Which properties could you use to solve the following expression?

Which of the following is the explicit rule for the sequence -3, 5, 13, 21 ... *

TiliK225 [7]

Answer:

$a_{n}$ = 8n - 11

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence, that is

5 - (- 3) = 13 - 5 = 21 - 13 = 8

This indicates the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 8 , thus

$a_{n}$ = - 3 + 8(n - 1) = - 3 + 8n - 8 = 8n - 11 ← note this is the second option, that is

f(n) = - 3 + 8(n - 1)

7 0

3 years ago

A statistics student records the servings of vegetables Natalia and Zane eat each weekday. The table shows the results.

Softa [21]

Answer:

The Answer is D)

Step-by-step explanation:

3 0

3 years ago

Identify any extrema of the function by recognizing its given form or its form after completing the square. Verify your results

Andrews [41]

Answer:

Step-by-step explanation:

Given that,

g(x, y) = 5 - (x - 3)² - (y + 2)²

Let find the grad of the function,

The grad of a function is defined as

∇g= ∂g/∂x •i + ∂g/∂y •j + ∂g/∂z •k

∇g = gx•i + gy•j + gz•k

gx = -2(x-3) = -2x+6

gy = -2(y+2) = -2y -4

∇g = (-2x+6) •i + (-2y-4)•j

We have a maximum or a minimum If g conservative, then, ∇g = 0i +0j

Then comparing this to the grad of the function

(-2x+6) •i + (-2y-4)•j = 0i +0j

Then, -2x+6 = 0

2x=6

x = 3

Also, -2y-4=0

-2y=4

y = -2

Then, g(x, y) = 5 - (x - 3)² - (y + 2)²

g(x, y) = 5 - (3 - 3)² - (-2 + 2)²

g(x, y) = 5

So the critical point is (3, -2, 5)

gx =-2x+6

Second derivative of gx with respect to x

gxx=-2

gy=-2y-4

Second derivative of gy with respect to y

gyy=-2

Second derivative of gx with respect to y

gxy =0

d =gxxgyy - (gxy)²

Then, gyy=gxx

d = -2×-2 -0²

d = 4-0=4

Since d>0

Since d is greater than 0, then, it is not a chair points.

Then, since gxx=-2<0, gyy=-2<0

Cause the second derivative in x (or in y) is less than zero, then the point is relatively maximum

So the maximum point is (3, -2, 5).

6 0

3 years ago

The perimeter of the triangle below is 10x - 3<br><br> Show how to solve

bezimeni [28]

10x - 3 = x + 2 + 2x - 1
10x - 3 = 3x + 1
-3x on both sides
7x - 3 = 1
-1 on both sides
7x - 4

(Check 7x - 4 by adding them all up to equal 10x - 3)
x + 2 + 2x - 1 + 7x - 4 = 10x - 3
combine liked terms
10x - 3 = 10x - 3

Answer:
D) 7x - 4

4 0

3 years ago

Please Help! Thanks!

svetlana [45]

Answer:

C, 20 units

Step-by-step explanation:

We see that both angles QRS and QTR are 90 degrees. In addition, angles SQR and RQT are equivalent (because they're both angle Q).

By AA Similarity, we know that triangle QTR is similar to triangle QRS.

With this similarity in mind, we can look at the ratios of corresponding lengths to set up a proportion. QR from triangle QTR is the hypotenuse, and it corresponds to hypotenuse QS from triangle QRS. So, we can write the ratio x/(9 + 16) = x/25.

Now, we see that long leg QT of triangle QTR corresponds to long leg QR of triangle QRS. So, another ratio we can write is: 16/x.

Finally, we set these two ratios equal to each other:

$\frac{x}{25} =\frac{16}{x}$

Cross-multiplying, we get: $x^{2} =16*25=400$ .

Thus, x = $\sqrt{400} =20$ . The answer is C, 20 units.

Hope this helps!

4 0

3 years ago

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