[tex]{x}^{18}={y}^{21}={z}^{28}[/tex]
3, [tex]3 log_y x [/tex], [tex]3 log_z y [/tex] and [tex]7 log_x z [/tex] are in?​

Answers

Answer 1
[tex]\large\bold{\underline{\underline{Question:-}}}[/tex]

[tex]{x}^{18}={y}^{21}={z}^{28}[/tex]

3, [tex]3 log_y x [/tex], [tex]3 log_z y [/tex] and [tex]7 log_x z [/tex] are in??

[tex]\large\bold{\underline{\underline{Answer:-}}}[/tex]

The Series in AP.

[tex]\large\bold{\underline{\underline{Explanation:-}}}[/tex]

[tex]{x}^{18}={y}^{21}={z}^{28} [/tex]

[tex]{x}^{18}={y}^{21}[/tex]

By taking LOG on both sides

[tex]log {x}^{18}=log {y}^{21} [/tex]

[tex]18 log x= 21 log y[/tex]

[tex]2 \ times 3 log x= 7 log y[/tex]

[tex] 3 \dfrac{log x}{log y} =\dfrac{7}{2}[/tex]

[tex]\bold{ 3 log_y x =\dfrac{7}{2}}[/tex]

Now,

[tex]{x}^{18}={z}^{28} [/tex]

By taking LOG on both sides

[tex]log {x}^{18}=log {z}^{28} [/tex]

[tex]18 log x =28 log z [/tex]

[tex] 9 log x =7 \times 2 log z [/tex]

[tex] 7\dfrac{log z}{log x} = \dfrac{9}{2}[/tex]

[tex]\bold{7 log_x z= \dfrac{9}{2}}[/tex]

Now,

[tex]{y}^{21}={z}^{28} [/tex]

By taking LOG on both sides

[tex]log {y}^{21}=log {z}^{28} [/tex]

[tex]21 log y=28 log z [/tex]

[tex] 3 log y = 4 log z [/tex]

[tex]3 \dfrac{ log y}{logz }= 4 [/tex]

[tex]\bold{ 3 log_z y = 4 }[/tex]

According to the question:-

3, [tex]3 log_y x [/tex], [tex]3 log_z y [/tex] and [tex]7 log_x z [/tex] are ...in??

we have,

[tex]\bold{ 3 log_y x =\dfrac{7}{2}}[/tex]

[tex]\bold{7 log_x z= \dfrac{9}{2}}[/tex]

[tex]\bold{ 3 log_z y = 4 }[/tex]

The series is,

[tex]3 , \: \dfrac{7}{2 } , \: 4 , \: \dfrac{9}{2}[/tex]

Here,

[tex]a_1 = 3 [/tex]

[tex]a_2 = \dfrac{7}{2 } [/tex]

[tex]a_3 = 4 [/tex]

[tex]a_2 = \dfrac{7}{2 } [/tex]

Let, us find common difference

[tex]d \implies a_2 - a_1 = = a_3-a_2 [/tex]

[tex]d \implies 2 a_2 = a_3+a_1 [/tex]

[tex]d \implies 2 \times \dfrac{7}{2}= 7 [/tex]

[tex]d \implies 7 = 7 [/tex]

Since, common difference is equal!

The series is in AP.

Related Questions

Is x = 15 a solution to the equation 8x − 8 = 120

Answers

Answer:

No

Step-by-step explanation:

if x = 15, 8 x 15 = 120

5 less than the number k

Answers

Answer:

5 less than the number k(k-5) is the right answer.

PLEASE HELP and explain! ill give brainliest if you do

Answers

Area of the rectangle

[tex] = l \times b[/tex]

[tex] = 8 \times 6[/tex]

[tex] = 48 {in}^{2} [/tex]

Area of the semicircles

[tex] = 2 \times ( \frac{1}{2} \pi {r}^{2} )[/tex]

[tex] = \pi {r}^{2} [/tex]

[tex] = \pi {3}^{2} [/tex]

[tex] = 9\pi[/tex]

[tex] = 9 \times 3.14[/tex]

[tex] = 28.26 {in}^{2} [/tex]

Area of the figure

[tex] = 48 + 28.26[/tex]

[tex] = 76.26 {in}^{2} [/tex]

= 76.3in²

(rounded)

Answer:

76.3in squared

Step-by-step explanation:


What is the value for x?
Angle A=73°
Angle B=(6x + 4)º
Angle C=(8y-7)° Enter your answer in the box.
X=

Answers

The value of x is 5 from the diagram.

The sum of angles in a triangle.

The sum of interior angle of a triangle is 180 degrees. Hence:

m<A + m<B + m<C = 180

From the information given,;

73 = 8y - 7 (base angles are equal)

8y = 80

y = 10

Take the sum of the angles:

73  + 6x + 4 + 73 = 180

6x + 150 = 180

6x = 30

x= 5

Hence the value of x is 5 from the diagram.

Learn more on triangles here: https://brainly.com/question/2938476

The value of x is 5.

Since triangle ABC is an isoceles triangle, angle A = Angle C(base angles of an isoceles triangle are equal)

Since angle A = 73° and angle C = (8y - 7)°

angle A = angle C

73 = 8y - 7

Adding 7 to both sides, we have

73 + 7 = 8y - 7 + 7

80 = 8y

Dividing both sides by 8, we have

y = 80/8

y = 10

Also, angle A + angle B + angle C = 180° (sum of angles in a triangle)

73 + 6x + 4 + 8y - 7 = 180

Collecting like terms, we have

73 + 4 - 7 + 6x + 8y = 180

6x + 8y + 70 = 180

Subtracting 70 from both sides, we have

6x + 8y + 70 - 70 = 180 - 70

6x + 8y = 110

Making x subject of the formula, we have

6x = 110 - 8y

x = (110 - 8y)/6

Substituting the value of y into the equation, we have

x = (110 - 8y)/6

x = (110 - 8 × 10)/6

x = (110 - 80)/6

x = 30/6

x = 5

So, the value of x is 5.

Learn more about angles in a triangles here:

https://brainly.com/question/7888180

Steven’s retirement income is $54,500. Assuming it is 70% of his final salary, what was his final salary?

$38,150
$54,500
$77,857
$81,985

Answers

Answer:

third choice

Step-by-step explanation:

His final salary must be 100% so to find it,

100%/70%×$54500

=$77857.14≈$77857

Answer:

77,857$

Step-by-step explanation:

correct on odyssey

Suzy's kitchen measures 21 feet by 3 feet. She would like to add a small tile border around the entire room. How much should she expect to pay if the tile strip costs $0.95 per foot.

Answers

Find the area of kitchen

21×3=63

if tile costs $0.95 per foot,

then 63÷0.95=66.36

thus the cost will be $66.36

Which is a solution to the system of inequalities? y > - 2x + 5 ; 3x - 4y ≤ - 24

Answers

Answer:

y > 2x+5  and y > 6+ 3z/4

Step-by-step explanation:

solve each inequality and then find the intersection

Answer:

y > - 2x

Step-by-step explanation:

When sandy and allen's mother decorates the house by herself, it takes her 5 hours.When both Sandy and Allen help, the three can finish the job in 2.5 hours.

Answers

If you're asking how this is possible,

Answer and explanation:

If Sandy and Allen's mother does the job in 5 hours

And Allen and Sandy's contributions completes the job in 2.5 hours

5 hours - 2.5 hours =2.5 hours

Allen and Sandy's contribution is half of the time it took only Allen and Sandy's mother= 2.5 hours

Therefore Allen and Sandy together will take 2.5×2 = 5 hours to complete the job alone without their mother

A similar example: if it takes one person 2 hours to peel 5 potatoes and it takes 1 hour to peel same number of potatoes if a second person helps, then this second person reduces the time used by 1 hour(50%) and would take 2 hours to complete the work.

PLEASE HELP!!!
Solve the inequality:
5 (2x-3) - 6x > -2 (x - 6) +3

Answers

Answer:

x>5

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

4x−15>−2x+15

Step 2: Add 2x to both sides.

4x−15+2x>−2x+15+2x

6x−15>15

Step 3: Add 15 to both sides.

6x−15+15>15+15

6x>30

Step 4: Divide both sides by 6.

Answer:

x>5 have a great day

Step-by-step explanation:

Find the next 4 terms in this sequence. Show your work to​

Answers

Answer:

[tex]a_2 = a_1 + 6 = -13 + 6 = -7[/tex]

[tex]a_3 = a_2 + 6 = -7 + 6 = -1[/tex]

Step-by-step explanation:

Can you find a₄ and a₅ yourself?

Answer:

a1=-13 so a-13-1+6=-8 continue with this formula and you will get the 3 left terms

and the next -8-1+6=-3

and the -3-1+6=2

the last one 2-1+6=7 that's all

Pls help due soon!!!

Answers

Answer:

B) 10 m

Step-by-step explanation:

Area is 20 and Height is 4

Ok so

AREA of a triangle is =1/2Base Times Height

work back

Area=20

Height=4

b=Base

20=1/2b*4

Simplify both sides of the equation.

20=2b

Flip equation

2b=20

Divide both sides by 2

b=10

Base=10 m

Answer:

10m

Step-by-step explanation:

Area of a triangle:  [tex]\frac{1}{2}[/tex]bh

where 'b' = base and 'h' = height

plug in known values:  20 = [tex]\frac{4b}{2}[/tex]

cross-multiply:  4b = 40

b = 10

HELP IM TIMED
What is the multiplicative rate of change of the function? One-third Two-thirds 2 9

Answers

One third two to thirds is going to 8/27

Answer:

B/2) Two-Thirds Or 2/3

Step-by-step explanation:

What is 24.5 divided by 2? Please show your work.

Answers

Answer: 12.25

Explanation:

12. Which of the following shows the domain and range of F(x) = 2 |x|?

Answers

Answer:

Step-by-step explanation:

Number 8 please thank you people>>>>>

Answers

Answer:

I believe the correct answer is C.

Step-by-step explanation:

When you put it in simplest firm they equal the same ratio:

1/5

translate into an algebraic expression and simplify if possible. what number exceeds m by five more than n

Answers

Answer:

If the number is x, then the equation is;

x-m = 5 + n

Step-by-step explanation:

Here, we want to write the given statement in algebraic form

What number exceeds m by five more than n

Let the number be x

x-m = n + 5

If 12 juice boxes cost $4.20 how much would fifteen juice boxes boxes cost

Answers

Answer:

$5.25

Step-by-step explanation:

Calculation for how much would fifteen juice boxes cost

Cost of fifteen juice boxes=15/12=x/$4.20

Cost of fifteen juice boxes=x=15*$4.20/12

Hence,

x=63/12

x=$5.25

Therefore the amount that the fifteen juice boxes would cost is $5.25

Answer:

$5.25

Step-by-step explanation:

First, we need to divide $4.20 by 12.

4.20 / 12 = 0.35

We now know that a juice box costs $0.35.

Now, multiply $0.35 by 15.

0.35 * 15 = 5.25

So the answer is $5.25.

I hope this helps!

Javier is helping his parents put up posters in their movie theater. Each poster has a thickness of 0.012 inch. How thick is a stack of 10 posters? 100 posters? 1,000 posters?
and why

Answers

Step-by-step explanation:

1=0.012inch

10=0.012x10

10=0.12inch

100=0.012x100

100=1.2inch

1000=0.012x1000

1000=12inch

because if 1 poster has a thickness of 0.012 inch

than you have to multiple the number of posters with 0.012 inch

9. Tell whether the table is a linear equation and explain why

Answers

The table is linear because the change because it had a constant slope when we solve for change in y / change in x for each of the data points given. That slope is -0.5 and it’s constant.

Write a real-word problem that can be modeled by 4*(-7).​

Answers

Answer:

Kimberly is hiking a huge canyon. Every very hour, she hikes down the canyon, and gets -7 feet deeper. How many feet deep is she in 4 hours?

Step-by-step explanation:

I hope this is good.

There will be 666 people at ellie's pie party. She wants to bake enough pie so that each person can eat at least \dfrac15 5 1 %e2%80%8b start fraction, 1, divided by, 5, end fraction of a pie. What is the minimum number of pies ellie should bake?

Answers

Answer: 2 pies

Step-by-step explanation:

Here is the correct question:

There will be 6 people at Ellie's pie party. She wants to bake enough pie so that each person can eat at least ​1/5 of a pie.What is the minimum number of pies Ellie should bake?

Since each person can eat at least 1/5 of the pie and there are 6 people, the 6 people would them eat at least (6 × 1/5) = 6/5 pie. Since we are talking about whole numbers with regards to the pie, it simply means that at least 2 pies should be baked.

Marissa drove 3000 miles in 75 hours. At this rate, how long will it take her to drive 4000 miles?

Answers

Answer:

88.33 hrs

Step-by-step explanation:

Answer:

100 hours

Step-by-step explanation:

You can divide 3000 miles by 75 hours to find the mile per hour. You get 40mph and you divide 4000 by 40 to get 100 hours for 4000 miles.

Write a positive or negative integer that represents the situation.

You earn 7 points in a game.

Answers

Answer:

what situation...there"s no any situation

i’m pretty sure the answer is positive 7

Please solve for x
y+x=89
y=11
x=???

Answers

Answer:

78

Step-by-step explanation:

11 + x = 89                Subtract 11

11 - 11 + x = 89 -11

x = 78

Step-by-step explanation:

Hey there!

Given;

y+x= 89.......(a)

y = 11

~ Substitute the value of y on equation (a)

11+x = 89

~ Subtract 11 from both sides.

11+X -11 = 89-11

x = 78.

Therefore, the value of x is 78.

Hope it helps....

At a quick-lunch counter, 3 pretzels and 1 soda cost
$2.75. Two pretzels and 1 soda cost $2.00.
What is the cost of a pretzel?

Answers

Answer:

I really did try man ;-;

Step-by-step explanation:

3x+7y=17
3x-6y=4
solve this by elimination method plzzzzzzzzzzzzz helppppppppppppp meeeeeeeeeee

Answers

Answer:

[tex](\frac{10}{3}, 1)[/tex]

Step-by-step explanation:

1) In order to solve a system of equations with the elimination method, you need to add or subtract the two equations and "eliminate" variables by canceling out terms. This leaves you with an equation with only one variable to solve. Then, once you solve that equation, you can substitute the answer you got into one of the system's equations to find either the x or y value.

This problem already has one 3x in each equation, so let's focus on canceling that term out, eliminating the x variable. To set up this situation, we need one 3x to be negative, so let's multiply the terms in 3x-6y = 4 by -1, which gets us to -3x + 6y = -4. Now let's "cancel out" those x variables by adding them together.  (This work is shown in the first picture.)

Remember to add the other terms. This leaves us with the equation 13y = 13. By isolating y, we can find its value, which leaves us with y = 1.

2) Next, let's substitute 1 for y in one of the two equations. In this case, I used 3x + 7y = 17. Then, isolate x to find its value:

[tex]3x + 7 (1) = 17\\3x + 7 = 17 \\3x = 10 \\x = \frac{10}{3}[/tex]

Therefore, the answer would be [tex](\frac{10}{3} , 1)[/tex].

Find the greatest common factor (GCF) of 16 and 56.
Use the GCF to factor 16+56.
GCF =
16 + 56 = _ x (_+_)

Answers

Answer:

GCF is 8

16 + 56

= 8(2 + 7)

Step-by-step explanation:

Here, we want to write the greatest common factor of 16 and 56

The greatest common factor is 8

We can use tie rewrite the sum as follows ;

16 + 56 = 8(2 + 7)

find the mode of the given data 4,6,5,9,9,9,9,10,12.
please answer me fast ​

Answers

Answer:

9

Step-by-step explanation:

This is the answer because:

1) The mode is the element that occurs most in the data set. In this case, 9  occurs 4 times.

Therefore, the answer is 9.

Hope this helps! :D

The answer is 9
The mode is the number that shows up most in the set of numbers . 9 shows up the most

what is the answer to the question?​

Answers

Substitute the given number into the equation

Sum = 180(15-2)

Solve brackets

180(13)

Which is equal to 2340

So, the sum of interior angles is 2340 degrees


What are the missing operations?


48 ? (-8) = (-6)

(-40) ? 8 =( -5)

12 ? (-2) = 14

18 ? (-12) = 6

18 ? (-20) = -2

22 ? (-0.5) = -11


If you answer this I will give 26 points please help me!!!!

Answers

Answer:

Solution in photo

Step-by-step explanation:

Answer:

Step-by-step explanation:

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