21

The number of band members in row 3, f(3) = f(2) + 8 = 21 + 8 = 29

The number of band members in row 4, f(4) = f(3) + 8 = 29 + 8 = 37

Therefore, given that the trumpet players are in row 4, the number of trumpet players = The number of band members in row 4 = 37 Trumpet players

The difference in the number of trumpet and clarinet = The number of more trumpet players than clarinet players = 37 - 13 = 24 more trumpet players than clarinet players

There are 24 more trumpet players than clarinet players.

3 0

3 years ago

What is the measure of z?

Ymorist [56]

Solving a system of linear equations, we conclude that the measure of side Z is 2√13

<h3>How to find the measure of side Z?</h3>

Remember the Pythagorean theorem. It says that the square of the hypotenuse is equal to the sum of the squares of the legs.

In the image, we can identify 3 right triangles, and with the Pythagorean theorem, we can write a system of 3 equations.

x^2 = y^2 + 4^2

z^2 = y^2 + 9^2

(4 + 9)^2 = z^2 + x^2

We want to solve that for z.

Now, the second equation can be rewritten to:

y^2 = z^2 - 9^2

Now let's replace the first equation into the third one, so we get:

(4 + 9)^2 = z^2 + (y^2 + 4^2)

Now we can replace y^2 by z^2 - 9^2

(4 + 9)^2 = z^2 + ((z^2 - 9^2) + 4^2)

Now we can solve this:

(13)^2 = z^2 + z^2 - 9^2 + 4^2

(13)^2 + 9^2 - 4^2 = 2*z^2

104/2 = z^2

52 = z^2

√52 = z

√(4*13) = z

√4*√13 = z

2√13 = z

We conclude that the measure of side Z is 2√13

If you want to learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

8 0

1 year ago

I need helpppp plss ❗️❗️❗️

katrin [286]

Answer:

f(x) = -2|x| + 1

Step-by-step explanation:

The graph shifts one unit up the y axis since there's a value outside the absolute value which directly adds 1 to it.

3 0

2 years ago

11. Circle the name of the student who correctly wrote the equation modeled below. Then, find the

Svet_ta [14]

Answer:

the student that is correct is Gene and the solution is x=10

3 0

2 years ago

Express the function graphed on the axes below as a piecewise function.

adoni [48]

Answer:

f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

f(x) = x-3 for x ≤ -1

__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

y -(-1) = -3(x -5)

y = -3x +15 -1 = -3x +14

The second piece can be written ...

f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

$\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}$

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

3 0

2 years ago