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3 years ago

A geometric sequence is shown on the graph below. What is the formula for the nth term of the sequence?

Mathematics

1 answer:

larisa [96]3 years ago

4 0

Answer:

$\boxed{u_n=40*(\frac{1}{2} )^{n-1})}\\$

Step-by-step explanation:

$u_1=40\\\\u_2=20=u_1*(\frac{1}{2} )^{2-1}\\\\u_3=10=u_1*(\frac{1}{2} )^{3-1}\\\\u_4=5=u_1*(\frac{1}{2} )^{4-1}\\\\u_5=2.5=u_1*(\frac{1}{2} )^{5-1}\\\\\\\boxed{u_n=40*(\frac{1}{2} )^{n-1})}\\$

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What is the value of z in the equation 2(4z − 6 − 6) = 170 − 46?

Vsevolod [243]

Answer:

Z=18.5

Step-by-step explanation:

2(4z - 6 - 6) = 170 - 46

2(4z - 12) = 124 Use distributive property: a(b - c) = ab - ac

8z - 24 = 124 Add 24 to both sides

8z = 148 Divide both sides by 8

4 0

3 years ago

Match the examples with the properties of equalities:

Nataly_w [17]

I'm assuming you're matching the property you'd use to solve each given equation.

The thing to remember is that when you're solving equations like these, you're going to always do the opposite operations (formally the "inverse" operation) to get the variable by itself.

Equation a: x÷3 = 52

Since this has division connecting the 3 to the x, you'll cancel out the division with multiplication, using the Multiplication property of equality (Property 3).

Equation b: 6x = 36

Since this has multiplication connecting the 6 to the x, you'll cancel out the multiplication with division, using the Division property of equality (Property 4).

Equation c: x+70 = 245

Since this has addition connecting the 70 to the x, you'll cancel out the addition with subtraction, using the Subtraction property of equality (Property 2).

Equation c: x-35 = 450

Since this has subtraction connecting the 35 to the x, you'll cancel out the subtraction with addition, using the Addition property of equality (Property 1).

5 0

3 years ago

|7| What does this mean?

Elza [17]

Absolute value of 7. Any real numbers in the absolute sign would equal to the positive value.

Definition

$\large \boxed{ |x| = \begin{cases} x \: \: \: \: (x \geqslant 0) \\ - x \: \: \: \: (x < 0) \end{cases}}$

If we substitute x = 7 in. Answer by using the definition of absolute value. Note that we only substitute x = 7 in x and not -x since 7 is greater than 0 and not less than 0.

$\large{ |7| = 7 \: \: \: \: (x \geqslant 0)}$

You may also be wondering what will happen if we substitute x = any negative numbers.

$\large{ | - 7| = - ( - 7) \: \: \: \: (x < 0)} \\ \large \boxed{ | - 7| = 7}$

Because -7 is less than 0. We substitute in -x and not x. This is the definition of absolute value. But to understand it easily, any numbers in absolute value have to equal to their positive value.

Conclusion

|7| means the absolute value of 7.
|7| is 7.
|x| is x when x ≥ 0 but -x when x < 0

Let me know if you have any doubts regarding the absolute value through comment!

7 0

3 years ago

Evaluate 5! + 2!. 60 122 5,040

ludmilkaskok [199]

! Means starting from that number multiply by every number down to 1.

5!= 5•4•3•2•1 = 20•6=120

2!= 2•1=2

120+2=122 :)

8 0

3 years ago

Calculate $1200 ÷ 415.00 = answer in weeks. Round your answer up to the nearest whole week.

Lisa [10]

Answer:

3 weeks

Step-by-step explanation:

$\frac{1200}{415}\\\mathrm{Write\:the\:problem\:in\:long\:division\:format}\\415\overline{|\smallspace1200}\\\\\mathrm{Divide}\:1200\:\mathrm{by}\:415\:\mathrm{to\:get}\:2\\\\\begin{matrix}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\415\overline{|\smallspace1200}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\$

$\mathrm{Multiply\:the\:quotient\:digit}\:\left(2\right)\:\mathrm{by\:the\:divisor}\:415\\$

$\begin{matrix}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 415\overline{|\smallspace1200}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\space\space\space\space\space\space\underline{\emptyspace8\emptyspace3\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}$

$\mathrm{Subtract}\:830\:\mathrm{from}\:1200$

$\begin{matrix}\space\space\space\space\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 415\overline{|\smallspace1200}\space\space\space\space\space\space\space\space\space\space\space\space\space\\ space\space\space\space\space\space\underline{\empty\space8\empty\space3\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\emptyspace3\emptyspace7\emptyspace0\space\space\space\end{matrix}$

$\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{1200}{415}\:\mathrm{is}\:2\:\mathrm{with\:remainder\:of}\:370\\\\2\quad \mathrm{Remainder}\quad \:370\\=2.89\\=3 weeks$

3 0

4 years ago