Expand the following expressions and write in standard form. Show your work.

The terms in a sequence are given by 3 + 2x. what are the first 6 terms in the sequence?

enyata [817]

First 6 terms are 5, 7, 9, 11, 13 and 15

Step-by-step explanation:

Step 1: Given terms in the sequence = 3 + 2x. Find the first 6 terms.

a(1) = 3 + 2 × 1 = 3 + 2 = 5

a(2) = 3 + 2 × 2 = 3 + 4 = 7

a(3) = 3 + 2 × 3 = 3 + 6 = 9

a(4) = 3 + 2 × 4 = 3 + 8 = 11

a(5) = 3 + 2 × 5 = 3 + 10 = 13

a(6) = 3 + 2 × 6 = 3 + 12 = 15

4 0

3 years ago

What is the answer to (-8x)÷(-2)

pav-90 [236]

(-8x) ÷ (-2)
= (-4x) ÷ (-1)
= 4x ÷ 1 = 4x

3 0

3 years ago

Help I need this ASAP

ddd [48]

Answer:

1. 7:1

2. 1:8

Step-by-step explanation:

1. Start by counting the number of triangles. We see: 56 triangles. Then, count the hearts. We see: 8 hearts.

So, the ratio of triangles to hearts is 56:8 which we simplify to get: 7:1.

2. Start by adding triangles to hearts. We get: 56+8 which equals 64.

The amount of hearts equals 8 so the ratio of hearts to (hearts + triangle) is! 8:64 which equals 1:8.

4 0

3 years ago

A discuss moves from P1 (4,8) to P2 (15,17). What is the lincar displacement in the horizontal and vertical directions? What is

Yakvenalex [24]

Answer:

The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.

Step-by-step explanation:

We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have

$\Delta s = s_2-s_1$

And apply it to get the horizontal and vertical displacements.

Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.

Linear displacements.

Using the definition of displacement, we can write the horizontal displacement as

$\Delta x = x_2-x_1$

So we can use the given points $P1:(x_1,y_2) \text{ and } P_2: (x_2,y_2)$ on the displacement formula

$\Delta x = 15-4\\\Delta x = 11$

In the same manner we can look at the y components of those points to find the vertical displacement

$\Delta y = 17-8\\\Delta y =9$

Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.

Projection angle.

The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write

$\tan(\theta) = \cfrac{\Delta y}{\Delta x}$

Solving for the angle we get

$\theta = \tan^{-1}\left(\cfrac{\Delta y}{\Delta x}\right)$

Replacing values

$\theta = \tan^{-1}\left(\cfrac{9}{11}\right)$

Which give us

$\theta = 39.3^\circ$

So the projection angle is 39.3 degrees.

7 0

3 years ago

If AD=BD, which of the following relationships can be proved and why?

myrzilka [38]

Answer: The answer would be b, the side-angle-side postulate. :)

Step-by-step explanation:

This would be due to the definition of a bisector, and the reflexive property.

3 0

3 years ago