⅗ Write the numerator and denominator of each of the following rational numbers​

You're looking for a number w such that the numbers

{1 + w, 7 + w, 15 + w}

form a geometric sequence, which in turn means there is a constant r for which

7 + w = r (1 + w)

15 + w = r (7 + w)

Solving for r, we get

r = (7 + w) / (1 + w) = (15 + w) / (7 + w)

Solve this for w :

(7 + w)² = (15 + w) (1 + w)

49 + 14w + w ² = 15 + 16w + w ²

2w = 34

w = 17

Then the three terms in the sequence are

{18, 24, 32}

and indeed we have 24/18 = 4/3 and 32/24 = 4/3.

Answer:

A - L = O

Step-by-step explanation:

A = L + O

Subtract L from each side

A-L = L + O - L

A - L = O

The way that the given formula A = L + O can be rewritten to solve for O is; O = A - L

We are given the formula to find A as;

A = L + O

Now, to make O the subject of the formula, let us use subtraction property of equality to subtract L from both sides to get;

A - L = L + O - L

O = A - L

Thus, the way the formula can be rewritten to solve for O is;

O = A - L

Read more about Subject of Formula at; https://brainly.com/question/10643782

#SPJ2

Answer:

Below.

Step-by-step explanation:

Area = 5(x + 3)

= 5x + 15

Perimeter = 2(x + 3) + 2(5)

= 2x + 6 + 10

= 2x + 16.

Answer:

207 tens

Step-by-step explanation:

If you mean

8,000 + 70 = 6000 + X tens

then it should be 207 tens

Answer:

Selling price=rs.600.

Profit of rs=100.

Step-by-step explanation:

C.P=500; profit%=20%

S.P.=100+profit%×C.P/100

S.P=120×500/100

=rs.600

S.P>C.P

Profit S.P-C.P

600-500=100

he gained for rs.100.

Answer:

$275 a month

Step-by-step explanation:

Let x represent how much each friend is paying.

The amount Jane pays can be represented by 2x, since she is paying double than her friends.

Add together these terms and set them equal to 550. Then, solve for x:

x + x + 2x = 550

4x = 550

x = 137.5

So, each friend is paying $137.50. Double this to find how much Jane is paying:

137.5(2)

= 275

So, Jane is paying $275 a month

Answer:

yep it's D

Step-by-step explanation:

I think it's (2,0).

Because u use the slope of line AB to go down from point C until one of the answers are met.

The point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).

Slope of AB = -(3/6)

Slope of AB = -1/2

Slope of from point (2, 0) to point C(-2, 2):

Slope = (2 - 0)/(-2 - 2) = 2/-4

Slope = -1/2

Therefore, the point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).

Learn more about slope of parallel lines on:

https://brainly.com/question/10790818

Question: -4 + 5x -7 = 10 + 3x -2x

⇒ 5x -11 = 10 + x

⇒ 5x - x = 10+11

⇒ 4x = 21

⇒ x = 21/4

Answer is Option D

x = 21/4

Must click thanks and mark brainliest

Answer:

...

Step-by-step explanation:

seeee the above picture

Step-by-step explanation:

Hey there!

From the given figure;

Angle FVT = 43°

VT = 53

Taking Angle FVT as reference angle we get;

Perpendicular (p) = FT = ?

Base (b) = VT = 53

Taking the of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep all values and simplify it;

[tex] \tan(43) = \frac{ft}{53} [/tex]

0.932515*53 = FT

Therefore, FT= 49.423.

Hope it helps!

Answer:

A. 49.42

Step-by-step explanation:

tan 43 = FT ÷ VT

0.932515086 = FT ÷ 53

49.42 = FT

9514 1404 393

Answer:

Step-by-step explanation:

The linear speed 12 mi/h translates to inches per minute as follows:

  (12 mi/h) × (5820 ft/mi) × (12 in/ft) ÷ (60 min/h) = 12,672 in/min

The relationship between arc length and angle is ...

  s = rθ

For a constant radius, the relationship between linear speed and angular speed is ...

  s' = rθ'

  θ' = s'/r = (12,672 in/min)/(12 in) = 1056 rad/min

There are 2π radians in one revolution, so this is ...

  (1056 rad/min) ÷ (2π rad/rev) = 168.068 rev/min

Answer:

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Step-by-step explanation:

Set up the expression.

[tex](x+7)*(\frac{1}{x}-13)[/tex]

Multiply using FOIL.

[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]

[tex]1-13x+\frac{7}{x}-91[/tex]

[tex]-13x+\frac{7}{x}-91[/tex]

Find the Domain.

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Answer:

In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?

There are 4 colours of balls - green, blue, yellow and white.

Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.

Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.

Check: Total number of balls = 12+6+4+26 = 48

Answer: 6 balls are blue....

Answer:

x = 150°

Step-by-step explanation:

Interior angle of a hexagon = 120° and interior angle of a square = 90°

so remaining angle, 360-120-90 = 150°

9514 1404 393

Answer:

  A.  $11 per week

Step-by-step explanation:

  $187 = (17)(weekly allowance) . . . . . Pete's savings after 17 weeks

  weekly allowance = $187/17 = $11 . . . . . divide by 17

Pete gets $11 each week.

Answer:11 per week

Step-by-step explanation:I did the test

Answer: Let the length of the hypotenuse be x

Applying the Pythagorean theorem we have :

x²=20²+48²

⇒x²=2704

⇒x=52( ∀ x >= 0 )

Step-by-step explanation:

Let assume the hypotenuse(longest side of right triangle) be x

By Pythagoras theorem

[tex] \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} [/tex]

Applying Pythagoras theorem

[tex] \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} [/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304[/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:2704[/tex]

[tex]\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} [/tex]

[tex]\bf \large \implies \: \: x \: = \: 52[/tex]

Hence , the length of hypotenuse is 52.

Mean:

[tex]E(X) = \displaystyle \sum_{x\in\{1,2,3,4\}}x\,P(X=x) = 1\times0.4 + 2\times0.1 + 3\times0.3 + 4\times0.2 = \boxed{2.3}[/tex]

Variance:

[tex]\displaystyle V(X) = E\left((X-E(X))^2\right) = E(X^2) - E(X)^2 \\\\ E(X^2) = \sum_{x\in\{1,2,3,4\}}x^2\,P(X=x) = 1^2\times0.4 + 2^2\times0.1 + 3^2\times0.3 + 4^2\times0.2 = 6.7 \\\\ \implies V(X) = 6.7 - 2.3^2 = \boxed{1.41}[/tex]

Standard deviation:

[tex]\sigma_X = \sqrt{V(X)} = \sqrt{1.41} \approx \boxed{1.19}[/tex]

Answer:

7x is monomial according to question.

Answer:

y = 4

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : √3 : 2

The sides in this triangle are in the order:

y : 4√3 : x

y/1 = 4√3/√3

y = 4

Answer: 3/8

Step-by-step explanation:

A=3

B=5

3/3+5=3/8

Answer:

x = 1

y = 2

Step-by-step explanation:

5x + 2y = 9

-5x + 4y = 3

==> 6y = 12 ==> y = 12/6 ==> y = 2.

we replace y by its value in the first or the second equation, so will have:

5x + 2×2 = 9

5x + 4 = 9

5x = 5

x = 1

Answer:

The answer closest to 36.10425. So 36.10 or 36.1

Step-by-step explanation:

x = 44.85 ( 1 - 0.195) = 36.10425

If this helps, it would be nice if 5 stars are given, and a brainliest :)

The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

For this case, we can assume the amount of bill without tip being A.

Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:

Total price of the bill = Bill amount before tip + Tip

44.85 = A + (19.5 % of A)

(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))

44.85 = A + (19.5 % of A)

or

[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]

Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.

Learn more about percent here:

https://brainly.com/question/11549320

90/-10

= 9/-1

= -9

So, -9 is the quotient.

Using the shell method, the volume integral would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]

That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].

The volume itself would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]

Using the disk method, the integral for volume would be

[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]

where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.

The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

[tex]\rm y = x^8[/tex]   or

[tex]x = \sqrt[8]{y}[/tex]

And  y = 256

By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.

[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]

Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]

[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]

After solving definite integration, we will get:

[tex]\rm V = \pi(\frac{4096}{5} )[/tex]  or

[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit

Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

Learn more about integration here:

brainly.com/question/18125359

Answer:

the correct answer is point b

Answer:

The Bison is faster by 10 miles per hour.

Step-by-step explanation:

The Bison runs at 3520 ft / min

= 3520/ 5280 miles / minute

= (3520/ 5280) * 60 miles per hour

= 40 miles per hour

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled