1/3 * 2 3 / 4 using distributive property

Show all work. find the missing terms of the arithmetic sequence... , 4, ?, ?, ?, 120, ...

denis23 [38]

Answer:

-25, 4, 33, 62, 91, 120, ...

Step-by-step explanation:

<h3>Given</h3>

<u>The arithmetic sequence</u>

.. , 4, ?, ?, ?, 120, ...

Missing terms

<h3>Solution</h3>

<u>Let the first term a₁ = x, and common difference = d then we have:</u>

a₁ = x
a₂ = x + d = 4
...
a₆ = x + 5d = 120

<u>The difference of the 6th and 2nd terms:</u>

a₆ - a₂ =
a + 5d - x - d = 120 - 4
4d = 116
d = 116/4
d = 29

<u>Then we get the first term and other missing terms:</u>

x = 4 - 29 = -25
a₁ = -25

-25, 4, 4+29 = 33, 33+29 = 62, 62 + 29= 91, 91+29 = 120, ...

6 0

2 years ago

At what x-values do the graphs of the functions y=cos 2x and y = cos^2 x-1 intersect over the interval 0 ≤ x ≤ pi. There must be

baherus [9]

Answer:

$x=\frac{\pi}{2}$ and $x=\frac{3\pi}{2}$

Step-by-step explanation:

We need to solve the 2 equations to figure out the x-values (intersecting points).

<em>Note: </em>The identity $cos^{2}x=\frac{1}{2}+\frac{1}{2}cos(2x)$

$cos(2x)=cos^{2}(x)-1\\cos(2x)=(\frac{1}{2}+\frac{1}{2}cos(2x))-1\\cos(2x)=\frac{1}{2}cos(2x)-\frac{1}{2}\\\frac{1}{2}cos(2x)=-\frac{1}{2}\\cos(2x)=-1\\2x=cos^{-1}(-1)\\2x=\pi, 3\pi\\x=\frac{\pi}{2}, \frac{3\pi}{2}$

So they intersect at $x=\frac{\pi}{2}, \frac{3\pi}{2}$

4 0

3 years ago

Read 2 more answers

Which equation represents: "Two times an unknown integer, multiplied by the unknown integer minus two times a different unknown

viva [34]

Answer:

$2 {x}^{2} - 4xy - 50 = 0$

Step-by-step explanation:

Let the first unknown integer be x

Let the second unknown integer be y

$2x(x - 2y) = 50 \\ 2 {x}^{2} - 4xy - 50 = 0$

5 0

2 years ago

The perimeter of a triangle is 17x−5 units. One side is 3x+5 units and another is 8x−3 units. How many units long is the third s

Inessa05 [86]

9514 1404 393

Answer:

6x -7 units

Step-by-step explanation:

Let c represent the length of the third side. The perimeter is the sum of the three side lengths.

P = a + b + c

(17x -5) = (3x +5) +(8x -3) +c

17x -5 = 11x +2 + c . . . . . . . . . . . . collect terms

6x -7 = c . . . . . . . . . . . . . . subtract 11x+2

The third side is 6x -7 units.

6 0

2 years ago

okay so ive got a ton of piecewise function things and I really suck at them so maybe someone wants to help me? :D thanks giving

algol [13]

[] signs mean that the number is included in the domain and () mean that the number is not included. Now,

1. [-1,5)
Because x is greater than or equal to -1 (included) but less than 5 (excluded

2. [-5,13)
When we plug in x = -1, we get the minimum value of -5, which is included because its x-value was included. The, we plug in x = 5 to find the range's maximum and this is excluded because its x-value was excluded.

3. 218
x = 6 lies in the domain of the first function so we will use it to evaluate the value of x = 6. We do this by simply substituting x into the function.

4. 12
x = 9 is included in the domain of the second function and the value of the second function at all points is 12.

5. 103
x = 10 is included in the domain of the second function so we will use it to evaluate the value of x = 10. This is done by substituting x into the equation.

4 0

2 years ago