The n term of a geometric sequence is denoted by Tn and the sum of the first n terms is denoted by Sn.Given T6-T4=5/2 and S5-S3=5.Calculate (a)the common ratio. (b)the first term of this geometric sequence

Answers

Answer 1

Answer: 1 step: $S_(5)=T_(1)+T_(2)+T_(3)+T_(4)+T_(5)$ , $S_(3)=T_(1)+T_(2)+T_(3)$ , then
$S_(5)-S_(3)=T_(4)+T_(5)=5$ .

2 step: $T_(n)=T_(1)*q^(n-1)$ , then
$T_(6)=T_(1)*q^(5)$
$T_(5)=T_(1)*q^(4)$
$T_(4)=T_(1)*q^(3)$
$T_(3)=T_(1)*q^(2)$
and $\left \{ {{T_(6)-T_(4)= (5)/(2) } \atop {T_(5)+T_(4)=5}} \right.$ will have form $\left \{ {{T_1*q^(5)-T_(1)*q^(3)= (5)/(2) } \atop {T_(1)*q^(4)+T_(1)*q^(3)=5} \right.$ .

3 step: Solve this system $\left \{ {{T_1*q^(3)*(q^(2)-1)= (5)/(2) } \atop {T_(1)*q^(3)*(q+1)=5} \right.$ and dividing first equation on second we obtain $(q^(2)-1)/(q+1)= ( (5)/(2) )/(5)$ . So, $((q-1)(q+1))/(q+1) = (1)/(2)$ and $q-1= (1)/(2)$ , $q= (3)/(2)$ - the common ratio.

4 step: Insert $q= (3)/(2)$ into equation $T_(1)*q^(3)*(q+1)=5$ and obtain $T_(1)* (27)/(8)*( (3)/(2)+1 ) =5$ , from where $T_(1)= (16)/(27)$ .

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Which of these equations is for a line perpendicular to y-3=5(x-2)?

An unknown number b is 10 more than an unknown number k. The number b is also k less than 8. The equations to find k and b are shown below:b = k + 10
b = −k + 8

Which is a correct step to find k and b?
Write the points where the graphs of the equations intersect the x-axis. Write the points where the graphs of the equations intersect the y-axis. Add the equations to eliminate k. Multiply the equations to eliminate b.

Answers

Answer:

Add the equations to eliminate k.

Step-by-step explanation:

When we add the equations we get

$2b =18$

$\boxed{b=9}$

next we put $b=9$ into $b=k+10$ and solve for k:

$9=k+10\n\n\boxed{k=-1}$

this way we have found k and b; therefore, adding the equations to eliminate k is a correct step for finding k and b.

Let us now look at other choices we were given.

Write the points where the graphs of the equations intersect the x axis.

These points may be the solutions to each equation, but they are not the solutions to the system of these two equations.

Write the points where the graphs of the equations intersect the y axis.

Same thing goes here: these points may be the solutions to each equation, but they are not the solutions to the system of these two equations.

Multiply the equations to eliminate b.

Multiplying the equations doesn't eliminate b, but rather it complicates the matter by producing a quadratic equation—we don't want to go down that road!

Insert 2 irrational numbers between 2/5 and 3/4

Answers

$(2)/(5) = 0.4$

$(3)/(4) = 0.75$

There are many irrational numbers between these two fractions.

Two of them are -

$0.40121121112...$

$0.40232232223...$

$(2)/(5)=0.4\n (3)/(4)=0.75\n$

$\boxed{\sqrt{(3)/(4)\pi}-1}\n \boxed{e-2}$

deepest part of a swimming pool is 12 feet deep. The shallowest part is 3 feet deep. What is the ratio of the depth of the deepest part of the pool to the depth of the shallowest part of the pool

Answers

Deepestpart of the swimming pool = 12 feet deep
Shallowest part of the swimming pool = 3 feet deep
Thus the ratio of both swimming pool depth is:
=> 12 : 3
12 – 3 = 9
The deepest part of swimming pool is 9 feet deeper compare to the shallowestpart of the swimming pool.
Ratio is simply mean the number of x is to the number of y
=> x : y

David bought 3 dvds and 4 books for $40 at a yard sale. Anna bought 1 dvd and 6 books for $18. How much did each dvd and book cost?

Answers

Answer: d=$12, b=$1

d represents DVDs

b represets books

Step-by-step explanation:

Whenever you have 2 examples of 2 different things (such as books and dvds), make a systems of equations.

Step 1: Write a system of equations

3d+4b= 40

d+6b= 18

Step 2: Eliminate any letter. I'll just choose d.

To elimiate d, you have to make them both equal to the biggest d variable. In other words, make both d terms equal to 3d. To do this, miultiply the 2nd equation by 3, and keep the 1st one the same.

3d+4b=40

3d+18b= 54

Now, elimiate d, by doing 3d-3d= 0. Now use subtraction to solve for b since we used this to get 3 and 3 to 0.

4b-18b=40-54

-14b= -14

b= -14÷-14

b= 1

Each book costs 1 dollar.

Step 3: Plug in b=1 to find how much each dvd costs (plug into any equation)

3d+4b=40

3d+4(1)=40

3d+4=40

3d=40-4

3d=36

d=36÷3

d=12

Each dvd is $12

Step 4: Checks--plug d=12 and b=1 into any equation

3d+4b=40

3(12)+4(1)=40

36+4=40

40=40

It's correct ✅

Also i know this was answered really late but id appreciate if i could get brainliest as i worked pretty hard for this :) Hope i could help the best i could :D

(Please help) Which statement(s) about translations, reflections, and rotations are true?•These transformations do not create a congruent image.
•These transformations do not change the shape of the image.
•These transformations do not change the location of the image.
•These transformations do not change the size of the image.

Answers

Answer:

These transformations do not change the size of the image.

Step-by-step explanation:

By going over the different properties of translations, reflections and rotations, we can determine what exactly is common about each of these.

- Translations: the shifting of a function on the coordinate plane without any change in congruence, shape or size.

In algebra, translations are seen most often in quadratic and linear functions, and always by adding or subtracting a number the function's $x$ and/or $y$ values.
ex.) In the parent function of standard-form quadratic equations, $f(x)=ax^2+bx+c$ , the value $c$ would be considered a value that determines the function's vertical translation. It is a value that would move the equation up or down if changed.

- Reflection: the flipping of a function without any change of its overall shape or size.

In algebra, a reflection is usually seen in vertical reflections across the $x$ -axis.
ex.) The $a$ in standard-form quadratic equations is an example of a reflection across the $x$ -axis. If it's sign is changed (if it is changed from negative to positive and vise-versa), then the equation would be flipped across the $x$ -axis.

- Rotation: the change of a function's rotation without any change in its size, shape or location.

Rotations, are most often seen in linear equations with a line's slope.
ex.) In the standard form linear function, $f(x)=mx+b$ , $m$ or the line's slope changes the rotation of the function.

Translation, reflection and rotation all do not change the size of the function/shape they are acting on. Thus, Answer D is correct.

WILL BE MARKED AS BRAINLIEST PLS JUST HELP ME!a)A local shoe store buys shoes at a wholesale price and then marks them up 80% to calculate the retail price. The wholesale price varies, depending on the quantity of shoes purchased.
b.) Using the formula from part a, calculate the retail price for each quantity range.

Answers

Answer:

since all the shoes get marked up by 80%

the equation for all of them would be :

y = new price

x = wholesale price

y = 1.8x

Step-by-step explanation:

The equation for them would be
y = the new price
x = the wholesale price
y = 1.8

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