You put a $625 necklace on layaway and put down a 15% deposit. What is the balance?

When the first side is 20 cm long, the second side is 30 cm long, and the angle is /6 radians, the angle between the sides is changing at a rate of -0.15 radians per second.

Let's denote the two sides of the triangle that are changing as x and y, where x is increasing at a rate of 3 cm/s and y is decreasing at a rate of 2 cm/s. Let A be the angle between these two sides, and let A be the area of the triangle, which is constant.

We can use the formula for the area of a triangle:

A = 1/2 xy sin(A)

where sin(A) is the sine of the angle A.

Taking the derivative of this equation with respect to time t, we get:

dA/dt = 1/2 [(dx/dt) y sin(A) + x (dy/dt) sin(A) + xy cos(A) (dA/dt)]

Simplifying this equation and plugging in the given values, we get:

0 = 1/2 [(3)(30) sin(π/6) + (20)(-2) sin(π/6) + (20)(30) cos(π/6) (dA/dt)]

Solving for dA/dt, we get:

dA/dt = [-45/(600 cos(π/6))] cm²/s

dA/dt = -0.15 cm²/s

Therefore, the angle between the sides is changing at a rate of -0.15 radians per second when the first side is 20 cm long, the second side is 30 cm long, and the angle is π/6 radians.

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Answer:

It is Linear

Step-by-step explanation:

We know the regular Linear equation is y = mx + b. In this case, the mx and the b switched places, but the equation still works the same way. y = -2x + 3

Answer:

yes

Step-by-step explanation:

Linear equations look like this

y=mx+b

where m is the slope

and b is the y intercept

if we switch -2x and the 3 we have the following

y= -2x+3

which looks like our y=mx+b

This expression for t1 does not depend on t2 and is expressed in terms of the given variables m, θ1, θ2, and the acceleration due to gravity g.

First, let's analyze the forces acting on the mass m.

There are three forces acting on the mass:
1. Gravitational force (mg) acting downwards
2. Tension force t1 acting at an angle θ1 from the vertical
3. Tension force t2 acting at an angle θ2 from the vertical

We can resolve these forces into their vertical and horizontal components.

For the vertical components, we have:
t1 * sin(θ1) + t2 * sin(θ2) = mg

For the horizontal components, we have:
t1 * cos(θ1) = t2 * cos(θ2)

Now we need to eliminate t2 from these equations. Divide the first equation by sin(θ2) and the second equation by cos(θ2):

t1 * sin(θ1) / sin(θ2) + t2 = mg / sin(θ2)
t1 * cos(θ1) / cos(θ2) = t2

Now we can substitute the expression for t2 from the second equation into the first equation:

t1 * sin(θ1) / sin(θ2) + t1 * cos(θ1) / cos(θ2) = mg / sin(θ2)

Factor out t1 from the left side:

t1 * (sin(θ1) / sin(θ2) + cos(θ1) / cos(θ2)) = mg / sin(θ2)

Finally, solve for t1:

t1 = (mg / sin(θ2)) / (sin(θ1) / sin(θ2) + cos(θ1) / cos(θ2))

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Answer:

\(\mathbf{ \dfrac{dr}{dt} = 0.03730 \ cm/min}\)

Step-by-step explanation:

The rate of the inflation of the balloon with time can be denoted as:

\(\dfrac{dv}{dt} = 500 \ cm^3/m\)

To determine; how fast does the radius change with time.

i.e.

\(\dfrac{dr}{dt}=???\)

where r = 40 cm and the volume of sphere = \(\dfrac{4}{3} \pi r^2\)

∴

\(\dfrac{dv}{dt}= \dfrac{4}{3} \pi 2(r^3) \dfrac{dr}{dt}\)

\(500= \dfrac{4}{3} \pi \times 2(40^2) \dfrac{dr}{dt}\)

\(500= 13404.13 \dfrac{dr}{dt}\)

\(\dfrac{500}{13404.13} = \dfrac{dr}{dt}\)

\(\mathbf{ \dfrac{dr}{dt} = 0.03730 \ cm/min}\)

The number of angles that are alternate exterior with angle 5 is one, which is angle 11.

Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.

The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.

Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.

Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.

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Answer:

20x + 12y

Step-by-step explanation:

4 times 5x = 20x

4 times 3y= 12y

Step-by-step explanation:

I am going to assume that the equivalent expression is fully simplified.

To simplify this expression, we use the distributive method.

Using this method we get:

4·(5x+3y) = 4·5x+4·3y

Now that we have the terms seperated, simplify each of them:

4·5x + 4·3y = 20x + 12y

Our expression is now fully simplified so our answer is:

20x + 12y

Answer:

B

Step-by-step explanation:

3 5/5 = 4 because 5/5 is equal to 1, and 3+1 = 4.

1/4 is not equal to 4 because it is equal to 0.25

4/1 = 4 because it is an identity

3 4/4 = 4 because 4/4 is equal to 1, and 3+1 = 4

Answer:

-6.3 is your slope.

Step-by-step explanation:

Hello, there! Nice to meet you.

This is a pretty easy question, as it's written in y = mx + b form.

When it's written like this, the m in replacement is your slope value.

So, in this case, -6.3 is your slope.

If I had y = 3x + 6, then 3 would be the slope, but that's just an example.

Once more, the m value is your slope.

Hope this helped, and best of luck with the rest of your assignment! (:

Answer: hi someone else answered this but you should report it its not an answer anyway here is the answer. 12

Step-by-step explanation:

write out the factors of both numbers:

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

then find the highest number in both, 12.

and thats the hcf. hope this helped but report that person they are not helping. :)

Answer:

1 mi/hr

Step-by-step explanation:

Given that:

Speed in still water, s = 5 mi/hr

Let speed of current = x

Time = distance /speed

Upstream (subtract speed of current) = 5 - x

Upstream time = 8 / 5 - x - - - (1)

Downstream (add speed of current) = 5 + x

Downstream time = 12 / 5 + x - - - (2)

Equate (1) and (2)

8 / (5 - x) = 12/ (5 + x)

8(5 + x) = 12(5-x)

40 + 8x = 60 - 12x

40 - 60 = - 12x - 8x

-20 = - 20x

x = 1

Spwed of current = 1 mi/hr

Answer:

decimal 0.42

percent 42%

Answer:

see explanation

Step-by-step explanation:

Using the product rule

Given

y = f(x)g(x) , then

\(\frac{dy}{dx}\) = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

let

f(x) = (3x - 1)³ , then using the chain rule

f'(x) = 3(3x - 1)² × \(\frac{d}{dx}\)(3x - 1) = 3(3x - 1)² × 3 = 9(3x - 1)²

let

g(x) = 2x + 5 ⇒ g'(x) = 2

Then

\(\frac{dy}{dx}\) = (3x - 1)³ . 2 + (2x + 5) × 9(3x - 1)²

    = 2(3x - 1)³ +9(3x - 1)²(2x + 5) ← factor out (3x - 1)²

    = (3x - 1)²[ 2(3x - 1) + 9(2x + 5) ]

    = (3x - 1)² [ 6x - 2 + 18x + 45 ]

    = (3x - 1)²(24x + 43)

--------------------------------------------------------------

(b)

let

f(x) = 3x - 2 ⇒ f'(x) = 3

let

g(x) = 2x² + 3 ⇒ g'(x) = 4x

Then

\(\frac{dy}{dx}\) = (3x - 2).4x + (2x² + 3). 3 ← distribute parenthesis

    = 12x² - 8x + 6x² + 9

    = 12x² - 8x + 9

Note

It is usual to simplify after differentiating the expressions

Answer:

432, 36, 3

Step-by-step explanation:

Divide each # by 12

Answer: 432, 36, 3

Step-by-step explanation:

You can divide 746,496 by 12 to get 62,208.

You can divide 62,208 by 12 to get 5,184.

You can continue dividing by 12 to get:

5,184 ÷ 12 = 432

432 ÷ 12 = 36

36 ÷ 12 = 3

Therefore, the next three terms are 432, 36, and 3.

I hope this helps!

The possible values of a for which x^2+ax+25 is the square of a binomial are +10 and -10

If x^2+ax+25 is the square of a binomial, then it can be expressed in the form (x+b)^2 = x^2+2bx+b^2. Comparing the two expressions, we get:

a = 2b

25 = b^2

Solving for b in the second equation, we get:

b = ±5

Substituting this into the first equation, we get:

a = ±10

Therefore, the possible values of a for which x^2+ax+25 is the square of a binomial are +10 and -10, and these values will make b equal to +5 or -5, respectively.

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The product of 4/6-2a x 3-a/2 is equal to 2a-1. To calculate this, the fractions must first be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Next, the two terms should be multiplied together, resulting in 2a-1.

The product of 4/6-2a x 3-a/2 can be found by expanding the terms and then solving the equation. First, the fractions must be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Once the fractions are simplified, the two terms should be multiplied together, resulting in 2a-1. Now that the two terms have been multiplied, the equation can be expanded by using the Distributive Property. The equation should be written as (2/3-2a) x (3-a/2). This can be simplified by distributing the 2/3 and 3 across the parentheses. This results in (2-6a+2a^2) x (3-1/2a). Finally, the equation should be simplified by combining like terms. This results in 2-6a+2a^2+3-1/2a, which simplifies to 2a-1. Therefore, the product of 4/6-2a x 3-a/2 is equal to 2a-1.

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Answer:

I don't know........................

Answer:

x < 33/4

Step-by-step explanation:

1.) -4x+35 > 2 (Move the constant to the right-hand scale side and change its sign)

-4x > 2 - 35

2.) -4x > 2 - 35 (Calculate the difference)

4x > -33

3.) -4x > -33 (Divide both sides of the inequality by -4 and flip the inequality sign)

x < 33/4

We can conclude that the statement (a !) != (a !)² is true for all positive integers a is the answer.

The statement (a !) != (a !)² is always true. The exclamation mark (!) in this context denotes the factorial operation. The factorial of a positive integer is the product of all positive integers less than or equal to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Given that a and b are positive integers, let's consider a specific value, say a = 5.

Therefore, (5 !) is equal to 5 x 4 x 3 x 2 x 1 = 120.

Now, let's calculate (5 !)². It will be equal to (5 x 4 x 3 x 2 x 1) x (5 x 4 x 3 x 2 x 1) = 120 x 120 = 14400.

As we can see, (a !) = 120 and (a !)² = 14400.

These two values are not equal, so the statement (a !) != (a !)² is true.

This holds true for any positive integer value of a.

Therefore, we can conclude that the statement (a !) != (a !)² is true for all positive integers a.

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Answer: add 7 each time

Step-by-step explanation:

no explanation lol

Answer:

add 7 to the previous number

Answer: 4x+40 dollars

Step-by-step explanation:

1. Define: since a ticket costs x dollars and 10$ for a drink and candy, your expression would be x+10 dollars.

2. Distrubute: Since there are 4 people, it would be:

4*(x+10)

3. Simplify: 4*(x+10) => 4x+40

Have a nice day! :D

Answer:

h = 4.41 feet

Step-by-step explanation:

\(V_{cone} = \frac{1}{3} \pi {r}^{2}h \\ \\ 220 = \frac{1}{3} \times 3.14 \times {5}^{2} \times h \\ \\ 220 \times 3 = 3.14 \times 25 \times h \\ \\ 660 = 78.5 \times h \\ \\ h = \frac{660}{78.5} \\ \\ h = 8.40764331 \\ \\ h = 4.41 \: feet\)

As per the two factor study, the value of s is 60.

Two factor study

In math, two factor study defined as an experimental design in which data is collected for all possible combinations of the levels of the two factors of interest.

Given,

Here we have that for a two-factor study with 2 levels of factor a, 2 levels of factor b, and a separate sample of 10 participants in each treatment condition, the two means for level a1 are 4 and 1, and the two means for level a2 are 3 and 2.

And we need to find the value of s between treatments.

As per the given question, we have identified that the values,

Number of participants = 10

And we also know that,  level a1 are 4 and 1, and the two means for level a2 are 3 and 2.

So, based on the two factor method, the value of s calculated as,

Here we have to multiple factors first,

=> 3 x 2 = 6

And then multiply that by n = 10,

=> 6 x 10 = 60

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Answer:

You can get 10 chesse pizzas and then you can get 1 meat pizza.

Step-by-step explanation:

Sorry if that wasn't what you were looking for. Hope this helped!

Answer:

6 meat pizzas and 4 cheese pizzas = $56

Step-by-step explanation:

The five large cities in India are:

The population of large cities in India are:

The distance between the large cities in India are:

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Answer:

D

Step-by-step explanation:

Answer:

C. 40 square meters

Step-by-step explanation:

The area for a kite can be figure out with this formula. pq/2. Substitute p for 8 & q for 10.

A = pq/2 {Substitutions made}

A = (8 * 10)/2 {Multiply 8 by 10 to get 80.}

A = 80/2 {Divide 80 by 2 to get 40.}

A = 40 square meters

The area of this kite of 40 square meters, which is C.

Step-by-step explanation:

Sum of arithmetic terms = n/2 × [2a + (n - 1)×d], where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.

this is the same as n/2 × (a1 + an), because

an = a1 + (n-1)×d

so, for the series above :

a or a1 = 2

d = 7, as every new term is the previous term plus 7.

for n

37 = a1 + (n-1)×d = 2 + (n-1)×7

and now solve for n

35 = 7n - 7

42 = 7n

n = 6

so, the sum of all terms is

6/2 × (2+37) = 3×39 = 117

The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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Answer:

3/14

Step-by-step explanation:

1 1/4 can be written as 5/4

5 5/6 can be written as 35/6

so divide (5/4)/(35/6)

= (5/4)*(6/35)

=(1/4)*(6/7)

=6/28

simplified = 3/14

Answer:

Im not 100% sure because I dont have paper, but the answer is..YELLOW and Dark blue

Step-by-step explanation:

If this isnt the answer pls forgive me, and if you can pls gimme brainliest