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3 years ago

13

Find x. 1.5 2

sqrt{3}" align="absmiddle" class="latex-formula">
3 $\sqrt{3}$

1 answer:

Vanyuwa [196]3 years ago

3 0

Answer:

1.5

Step-by-step explanation:

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3. What is the 9th term in the following sequence? 11, 17, 23, 29, . . . (1 point) 47 53 59 65

KatRina [158]

Since the common difference is 6, we can assume that the sequence is arithmetic, with rule
T(n)=6n+5 where T(1)=11
T(9)=6(9)+5=59

5 0

3 years ago

What is the value of the expression f(-3) + 2f(-1) - f (4)<br><br> PLEASE HELP NO LINKS

Bas_tet [7]

Answer:

22

Step-by-step explanation:

Find f(-3) :

f(x) = x² + 2x for x ≤ -3

That means for those values of x, less than or equal to -3, this is the function.

So, f(-3) = (-3)² + 2(-3) = 9 - 6 = 3

Now, f(-1) :

From the given data, we see it is: f(x) = 2 $(\frac{1}{3} )^{2x}$

We take this because -1 lies between -3 and 4.

Now, f(-1) = 2 $(\frac{1}{3} )^{2(-1)}$

=> $f = (-1) = 2(3)^{2} = 2 (9) = 18$

For f(4) :

Clearly, the function is: $f (x) = \frac{2x - 5}{x-7}$

$f (4) = \frac{2(4)-5}{4-7} = \frac{3}{-3} = -1$

Therefore, <u>f(-3) + f(-1) - f(4) = 3 + 18 - (-1) = 3 + 18 + 1 = 22.</u>

5 0

3 years ago

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

8 0

3 years ago

Select the proper inverse operation to check the answer to 14 + 17 = 31.

vivado [14]

The correct answer ids 100% answer choice D

4 0

3 years ago

Find the distance between the points <br> (-8,-6) and (4, 10)

never [62]

Answer:

d=20

Step-by-step explanation:

To find the distance between 2 points we use the distance formula

d = √(x2 - x1)²+(y2 - y1)²

The given points are (x1= -8, y1 = -6) and (x2 = 4, y2 = 10).

Substitute the given points into the distance formula.

d = √(4 + 8)²+(10 +6)²

d = √144+252

d= √400

d = 20

3 0

3 years ago