Form a union for the following sets.
M = {1, 2, 4, 8)
N = (2,5,8)

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: 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.

because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.

By distributing the power of 2, we will get y^2(6).

Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.

summary:

multiply exponents if they are being raised to a power.

add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)

(-4/9)*3×(-27/20)*4= 7.2

Step-by-step explanation:

here's the answer to your question

Answer

20%

Step-by-step explanation:

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:

Step-by-step explanation:

For each game played the chance of winning is 0.05 and losing is 0.95.

If the student wins, they get $5 -$1 = $4, but they lose $1.

Expected value is:

It means you will make $0.75 per average game.

Answer:

21.8

Step-by-step explanation:

Step 1

This is a problem on finding the mean of continuous grouped data. We first find the midpoint of each interval. For example, the first interval or class is 0 - 10. The mid-point of this class will be (0 + 10)/2 = 5.

fullscreen

Step 2

We now calculate the product of mid-point and frequency for each class. Here, the number of athletes in each class is the frequency of that class. For example, for the first class 0 – 10, its frequency is 3.

fullscreen

Step 3

We can now use the formula to calculate mean. Note that t...

Answer:

x = 138

Step-by-step explanation:

A straight line is 180

x+ 42 = 180

X = 180-42

x = 138

Step-by-step explanation:

you cannot just put the actual numbers in and calculate ?

and you can't provide the correct problem statement, as it seems.

I assume you mean

an = 3n² - 1

a sequence starts with a1, so, n>=1

a1 = 3×1² - 1 = 3-1 = 2

a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11

a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26

a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47

a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74

there, that is all there is to it. you really needed help with that ?

Answer:

207 tens

Step-by-step explanation:

If you mean

8,000 + 70 = 6000 + X tens

then it should be 207 tens

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

c.write the fact,organize your thoughts and define your strategy.

Answer:

c

Step-by-step explanation:

HA

See In Triangle DEF and Triangle XZY

[tex]\because\begin{cases}\sf \angle E=\angle Z=90° \\ \sf \ FD\sim XY=Hypotenuse\end{cases}[/tex]

Hence

[tex]\sf \Delta DEF\sim \Delta XZY(Angle-Angle)[/tex]

The theorems that verify that Δ DEF ~ Δ XZY is AA theorem of similarity.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given that, two triangles, Δ DEF and Δ XZY, we need to find a theorem that will verify that, Δ DEF and Δ XZY are similar,

So, we have, ∠ X = 40°,

Therefore, ∠ Y = 90°-40° = 50°

Now, we get,

∠ Y = ∠ F = 50°

∠ E = ∠ Z = 90°

We know that,

if two pairs of corresponding angles are congruent, then the triangles are similar.

Therefore, Δ DEF ~ Δ XZY by AA rule

Hence, the theorems that verify that Δ DEF ~ Δ XZY is AA theorem of similarity.

Learn more about Similar triangles click;

https://brainly.com/question/14926756

#SPJ7

Answer:

$9

Step-by-step explanation:

30*(100%-70%)=9

Answer:

9

Step-by-step explanation:

Take the original price

Multiply by the discount percent

30 *70%

30 *.70

21

The discount is 21 percent

Subtract this from the original amount

30-21

9

Answer:

Below.

Step-by-step explanation:

Area = 5(x + 3)

= 5x + 15

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

= 2x + 6 + 10

= 2x + 16.

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Hi,

no need to use discriminant for that.

3(m)^2 = -6

m^2 = -6/3

m^2= -2

in R, there is no

solution as a square can not be negative.

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

Hi

let's call X amount of second going and Y the height reach by the ballon.

so Y=8X+94

f(x) = 8X+94

If you want to know how high will the ballon be in 25 seconds, remplace X by 25 and do the math. Have fun .

Answer:

78,073

Step-by-step explanation:

Subtract 8,420 from 86,493...86,493-8,420=78,073 is the answer

Double check by using inverse operations...78,073+8,420=86,493

It is correct, as I ended up with 86,493, the starting number of the equation.

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

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

Answer:

Amount of tickets

Step-by-step explanation:

The variable is the amount of tickets purchased because that is the only thing that changes, according to the statement that says that daily tickets are $50.

Answer:

[tex]1.5,1.2,0.96,0.768[/tex]

Common ratio between successive terms

[tex]=\frac{1.2}{1.5}[/tex]

[tex]=0.8[/tex]

OAmalOHopeO

The value of the common ratio between successive terms in the sequence is,

⇒ 0.8

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The sequence is,

⇒ 1.5, 1.2, 0.96, 0.768,...

Hence, The value of the common ratio between successive terms in the sequence is,

⇒ 1.2 / 1.5

⇒ 12/15

⇒ 0.8

Thus, The value of the common ratio between successive terms in the sequence is,

⇒ 0.8

Learn more about the geometric sequence visit:

https://brainly.com/question/25461416

#SPJ7

Answer:

The degree of this polynomial is 2.

Step-by-step explanation:

The degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.

The given polynomial is:

[tex]9m^2+11m^2+2m^2[/tex]

The only variable is m.

The power of m in all terms is 2.

So, the degree of this polynomial is 2.

Answer:

x = -5

Step-by-step explanation:

4-2(x+7) = 3(x+5)

Distribute

4 - 2x-14 = 3x+15

Combine like terms

-2x-10 = 3x+15

Add 2x to each side

-2x-10 +2x =3x+2x+15

-10 = 5x+15

Subtract 15 from each side

-10-15 = 5x+15-15

-25 = 5x

Divide by 5

-25/5 = 5x/5

-5 =x

90/-10

= 9/-1

= -9

So, -9 is the quotient.