Question
A hot-air balloon is 1200 feet off the ground and its altitude is slowly changing at a constant rate of −712 feet per second.

How many seconds, s, will it take for the balloon to drop to below 310 feet?

Drag and drop a symbol and value to correctly complete the solution to this inequality.

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We find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

What is the tangent of the angle?

The ratio of the right-angle triangle's base or perpendicular is known as the tangent of the angle.

The ratio of two of the right-angled triangle's three sides is used to define the sine, cosine, and tangent of an acute angle.

Here,

We have to find out how is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used.

We concluded that a right triangle can be used to determine the tangent of any acute angle, by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

Hence, we find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

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Answer:

$68

Step-by-step explanation:

So, we will start off by putting our original price as a variable, x. Now, we will need an equation to show the relationship between the current price and three-fourths of the original price. The equation will look like this:

[tex]\frac{3}{4} x = 51[/tex]

Then, we will multiply both sides by 4 to get rid of the fraction, giving us:

3x = 204

Finally, we will divide by 3 to find the original price of the sneakers:

x = 68

So the pair of shoes originally cost $68.

Hope this helped!

The number line is drawn to find the open end point interval is infinity.

Number Line of an Open endpoint to the endpoint of number line =?

Selection of Open endpoint to the endpoint of the number line is  fit for the following intervals as such determined below :

basically the intervals are mentioned as follow

( ), [ ], ( ], [ )  

An open interval is mentioned (a, b), is an interval that does not contain its endpoints. When an interval involves infinity or negative infinity, hence the following rules for whether it is an open or closed interval. (a, and

(-a , a) are open intervals.

For instance [a,∞) doesn't contain all of its endpoints as mentioned . It's a real number where The interval has only one endpoint - a, so it contains all of its endpoints (however it only has one).

Secondly, the definition forgot to add that (−∞,∞) is also open

Take numbers as follows:

Final Answer  as followed  in intervals

(-2, 2)

[-2, 2]

(-∞, 2]

[2, ∞)

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Answer:

x = 60

Step-by-step explanation:

Let the two opposite angles be equal and let's call them y.

Because of the theory of angles on a straight line 120 +y = 180

y = 60

Because of the theory of angles on a straight line 2x + y = 180

2x + 60 = 180

2x =  120

x = 60

Alternatively. (also a lot easier)

120 and 2x are opposite angles so they are equal and so;

2x = 120

x = 60

Please mark as brainliest if this answer is helpful.

-6,7 is in 2nd Quadrant of a coordinate plane because the coordinate of x is negative integer and the coordinate of y is positive integers.

It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. We may have observed the use of grids in mathematics. We can plot any point using these grids and its coordinates.

Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identify a specific point's precise location on a grid. This grid is referred to as a coordinate plane.

The X-axis is the horizontal axis and the Y-axis is the vertical axis of a coordinate plane, which has four quadrants.

To plot -6, 7 point on coordinate first we find the point -6 on the left side of plane on x axis. the we go upward and find point y=7 parallel to y axis.

this point is -6,7.

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$1862  is Devi red from his biweekly paycheck for medical insurance

percentage, a relative value indicating hundredth parts of any quantity.

The annual cost of Randall coverage is 4900.

The college pays 62% of the cost.

We need to find How much is Devi red from his biweekly paycheck for medical insurance

Let us convert 62% to decimal value by dividing with 100

62/100=0.62

Now multiply 0.62 with 4900

0.62×4900

3038

Now subtract 3038 from 4900

4900-3038

1862

Hence, $1862  is Devi red from his biweekly paycheck for medical insurance

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Relief refers to the highest and lowest point elevation in an area.

Relief

Relief is the term used for the differences in height from place to place on the land’s surface and it is greatly affected by the underlying geology. Relief relies on the hardness, permeability and structure of a rock.

elevation

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface.

geology

Geology describes the structure of the Earth on and beneath its surface, and the processes that have shaped that structure. It also provides tools to determine the relative and absolute ages of rocks found in a given location, and also to describe the histories of those rocks.

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Answer: Relief

Step-by-step explanation:

Relief refers to the highest and lowest point elevation in an area.

Slope is the measure of steepness

Topography refers to the arrangement of the land in an area

Elevation on the other hand is the distance above sea level

Answer:

5 × x + 8

Would be the equation you are looking for.

Answer:

  Manuel can make 5 batches of muffins using Recipe 1

Step-by-step explanation:

You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.

Divide both sides of the given equation by 2 so solve for the value of b.

  (2b)/2 = (10)/2

  b = 5

Manuel can make 5 batches of muffins using Recipe 1.

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The value of x in the triangle WXY is 27°

An equation shows how two or more numbers and variables are related to each other.

∠VWY + ∠XWY = 180° (sum of angle in straight line)

6x + ∠XWY = 180°

∠XWY = 180 - 6x

∠XYW + ∠ZYW = 180° (sum of angle in straight line)

∠XYW + 4x = 180°

∠XYW = 180 - 4x

∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)

(180 - 6x) + (180 - 4x) + 90 = 180

450 - 10x = 180

10x = 270

x = 27°

The value of x is 27°

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Answer:

15:18.75:26.25

Step-by-step explanation:

4:5:7

Total=16

60/16 = 3.75

4 x 3.75 = 15

5 x 3.75 = 18.75

7 x 3.75 = 26.25

15:18.75:26.25

Answer: $15 : $18.75 : $26.25

Step-by-step explanation:

4 + 5 + 7 = 16

4/16 × $60 = $15

5/16 × $60 = $18.75

7/16 × $60 = $26.25

Answer:

x^2-9

Step-by-step explanation:

-3 + 3 = 0 so the x terms cancel out.  This leaves you with only x^2-9

Answer:

[tex] \sf \: 7.31[/tex]

Step-by-step explanation:

Now we have to,

→ round a number to 2 decimal places.

The number is,

→ 7.3084

Let's solve the problem,

→ 7.3084

→ ≈ 7.308

→ [tex] \boxed{ \sf ≈ 7.31} [/tex]

→ ≈ 7.3

Hence, the answer is 7.31.

The equation is y = 2x and the constant of variation k = 2

Therefore, the correct answer is option d.

Here, we can clearly see that y varies directly with x, because as x increases, y increases with the same proportion and vice versa. The constant of variation, k, is the coefficient of proportionality between x and y. To find the constant of variation, we can divide the value of y by the value of x for any one of the given points.

For example, for the point (-2, -4) we have:

k = -4 / -2 = 2

So the equation relating x and y is: y = kx = 2x

Hence, the equation is y = 2x and the constant of variation k = 2

Therefore, the correct answer is option d.

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The complete question is -

Determine whether y varies directly with x. If so, find the constant of variation and write the equation.

x | y

-2 | -4

-4 | -8

-16 | -32

a. No

b. yes; k=-2 and y=-2x

c. yes; k=1/2 and y=1/2x

d. yes; k=2 and y=2x

No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.

An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.

To estimate a few terms of the sequence in order to obtain a feel how it looks like.

In our case, the definition is that [tex]$\forall$[/tex] (for all) [tex]$n > 1: a_n=a_{n-1} a_{n+1}-1$[/tex].

This can be rewritten as [tex]$a_{n+1}=\frac{a_n+1}{a_{n-1}}$[/tex].

We have [tex]$a_1=x$[/tex] and [tex]$a_2=2000$[/tex], and we estimate:

[tex]$& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\[/tex]

[tex]$& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\[/tex]

[tex]$& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\[/tex]

[tex]$& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\[/tex]

[tex]$& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000[/tex]

At this point we see that the sequence will become periodic: we contain [tex]$a_6=a_1, a_7=a_2$[/tex], and each subsequent term exists uniquely determined by the previous two.

Hence 2001 appears, it contains to be one of [tex]$a_1$[/tex] to [tex]$a_5$[/tex].

As [tex]$a_2=2000$[/tex], we only have four possibilities left.

Clearly [tex]$a_1=2001$[/tex] for x = 2001, and [tex]$a_3=2001$[/tex] for x = 1.

The equation [tex]$a_4=2001$[/tex]

solves to [tex]$x=\frac{2001}{2000 \cdot 2001-1}$[/tex], and the equation [tex]$a_5=2001$[/tex] to [tex]$x=2000 \cdot 2001-1$[/tex]

There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.

Therefore, the correct answer is option (D) 4.

The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........  in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?

(A) 1

(B) 2

(C) 3

(D) 4

(E) more than 4

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Answer:

70 members

Step-by-step explanation:

Let's call the number of total members x. We know that 30% or  [tex]\frac{3}{10}[/tex] of the members forgot, so our equation looks like this:

[tex]\frac{3}{10}x = 21[/tex]

Then, we will multiply both sides by 10 to get rid of the fraction:

3x = 210

Finally, we will divide both sides by 3 to find out our variable, x:

x = 70

So, there are 70 members in total.

Hope this helped!

Answer:

g (x) = −7 x 2 + 26 x + 8

Step-by-step explanation:

Answer:

It can't add a plot for those numbers-

Step-by-step explanation:

Use synthetic division to divide (3x2 + 7x - 18) by (x - 3).The result of the division is (3x + 5)/(x - 3).

The first step is to write out the dividend and the divisor, and put a 0 in the box below the dividend.

3x2  +7x  -18

x - 3   0

The next step is to divide the divisor into the first term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9

Next, we multiply the divisor by the result from the previous step and subtract it from the second term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9  5

Next, we multiply the divisor by the result from the previous step and subtract it from the third term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9  5  -15

Finally, we divide the last result by the divisor.

3x2  +7x  -18

x - 3   0

3  -9  5  -15  3

The result of the division by synthetic division is (3x + 5)/(x - 3).

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the equation of the desired line is x = 3y + 6.

To find the equation of a line that is parallel to the given line

y = 1\3x + 10

and passes through the point (3,-1), since parallel lines have the same slope.

Therefore, the slope of the desired line is also 1\3.

Since the desired line passes through the point (3,-1), we can use the point-slope formula to write its equation:

y - (-1) = 1\{3}(x - 3)

Simplifying, we get

y + 1 = 1\ 3x - 1

Multiplying both sides by 3, we get

3y + 3 = x - 3

Adding 3 to both sides, we get

3y + 6 = x

Therefore, the equation of the desired line is x = 3y + 6.

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Answer: The table shows the number of pictures that a printer can print at different intervals of time (measured in minutes). To find the rate in pictures per minute, we need to divide the number of pictures printed by the number of minutes it took to print them.

For example, at 2 minutes the printer printed 16 pictures. The rate of pictures printed per minute is 16 pictures / 2 minutes = 8 pictures/minute.

Similarly, at 4 minutes the printer printed 32 pictures. The rate of pictures printed per minute is 32 pictures / 4 minutes = 8 pictures/minute

And, at 6 minutes the printer printed 48 pictures. The rate of pictures printed per minute is 48 pictures / 6 minutes = 8 pictures/minute.

And, at 8 minutes the printer printed 64 pictures. The rate of pictures printed per minute is 64 pictures / 8 minutes = 8 pictures/minute.

From this it can be seen that the printer has a constant rate of 8 pictures per minute, independent of the number of minutes, it is producing 8 pictures/min.

The value 15 is not related to the table, so it's not the rate, and 16 is not the rate either, it is the number of pictures printed at 8 minutes.

Step-by-step explanation:

Answer: To solve this system of equations, you can use the substitution method.

First, you can solve one of the equations for one of the variables in terms of the other. For example, you can solve the first equation for y:

y = (-4x - 8)/4

Then, you can substitute this expression for y into the second equation to find the value of x:

-2x - 2((-4x - 8)/4) = 4

-2x + 4x + 8 = 4

2x = -4

x = -2

You can then substitute this value of x back into the first equation to find the value of y:

y = (-4(-2) - 8)/4 = (8 - 8)/4 = 0

Thus, the solution to the system of equations is x = -2 and y = 0.

Step-by-step explanation:

The number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

To determine this:

Each cow has 4 legs, so the cows have 3 cows * 4 legs/cow = 12 legs.

Each chicken has 2 legs, so the chickens have 8 chickens * 2 legs/chicken = 16 legs.

We know the total number of farm animal legs is 40 legs.

So the number of duck legs can be calculated by subtracting the number of cow legs and chicken legs from the total number of farm animal legs: 40 legs - 12 legs - 16 legs = 12 legs.

Since each duck has 2 legs, the number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

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The correct option is (d). The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis

The difference between the areas beneath the two curves that form a boundary is the area between the curves. You will then have the area between the two curves, or the difference, between them.

The washer method enables us to use cylindrical discs with holes to compute the volume of solids in a rotation.

[tex]$$\begin{aligned}& V=\int_a^b \pi\left(x_1^2-x_2^2\right) d y \\& =\int_0^1 \pi\left(y^2-\left(y^2\right)^2\right) d y \\& =\int_0^1 \pi\left(y^2-y^4\right) d y\end{aligned}$$[/tex]

Therefore, the solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y² around the y axis.

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The amount of the proposed increase is, Rs 1071.4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The annual gym subscription for a single member is Rs.1000,

And, An annual family membership is Rs.1500.

Here, A single membership increased cost 5/7 of a family membership.

Hence, The increased cost = 5/7 of 1500

                                          = 1071.4 Rupees

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Answer: 88

Step-by-step explanation:

Answer: 88

Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88