what is the first term of an infinitely decreasing G.P whose sum is 16 and the second term is -0.5?​

Answers

Answer 1

Answer:

8 + 6√2  

Step-by-step explanation:

Sum of infinite GP is:

a/(1 - r) = 16 and

The second term is:

ar = -0.5

Eliminate r in the system:

a/(1-r) = 16 ⇒  a = 16 - 16r ⇒ 16r = 16 - a ⇒ r = 1 - a/16ar = -0.5 ⇒ r = -0.5/a

Compare the two equations and solve for a:

1 - a/16 = -0.5/a

Multiply both sides by 16a:

16a - a² = -8a² - 16a = 8 a² - 16a + 64 = 72(a - 8)² = 72a - 8 = ±√72a = 8 ± √72a = 8 + 6√2  a = 8 - 6√2, excluded as it is negative and makes common difference positive and so an increasing function

a = 8 - 6√2 = -0.4852 ⇒ r = -0.5/a = -0.5/-0.4852 = 1.03 > 1


Related Questions

If you borrow $400,000 at an APR of 4% for 15 years, you will pay more per month than if you borrow the money for 30 years at 4%. However, you will pay much more in interest over the life of the loan. Answer the questions below (10 points) a. What is the monthly payment on the 15-year mortgage, to the nearest cent? (Be sure to use Excel to calculate the monthly payment.) b. What is the total interest paid on the 15-year mortgage? C. What is the monthly payment on the 30-year mortgage, to the nearest cent? d. What is the total interest paid on the 30-year mortgage? e. How much more interest in paid on the 30-year loan?​

Answers

Answer:

If if i did the match correctly then you would be paying $53.33

Step-by-step explanation:

hope this helps!!!!!!! :D

What is the fourth root of -16/81?​

Answers

Answer:

The fourth root of -16/81, whose result is -0.19, is -0.66.

Step-by-step explanation:

To determine the fourth root of -16/81, you must first perform this mathematical operation, and then perform the radication of the result of it. Thus, the following process must be carried out:

-16 / 81 = X

-0.19 = X

4√0.19 = -X

0.66 = -X

-0.66 = X

Therefore, the fourth root of -16/81, whose result is -0.19, is -0.66.

What is a formula for the nth term of the given sequence? 50, -20,8...​

Answers

Answer:

L = 50 * (-0.4)^(n - 1)

Step-by-step explanation:

r = t2/t1 = -20/50 = - 0.4

a = 50

L = 50 * (r)^(n - 1)      Let's  see if we can get the answer when n = 3

L=50 * (-0.4)^(3 -1)

L =50* (-0.4)^2

L = 50 * 0.16

L = 8 which is correct

Help me out here pleaseeeeeeee

Answers

Answer:

if gray is what's left then it is C if white is what's left it is A

Step-by-step explanation:

Step-by-step explanation:

A because it shows the 2/3 of the pie colored meaning eaten

Write the following in point-slope form using the given information: Slope: 2 points
1/15; Point: (3,-5)

Answers

Answer:

[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]

Step-by-step explanation:

Given

[tex]m = \frac{1}{15}[/tex] -- Slope

[tex](x_1,y_1) = (3,-5)[/tex] --- Point

Required

Write an equation in point slope form

The point slope form of an equation is:

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

Substitute values for y1, x1 and m

[tex]y-(-5) = \frac{1}{15}(x - 3)}[/tex]

[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]

Hence, the equation in point slope form is:

[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]

A store sells candles. Each candle costs the same amount. During a sale, the store reduces the price of each candle by $1.70. Owen spends $11.96 on 4 candles at the sale price. what was the price of 1 candle before the sale?

Answers

Answer:

The regular sales price was $4.69

Answer:

4.69

Step-by-step explanation:

I had the maps test

Can someone help me with this

Answers

No because 3^2 is 3x3 which is 9 not 6.

Two parallel lines are cut by transversal x and a transversal Y so that x and y intersect at point Q as shown. Wong constructs the following argument : A) Reason 1: an alternating exterior angel with one angle in the triangle ...etc

Answers

Answer:

A

Step-by-step explanation:

PLzzz help meeeeeeeeeeeeeeeeeeeeee


In rhombus MATH, the coordinates of the endpoints of the diagonal MT are M(0, 2) and T(4, 6). Write an equation of the line that contains diagonal AH. Give your answer in slope-intercept form.

Answers

Answer:

y = - x + 6

Step-by-step explanation:

-- Rhombus diagonals are perpendicular and bisect each other.

-- A( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

Coordinates of the midpoint of a segment AB are

( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

and formula of a slope of the line segment AB is

m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

-- If AB ⊥ CD then [tex]m_{AB}[/tex] × [tex]m_{CD}[/tex] = - 1

-- Slope-point of linear equation is

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~~~

M(0, 2)

T(4, 6)

[tex]m_{MT}[/tex] = [tex]\frac{6-2}{4-0}[/tex] = 1

[tex]m_{AH}[/tex] = - 1

Coordinates of the intersection of the diagonals are ( [tex]\frac{4+0}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = (2, 4)

y - 4 = - 1(x - 2)

y = - x + 6 is slope-intercept form of the diagonal AH

Together, Lee and Joanna have 19 computer games. Joanna has 3 more games than Lee. Write and solve an equation to find the number of games each friend had.

Answers

Answer:

L=8 and J=11

Step-by-step explanation:

If Lee is L and Joanna is J we get: L+J=19.

And since Joanna has 3 more than Lee we get: J=L+3

When we substitute J for L+3 we get: 2L+3=19

When we solve we get: L=8

Finally, since J=L+3 we get: J=11

which is the correct answer?​

Answers

Step-by-step explanation:

Options B and C are wrong because 0 as a numerator is totally fine as a real solution.

In Option A,

15(x² - 1) = 10(3x - 3)

15x² - 45x + 30 = 0

x² - 3x + 2 = 0

(x - 1)(x - 2) = 0

x = 1 or x = 2.

This is correct as x cannot be 1 (dividing by zero).

In Option D,

(x + 2)(x - 1) = 40

x² + x - 42 = 0

(x - 6)(x + 7) = 0

x = 6 or x = -7.

In here x = 1 does not even appear in our working so it is not an extraneous solution (even though it is dividing by zero)

Hence the answer is A.

Which graph represents the function y = 2/3x-2

Answers

Answer:

C

Step-by-step explanation:

so the y-int is where the point is on the y-axis (0,X). Or, in this situation-2.

for slope, you just need to do rise over run, or up and down first then, left and right. If I do that for C, I go 2 up and 3 right. So the slope os 2/3 (P.S. up and right is positive, and down and left is negative)

Need help ASAP!!
HELP!!!!!

Answers

Answer:

Option D

Step-by-step explanation:

Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the formula,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

From the graph attached,

Since, the given line passes through two points (-3, 0) and (0, 2),

Slope of the line = [tex]\frac{2-0}{0-(-3)}[/tex]

                           = [tex]\frac{2}{3}[/tex]

y-intercept of the line is the point of intersection of the line and y-axis.

Therefore, y-intercept of the line given in the graph is,

y = 2 units

Option D is the answer.                    

What is the value of x?
x= -8
2x + 5 – įx = 3
O x =
0.x = -2
0 x = 1/2
x = 8

Answers

Dude doesn’t x basically equal 8 X=8 ? Or am I just wrong

sum of
5 3/7 - 2 1/5

Answers

Answer:

Step-by-step explanation:

5 3/7= 38/7 (move the wholes into the fraction)

2 1/5=11/5

38/7- 11/5  we need the common denominator=35

190/35 -77/35= 113/35

=3 8/35

Help..I’m useing all my points TELL ME ALL THE AWNSERS TO THE LOWER PART

Answers

Answers:

Lazy Butcher: M E A T L O A F E R

Rubber Raft: P L A Y B U O Y

Corn Salesman:  S T A L K B R O K E R

T = 6(3*4 - 5) - 9*4 = 6

U = 4 - 8(-2 -6*-1) = -28

Y = -3*-3 + 2(-5 * -3 + 1) = 41

R = -7(7 +6) + 12 = 79

F = 4(8 + 5 * -2) + 2* -2 = -12

S = -5 -3(4 - 9) = 10

E = 7 - 6(-8 + 2 * -6) + -6 = 121

P = 8 * -8 - 9 * -8 + 2(-3 * -8 - 4) = 48

K = -4(4 + 7 * 2) + 5 + 3 * 2 = -61

B = 5(--5 - 3) + 4 * -5 - 10 = -20

M = -1 + 9(4 * -1 - 2)  - 6 * -1 = -49

A = 6 - 2 * 3 - 6(-3 * 3 + 7) = 12

O = -8(9 + 2 * 6) + 8 * 6 + 6 = -114

L = -1 - 5 + 5(-5 * 1 + 9) = 14

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I need help please I have to finish this

Answers

Answer:

Hey,

Let A be (-1,7)

Let B be (5,1)

In order to find the distance we need to do

[tex]d = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } [/tex]

Once we plug x2=5 and x1=-1

and y2=1 and y1= 7

You get

[tex]6 \sqrt{2} [/tex]

Now to find the midpoint:

[tex]( \frac{x1 + x2}{2} \frac{y1 + y2}{2} )[/tex]

Using the same values defined above we get:

(2,4)

Please rate brainlist and give a positive review

Select the correct answer.
What is the slope of the linear relationship shown in this table of values?
a.-3
b.-2
c.2
d.3

Answers

Answer:

c

Step-by-step explanation:

I agree with c.2 as well

Tyler needs to complete this table for his consumer science class. He knows that 1 tablespoon contains 3 teaspoons and that 1 cup contains 16 tablespoons. Write an equation that represents the number os teaspoons tcontAINED IN A CUP C.

Answers

Answer:

([tex]\frac{t}{3}[/tex])÷16=C

what is 344.7234 to 1 decimal point​

Answers

Answer: 344.7

Explanation:

344.7∣234

  (Cut ^off point at the line)

The digit to the right of the cut of the point is less than 5. So the digit to its left (the 7) is not changed and all those to the right are changed to 0 gives you:

344.7000

Written as 344.7

Hope this helps and hope you have a wonderful day :)

Rolling a 2 on a number cube is
1. likely
2. unlikely
3. as likely as not (50/50)
4. impossible
5. certain

Answers

Answer:

2. unlikely

Step-by-step explanation:

The probability of rolling a 2 is 1/6, 0r 0.1666...  .

Probabilities and their meanings:

0   -   impossible

between 0 and 0.5   -   from unlikely to almost as likely as not

0.5   -   as likely as not

between 0.5 and 1   -   from as likely as not to almost certain

1   -   certain

This probability is 0.1666... which is in the category from 0 to 0.5. It is closer to 0 than to 0.5, so although it is not impossible, it is unlikely.

Answer: 2. unlikely

In the group of ordered pairs shown, the x-values are inputs and the y-values are outputs. Which statements are true about the inputs and outputs? Select all that apply. (2, 4), (6, 3), (5, 4), (7, 3), (8, 2)

Answers

Answer:

I dont see the statements but this is a parabola. As you can see some of the ys repeat.

Step-by-step explanation:

Match the correct equation for the variable n with * for number of times compound interest is figured. quarterly d.___ semi-annually a.___ monthly b.___ annually c.____

I have to put the correct answer on the lines and they gave me a. N =2 b. N= 12
C. N=1 and D. N=4

Answers

Answer:

quarterly N = 4

semi-annually N = 2

Monthly N = 12

annually N = 1

Step-by-step explanation:

Given the following compound interest times :

N = number of times interest is compounded per period :

A period is regarded as a whole year.

Interest compounded;

QUARTERLY = Every 4 months per period = 12/3= 4

SEMI ANNUALLY = Every 6 months per period = 12/6 = 2

MONTHLY = Every month = 12 / 1 = 12

ANNUALLY = Every 12 months = 12 /12 = 1

Find the commission on a $1250 sale with a commission rate of 5%

Answers

Answer:

He will have in total $1312.50

He earns a total of $62.50

Step-by-step explanation:

1250 x 1.05 = 1312.50

1250 x 0.05 = 62.50

Is (-4,2) a solution of 4x+5y<-7

Answers

Answer:

(-4,2) is NOT a solution

Step-by-step explanation:

In this question, we have to see if the coordinate is a solution to the inequality.

To do this, plug in and solve:

4(-4) + 5(2) < -7

-16 + 5(2) < -7

-16 + 10 < -7

-6 < -7

Since -6 is not less than -7, this would be false.

Therefore, (-4,2) is NOT a solution.

coordinates are (-4,2)

equation :

[tex]4x + 5y < - 7[/tex]

substituting values of x and y in equation :

[tex]4( - 4) + 5(2)[/tex]

[tex] = - 16 + 10 \\ = - 6 > - 7[/tex]

which is not the required solution as - 6 is greater than -7

therefore (-4,2) is not the solution

Kirby is packing granola bars for a filed trip. He already packed 2 bags with 5 granola bars in each bag. He has 10 more granola bars to pack. How many granola bars will Kirby pack in all

Answers

Answer:

20 granola bars

Step-by-step explanation:

1.298 -
Prime number

Answers

Answer:

what are you asking rlly

Help ASAP Please. Working on this now. Look at picture for question and answer A, B, C. No Plagiarism Please. Will Mark Brainliest. ​

Answers

Answer:

Please check explanations for answer to the question

Step-by-step explanation:

The exponential relation can generally be represented as ;

y = I (1 + x)^n

where I is the initial value

1 + x represents the growth rate

n represents the time such as number of years

y represents the value after n count

a) The value 1200 represents the initial count of bacteria in the study

b) 1.8 represents the growth rate of the bacteria population in the culture

c) 1000 represents the initial bacteria population in the second function

The difference mean that the initial population in the first case study is greater than what we have in the second function

An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location in the sea. It then flies 483 miles from the sea at a bearing of S 55° W to another location. Finally, the aircraft flies straight back from the second location to its base. What is the total distance it flies, rounded to the nearest mile?


A.
550 miles
B.
1,033 miles
C.
1,583 miles
D.
1,692 miles
E.
2,210 miles

Answers

Answer: D) 1692 miles

============================================

Explanation:

A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram

Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.Plot the points E and F, which are north and south of point B.Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.

The diagram below shows all of this visually summarized. We have the segments

AB = 550 milesBC = 483 milesAC = x miles

And we have these angles

Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)Angle ABC = 79 degrees (red)Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)

Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.

------------------------------

Once the diagram is set up, we'll use the law of cosines to find x.

Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.

The interior angles of triangle ABC are

A = 46 degreesB = 79 degreesC = 55 degrees

The sides opposite the angles are

a = 483 (opposite angle A)b = x (opposite angle B)c = 550 (opposite angle C)

Now we can apply the law of cosines

b^2 = a^2 + c^2 - 2*a*c*cos(B)

x^2 = 483^2 + 550^2 - 2*483*550*cos(79)

x^2 = 434412.180756441

x = sqrt(434412.180756441)

x = 659.099522649229

x = 659

Side AC, or CA, is roughly 659 miles long.

------------

To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)

Distance Traveled = AB + BC + CA

Distance Traveled = 550 + 483 + 659

Distance Traveled = 1692 miles

Diana creates a graph of money she earns y for working x hours the graph contains the points 34,408 40,489 46 588

Answers

Answer:D and E I think

Step-by-step explanation:

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