if y varies directly as the square root of x and y=87 when x=625, find y if x =390625. Round off your answer to the nearest hundredth

Answer:

14w

Step-by-step explanation:

I don't know how to explain it any simpler than just to give you the answer which is 14w.

There is a more mathematical way of getting the 14w, but I'm guessing you won't like it. Use the distributive property. Put brackets around the given expression

7w + 7w = (7w + 7w)  

On each side of the plus sign there is a common factor and that common factor is w

w(7 + 7)  Now add the two 7s together.

14w

You could say to me, why didn't you take out the 7 to start with. You could

7 ( w + w)  but w and w add up to 2w

7*2w

14 w

Step-by-step explanation:

n(AUB)=n(A)+n(B)-n(AnB)

hope it helps

Answer:

Assuming that x is in degrees (you could generalize this to any unit)

For an equation like:

sin(a*x) = K

The principle solutions are the values of x in the range:

0° ≤ x < 360°

And the symmetric ones are the solutions:

xₙ = x + n*360°

where n is an integer.

Ok, first let's solve:

2*cos(x) = -1

isolating the cosine part, we get:

cos(x) = -1/2

Now we can use the inverse cosine function, Acos(x)

If we apply this function to both sides, we get:

Acos (cos(x)) = Acos(-1/2)

x = Acos(-1/2) = 120°

x = 120° is the princpiple solution.

And the symmetric solutions are:

xₙ = 120° + n*360°

So for example:

x₁ = 120° + 1*360° = 480°

x₃ = 120° + 3*360° = 1200°

etc...

Answer:

B

Step-by-step explanation:

You always have to use the Big Three trig functions (those that are on your calculator when answering this kind of question involving right angle triangles).

y is the adjacent side of the triangle. It is the side (other than the hypotenuse -- which is the longest side of the right triangle) that makes up the cosine.

Cos(45) = y / 4 sqrt(2)

Cos(45) = sqrt(2)/2

Multiply both sides by 4 sqrt(2)

4*sqrt(2) * cos(45) = y

4*sqrt(2) * sqrt(2)/2 = y

2*2 = y

y = 4

I can't tell you where all the other choices are coming from.

Answer:

4, or B

Step-by-step explanation:

The average rate of change for the interval from x = 1 to x = 3 is 5. therefore, option B the most appropriate choice.

The average Rate of Change of the function f(x) can be calculated as;

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]

Rate is defined as the ratio between two related quantities in different units.

Average rate of change = f(b) - f(a) / (b - a)

We were given a = 1, f(a) = 7 ,b = 3, f(b) = 13

We need to find the average rate of change for the interval from x = 1 to x = 3.

So,

Average rate of change = 13 - 3 / 3 - 1

Average rate of change = 10 / 2 = 5.

Hence, The average rate of change for the interval from x = 1 to x = 3 is 5.

therefore, option B the most appropriate choice.

Read more about Rate of change here;

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Answer:

16 3/2

Step-by-step explanation:

So lets go thru each one.

16 3/2 is just 17.5

A square root cancels out a square.

A cubed root cancels out a cube.

So, in the next answer:

16 squared, to the square root is just 16, since the squaring and root cancels out.

64 sqaured to the cube root must be 16. Lets break it all down:

2^6=64.  We need to square this, so we can rewrite it as:

64^2 = [tex](2^6)^2[/tex]

Normally we add/subtract exponents, but since the 6 exponent is in parethesese, it is multiplied by the 2 exponent. This makes it 2^12. So we can rewrite [tex]\sqrt[3]{64^2}[/tex] as:

[tex]\sqrt[3]{2^1^2}[/tex]

Now, when we divide a exponent by a exponent, we subtract.

However, when we root a exponent, it is division.

So it is the 2 [tex]\frac{^1^2}{^3}[/tex]

=

[tex]2^4[/tex]

Or

16

Finally we have the cubed root of 8^4.

using the same steps as above, 8^4 = [tex](2^3)^4[/tex]. This equals [tex]2^1^2[/tex]

Then again, we cube root it.

This is division of the 12 exponent by the 3 root, so we get:

[tex]2^4[/tex]

=

16

So in the end:

A - 17.5

B - 16

C - 16

D - 16

So a is the largest number

Hope this helps!

Answer:

I think it's simple sentence

Answer:

Scale factor = 3

Step-by-step explanation:

Scale factor used for the dilation = the ratio of the corresponding side length of the new figure to the side length of the original figure

Scale factor = B'C'/BC

B'C' = 9 units

BC = 3 units

Scale factor = 9/3 = 3

Answer:

34

Step-by-step explanation:

The angles of a triangle add to 180

56+ F + 90 = 180   ( the box means 90 degrees)

Combine like terms

146+F = 180

Subtract 146 from each side

F = 180-146

F = 34

Answer:

See image below for answer:)

Step-by-step explanation:

The inequality b < - 1.4 written as interval notation is b ∈ (- ∞, - 1.4).

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality b < - 1.4.

We know in interval notation if x is greater than a and less than b we write

a < x < b.

Therefore, The inequality b < - 1.4 can be written as,

- ∞ < b < - 1.4 Or b ∈ (- ∞, - 1.4).

learn more about inequalities here :

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Answer:

A ∩ C   [ -6, -4 )

Step-by-step explanation:

A ∩ C

-6 ≤ x < -4

[ -6, -4 )

9514 1404 393

Answer:

  the correct choice is marked: x = 11; Q = 55°

Step-by-step explanation:

If P and Q are supplementary, then ...

  Q = 180° -P

  Q = 180° -125°

  Q = 55°

Then we have ...

  5x = 55°

  x = 11°

This question is incomplete, the missing diagram is uploaded along this answer below;

Answer:

horizontal V₁ ( 141.37 in³ ) is less than vertical V₂ ( 235.62 in³ )

Step-by-step explanation:

Given the data in the question and as illustrated in the image below;

from the image,

We find the volume of the solid obtained by rotating the card around a horizontal line;

Volume of the cylinder V₁ = πr²h

given that; radii = 3 in and height = 5 in

we substitute

V₁ = π × (3)² × 5

V₁ =  π × 9 × 5

V₁ = 141.37 in³

Next we find the volume of the solid obtained by rotating the card around a vertical line;

Volume of the cylinder V₂ = πr²h

given that; radii = 5 in and height = 3 in

we substitute

V₂ = π × (5)² × 3

V₂ =  π × 25 × 3

V₂ = 235.62 in³

Hence horizontal V₁ ( 141.37 in³ ) is less than vertical V₂ ( 235.62 in³ )

Answer:

the area is 27

Step-by-step explanation:

Answer:

the base of this shape is 6

lets break it up into a rectangle and a triangle

the rectangle is 6(base) time 3(height)=18

the triangle is 6(base) times 3(height) divided by two = 9

18 plus 9 = 27

Answer:

NUMBERS end in 12581... YEP.

Answer:

End 12581 yes

Answer:

im pretty sure the radius is 1.9 :)

Step-by-step explanation:

have a good day

Answer:

3,770,461,100,000 different playlists are possible.

Step-by-step explanation:

To solve this question, the arrangements formula and the combinations formula are used. The arrangements formula is used considering the order of the musics being played, and the combinations formula is used to find the number of possible combinations of musics.

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

[tex]A_{n} = n![/tex]

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

0 pop songs

10 non-pop from a set of 8 + 4 + 4 = 16.

Arrangements of 10(order in which the musics are played). So

[tex]P(0) = 10!C_{16,10} = 10!\frac{16!}{6!10!} = \frac{16!}{6!} = 29059430400[/tex]

1 pop song:

9 non-pop from a set of 16, 1 pop from a set of 7. So

[tex]P(1) = 10!C_{16,9}C_{7,1} = 10!\frac{16!}{7!9!}\frac{7!}{1!6!} = 290594304000[/tex]

2 pop songs:

8 non-pop from a set of 16, 2 pop from a set of 7. So

[tex]P(2) = 10!C_{16,8}C_{7,2} = 10!\frac{16!}{8!8!}\frac{7!}{2!5!} = 980755776000[/tex]

3 pop songs:

7 non-pop from a set of 16, 3 pop from a set of 7. So

[tex]P(3) = 10!C_{16,7}C_{7,3} = 10!\frac{16!}{7!9!}\frac{7!}{3!4!} = 1452971500000[/tex]

4 pop songs:

6 non-pop from a set of 16, 4 pop from a set of 7. So

[tex]P(4) = 10!C_{16,6}C_{7,4} = 10!\frac{16!}{6!10!}\frac{7!}{3!4!} = 1017080100000[/tex]

How many different playlists are possible?

[tex]T = P(0) + P(1) + P(2) + P(3) + P(4) = 29059430400 + 290594304000 + 980755776000 + 1452971500000 + 1017080100000 = 3770461100000[/tex]

3,770,461,100,000 different playlists are possible.

Answer:

55

Step-by-step explanation:

It is 55 minutes more because 1 1/2 hrs = 90 minutes and when you add 20 plus quarter of an hour it equal to 35. SO than you subtract 35 from 90 and you get 55 which is the more minutes .

Answer:

a. {(1,3), (1,4) ,(2,3), (2,4) }

b. {(1,4), (1,5), (2,4), (2,5)}

Answer:

PxR={(1,4)(1,5)(2,4)(2,5)}

PxQ={(1,3)(1,4)(2,3)(2,4)}

Step-by-step explanation:

Each of the members of set P is multiplying by each member of set Q or R,

so, 1 in set P has to multiply by 3 and 4 in set Q or 4 and 5 in set R. (We do the same for 2)

When a member of a set multiplies with another, we put the two members of two sets we are multiplying in parentheses.

Answer:

4 and 2

Step-by-step explanation:

These are considered to be constant because the values cannot change. For example, the values of  5 and 9 can change depending on what w and m are.

Answer:

4 and 2

Step-by-step explanation:

Answer:

a. m<Q = 75°

b. m<M = 60°

Step-by-step explanation:

a. The triangle has two equal sides, therefore it is an isosceles triangle. Thus, its base angles would be equal also. m<Q = m<S

Therefore:

m<Q = ½(180 - 30)

m<Q = 75°

b. All sides of the triangle are equal. Therefore, it is an equilateral triangle with equal angles measuring 60° each.

m<M = 60°

Answer:

20x² + 40y²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4x(2x + 3x) + 5y(5y + 3y)

Step 2: Simplify

Answer:

20 x ² + 40 y ²

Step-by-step explanation:

4 x ( 2 x + 3 x ) + 5 y ( 5 y + 3 y )

Combine likes term

4 x ( 5 x ) + 5 y ( 8 y )

multiply, we get

20 x ² + 40 y ²

Answer:

c

Step-by-step explanation:

Answer:

200,000

Step-by-step explanation:

just divide

Answer:

200,000

Step-by-step explanation:

Answer:

[tex]36 - 3m[/tex]

Step-by-step explanation:

[tex]3(12−m)[/tex]

[tex]3 \times 12+3(−m)[/tex]

[tex]36+3(−m)[/tex]

[tex]36−3m[/tex]

Answer:

[tex]2 + b >z > 2 -a[/tex]

Step-by-step explanation:

Given

[tex]z - b < 2 < a + z[/tex]

Required

Solve for z

Split the inequality

[tex]z - b < 2[/tex] or [tex]2< a + z[/tex]

Make z the subject

[tex]z < 2 + b[/tex] or [tex]2 - a < z[/tex]

Rewrite as:

[tex]2 + b >z[/tex] or [tex]z > 2-a[/tex]

Combine the inequalities

[tex]2 + b >z > 2 -a[/tex]