Y varies inversely with the square of x. When x=4, then y=3. Find y when x=2

In order to find the value of x in the expression, we need to isolate the terms with the variable 'x' in one side of the equation, and the variables without 'x' in the other side.

Then, we divide the whole equation by the number multiplying 'x', so we have just 'x' in one side of the equation.

So we have that:

a)

So the value of x is -1.

b)

So the value of x is 3

First, let's remember that the zeros of a function are the points where the graph intersects the x-axis, that is, those points where an x-coordinate intersects the x-axis since its output is y=0.

Therefore, the following paragraph should be filled in as follows:

You find a zero of a linear function from a graph identifying the x coordinate of any point of intersection with the x-axis, from an equation by setting the output equal to 0, and from a table by identifying the input values when the output is 0.

The solution to the equations are

Weeks (w)     Amount remaining

6                          62

10                        20

From the question, we have the following parameters

Savings = $125

Bus fare = $10.5

The equation of the amount remaining is represented as

Amount remaining = Savings - Bus fare x Number of weeks

Substitute the known values in the above equation

So, we have the following equation

s = 125 - 10.5w

Where w represents the number of weeks

Also, we have

w = 6 and w = 10

So, we have

s = 125 - 10.5 * 6 = 62

s = 125 - 10.5 * 10 = 20

So, the table is

Weeks (w)     Amount remaining

6                          62

10                        20

In (a), we have

s = 125 - 10.5w

Express as a function notation

s(w) = 125 - 10.5w

See attachment for the graph

We have

s(w) = 125 - 10.5w

This gives

125 - 10.5w = 41

So, we have

10.5w = 84

Evaluate

w = 8

This means that the amount remaining after 8 weeks is $41

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Given the segment on the picture, we can write the following 3 equations:

If the purchases of streamed music can be modeled by function f(t) = 3.7+0.84 ln(t+1)

Part a

The amount spent by consumers on streamed music in 2014 is 4.62 billion

Part b

The amount spent by consumers on streamed music changing in 2014 at the rate of 0.28 billions per year

The purchases of streamed music  model

f(t) = 3.7+0.84 ln(t+1)

Where f(t) is measure in billion of dollar

t is the measured in years

Part a

We have to find the amount spent by consumer on streamed music in 2014.

t = 0 corresponding to the year 2012

Then 2014 corresponding to t = 2

Substitute the value of t in the equation

f(2) = 3.7+0.84 ln(2+1)

f(2) = 3.7+0.922

f(2) = 4.62 billion

Part b

Differentiate the model with respect to x

f'(t)  = 0.84×[tex]\frac{1}{t+1}[/tex]

t = 2

Substitute the value in the equation

f'(2) = 0.84×[tex]\frac{1}{2+1}[/tex]

f'(2) = 0.28 billions per year

Hence, if the purchases of streamed music can be modeled by f(t) = 3.7+0.84 ln(t+1)

Part a

The amount spent by consumers on streamed music in 2014 is 4.62 billion

Part b

The amount spent by consumers on streamed music changing in 2014 at the rate of 0.28 billions per year

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First, we compute the population increase:

Now we divided the above result by the initial population:

Finally, we multiply by 100 and round to the nearest tenth of percent:

Answer: 23.1%

The growth rate of real gdp per capita from 2019 to 2020 is 40%

Given,

The real gdp of an economy in 2019 = 100 billion = 100, 000, 000, 000

The real gdp of an economy in 2020 = 240 billion = 240, 000, 000, 000

The population in 2019 = 15 million = 15, 000, 000

The population in 2020 = 15 million = 15, 000, 000

Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)

Here,

Initial gdp = 100,000,000,000 / 15,000,000 = 6666.67

Increased gdp = 240,000,000,000 / 15, 000, 000 = 16000

Now,

Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)

Growth rate of real gdp per capita = (16000 × 100) / 6666.67 = 240

That is,

The growth rate of real gdp per capita from 2019 to 2020 is 40%

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Solution

For this case the answer is:

Side-Angle-Side (SAS)

Since we have two sides congruent and also one angle

SOLUTION

The diagram for this is shown below

From the diagram above, considering triangle BPC, let us find angle C

Using sine rule, we have

From the same triangle BPC to get angle B, we have

From the same triangle BPC, using sine rule to get the side PC, which I called x, we have

This makes the side AC to become

So, to get the area of the triangle ABC, we have that

Applying we have

Hence the answer is approximately 1402.94 square-millimeters to the nearest hundredth

the y intercept of the curve of the function is 0.

y intercept is the point at which the curve of the function intersects the y axis.

here,

the curve intersects the Y axis at the origin.

coordinates of the origin are:

(0, 0)

So, the y intercept will be:

y = 0

Therefore, we get that, the y intercept of the curve of the function is 0.

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The perimeter of a geometric figure is the sum of it's side lengths.

We have a pentagon with side lengths equal to:

x, x, x, 3x, and 3x

a)

The perimeter of this pentagon is:

P = x + x + x + 3x + 3x

Since the perimeter is given as 54 cm:

x + x + x + 3x + 3x = 54

Answer: Option A

b) Solve the equation in part a)

Collecting all like terms:

9x = 54

Dividing by 9:

x = 54 / 9

x = 6 cm

c) Find the length of each side.

The sides are

x=9 cm

x=9 cm

x=9 cm

3x=27 cm

3x=27 cm

The given equations are-

These equations represent straight lines, where the coefficients of x are the slope of each one.

When two lines are parallel, they have the same slope, which is not the case here because the first one has a slope of 3, and the second one has a slope of -1.

Additionally, if two lines are perpendicular, their slopes are totally opposite in number and sign, which is not the case here because 3 is not opposite to -1.

Therefore, the answer is neig

The best estimate of the diameter of the moon is 3.474×10⁶.

The best estimate of the diameter will be calculated by converting the number into scientific notation. To convert the number into scientific notation it is broken into two parts.

First number is coefficient which has to range between 1 and 10. So, as per the digits, 3.474 will be the coefficient.

The 10 will be written along with exponent. There are three digits after the decimal followed by three zeroes. Therefore, the 10 and exponent will be written as 10⁶.

So, the complete number estimating the diameter of moon is 3.474×10⁶.

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Given:

To find:

The angle BOC.

Explanation:

Using the length of the arc formula,

The angle is

Final answer:

The angle is

Recall the definitions of the magnitude and direction of a vector:

Answer:

8.

Step-by-step explanation:

A little trick is to multiply 2 and 8, then divide by two because a triangle is half a square.

2 x 8 = 16

16 divided by 2 is 8.

Answer = 8

Given:

• Length of top base of figure A = 3

• Length of top base of figure B = x

• Scale factor = 1.75

Given that figure A is a scale image of figure B, let's find the value of x.

To find the value of x since figure A is a scale image of figure B, multiply the corre

John's account balance after considering the withdrawal and the overdrawn fee is -$35

What does it mean for an account to be overdrawn?

An account is overdrawn if the money withdrawn from it is more than the account balance, in this scenario, the check presented whose value is $110 is more than the account balance, which was the account by which the account was opened initially, hence, John's account can be said to be overdrawn.

Account balance=initial balance-amount withdrawn-overdrawn fee

Note overdrawn fee and amount withdrawn would be shown as negative values because they are obligations against the account balance

initial balance=$100

amount withdrawn=$110

overdrawn fee=$25

Account balance=$100-$110-$25

Account balance=-$35

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there is a zero at x = 1 (option D)

Explanation:

a) The graph shows it is going up (increasing towards both the y axis and x axis).

This graph will give a positive leading coefficient.

As a result, the equation will have a positive leading coefficient not a negative one.

b) zeros of a polynomial are the values of x when the line crossses the x axis.

From our graph, the line doesn't cross the x axis at x = 6.

As a result, there is no zero of -6.

Multiplicity tells us the number of times the number of times a factor occurs.

Since part of the statement is wrong, it makes the whole statement wrong

c) The degree of this graph is odd. Its equation is 3rd degree

d) From the graph, the line crosses the x axis at x = 1 (2nd tick line)

Each tick line represents 0.5

The zero is the value of x when it crosses the x axis

As a result the polynomial has a zero at x = 1

The correct option is there is a zero at x = 1 (option D)

We will solve as follows:

So, the value that is a solution for the inequality is:

[Option A]

The distance by which Mika will be ahead is equal to 36 m from present location.

According to the question Gretchen and Mika are at the same point when Gretchen runs backward at the speed of 4 m/s in opposite direction to pick her baton and Mika runs in the direction of the race at the speed of 3 m/s. We need to find the distance covered by Mika form the current location in the time when Gretchen picks her baton up. Let us assume that the time taken by Gretchen to pick up her baton be equal to t. It is given that 48 meters from her current location she dropped her baton. Since she is running at the speed of 4 m/s then the time will be equal to t = 48/4 = 12 seconds. Now, Gretchen will be able to pick up the baton in 12 seconds. Thus, the distance covered by Mika in 12 seconds will be equal to 3×12 = 36m.

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Complete Question:

Gretchen and Mika are involved in a relay race. Both runners are at the same point on the course when Gretchen realizes that she dropped her baton and has to turn around to retrieve it. Gretchen runs backwards at a speed of −4 m/s, relative to the direction of the race. Mika continues running at a speed of 3 m/s. If Gretchen dropped her baton −48 meters from her current location, relative to the direction of the race, how far ahead will Mika be when Gretchen picks her baton up?

The equation of the parabola from its focus and vertex is 5x = 4y² .

A parabola is a mirror-symmetrical, roughly U-shaped planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.

A line and a point (the focus) are two components of one definition of a parabola (the directrix). There is less emphasis on the directrix. The parabola is the location of the endpoints in that plane that are equally spaced away from the directrix and the focus.

Another approach to define a parabola is as a conic section formed by the union of a right circular conical area with a plane parallel to another axis perpendicular to the conical surface.

from the figure the parabola is opening on the right side.

Hence the general equation of the parabola is is y² = 4ax

Now from the focus we get 4a = 5

or, a = 5/4

Hence the equation of the parabola is 5x = 4y².

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Answer:

7√8

Step-by-step explanation:

3+√3+4√5

3+4+√3+√5

7+√8

Donna is right. 115° angle and ∠3 are supplementary.

From the figure, we are discussing about the 115° angle and ∠3.

Donna says that m∠3 = 65° because the 115° angle and ∠3 are supplementary. That is their sum = 180°.

From the figure, it is clear that the 115° angle and ∠2 are supplementary.

So ∠2 = 180° -115° = 65°.

Now ∠2 and ∠3 are corresponding angles formed between the parallel lines m and q. Since corresponding angles are equal, m∠2 = m∠3.

Thus m∠3 = 65°.

Thus 115° + m∠3 = 115° + 65° = 180°

As the sum of the 115° angle and m∠3 = 180°, they are supplementary.

Hence Donna is correct.

Luis said that 115° and ∠3 are alternate but they are not. Alternate angles are those which are formed in the interior and on the opposite sides of the transversal cutting two parallel lines. They are of same size. But here, m∠3 ≠ 115°.

So Luis is not right.

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Answer:

Explanation:

Here, we want to get the measure of the other three angles in a parallelogram

The angle rules in a parallelogram are:

i) Opposite angles are equal to each other

ii) The two adjacent angles add up to 180 degrees

From what we have, one of the angles is 24 degrees

The measure of the last two angles would be:

The triangles are not similar.

Triangles that are comparable to one another are those that have an equal number of corresponding sides and corresponding angles.

If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be comparable. To put it another way, similar triangles have the same shape but may differ in size. In addition, if the corresponding sides of the triangles are identical in length, the triangles are congruent.

Here, the ratio of the sides are not similar

AB/AC= 4/10 = 2/5

DE/DF= 8/19

Hence, 2/5≠8/19

therefore, the triangles are not similar.

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Investment = $5,000

Price of the product or sale price = $3.49

Production cost = $2.16

Profit = 3.49 - 2.16 = $1.33

We need to sell X items to get our investment back, therefore

X * Profit = Investment

1.33 * X = 5,000

X = 5,000 / 1.33 =3759.4

Therefore you need to sell at least 3760 articles to break even

Additionally, if you want to make a $10,000 profit, then you need to sell those items plus Y more or in other words, you want to sell as many items to get your $5,000 investment plus $10,000

This is...

5,000 + 10,000 = K * (1.33)

15,000 = 1.33 * K

K = 15,000 / 1.33 = 11,278.2 ;

Therefore, you need to sell 11,279 items

Given the points:

(x1, y1) ==> (1, 1)

(x2, y2) ==> (3, 7)

To find an equation of the line that goes through the points, first find the slope using the slope formula below:

Substitue values into the formula and solve for the slope, m:

The slope of the line, m is = 3.

Now, use the point slope form:

(y - y1) = m(x - x1)

Substitute 1 for y1, 1 for x1, and 3 for m:

(y - 1) = 3(x - 1)

Let's rewrite the equation to slope intercept form: y = mx + b

Where m is the slope and b is the y-intercept

y - 1 = 3(x) + 3(-1)

y - 1 = 3x - 3

Add 1 to both sides:

y - 1 + 1 = 3x - 3 + 1

y + 0 = 3x - 2

y = 3x - 2

Therefore, the equation of the line in slope intercept form is:

y = 3x - 2

ANSWER:

y = 3x - 2

The amount that he borrow (PV)  if interest rate is 13% (interest rate) per annum compounded monthly (P/YR)​ is: $12,235.90.

First step is find to  the number of months

n = 20 months / 12

n = 1.66666666

Now let find the amount borrowed

A= P/ ( 1+ r) ^ n

Where:

A = Amount

P = Principal

r = interest rate

n =  time

Hence.

A = 15,000 / ( 1+ 0.13) ^ 1.66666666

A = 15,000 / (1.13)^ 1.66666666

A = 15,000 /  1.2259

A = $12,235.90

Therefore $12,235.90 is the amount borrowed.

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