The GM of a series of a three positive numbers is 4 by including fourth number it becomes 2 what is fourth value

Answers

Answer 1

Answer:

1/4

Step-by-step explanation:

Let a₁, a₂, a₃ and a₄ be the four numbers. Since the geometric mean of the first 3 positive numbers is 4, we have that

∛(a₁a₂a₃) = 4. (1)

Also the geometric mean of the four numbers is 2, we have that ⁴√(a₁a₂a₃a₄) = 2   (2).

So, taking the cube of (1), we have

[∛(a₁a₂a₃)]³ = 4³

a₁a₂a₃ = 64  (3)

Also, taking the fourth power of equation (2), we have

[⁴√(a₁a₂a₃a₄)]⁴ = 2⁴  

a₁a₂a₃a₄ = 16  (4)

Dividing (4) by (3), we have

a₁a₂a₃a₄/a₁a₂a₃ = 16/64

a₄ = 1/4

The fourth value is 1/4


Related Questions

the top says for the first box : Part A Explain how Mrs. Soto could apply the
following theorem to the problem of restoring
the gate to its original rectangular shape.

Answers

Answer:

The given theorem proves that the door is not a rectangle right now since, the door came out of shape, it can be proved by the Pythagorean theorem. If the length is set to a certain shape, and the width is set to a certain shape, and drawn to diagonals. If solved by the Pythagorean Theorem, if the length of two diagonals are similar then and only then the door would be a rectangle.

Hope this helps!

which is a solution of the equation y=2x+8

Answers

To find the y-intercept, plug in 0 for x and you solve to get 8

y=−2x+8

y=−2(0)+8

y=0+8

y=0

To find the x-intercept, plug in 0 for y and you solve to get 4

y=−2x+8

0=−2x+8

2x=8

x=0

Step by step below in the pic

Help pls , will give brainliest!

Answers

Answer:  6

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

Work Shown:

1 liter = 1000 mL

3 liters = 3000 mL

I multiplied both sides by 3.

Divide that result over 500 to get 3000/500 = 6

So she'll need to buy 6 cartons.

-------

You could also solve like this:

(1 carton)/(500 mL) = (x cartons)/(3000 mL)

1/500 = x/3000

1*3000 = 500*x ... cross multiply

3000 = 500x

500x = 3000

x = 3000/500 .... dividing both sides by 500

x = 6

What is the value of y?
O A. 36°
O B. 72°
C. 54°
O D. 1080

Answers

sorry but can u show a picture of y?

Answer:

but where is que plz show your que

What is the measure of arc XZ?​

Answers

ohh dear u still have school i have a holiday for two months

What is parallel to y=-5+4.2x

Answers

Any line that has the same slope as the given equation , 4.2

B E
400
(51)
А
C D
3t
Find the measure of ZF if mZD=88º.
A. 8°
B. 40°
C. 52°
D. 90°

Answers

the answer is c because you have to take the zf an time it by the zd

Answer:

C

Step-by-step explanation:

for the top of the triangle it has to be 40 and angle d has been declared as 88

so it is 40+88 = 128    now 180 -128 = 52 so the answer is C

Please help me, please and thank you it would mean a lot.

Answers

Hey! 576 feet of lacquer will be needed to cover the floor. I know this because the formula to find this shape is base * night and 12 * 48 is 576.

For the next question the answer is that she needs 120 ft.

This confuses me a little because it keeps saying like “will the person have enough” but it does not say what the number is. I might be wrong for the second one and I am sorry if I am. Have a great summer!!!!

Mike wants to work out the height of a tree which has a fence around it. From A he sees that the angle of elevation of the top is 19° From B, 18m closer, the angle of elevation is 32° Workout the height of the tree

Answers

Answer: 13.8 m

Step-by-step explanation:

Given

From point A, angle of elevation is [tex]19^{\circ}[/tex]

From point B which is 18 m closer, it changes to [tex]32^{\circ}[/tex]

Suppose the height of tree is h

From figure, we can write

[tex]\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}[/tex]

Similarly

[tex]\Rightarrow \tan19^{\circ}=\dfrac{h}{x+18}\\\\\Rightarrow h=(x+18)\tan 19^{\circ}\\\text{Substitute the value of h}\\\Rightarrow x\tan 32^{\circ}=x\tan 19^{\circ}+18\tan 19^{\circ}\\\Rightarrow x(\tan32^{\circ}-\tan 19^{\circ})=18\tan 19^{\circ}\\\\\Rightarrow x=\dfrac{18\tan 19^{\circ}}{\tan32^{\circ}-\tan 19^{\circ}}\\\\\Rightarrow x=22.09\approx 22.1\ m[/tex]

Deduce the value of h

[tex]\Rightarrow h=22.092\times \tan 32^{\circ}\\\Rightarrow h=13.8\ m[/tex]

Thus, the height of the tree is 13.8 m

For the function y = -2x + 4, the input is 3. What is the output?​

Answers

Answer:

The output is -2 when the input is 3.

Step-by-step explanation:

You're actually being asked to evaluate y = -2x + 4 at x = 3.  x is the 'input' and y is the 'output.'

At x = 3, y = -2(3) + 4 = -2

The output is -2 when the input is 3.


Can someone pleaseeee help and if you’re correct i’ll give brainliest

Answers

Answer:area of the circle=πr²

3.14 =3.14 ×r²

= 1

r. =1 millimeters

What is the distance between (4,6) and (9,15)?

Answers

Answer:

10.2956

Step-by-step explanation:

The distance  between (4,6) and (9,15) is √87.

What is distance formula?

The distance between the points P ([tex]x_1, y_1[/tex])and Q ([tex]x_2, y_2[/tex]) is

PQ = √[tex](x_2 - x_1[/tex]) ² + ([tex]y_2 - y_1[/tex])² , which is called the distance formula.

Given coordinates: (4,6) and (9,15)

Using distance formula:

=√[tex](x_2 - x_1[/tex]) ² + ([tex]y_2 - y_1[/tex])²

= √[tex](9 -5[/tex]) ² + ([tex]15 -6[/tex])²

=√[tex](4[/tex]) ² + (9)²

= √16 + 81

=√87.

Hence, the distance between  (4,6) and (9,15) is √87 units.

Learn more about distance formula here:

https://brainly.com/question/2287272

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MARKING BRAINLIEST

PLS HELP

Answers

Answer:

25

Step-by-step explanation:

Moving it down does not change the length.

can anyone help me please?

Answers

Answer:

yes i can help you with all the time

Which correctly uses bar notation to represent the repeating decimal for
fi
O 0.54
O 05454
O 054
O 0.545

Answers

0.45 I took the test

Write as a single power: (x^4)(x^10)/(x^3)^5​

Answers

X^22
Because, (x^4) (x^10) (x^3) (x^5)
= x^22 . I hope u have a great summer

The solution of the expression as a single power is X²⁹.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is (x⁴)(x¹⁰)/(x³)⁵. The equation will be solved by the property of exponents.

E = (x⁴)(x¹⁰)/(x³)⁵

Add all the powers of the same base x.

E =  (x⁴)(x¹⁰)/(x¹⁵)

E = x⁽⁴⁺¹⁰⁺¹⁵⁾

E = x²⁹

Therefore, the solution of the expression as a single power is X²⁹.

To know more about an expression follow

https://brainly.com/question/8844911

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4,570= 3thousands+___hundreds+ 7 tens

Answers

Answer: 4 thousands, 5 hundreds, 7 tens

Step-by-step explanation: 4,570 is pretty easy to break down. The first place value is 0 so nothing for that. As you have it there the tens place values has 7. Next is hundreds and there's a 5 there so 5 hundreds. If the number is 4,570 then it should be 4 thousands not three.

a 25% tip was payed on a 30$ meal what is the amount of the tip

Answers

Answer:

$7.50

Step-by-step explanation:

30 x 0.25= 7.50

the tip is 7.50 because 20% of 30 is 7.50

The expression 2 - x-1/x+2
is equivalent to

A. 1 - 3/x+2
B. 1 + 3/x+2
C. 1 - 1/x+2
D. 1 + 1/x+2

Answers

The answer is b I think

The expression [tex]2- \dfrac{x-1}{x+2}[/tex]  is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].

We have to find, which equation is equivalent to the given expression.

The given expression is,

[tex]= 2- \dfrac{x-1}{x+2}[/tex]

To determine the equivalent expression following all the steps given below.

Step1; Taking LCM in the equation,

                   [tex]\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\[/tex]

Step2; Solving the equation,

                    [tex]= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\[/tex]

Step3; rewrite the equation in the small factors,

                    [tex]=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\[/tex]

Step4; By using partial fraction rewrite the equation,

                    [tex]= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}[/tex]

Hence, The expression [tex]2- \dfrac{x-1}{x+2}[/tex]  is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].

For more details refer to the link given below.

https://brainly.com/question/2264568

Aaron as 3 times as many sweets as Bola Aaron gives Bola 6 sweets and now he has twice as many as her new total How many sweets did they each begin with

Answers

Answer:

Aaron = 54

Bola = 18

Step-by-step explanation:

Let

[tex]A \to Aaron[/tex]

[tex]B \to Bola[/tex]

From the first statement, we have:

[tex]A = 3B[/tex]

After given Bola 6 sweets,

[tex]A - 6 = 2(B + 6)[/tex]

Required

The initial number of sweets each has

Substitute [tex]A = 3B[/tex] in [tex]A - 6 = 2(B + 6)[/tex]

[tex]3B - 6 = 2(B + 6)[/tex]

Open bracket

[tex]3B - 6 = 2B + 12[/tex]

Collect like terms

[tex]3B -2B = 12+6[/tex]

[tex]B = 18[/tex]

Substitute [tex]B = 18[/tex] in [tex]A = 3B[/tex]

[tex]A = 3 * 18[/tex]

[tex]A = 54[/tex]

What is the remainder when 19x^2+15x+12 is divided by x-2?

Answers

Answer:

118

Step-by-step explanation:

Please help me. Study island is hard

Answers

Answer: 5/12

Step-by-step explanation:

13-7 = 5

16-4 = 12

A the answer is A have a nice day

What effects do the values of a and b have on the graph of the linear relation y = ax + b?

Answers

a is the coefficient of x. It changes the slope of the line/the steepness. The b changes the point where the line crosses the y-axis. For instance if we had the equation y = x + 4 then the function would cross at the point (0,4)

Question 1:

Solve this system of equations using any method.

4x – y = 5
3x + y = 16

a. (3, 5)

b. (4, 11)

c. (4, 4)

d. (3, 7)

Question 2:

Solve the following system of equations.

d + e = 6
d – e = 4

a. no solution

b. (5, 1)

c. (3, –1)

d. infinite number of solutions

Question 3:

Solve the following system of equations by linear combination:

4x + 3y = 12
y = x – 10

a. (3, –7)

b. (6, –4)

c. (–7, 3)

d. (–4, 6)

Answers

Answer:

Question 1: d. (3, 7)

Question 2: b. (5, 1)

Question 3: b. (6, –4)

Step-by-step explanation:

Question 1:

Solve this system of equations using any method.

4x – y = 5

3x + y = 16

Add the equations.

7x = 21

x = 3

4(3) - y = 5

-y = -7

y = 7

d. (3, 7)

Question 2:

Solve the following system of equations.

d + e = 6

d – e = 4

Add the equations.

2d = 10

d = 5

5 + e = 6

e = 1

b. (5, 1)

Question 3:

Solve the following system of equations by linear combination:

4x + 3y = 12

y = x – 10

4x + 3y = 12

-x + y = -10

Multiply the second equation by 4 and add to the first equation.

          4x + 3y = 12

(+)      -4x + 4y = -40

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

                  7y = -28

y = -4

-4 = x - 10

x = 6

b. (6, –4)

Given the points Q(-3, -4) and R(2, 0), find the coordinates of the point P on directed line segment QR that partitions segment QR such that the ratio of QP to PR is 2

Answers

Step-by-step explanation:

the answer in photo above

Please answer properly.

Answers

Answer:

1) [tex]b=6[/tex]

2) [tex]m=4[/tex]

3) [tex]p=12[/tex]

4) [tex]x=-1\frac{2}{6}[/tex]

Step-by-step explanation:

[tex]b+6=12[/tex]

subtract 6 from both sides

[tex]b=6[/tex]

---------->>>>

[tex]9m=32+4[/tex]

combine like terms

[tex]9m=36[/tex]

divide both sides by 9

[tex]m=4[/tex]

---------->>>>

[tex]21=p+9[/tex]

Subtract 9 from both sides

[tex]12 = p[/tex]

---------->>>>

[tex](10+5)+3x=0[/tex]

Add within the parenthesis

[tex]5+3x=0[/tex]

subtract 5 from both sides

[tex]3x=-5[/tex]

divide both sides by 3

[tex]x=-1\frac{2}{6}[/tex]

Hope this is helpful to you.

A jar contains quarters and nickels. There are 5 fewer quarters than nickels. The
total value of the coins is $4.45. Which system of equations can be used to
determine the number of quarters, q, and the number of nickels, n?

Answers

Given:

In a jar, there are 5 fewer quarters than nickels.

The total value of the coins is $4.45.

To find:

The system of equations can be used to determine the number of quarters, q, and the number of nickels, n.

Solution:

Let q be the number of quarters and n be the number of nickels.

It is given that there are 5 fewer quarters than nickels.

[tex]q=n-5[/tex]           ...(i)

We know that,

1 quarter = $0.25

1 nickel = $0.05

Using these conversions, we get

q quarters = $0.25q

n nickels = $0.05n

The total value of the coins is $4.45.

[tex]0.25q+0.05n=4.45[/tex]           ...(ii)

The equations (i) and (ii) are equations of required system of equations.

Therefore, the system of equations is:

[tex]q=n-5[/tex]  

[tex]0.25q+0.05n=4.45[/tex]

What are the solutions of this quadratic equation? X2 − 10x = -34 A. X= -8, -2 B. X= 5 + 3i C. X= -5 + 3i D. X= -5 + square root of 59

Answers

Answer:

B. X= 5 + 3i

5 + 3i

Step-by-step explanation:

We are given the quadratic equation

x² - 10x = -34

x² - 10x + 34 = 0

Using Almighty formula

x = -b ± √b² - 4ac/2a

When given equation: ax² + bx + c

Where: a = 1, b = -10 , c = 34

x = -10 ± √-10² - 4 × 1 × 34/2 × 1

x = 10 ± √100 - 136/2

x = 10 ± √-36 /2

x = 10/2 ±. √-36/2

x = 5 ± 6i /2

x = 5 ± 3i

Hence: the roots of the equation are:

x = 5 - 3i , x = 5 + 3i

Owen bought 4 pizzas for a class party. If each person ate 1/5 of a pizza, how many people could be served? Division and multiplecation please right the correct equation.

Answers

9514 1404 393

Answer:

  20 people

Step-by-step explanation:

Let n represent the number of people served. If each ate 1/5 of a pizza and there are 4 pizzas, we have ...

  (1/5)·n = 4

The solution can be found by multiplying both sides of the equation by 5.

  5(1/5)n = 5(4)

  n = 20

20 people could be served.

Which equation does not describe a linear function?
y = 7
y = 2x2 – 5
2y = 3x - 9
4x – 6y = 13

Answers

Answer:

The second option

Step-by-step explanation:

All the other choices can be graphed as straight lines, but only the second option is a parabola

Answer:

y = 2x² – 5

Step-by-step explanation:

y = 2x² – 5 is not lineal function since x is raises to an exponent.

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