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enyata [817]
3 years ago
13

I’m stuck on this please someone help

Mathematics
1 answer:
kakasveta [241]3 years ago
6 0

Answer:   \bold{a_{n+1}=\dfrac{1}{2}a_n}

<u>Step-by-step explanation:</u>

Term-to-term rule is also called the recursive rule.

The recursive rule for a geometric sequence is: a_{n+1}=a_n\cdot r  where

  • a_n\ \text{is the previous term}
  • r is the common ratio

The common ratio (r) is the second term divided by the first term <em>(which is the same ratio for each term divided by its previous term) </em>

In the given sequence {64, 32, 16, 8, 4}, r=\dfrac{32}{64}\quad \rightarrow \quad r=\dfrac{1}{2}

So, the recursive rule is: {a_{n+1}=a_n\cdot \dfrac{1}{2}

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I need help answering this question
Gekata [30.6K]

ANSWER:

[a] A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

[b] In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the “Slope-intercepts form”.

NOTE: See picture attached.

7 0
3 years ago
The sum of three numbers is 26. Twice the first minus the second is the third less 2. The third is the second minus 3 times the
Agata [3.3K]

Let a, b, c represent the three numbers. The problem statement gives rise to three equations:

  • a +b +c = 26
  • 2a -b = c -2
  • -3a +b = c

Adding the first two equations gives

... (a +b +c) +(2a -b) = (26) +(c -2)

... 3a +c = 24 +c . . . . . simplify

... 3a = 24 . . . . . . . . . . subtract c

... a = 8 . . . . . . . . . . . . divide by 3

Adding the second and third equations gives ...

... (2a -b) +(-3a +b) = (c -2) +(c)

... -a = 2c -2 . . . . simplify

... -6 = 2c . . . . . . add 2, substitute for a

... -3 = c . . . . . . . . divide by 2

Using the third equation we can find b.

... -3·8 +b = -3 . . . . substitute for a and c

... b = 21 . . . . . . . . .add 24

The numbers are 8, 21, -3.

_____

The method above is sort of "ad hoc", taking advantage of the numbers in this particular set of equations. You can use more formal methods of Gaussian elimination or Cramer's Rule to solve these by just following a procedure. Or, your graphing calculator can do it for you.

6 0
3 years ago
What is the sin inverse of (sine 9pi/7)?
Sveta_85 [38]
For the answer to the question above, I've used my calculator to inverse your given equation because my brain can't do that.
The answer to your question is
In radians, arcsin(sin(9π) / 7) = 0.
 i hope my answer helped you.

7 0
3 years ago
Confusion...help please
kifflom [539]

Given:

In triangle KLM, KL = 123 cm and measure of angle K is 35 degrees.

To find:

The length of the side KM to the nearest tenth of a centimeter.

Solution:

In a right angle triangle,

\cos \theta =\dfrac{Base}{Hypotenuse}

In the given right triangle KLM,

\cos K=\dfrac{KM}{KL}

\cos (35^\circ)=\dfrac{KM}{123}

0.819152=\dfrac{KM}{123}

Multiply both sides by 123.

0.819152\times 123=KM

100.755696=KM

KM\approx 100.8

The measure of side KM is 100.8 cm.

Therefore, the correct option is (2).

8 0
2 years ago
Pam needs 3 1/2 cups of sugar to make 50 cupcakes. A 5- pound bag of sugar coats $3.69. There are about 2 cups of sugar in a pou
Lorico [155]

Answer:

The answer to your question is $1.29

Step-by-step explanation:

Data

Total amount of cupcakes = 50

Total amount of sugar = 3 1/2 cups = 3.5 cups

Cost of 5-pound bag = $3.69

2 cups = 1 pound

Total cost = ?

Process

1.- Calculate the amount of pounds needed

                  2 cups ------------------ 1 pound

                  3.5 cups ---------------  x

                  x = (3.5 x 1) / 2

                  x = 3.5 / 2

                  x = 1.75 pounds

2.- Calculate the price of 1.75 pounds

                  5 pounds -------------- $3.69

                  1.75 pounds ----------    x

                  x = (1.75 x 3.69)/5

                  x = 6.46/5

                 x = $1.29

3.- Conclusion

The cost of sugar to prepare 50 cupcakes is $1.29

3 0
3 years ago
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