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Keith_Richards [23]
4 years ago
15

The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to mode

l the same sequence?
Mathematics
1 answer:
astraxan [27]4 years ago
7 0

Answer:

The explicit formula is Tn = 18[(2/3)^(n-1)]

Where n is the term we are looking for

Step-by-step explanation:

Here, we want to get an explicit formula to model the equation

Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12

F(3) = 2/3 * f(2) = 2/3 * 12 = 8

F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3

F(5) = 2/3 * 16/3 = 32/9

Thus, seeing how the equations are progressing, we can definitely see a pattern.

That is Tn = (2/3)^(n-1)(18)

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Find the values of x, y, and z. The diagram is not to scale.
Kruka [31]

we know that

The sum of the internal angles in the triangle must be 180 degrees

see the attached figure with letters to better understand the problem

Step 1

<u>Find the measure of the angle x</u>

In the triangle ABC

63\°+36\°+x\°=180\°

solve for x

99\°+x\°=180\°

x\°=180\°-99\°

x=81\°

therefore

<u>the answer Part a)  is</u>

the measure of angle x is 81\°

Step 2

<u>Find the measure of the angle z</u>

we know that

x+z=180\° --------> by supplementary angles

substitute the value of x

81\°+z=180\°

z=180\°-81\°

z=99\°

therefore

<u>the answer Part b)  is</u>

the measure of angle z is 99\°

Step 3

<u>Find the measure of the angle y</u>

In the triangle ACD

13\°+z\°+y\°=180\°

solve for y

13\°+99\°+y\°=180\°

112\°+y\°=180\°

y\°=180\°-112\°

y\°=68\°

therefore

<u>the answer Part c)  is</u>

the measure of angle y is 68\°

5 0
3 years ago
Read 2 more answers
If 15% of the total ticket sales is $375, what is the value of the total ticket sales?
Arisa [49]

Answer:

The value of the total ticket sales is, 2500

Step-by-step explanation:

Let x be the total ticket sales.

As per the statement:

if 15% of the total ticket sales is $375

\text{15 \% of total ticket} = \frac{15}{100} \times x = \frac{15x}{100}

then;

\frac{15x}{100} = 375

Divide both sides by 15 we have;

\frac{x}{100} =25

multiply both sides by 100 we have;

x = 2500

Therefore,  the value of the total ticket sales is, 2500

5 0
3 years ago
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What is the value of x ? write your answers in the blanks 5x+5+95=180
katrin [286]

Answer:

............................................

7 0
3 years ago
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What is the simplified of 2160x^8/60x^2
olga nikolaevna [1]
X=6x to the third power.
3 0
4 years ago
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The largest taco contained approximately 1 kg of onion for every 6.8 kg grilled steak. The total weight of these two ingredients
erastovalidia [21]

Answer: Onion = 79.17 kg

Grilled steak = 538.356 kg

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

1 k + 6.8 k = 617.6  

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.6

k = 617.6 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.8 (79.17) = 538.356 kg

Feel free to ask for more if needed or if you did not understand something.

6 0
4 years ago
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