The sum of first four terms is a G.P. is 30 and that of the last four terms is 960. if its first term is 2 find the common ratio .

Answers

Answer 1

If the sum of first four terms in a G.P. is 30 and that of the last four terms is 960, then the sum of the first 8 terms is 990

We also know that a = 2

sum of first 4 terms

= 2(r^4 - 1)(r-1) = 30

r^4 - 1 = 15r - 15

r^4 - 15r + 14 = 0

r = 1 works for the equation , but r = 1 would make all the terms of the

GP the same, so clearly not a solution

r^4 - 15r + 14 = 0 , a bit of trial and error ....

(r-1)(r - 2)(r^2 + 3r + 7) = 0

so r = 2 or r = not real

check: sum(4) = 2(2^4 - 1)/(2-1) = 30 , as needed

so r = 2 , BUT it does not work for sum(8)

sum(8) = 2(2^8 - 1)(2-1) = 510 , not 990 as necessary according to your second part of the question.

check your question.


Related Questions

Write an equation of a line
that passes through the
points
(-6,0) and (0,-24).

Answers

Answer:

y= -4x-24

Step-by-step explanation:

change in y/change in x = 0- -24/-6-0 = 24/-6 = -4

gradient is -4

then you put a set of coradinates into the formular y-y=m(x-x)

y - 0= -4 (x+6)

y-0=-4x-24

y=-4x-24

Answer:

  4x +y = -24

Step-by-step explanation:

The given points are the x- and y-intercepts. It is convenient to write the equation in intercept form:

  x/a +y/b = 1 . . . . . . x-intercept 'a', y-intercept 'b'

  x/-6 +y/-24 = 1 . . . . . equation in intercept form

  4x +y = -24 . . . . . . . equation in standard form (multiply by -24)

20 points! :D

Help is much appreciated. :D

Answers

Answer:

I think it's 32x

Step-by-step explanation:

hope I got it right Im not to good at this


Find the equation of this line.
(0,1)
(-3,0)|
y =
x+

Answers

Answer:

y = 1/3x +1

Step-by-step explanation:

y intercept is 1 and the rise is one with a run of 3

7.90×10^−2/1.0×10^−5

Answers

Answer:

[tex] \frac{7.90 \times {10}^{ - 2} }{1.0 \times {10}^{ - 5} } \\ = 7.9 \times {10}^{5 - 2} \\ = 7.9 \times {10}^{3} [/tex]

Can someone help me with this?

Answers

Answer:

y = 3x + 7.

Step-by-step explanation:

The slope = 6/2 = 3

y-intercept = 7.

Answer:

y = 3x + 7

Step-by-step explanation:

y-intercept = 7    {where the line intersect at y-axis (0,7)}

Plot a point:  (-1 ,4 )

Slope intercept form: y = mx + b

y = mx + 7

4 = m*(-1) + 7

4 = -m + 7

4 - 7 = -m

-m = -3

m = 3

y = 3x + 7

h=19+3.5w. What could the number 3.5 represent in the equation?

Answers

This number could represent the height of 19 and then you add 3.5 of something :)

Answer:

the slope of the equation

Step-by-step explanation:

ANSWER ASAP PLEASE!!!!!
What is the domain of the square root function graphed below?
A. x is less than or equal to -1
B. x is greater than or equal to -1
C. x is less than or equal to 0
D. x is greater than or equal to 0

Answers

Answer:

Step-by-step explanation:

A. If you need proof message me.

Answer:

D

Step-by-step explanation:

its correct

A rectangular field is four times as long as it is wide. If the perimeter of the field is 410 yards, what are the​ field's dimensions?

Answers

The length of the rectangular field is 164 yards and the width is 41 yards

From the question,

We are to determine the fields dimensions

From the given information

A rectangular field is four times as long as it is wide

That is

l = 4w -------- (1)

The perimeter of a rectangle is given by

P = 2(l + w)

Where

P is the perimeter

l is the length

and w is the width

From the given information

The perimeter of the field is 410 yards

∴ 2(l + w) = 410 ------ (2)

Substitute equation (1) into equation (2)

2(4w + w) = 410

2(5w) = 410

10w = 410

∴  w = 410 ÷ 10

w = 41 yards

Substitute the value of w into equation (1)

l = 4(41)

l = 164 yards

Hence, the length of the rectangular field is 164 yards and the width is 41 yards.

Learn more here:  https://brainly.com/question/4958695

Solve pls brainliest

Answers

Answer:

a is 0.085 b is 19.6%

Step-by-step explanation:

1% = 0.01 so 8.5 = 0.085

0.20 = 20% so 0.196 = 19.6%

Tell whether the given value is a solution of the inequality.

Answers

Answer:

Step-by-step explanation:

8p < -3

  if p = -2

8* -2 < -3

  -16 < -3 TRUE so p= -2 is a solution to the inequality 8p < -3

Which expression is equivalent to this expression?

34(4h – 6)
A. 3h – 92
B. 4h + 92
C. 3h – 6
D. 4h + 6

Answers

Answer:

the answer is d

Step-by-step explanation:

What is the value of x?

Answers

C. x = 36

explanation it is a straight angle which means it adds up to 180.
180-72=108
3x=108
x=36

Answer:

AC is straight line.

72°+3x=180°[linear pair]

3x=180°-72°

3x=108°

x=108°/3

x=36°

option c.

One theme in “Thank You, Ma’am” is that respectful treatment encourages mutual respect. Which passages from the story support this theme?

Select all that apply.

Thank You, Ma’am


He did not trust the woman not to trust him. And he did not want to be mistrusted now.
He did not trust the woman , not, to trust him. And he did not want to be mistrusted now.

The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him.
The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him.

The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next.
The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next.

“Then, Roger, you go to that sink and wash your face,” said the woman, whereupon she turned him loose—at last. Roger looked at the door—looked at the woman—looked at the door—and went to the sink.

Answers

Answer:

Either B. 'The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him' or A. 'He did not trust the woman not to trust him. And he did not want to be mistrusted now.'.

Step-by-step explanation:

Brainliest Please!

The passages from the story "Thank You, Ma'am" that support the theme that respectful treatment encourages mutual respect are: "The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him." "The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next." and "Then, Roger, you go to that sink and wash your face,” said the woman, whereupon she turned him loose—at last. Roger looked at the door—looked at the woman—looked at the door—and went to the sink." Correct options are 2, 3 and 4.

These passages highlight how the woman treats the boy, Roger, with kindness and respect despite his attempt to steal her purse. Her understanding and respectful treatment lead Roger to reflect on his actions and ultimately decide to follow her guidance. This illustrates how respectful treatment encourages mutual respect between the characters.

To know more about respectful treatment :

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which ordered pair is a solution to the equation?

Answers

B bc I need points !
If you have the time, it is easiest to just plug in the first part of the coordinate pair (the x value) into the x variable into the equation,
and the y value into the y variable.
A. 10 = (-2/3)(-3/2) + 9
10 = (6/6) + 9
10 = 1 + 9
10 = 10
choice a is correct

Dan is buying turkey cutlets for $2.69 per pound. The package weighs 4 pounds, 8 ounces.
How much will the cutlets cost?

Answers

if I did it right then it's $32.38.

Write an equation in point-slope form of the line that passes through (-3, 2) and (6, - 1)

Answers

Answer:

y - 2 = -1/3 (x + 3)

Step-by-step explanation

Sorry!

 Point-slope form )

Slope = (-1 -2)/(6 - (-3)

Slope = -3/9

Slope = -1/3

 Using the point-slope formula and point (-3, 2)

y - 2 = -1/3(x - (-3)

y - 2 = -1/3 (x + 3)  This is = to y = -1/3(x + 3) +2

Which equation matches the graph shown?

Answers

Answer:

Vertex form:  y = -2(x - 1)²

Standard form: y = -2x² + 4x - 2

Step-by-step explanation:

Given the x-intercept as the vertex, (1, 0), and the y-intercept, (0, -2) as the two points on the graph of a parabola:

We can determine the equation by substituting these given values into the vertex form of the quadratic equation:

y = a(x - h)² + k

where:

a = determines the direction of where the graph opens, and the wideness or narrowness of the parabola.

(h, k) = vertex

Solve for the value of a:

Use vertex: (1, 0) and y-intercept, (0, -2):

y = a(x - h)² + k

-2 = a(0 - 1)² + 0

-2 = a(-1)²

-2 = a(1)

-2 = a

Quadratic Equation:Vertex form:

The quadratic equation in vertex form that matches the graph is:

y = -2(x - 1)² + 0 or  y = -2(x - 1)² This is the quadratic equation in vertex form.

Standard form:

To transform the vertex form into the standard form, y = ax² + bx + c:

Simply expand the perfect square, (x - 1)², through FOIL method before distributing -2:

y = -2(x - 1)²

y = -2(x - 1)(x - 1)

y = -2(x² -2x + 1)

y = -2x² + 4x - 2 ⇒ This is the quadratic equation in standard form.  

What is y=6-2x-4x^2+5x^3 in standard form?

Answers

Y=6-2x-4x^2+5x^3
In standard form is……

Y=5x^3-4x^2-2x+6

question below on photo pls quick

Answers

I hope youre asking for the y=mx+b kind of equation… if so its y=2x-1

the sum of two rational numbers is 17/18 If one of the numbers is 5/24 find the other number

Answers

Step-by-step explanation:

x + y = 17/18

x = 5/24

5/24 + y = 17/18

to bring both fractions to the same denominator (I see it is 72, but let's do it formally correct for you to learn), we look for the LCM, the lowest common multiple of both.

for this we split both numbers into their prime factors and then build the the combination of the longest chains per prime factor :

24 = 2×2×2×3

18 = 2×3×3

the LCM (and the new denominator) is then

2×2×2×3×3 = 8×9 = 72

so,

15/72 + y = 68/72

y = 53/72

53 is a prime number, so the fraction cannot be further refined.

8. The sum of two numbers is 52. Find the larger number if their ratio is 1: 3.

Answers

Answer:

39

Step-by-step explanation:

Lets solve for x:

We know the ratio is 1:3

1x+3x = 52

4x = 52

x = 13

Since the ratio is 1:3:

13(3) = 39

13:39

Which makes 39 the larger number

Rose spent 124 on 10 cars & 4 cats what is the cost for 1 car & 1 cat.

Answers

Answer:

$6 per cat, $10 per car

Step-by-step explanation:

I guess and checked my work.

3. A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.​

Answers

Answer:

Length of floor = 5 m and breadth of floor = 4 m

Area of floor = length x breadth

= 5 m x 4 m = 20 m.sq

Now, Side of square carpet = 3 m

Area of square carpet = side x side = 3 x 3 = 9 m.sq

Area of floor that is not carpeted = 20 m – 9 m = 11 m.sq

Answer:

[tex]11 {m}^{2} [/tex]

Step-by-step explanation:

First Condition:

Given ,

Length of a floor = 5 m

Width of the floor = 4 m

Therefore,

Area of the floor

= l × b

= 5m × 4m

[tex] = 20 {m}^{2} [/tex]

Second Condition:

Given,

Sides of a square carpet = 3 m

Therefore,

Area of the carpet

= s × s

= 3m × 3m

[tex] = {9m}^{2} [/tex]

At last:

Now,

Area of the floor that is not carpeted is

= Area of the floor - Area of the carpet

[tex] = {20m}^{2} - {9m}^{2} [/tex]

[tex] = 11 {m}^{2} (ans)[/tex]

What is an equation of the line that passes through the points (-6, -4)
and (-4, 0)?

Answers

Answer:

y=2x+8

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the points (-6, -4) and (-4, 0).

There are 3 ways to write the equation of the line:

Slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptPoint-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a pointStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be equal to zero, and a cannot be negative

Let's write the equation in slope-intercept form, which is the most common way to do it.

We'll need to start by finding the slope of the line

The formula for the slope calculated from two points is [tex]\frac{y_2- y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Even though we are already given two points, let's label their values in order to avoid any confusion and mistakes for later:

[tex]x_1=-6\\y_1=-4\\x_2=-4\\y_2=0[/tex]

Substitute these equations into the formula to find the slope (m):

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

Substitute (remember: we have NEGATIVE numbers and SUBTRACTION, so we'll end up subtracting a negative):

m=[tex]\frac{0- -4}{-4--6}[/tex]

Simplify

m=[tex]\frac{0+4}{-4+6}[/tex]

Add the numbers together

m=[tex]\frac{4}{2}[/tex]

Divide

m=2

The slope of the line is 2

We can immediately plug it into the formula for slope-intercept form  as m:

y=2x+b

Now we need to find b

As the equation passes through both (-6, -4) and (-4, 0), we can use either one of them to solve for b

Taking (-4, 0) for example:

Substitute -4 as x and 0 as y:

0=2(-4)+b

Multiply

0=-8+b

Add 8 to both sides

8=b

Substitute 8 as b into the equation

y=2x+8

Hope this helps!

Write 2549 correct to the nearest 10​

Answers

Answer:

2550

Step-by-step explanation:

Answer this and explain please

Answers

Answer:

x = 3

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that's supplementary to the third interior angle:

15x + 5 + 22x + 4 = 120 add like terms

37x + 9 = 120 subtract 9 from both sides

37x = 111 divide both side by 37

x = 3 and to find the angles replace x with 3 in given expressions

a number y divided by 4 is greater than 22

Answers

Answer:

y ÷ 4 ≥ 22

Step-by-step explanation:

I can't find the greater than symbol, but just write the "≥" without the line underneath

Answer:

44

Step-by-step explanation:

Let the number be X

B/P,

X/4=22  Or, X=22*4

X=88

X/2=88/2=44

So the quotient of the number when divided by 2 is 44.

Hope it help and if it its correct please give brainliest

Stay Safe and healthy

Thank You

Classify the sample space as finite or infinite. If it is finite, write the sample space. If it is infinite, classify whether it is discrete or continuous.

A letter is randomly chosen from the alphabet.

Answer 1:

A. Infinite

B. Finite

Answer 2:

A. Discrete

B. Continuous

Answers

Answer:

Answer 1

Because the alphabet can end,it is not unlimited


ANSWER FAST PLEASE !!




Use synthetic division and the remainder theorem to find P(a).
P(x) = x^3 + 5x^2 - 6x +6; a = 4
P(a) =
Simplify your answer

Answers

Answer:

[tex]1 + 2 = [/tex]

answer

Hello, ive been having issues with a quite easy topic. Slopes of lines? I dont really know how to solve this.

Answers

you would count the amount of squares going up then count the squares going horizontal, so then it would be 5/3 hole this helps:)
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