the sum of the first six terms of a geometric series is 21/16 . if the common ratio is -1/2 , what is the first term?

Answers

Answer 1

Answer:

-84

Step-by-step explanation:

The formula for the nth term of a geometric progression is

Un = ar^n- 1

The sum of the first six terms of a geometric series (U6) = 21/16

Common ratio = -1/2 ,

a = First term ??

21/16 = a × (-1/2 )^6- 1

21/16 = a ×(-2^-1)^5

21/16 = a × -2^-6

Cross Multiply

16 × a × -2^-6 = 21

a = 21/16 × -2^-6

a = 21/16 ×- 1/2⁶

a = 21/16 × -1/64

a = 21 ÷(-1/4)

a = 21 × -4

a = -84

The first term = 84


Related Questions

Marco paid $42.40 for 6.4 Gallons of gas. What is the price of 1 gallon of gas? Group of answer choices

Answers

Answer:

6.63

Step-by-step explanation:

Write equations (both, Point Slope & Slope Intercept Forms) of the line with
slope of -2 and point (9,2).

Answers

Answer:

Equation of line in Point Slope Form is [tex]\mathbf{y-2=-2(x-9)}[/tex]

Equation of line in Slope Intercept Form is: [tex]\mathbf{y=-2x+20}[/tex]

Step-by-step explanation:

We need to write equation of line having slope -2 and point (9,2)

a) Equation in Point Slope Form

The general equation of point slope form is: [tex]y-y_1=m(x-x_1)[/tex]

Where x₁ and y₁ are the points of line and m is slope.

x₁=9 and y₁=2 and m=-2

Putting values in formula and finding equation:

[tex]y-y_1=m(x-x_1)\\y-2=-2(x-9)[/tex]

So, Equation of line in Point Slope Form is [tex]\mathbf{y-2=-2(x-9)}[/tex]

b) Equation in Slope Intercept Form

The general equation of Slope Intercept Form is: [tex]y=mx+b[/tex]

where m is slope and b is y-intercept

Finding y-intercept using slope m=-2 and point(9,2)

[tex]y=mx+b\\2=-2(9)+b\\2=-18+b\\b=2+18\\b=20[/tex]

The equation in slope m=-2 and b=20 is:

[tex]y=mx+b\\y=-2x+20[/tex]

So, equation of line in Slope Intercept Form is: [tex]\mathbf{y=-2x+20}[/tex]

Helpppppppppppppp
asappppppppppp

Answers

Answer:

180-112=68

Step-by-step explanation:

a rectangular parking lot has length that is greater than the width the area of the parking lot is 160 square yards find the length and the width use formula area=length*width the parking lot length

Answers

let 'w' represent the width of the parking lot, then 'w+6' represents its length



area = width * length



160 = w * (w+6)

solving for 'w' we have a positive value of w=10



10+6=16



the width of the parking lot is 10 yards, the length of the parking lot is 16 yards

In the triangle shown, let AB = DE, BC = EF, and CA = FD. Use Rigid Motions to show (triangle)ABC onto (triangle) DEF.

Answers

Answer:

Step-by-step explanation:

Given: AB≅DE, BC≅EF, CA≅FD

Since those are the given it is maped A to D, B to E, C to F

This is a rigid transformation because the distance is preserve (givens) and the triangle ABC is map to triangle DEF.

Rigid transformations produce congruent figures so triangle ABC is congruent to triangle DEF

please help 8x -4 - 6x + 9 ​

Answers

Answer:

[tex] \huge{ \boxed{ \bold{ \tt{2x + 5}}}}[/tex]

☃️Question : Simplify

[tex] \text{8x - 4 - 6x + 9}[/tex]

Step by step explanation :

First, combine like terms :

Like terms are those which have the same base.

[tex] \longrightarrow{ \sf{8x - 6x - 4 + 9}}[/tex]

[tex] \longrightarrow{ \sf{2x - 4 + 9}}[/tex]

Remember : The negative and positive integers are always subtracted but posses the sign of the bigger integer.

[tex] \longrightarrow{ \boxed{ \sf{2x + 5}}}[/tex]

And we're done!

Hope I helped!

Best regards! :D

~[tex] \text{TheAnimeGirl}[/tex]

Write the slope-intercept form of the equation of the line described. through (2, -5) perpendicular to y = 1/3x -1

Answers

Answer:

y = -3x + 1

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be -3.

Plug in the slope and given point into y = mx + b

y = mx + b

-5 = -3(2) + b

-5 = -6 + b

1 = b

Then, plug in the slope and y intercept into y = mx + b again:

y = -3x + 1 will be the equation of the line

Which of the following is not a reason used in this proof?

A) Definition of perpendicular

B) Vertical angles are equal

C) Reflexive

Answers

Answer:

Reflexive

Step-by-step explanation:

Because C and D are right angles. That’s def of perpendicular. I’m not sure about the vertical angles but it’s shown in the proof

Answer:

Reflexive

Step-by-step explanation:

Find the values of a and b such that x² - 2x + 2 = ( x - a )² + b

Answers

Answer:

a = b = 1

Step-by-step explanation:

x² - 2x + 2 = ( x - a )² + b

x² - 2x + 2 = ( x² - 2x + 1) - 1 + 2 = (x - 1)² + 1

a = b = 1  

(I'LL BE GIVING BRAINLIEST AND EXTRA POINTS TO WHO EVER HELPS ME!! :D)



Petra eats five and three fifths pies in a pie-eating contest. Paulie eats three and fourteen sixteenths pies in the contest. How many more pies did Petra eat?

A) one and fifty eight eightieths pies

B) one and seventeen twenty firsts pies

C) two and fifty eight eightieths pies

D) two and seventeen twenty firsts pies


(Here is an image if needed) :

Answers

Answer:

2 7/20

Step-by-step explanation:

5 yds=? Ft (PLEASE HELPP!!!)

Answers

Answer:

5 yards = 15 feet

Step-by-step explanation:

Following the formula that for every 1 yard we have 3 feet.

x = amount of yards

y = amount of feet per yard

z = amount of feet total

[tex]x * y = z[/tex]

Substitute:

[tex]5 * 3 = z[/tex]

[tex]15 =z[/tex]

Final answer:

5 yards = 15 feet

Mia has 12 boxes of cookies. Each box contains 36 cookies. she has another 258 cookies in the pantry. How many cookies does she have in all?

Answers

690

12×36 + 258 = 690 For extending to 20 characters

Find the equation of the linear function represented by the table below in slope-intercept form.

Answers

First find slope: (y2-y1)/(x2-x1)
pick 2 points: (-3,9), (1,-7)
(-7-9)/(1+3) = -16/4 = -4
Slope intercept form: y = mx + b
y = -4x + b, plug in a point
9 = -4(-3) + b
9 = 12 + b, b = -3
Equation: y = -4x -3

Here is a rectangle ABCD. The length of the rectangle is increased by 10%. The width of the rectangle is increased by 5%. Find the percentage increased in the perimeter of tge rectangle.

Answers

Answer: Width would become 21 and length would become 33. Original perimeter is 100, increased perimeter is 108 which is a 7.69% increase

The diagram compares the ratio of girls in the chorus to boys in the chorus. What is the ratio of girls to boys? If there are 30 students in the chorus, how many are girls and how many are boys.

girls 3 parts
boys 2 parts

Answers

Answer:

it should be girls 12 to 18

Step-by-step explanation:

i just messed around with a calculator and found it.

2. Soive: (14x - 8) - 2(3x - 6)
a. 8x + 4
b. 20x + 4
19x + 14
d. 8x - 20

Answers

Answer:

A

Step-by-step explanation:

Distribute the -2 into (3x-6)

combine like terms!!

8x+4

Answer:

A.) 8x + 4

Step-by-step explanation:

State the number of complex roots and the possible number of real and imaginary roots for each equation. The find all roots? If possible.

Answers

Answer:

x =2

x = -2

Step-by-step explanation:

(x - 2)(x + 2)(x^2 + 4) = 0

(x - 2) = 0

x = 0 + 2

x =  2

(x + 2) = 0

x = - 2

x = - 2

(x^2 + 4) = 0

x^2 = 4

x = [tex]\sqrt{4}[/tex]

x = 2

Regional erosion occurs at a rate of 2 m per 1,000 years.

How much regional erosion will occur over 1,000,000 years?


A) 20 m

B) 200 m

C) 2,000 m

D) 100,000 m

Answers

Answer:

200

Step-by-step explanation:

It's 200 because you would take the 1,000 and multiply it by the power of 3, which is 100,000. So therefore you would do the same thing with the 2, which 2 to the power of 3 is 200. There is your explanation.

How many solutions does 5x-7=5x have

Answers

Answer:

[tex] \huge{ \boxed{ \bold{ \sf{no \: solution}}}}[/tex]

Step-by-step explanation:

Question :How many solutions does 5x - 7 = 5x have ?

Step by step explanation[tex] \bold{ \sf{5x - 7 = 5x}}[/tex]

Remember that the equal terms on both side should be cancelled.

[tex] \dashrightarrow{ \sf{ \cancel{5x} \: - 7 = \cancel{ 5x }}}[/tex]

[tex] \dashrightarrow{ \sf{ - 7 = 0}}[/tex]

The statement is false for any value of x. It cannot be further solved! So , 5x - 7 = -5x doesn't have any solution.

Hope I helped!

Have a wonderful time ! ツ

~TheAnimeGirl

add on sc alawad2003

Answers

Answer:

Mkay?

Step-by-step explanation:

PLEASE HELP!!

Use the expression 9i+2(7+3i) to answer this question!
Which property or properties should you use to simplify this expression?

Apply those properties to each term

Answers

Answer:

Please check the explanation.

Step-by-step explanation:

Considering the expression

[tex]9i+2\left(7+3i\right)[/tex]

Applying the distributive law

        [tex]a\left(b+c\right)=ab+ac[/tex]

so the expression becomes

[tex]=9i+2\cdot \:\:\:7+2\cdot \:\:\:3i[/tex]

Group like terms

[tex]=9i+14+6i[/tex]

Add similar elements: 9i+6i=15i

[tex]=15i+14[/tex]

Please help I will give Brainliest!!
Part A: Using x and y, write two different expressions that represent the perimeter of rectangle #1.
please do part B as well
Part B: Which two rectangles have equal area? Justify your answer using properties of operations.

Answers

Answer:

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. To find the area of a rectangle, multiply the length by the width.

A rectangle with four sides of equal length is a square.

Following image represents the area of a rectangle.

A perimeter is a path that surrounds a two-dimensional shape. The word comes from the Greek peri (around) and meter (measure). The perimeter can be used to calculate the length of fence required to surround a yard or garden. Following image represents the perimeter of a rectangle.

Step-by-step explanation:

Sorry if this is wrong.

I have no idea if this is right but i tried.

Sorry im dumb.

If its right Yw.

:)

Answer:

Part A:  2(4x)+2(y)+2(2) and 2(4x+y+2)

Part B:  #2 and #4

Step-by-step explanation:

Part B:

- #2:     4 x 3 is 12 and 4 x 6 is 24

- #3:      2 x 6 is 12 and 6 x 4 is 24

Bothe are the same.

what is 4 divided by 0.576

Answers

That will equal to 0.144!
Hope this helped.

4 divided by 0.576 is approximately equal to 6.9444.

To find the result of 4 divided by 0.576, we can perform the division by dividing the numerator ( 4 ) by the denominator ( 0.576 ).

When we divide 4 by 0.576, we get approximately 6.9444.

Therefore, 4 divided by 0.576 is approximately equal to 6.9444.

In decimal form, this indicates that 4 can be divided into 0.576 approximately 6.9444 times. The result is a decimal number that extends to multiple decimal places. To obtain a more precise or exact answer, additional decimal places may need to be considered in the calculation.

Learn more about division here

https://brainly.com/question/29168241

#SPJ6

The sum of twice a number, m, and 7 is equal to 15 less than the number,
m. What is the value of m?

Answers

Answer:

2m+7 = m-15

2m-m+7 = -15

1m = -15-7

1m = -22

m = -22

covent 13/10 to a mixed number

Answers

Answer:

1 whole number 3/10. Above is the answer

Which word describes the slope of the line?

positive
negative
zero
undefined

Answers

Answer:

Negative

Step-by-step explanation:

the slope in this equation is negetive as it is pointing in a downwards position.

Zero would be horizontal, undefined would be vertical and positive would be going in an upwards motion

Answer:

b

Step-by-step explanation:

aye

Please help it would help alot

Answers

First space is 6
Second one is 5

Hope this helps

anybody kniws the answer??

Answers

It’s the red one, corresponding

What is 8.15 rounded to the nearest whole number

Answers

Answer:

the answer is 8.

Step-by-step explanation:

Brainliest? uwu

Answer:

8 :)

You round down. If it was 8.5 then you'd round up, anything below would be rounded down, for example, 8.4, 8.3, 8.2, 8.1.

(11 POINTS!! ) CAN SOMEONE PLEASE DO NUMBERS 19-22 FOR ME, I’LL MARK YOUR ANSWER BRAINIEST!! Thanks in advance❤️

Answers

Answer:

19. x=2

20. y= - 72

21. y=4

22.x= - 1

Step-by-step explanation:

19.x=2
20.x=-7
21.x=1
22.x=-1
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