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3 years ago

Complete the recursive formula of the geometric sequence -0.6, 3, -15, 75, ...

Mathematics

2 answers:

lara [203]3 years ago

7 0

Answer:

$\boxed{Un = 3(-5)^{n - 2}}$

Step-by-step explanation:

We know that

a = -0,6 = $-\frac{3}{5}$ and r = $\frac{3}{-0,6}$ = -5

$Un = ar^{n - 1}$

$Un = (-\frac{3}{5} )(-5)^{n - 1}$

$Un = (3)(-5)^{-1}(-5)^{n - 1}$

$Un = 3(-5)^{n - 2}$

KatRina [158]3 years ago

6 0

Answer:

use this form 》Un = ar^(n - 1)

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Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 10, ST = 13, TU = 11, UV = 12, and VR = 12?

Kobotan [32]

Answer:

Step-by-step explanation:

The value of x is 7 ⇒ 1st answer

Step-by-step explanation:

* Lets revise a fact in the circle

- The two tangents drawn from a point out side the circle are equal

∵ RSTUV is circumscribed about a circle

∴ Each side of the pentagon is a tangent to the circle

- Look to the attached figure to know how we will solve the problem

- Each tangent divided into two parts

# RS = x + y

∵ RS = 8

∴ x + y = 8 ⇒ (1)

# RV = x + n

∵ RV = 12

∴ x + n = 12 ⇒ (2)

- Subtract (2) from (1)

∴ y - n = -4 ⇒ (3)

# ST = y + z

∵ ST = 12

∴ y + z = 12 ⇒ (4)

# TU = z + m

∵ TU = 15

∴ z + m = 15 ⇒ (5)

- Subtract (5) from (4)

∴ y - m = -3 ⇒ (6)

# UV = m + n

∵ UV = 9

∴ m + n = 9 ⇒ (7)

- Add (6) and (7)

∴ y + n = 6 ⇒ (8)

- Lets solve equation (3) and equation (8) to find y

∵ y - n = -4 ⇒ (3)

∵ y + n = 6 ⇒ (8)

- Add (3) and (8)

∴ 2y = 2 ⇒ divide two sises by 2

∴ y = 1

- Lets substitute the value of y in equation (1)

∵ x + y = 8 ⇒ (1)

∵ y = 1

∴ x + 1 = 8 ⇒ subtract (1) from both sides

∴ x = 7

* The value of x is 7

plz mark me as brainlyist thxx

7 0

3 years ago

Read 2 more answers

The distribution of a sample of the outside diameters of PVC pipes approximates a normal distribution. The mean is 14.0 inches,

lakkis [162]

Answer:

A. 13.9 and 14.1 inches

See explanation below.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the outside diameters of a population, and for this case we know the distribution for X is given by:

$X \sim N(14,0.1)$

Where $\mu=14$ and $\sigma=0.1$

If we want the middle 68% of the data we need to have on the tails 16% on each one

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.84$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.994$

And if we solve for a we got

$a=14 -0.994*0.1=13.9$

And since the distribution is symmetrical for the upper limit we can use z = 0.994 and we have:

$z=0.994$

And if we solve for a we got

$a=14 +0.994*0.1=14.1$

So the correct answer for this case would be:

A. 13.9 and 14.1 inches

3 0

3 years ago

The range of a relation is (1 point)

postnew [5]

Hi there!

The answer is:
The range of a relation is the output (y) values of the relation. The range represents the set of the y-coordinates from the ordered pairs.

~ Hope this helps you!

3 0

3 years ago

If an equation is an identity, then how many solutions does it have? zero one infinite

dezoksy [38]

Answer:

Infinite solutions.

Step-by-step explanation:

If an equation is an identity, then there will be infinite solutions that the identity will have.

Let, us assume that an identity equation is given by

(a + b)² = a² +2ab + b².......... (1)

Now, putting any real values of a and b the identity will be satisfied.

Therefore, there are infinite solutions for an identity equation. (Answer)

3 0

3 years ago

Read 2 more answers

Rewrite the following quadratic function in vertex form. Then, determine if it has a maximum or minimum and say what that value

alexira [117]

Discussion

1. Put brackets around the first two terms

y = (-x^2 + 6x) + 5

2. Take out the common factor of -1

y = -(x^2 - 6x) + 5

3. Inside the brackets, take 1/2 of - 6 and square it

y = -(x^2 - 6x + ( - 6 / 2)^2 ) + 5

y = -(x^2 - 6x + (- 3)^2 ) ) + 5

y = -(x^2 - 6x + 9 ) + 5

Note: Step 3 is very long. Make sure you work your way through it

4. You have added 9 inside the brackets. It is actually - 9. So add 9 outside to balance the equation out. This is the key step. Make sure you understand it.

y = - (x^2 - 6x + 9) + 5 + 9

5. Express the brackets as a square.

y = - (x + 3)^2 + 14

Discussion

The equation is now in vertex form. The minus tells you that the equation is a maximum. The maximum is located at ( - 3, 14 )

A graph follows to show the results.

3 0

3 years ago