solve: 9^8-x= 27^x-3

Answer:

1

Step-by-step explanation:

The greatest common factor GCF of 9 and 14 is 1.

Given the numbers in the question:

9 and 14

To find the greatest common factor of two numbers, we need to identify all the factors of each number and then determine the greatest number they have in common.

First:

Factors of 9 are 1, 3, and 9, as these are the whole numbers that divide 9 without leaving a remainder.

Next,

Factors of 14 are 1, 2, 7, and 14, as these are the whole numbers that divide 14 without leaving a remainder.

The common factors of 9 and 14 are 1 since it is the only number that divides both 9 and 14.

Therefore, the greatest common factor of 9 and 14 is 1.

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Answer:

[tex]x=\frac{6}{5}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5} / 2=\frac{3}{10}[/tex]

[tex]\frac{3}{10} =\frac{1}{4} x[/tex]

[tex]x=\frac{6}{5}[/tex]

Answer:

x=

[tex] \frac{5}{6} [/tex]

Step-by-step explanation:

(3/5)/2=(1/4)x

3/10=1/4x

12x=10

x=10/12=5/6

Answer:

Average monthly interest = $ 122.04

% total interest =36.94 %

Step-by-step explanation:

There are 120 cumulative payments and the total interest paid was $ 14,644.95.

Hence, the average monthly interest is :

Average monthly interest = $ 14,644.95 / 120

Average monthly interest = $ 122.04

% total interest

= ($ 14,644.95) / $ 39,644.95 x 100

% total interest =36.94 %

Answer:

Step-by-step explanation:

Answer:

54 π cubic centimeters

Step-by-step explanation:

Formula for the volume of a cylinder: πr²h

π×3²×6=

9×6×π=

54π cm³

Answer:

168

Step-by-step explanation:

You do 5 times 32 then divided 60 by 15 to figure out how much of 1 min is 15 sec its 1/4 so u do 1/4 of 32, 8 and add that to 5 times 32

Answer:

CCCC

Step-by-step explanation:

Answer:

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

Step-by-step explanation:

The height of the ball after t seconds is given by the following equation:

[tex]h(t) = -4.9t^{2} + 5t + 1[/tex]

How long will it take the ball to hit the ground if no other players touch it?

This is t when h(t) = 0. So

[tex]-4.9t^{2} + 5t + 1 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]-4.9t^{2} + 5t + 1 = 0[/tex]

So [tex]a = -4.9, b = 5, c = 1[/tex]

So

[tex]\bigtriangleup = 5^{2} - 4*4.9*1 = 44.6[/tex]

[tex]t_{1} = \frac{-5 + \sqrt{44.6}}{2*(-4.9)} = -0.17[/tex]

[tex]t_{2} = \frac{-5 - \sqrt{44.6}{2*(-4.9)}  = 1.19[/tex]

Since we want a time measure, the answer cannot be negative.

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

Answer:

  see below

Step-by-step explanation:

You have 3 chances in 5 of drawing a white counter, so the probability is ...

  3/5 = 0.6

Your mark will go at 0.6 on the probability scale.

Answer:

(2x)/(x-1)

x = y/(y-2)

(y-2)x = y

yx - 2x =y

yx-y = 2x

y(x-1) = 2x

y= 2x/(x-1)

Answer:

[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]

Step-by-step explanation:

Givens

First, we need to find the radius, which is the distance between the given points.

[tex]d=\sqrt{(3-5)^{2} +(10-2)^{2} } =\sqrt{4+64}=\sqrt{68}[/tex]

Therefore, the radius of the circle is

[tex]r \approx 8.25[/tex]

The explicit form of the equation of the circle would be

[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]

Answer:

w = 20

Step-by-step explanation:

Add 18 on both sides:

[tex]\frac{w}{4} =5[/tex]

Multiply by 4 on both sides:

w = 20

Answer:

20

Step-by-step explanation:

Let's solve your equation step-by-step.

−13=−18+ w/ 4

Step 1: Simplify both sides of the equation.

−13=−18+ w/ 4

−13=−18+ 1/ 4 w

−13= 1/ 4 w−18

Step 2: Flip the equation.

1/ 4 w−18=−13

Step 3: Add 18 to both sides.

1/ 4 w−18+18=−13+18

1/ 4 w=5

Step 4: Multiply both sides by 4.

4*( 1/ 4 w)=(4)*(5)

w=20

Answer:    Sally recieves £60 more than Megan

Step-by-step explanation:

Add the  ratio together 1+3+2=6

£180 divided by 6 = 30

Megan gets 30

Sally gets 30x3=90

Tom gets 30x2=60  30:90:69

Answer:

y = 4 (x - 9/2) +0

Step-by-step explanation:

hope ot helps you

Answer:

here

Step-by-step explanation:

Answer:

3

Explanation

There are 3 digits in the number 248 which is the square root of 61504.

√61504 = 248 --- 3 digits in 248

Answer:

8 cm and 10 cm

Step-by-step explanation:

Hello, I can help you with this.

Step 1

According to the question there are two rectangles A and B,

Rectangle A is a scale drawing of Rectangle B and has 25% of its area

in other words

[tex]Area_{A}=0.25*Area_{B} (Equation\ 1)\\[/tex]

Step 2

Let

Rectangle A

length (1)= 4 cm

length (2)= 5 cm

[tex]Area_{A}=4\ cm * 5\ cm\\Area_{A}=20\ cm^{2}[/tex]

put this value into equation 1

[tex]Area_{A}=0.25*Area_{B} (Equation\ 1)\\\\20\ cm^{2} =0.25*Area_{B} \\divide\ each\ side\ by\ 0.25\\\frac{20\ cm^{2} }{0.25}=\frac{0.25}{0.25}*Area_{B}\\ Area_{B}=80\ cm^{2}[/tex]

Now, we know the area of rectangle B, to know its length we need to formule other equation

Step 3

[tex]Area_{B}=80\ cm^{2}\\length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\[/tex]

the ratio between the lengths must be constant, so the ratio of A must be equal to ratio in B, then

[tex]\frac{length(1A)}{length(2A)}=\frac{length(1B)}{length(2B)} \\\\\\frac{4}{5}= \frac{length(1B)}{length(2B)}\\0.8=\frac{length(1B)}{length(2B)}\\length(1B)=0.8*length(2B) (Equation 3)[/tex]

Step three

using Eq 1 and Eq 2 find the lengths

put the value of length(1B) into equation (2)

[tex]length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\(0.8*length(2B)) (*length (2B)=80\ cm^{2} \\\\0.8*(length (2B))^{2} =80\ cm^{2}\\(length (2B))^{2} =\frac{80\ cm^{2}}{0.8} \\(length (2B))^{2}=100\\\sqrt{(length (2B))^{2}}=\sqrt{100\ cm^{2}} \\ length (2B)=10\ cm[/tex]

Now, put the value of length(2B) into equation 3 to know length (1B)

[tex]length(1B)=0.8*length(2B)\\length(1B)=0.8*10\ cm\\length(1B)=8 cm[/tex]

I really hope this helps you, have a great day.

Answer:

4,500

Step-by-step explanation:

To find the number of students majoring in economics, you must turn 90% into a decimal making it .9.

Then you multiply the decimal to how many students there are (5000x.9) and that gives you 4,500.

Answer:

100:59

Step-by-step explanation:

For every pound a company spends on advertising, it spends £0.59 on its website.

Amount Spent on Advertising = £1

Amount Spent on Website = £0.59

Therefore:

Amount Spent on Advertising : Amount Spent on Website

= 1 : 0.59

Multiply both sides by 100

= 100: 59

The ratio of the amount spent on advertising to its website as a ratio in its simplest form is 100:59 in its simplest form.

Answer:

£100 : £59

Step-by-step explanation:

The said company spends £0.59 on its website for every pound spent on advertisement. This implies that out of £1.00 spent on advertisement by the company, £0.59 is for website placements.

Thus, the rate of the amount spent on advertisement to amount spent on website is given as:

             £1.00 : £0.59

To convert this to the nearest whole number, multiply through by 100, so that the ratio becomes;

£100.00 : £59.00

Therefore, the ratio expressed in its simplest form is £100 : £59

Answer:

The population is everyone listed in the city phone directoy; the sample is the 75 people selected

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

100/10=10

4030/10=403

Answer:

sin=0

cos=-1

tan=0

csc=undefined

sec=-1

cot=undefined

Step-by-step explanation:

On the unit circle, [tex]-\pi=\pi[/tex]. The sin of theta is therefore 0, the cosine is -1, and the tangent is 0/-1=0. Since the following functions are just the reciprocals of the previous ones, the cosecant is 1/0=undefined, the secant is 1/-1=-1, and the cotangent is 1/0= undefined. Hope this helps!

All six trigonometric ratios were calculated using a unit circle and comes out to be

[tex]sin(-\pi )= -sin\pi =0\\cos(-\pi )= cos\pi =-1\\tan(-\pi )= -tan\pi=0 \\cosec(-\pi )= -cosec\pi =infinity\\sec(\pi )= sec\pi =-1\\cot(-\pi )=-cot\pi=infinity[/tex]

I have attached a unit circle diagram.

In this unit circle corresponding values of sine and cosine have been written near the angle 'α' in form (cosα,sinα)

x-coordinate is cosα

y-coordinate is sinα

now,

one can find other trigonometric ratios

[tex]tan\alpha =\frac{sin\alpha }{cos\alpha } \\\\cot\alpha =\frac{1}{tan\alpha } \\\\cosec\alpha =\frac{1}{sin\alpha } \\\\sec\alpha =\frac{1}{cos} \\[/tex]

Hence, we can find the rest of the trigonometric ratios by using the coordinates (cosα,sinα) for a particular angle 'α'.

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Answer:-3/5x(squared)+17

Step-by-step explanation:

Simplify and combine like terms

Answer:

We are expected to find 1,080,000 right handed people in that group of people

Step-by-step explanation:

In this question, we are given the ratio of right handed to left handed people and we are asked to calculate the number of right handed people we can find in a given population.

First, we check the ratio given.

The ratio is said to be that of left handed individuals to right handed individuals and this sits at 2 to 9.

Thus out of 1,320,000 people , the number of right handed individuals will be ;

9/(2+9) * 1,320,000

9/11 * 1,320,000

= 1,080,000 people

Answer:

Zero

Step-by-step explanation:

Since all the ice cream sold has exactly one flavor and one treat, a chocolate ice cream can't have a blue swirl. This means that the number of chocolate ice cream with blue swirl is zero. Therefor the probability is zero.

Answer:

A line that passes (2, 0) and (-6, 3) has slope:

S1 = (-6 -2)/(3 - 0) = -4/3

Another line that is perpendicular with above line has slope:

S2 = -1/S1 = -1/(-4/3) = 3/4

=> Option B is correct

Hope this helps

:)

The segment with endpoints (2,0) and (-6,3) has a line perpendicular to it with a slope of 4/3.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

From the general formula of the slope:

slope = (change in y) / (change in x)

The change in y is 3 - 0 = 3, and the change in x is -6 - 2 = -8. So the slope of the segment is:

slope = (3 - 0) / (-6 - 2) = -3/4

To find the slope of the line perpendicular to the segment, we know that it must have the opposite reciprocal slope. That is:

the slope of perpendicular line = -1 / slope of segment

slope of perpendicular line = -1 / (-3/4) = 4/3

Therefore, the slope of the line perpendicular to the segment with endpoints (2,0) and (-6,3) is 4/3.

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Answer:

See explanation below

Step-by-step explanation:

In this case, I'm assuming you want to know the price of all items purchased by Andrea.

Let's gather all the data.

Andrea has initially 54$. From that she got a Brush (B), a sketchbook (S) and a paint set (P). At the end, she has a left over of 1.5$, so she actually spends 52.5$, and our first equation would be:

B + S + P = 52.5  (1)

Now, the B cost 1/6 as the S, and S was 3/4 the paint set, so oru equations here would be:

B = 1/6S (2)

S = 3/4P (3)

Now, according to this we can write the (1) expression in function of (2) and (3).

Replacing (3) in (2):

B = 1/6 (3/4P)

B = 3/24P

B = 1/8P  (4)

And replacing (3) and(4) in (1) we have:

1/8P + 3/4P + P = 52.5

From here we can solve for P:

15/8P = 52.5

P = 52.5 * 8 / 15

P = 28.16$

Now we can replace this value to get the Sketchbook, and then, the brush:

S = 3/4 * 28.16

S = 21.12$

B = 1/6 * 21.12

B = 3.52$

These values would be the price of all items.

Answer:

0.45.

Step-by-step explanation:

To find the solution to this question, we will first need to determine how many cards are neither Cincinnati Reds and Cleveland Indians. We can do this by:

100 - 22 - 33 = 45. This is the number of cards that are neither the two teams.

To convert this to a decimal, simply divide by 100, giving us:

45 ÷ 100 = 0.45.

Answer:

31.5×10.51

315/10×1051/100

331065/1000

331.065

Answer:

John will need 34 more tickets to be able to go on all the rides he wants

Step-by-step explanation:

To solve this, we need to first of all know the total cost in terms of tickets of all the rides that john wants to have.

This will be

cost of roller coaster ride = 19 tickets

cost of bumper car ride = 3 tickets

cost of merry-go-round ride = 33 tickets

Total cost of rides = 19 + 3 + 33 =55 tickets

Next, we will need to find the number of tickets that John has left after losing 10 of them.

This will be 31 - 10 = 21 tickets left

To find the number of more tickets that John needs , we will subtract the number of tickets he has left from total ride ticket cost.

This will be 55-21 = 34 tickets.

Hence, John will need 34 more tickets to be able to go on all the rides he wants

Answer:

8πcm² = 8pi cm²

Step-by-step explanation:

The formula for area of a sector = ½r²θ

Where r = radius = 6cm

θ = central angle = 4pi/9 in radians = 4π/9

Area of the sector = 1/2 × 6² × 4π/9

Area of the sector = (144π/18)cm²

Area of the sector = 8πcm²

Therefore, Area of the sector =

8πcm² = 8pi cm²

Answer:

8πcm² = 8pi cm²

Step-by-step explanation:

trust