Is there any number that can be expressed as a ratio of two integers?

a) The required equation is h(t)=10−8×sin⁡(2×π×t/12). b) The sandbar at the latest at 7:00 pm. c) Captain Highliner will be able to return to the harbour at the earliest at 7:00 am.

a) The depth of water over the sandbar can be expressed as a function of time, t, in hours, using the following equation:

h(t)=10−8×sin⁡(2×π×t/12)

This equation describes a sinusoidal function with a period of 12 hours, a maximum value of 10 metres (at high tide) and a minimum value of 2 metres (at low tide).

b) To find the latest time of day that Captain Highliner will be able to get his trawler over the sandbar, we need to find the time when the depth of water is at least 4 metres.

We can do this by setting h(t) equal to 4 and solving for t:

4=10−8×sin⁡(2×π×t/12)

6=8×sin⁡(2×π×t/12)

3/4=sin⁡(2×π×t/12)

The value of sin⁡(2×π×t/12) is positive between 0 and 6 hours, and negative between 6 and 12 hours. Therefore, the only solution to this equation is t=3/4×12=9 hours.

This means that Captain Highliner will be able to get his trawler over the sandbar at the latest at 10:00 am + 9 hours = 7:00 pm.

c) To find the earliest time of day that Captain Highliner will be able to return, we need to find the time when the depth of water is at least 4 metres.

We can use the same equation as before:

4=10−8×sin⁡(2×π×t/12)

6=8×sin⁡(2×π×t/12)

34=sin⁡(2×π×t/12)

The value of sin⁡(2×π×t/12) is positive between 0 and 6 hours, and negative between 6 and 12 hours.

Therefore, the only solution to this equation is t=3/4×12=9 hours.

This means that Captain Highliner will be able to return to the harbour at the earliest at 10:00 am + 9 hours + 12 hours (to complete one full tidal cycle) = 10:00 pm + 9 hours = 7:00 am the next day.

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For slope equals to 1/3 the value of k in the line is 3 by slope intercept form.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The equation of the line :

3y - 5 = 1/9 kx

The slope of line is 1/3

3y - 5 = 1/9k x

by slope intercept form

1/9k = 1/3

k = 3

So, for slope equals to 1/3 the value of k in the line is 3 by slope intercept form.

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The graph of a quadratic function is called a parabola.

A parabola is a type of graph that is in the shape of a symmetrical "U" or "V", and it can be defined as a set of all points that are equidistant to the focus point F and the directrix.

The graph of a quadratic function is a parabola. A parabola can open upward or downward, depending on the sign of the quadratic term.

A parabola can be either concave up or concave down. A parabola that opens upwards is called an "upward-opening parabola" and a parabola that opens downwards is called a "downward-opening parabola".

It is also commonly referred to as a parabolic curve or a parabolic reflector.

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We can do it by splitting the coins into 2 piles. A small pile consists of 10 coins, and the other pile consists of 90 coins. Then, flip over all the coins in the small pile.

By picking any 10 coins and make a small pile, we now have 90 coins in the large pile. We do not know where the heads are, yet we do know that there are 10 coins in total, and thus, no matter how many heads there are in the large pile, there is 10 minus this many in small pile.

So, now we know that:

Small pile contains:

- n heads

- 90 – n tails

Large pile contains:

- 10 – n heads

- the balance tails = n tails. Since out of 10 coins, 10 – n are heads, it means the number of tails is 10 – (10 – n) = n tails.

Thus, the large pile has n heads and the small pile has n tails. So, we know that there are always the same number of heads in the large pile as there are tails in small pile, even if we do not know what number that is to be exact. Hence, flip over all the coins in small pile, now we have the same number of heads in both piles.

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Answer:

y = -24

Step-by-step explanation:

Solve for y:

y/8 + 38 = 35

Put each term in y/8 + 38 over the common denominator 8: y/8 + 38 = y/8 + 304/8:

(y/8 + 304/8) = 35

y/8 + 304/8 = (y + 304)/8:

((y + 304)/8) = 35

Multiply both sides of (y + 304)/8 = 35 by 8:

(8 (y + 304))/8 = 8×35

(8 (y + 304))/8 = 8/8×(y + 304) = y + 304:

y + 304 = 8×35

8×35 = 280:

y + 304 = 280

Subtract 304 from both sides:

y + (304 - 304) = 280 - 304

304 - 304 = 0:

y = 280 - 304

280 - 304 = -24:

Answer: y = -24

The function x3 + 4x²-3x - 12 in factored form knowing that one of the roots is -4 [tex]$$(x-4)\left(x^2+3\right)$$[/tex]

Group the first two terms and the last two terms.

[tex]$$\left(x^3-4 x^2\right)+3 x-12$$[/tex]

Factor out the greatest common factor (GCF) from each group.

[tex]$$x^2(x-4)+3(x-4)$$[/tex]

Factor the polynomial by factoring out the greatest common factor, x-4.

[tex]$$(x-4)\left(x^2+3\right)$$[/tex]

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The solution to the system of equations is (1, 8).

From the question, we have the following parameters that can be used in our computation:

y-x=7 y=3x+5

To find the solution to the system of equations y - x = 7 and y = 3x + 5, we can substitute the second equation into the first equation to eliminate y:

y - x = 7

y = 3x + 5

Substituting y = 3x + 5 into the first equation:

3x + 5 - x = 7

2x = 2

x = 1

Now that we have found x = 1, we can substitute it back into either equation to find y:

y = 3x + 5

y = 3 * 1 + 5

y = 8

So the solution to the system is (x, y) = (1, 8).

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A. (6,1) and D. (5,1) are the solutions that satisfy the linear inequality 2x - 3y < 6.

A. 2(6) - 3(1) = 12 - 3 = 9 < 6

D. 2(5) - 3(1) = 10 - 3 = 7 < 6

The given linear inequality 2x - 3y < 6 can be solved by first isolating the variable y on one side of the inequality. This can be done by adding 3y to both sides of the inequality, resulting in 2x < 6 + 3y. Then, divide both sides of the inequality by 2, resulting in x < 3 + 1.5y. This is the equation of a line in the x-y plane, which has a slope of -1/2 and a y-intercept of 3. To find the solutions that satisfy the inequality, the coordinates of points that are located below the line must be found.

The coordinates of point (6,1) can be plugged into the equation of the line, resulting in 6 < 3 + 1.5(1), which is true, so (6,1) satisfies the inequality. The coordinates of point (5,1) can be plugged into the equation of the line, resulting in 5 < 3 + 1.5(1), which is also true, so (5,1) satisfies the inequality. The coordinates of point (2,-7) can be plugged into the equation of the line, resulting in 2 < 3 + 1.5

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Therefore , the solution of the given problem of inequality comes out to be  Rosa's age is 17 .5 and her fathers age is 52.5 years.

In mathematics, an inequality is a relationship of linear solution or integers without the equal sign. Inequity inevitably leads to imbalance. When two numbers are not equal, there is an inequality between them. Between equality and inequality, there are differences. In instances when the variables aren't similar or equal, I've used the most common symbol (). There are many inequalities that may be utilised to compare values regardless of how small or huge they are.

Here,

Given :

Let Rosa age = x

Rosa's father age =  3x

and

=> 3x -x < 35

=> 2x < 35

=> x <35/2

=> x < 17.5

Thus , Rosa's age is 17 .5 and her fathers age is 3*17.5 = 52.5 years

Therefore , the solution of the given problem of inequality comes out to be  Rosa's age is 17 .5 and her fathers age is 52.5 years.

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James was able to save $15 by dividing $30 by 2. James and money equal 3/4 (money with sister) x/2 + 30 = 3/4 (x + 30) in the equation.

The statistic is said to be in its simplest form when cut into its smallest equivalent fraction. What to do to find the most basic form. Look for common factors in the denominator. Examine a fractional integer to verify if it qualifies as a real number. A statement having two equal sides and an equal sign in the middle is called an equation in algebra. The general form of almost any equation contains the quantities of all the variables in descending order. The conventional form of an equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditioned equations. An identity holds true regardless of the value given to the variables.

given

Sister's money saved should equal x.

James has saved only half as much money as his sister.

James saved x/2 in money.

They both saved a total of x + x/2 dollars.

If they each save thirty more

Then

sisters' money = x + 30

cash with James = x/2 + 30

Given that James will have saved half as much as her sister if they both save 30 more

thus,

James and money equals 3/4 (money with sister)

x/2 + 30 =3/4( x + 30 )

=> 4(x+30*2) /2 = 3x+90

=> 2x + 120 = 3x + 90

=> 3x-2x = 120-90

=> x = 30

James was able to save $15 by dividing $30 by 2. James and money equal 3/4 (money with sister) x/2 + 30 = 3/4 (x + 30) in the equation.

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Answer:

(-infinity, 4] U [7,infinity)

Step-by-step explanation:

domain is everywhere where x exists and by inspection of the graph x exists from negative infinity noninclusive to 4 inclusive and 7 inclusive to infinity noninclusive

If the layer sum of wxyz equals 2014, then the value of w + x + y + z = 13.

If wxyz is a four-digit positive integer with w ≠ 0, the layer sum of this integer equals wxyz+xyz+yz+z.

We are given the example -

The layer sum of 4089 is 4089+089+89+9 = 4276.

And that the layer sum of wxyz = 2014

Now we will find the values of w, x, y, and z using the given layer sum formula by guessing.

we have, 2014 = wxyz + xyz + yz + z

Here, we can clearly see that we have four z which should equal 4 from 2014. This is possible only when z = 1 or z = 6.

let us consider,

when z = 1, we will have

wxy1  + xy1 + y1 + 1 = 0004

Here, we will have no carryover from the sum of digits in units place, so the next step would be to find the value of y such that we could get 1 as the answer, which is possible only when y = 7 which gives the value of 3y = 21 from which 2 will be carried over.

wx71  + x71 + 71 + 1 = 0014

Now to find the value x such that 2x + 2(carried over) gives 0. This is possible when only when x = 4 which would give us

2x + 2 = 2(4) + 2 = 10 from which 1 will be carried over.

w471  + 471 + 71 + 1 = 0014

Finally, we are given that w ≠ 0 and we know that w cannot be 2 as it will not fit our tailored solution.

So the only possibility is w = 1, also it fits as we add the carried-over 1 to the w=1 to get 2014.

1471  + 471 + 71 + 1 = 2014

Since z = 1 satisfies our answer, the other case of z = 6 would not be possible.

Now, we have w = 1, x = 4, y = 7, z = 1.

Hence, the value of w + x + y + z = 1 + 4 + 7 + 1 = 13.

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The complete question is -

If wxyz is a four-digit positive integer with w ≠ 0, the layer sum of this integer equals wxyz+xyz+yz+z. For example, the layer sum of 4089 is 4089+089+89+9 = 4276. If the layer sum of wxyz equals 2014, what is the value of w + x + y + z?

We can utilise the laws of cosines to find the missing side of a scalane triangle c2 = a2 + b2 - 2ab cos(c),

A scalene triangle is a type of triangle in which all the three sides have different lengths.

A triangle with three uneven sides is known as a scalene triangle. Because there are differences between the three sides, it follows that there are likewise differences between the three angles. It is one of three different kinds of triangles that may be identified by the characteristics of their sides. So, a triangle is said to be scalene when none of its sides are equal.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. However, the sum of all the internal angles of the scalene triangle is unaffected by the various measurements. Scalene triangles satisfy the angle sum property of triangles because the sum of their three internal angles is always 180 degrees.

To determine a scalene triangle's missing side, we can utilise the laws of cosines. The equation is: c2 = a2 + b2 - 2ab cos(c), where c is the angle across from the third side.

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Answer:

Probability of there being two heads would be 1/4.

Math:

1/2 * 1/2 = 1/4.

Hope this helps^^

The minimum value for the given linear equation will be 19.

What are linear equations?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

For the minimum value of C=2x+3y

we have to find the area in the graph where given inequalities intersect and that's where C will have minimum value i.e. (5,3)

Hence,

For (5,3)  C=2*5+3*3

C=19

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Step-by-step explanation:

1. 605 feet = 7260 inches

  15:7260 = 1:484 = Circle number 2

2. 8/12 = 2/3

    10/15=2/3

   14/21 = 2/3

The correct similarity statement is Circle C, ABC is similar to DEF

3. 2.5/1.5 = 25/15=5/3

    8/4.8=80/48=10/6=5/3

   These 2 statements show that the quadrilaterals are similar.

Similarity statement = Circle 2 = JKML is similar to PQRS

4. ABC is similar to ACE, which is similar to CBE, therefore, the correct answer is Circle 3.

5. Using the similarity of triangle ADB and BDC, 5/y = 3/x = 4/3.

   5/y = 4/3, 15 = 4y, y = 15/4

   3/x = 4/3, 9 = 4x, x = 9/4

 The correct answer is Option 2

6.  Does your diagram mean that Angle PQS and SQR are equal?

7. You can use AA similarity to prove they are equal. (They both have a 72 degree angle, and the opposite angles of the intersection of the lines are equal.

The opposite sides of a parallelogram are congruent so a is 15.

3a+7a+2a=180 because the sum of the angles in the triangle BCD is 180 degrees.

3a+7a+2a=180

12a=180

a =180/12

a= 15

(I. e) 3a= 3(15)= 45

7a=7(15)=105

2a=2(15) =30

As a result, angle A=angle C (OPP. Angles of a Parallelogram are Equal) = A = B, D = A (OPP. angles of a parallelogram are equal)

In light of this, 7a=c = c = 105.

OPP sides in a parallelogram are parallel and equal, therefore AB is parallel to CD and BD is a transversal; as a result, angle d=2a (alternative internal angles are equal) translates to d=30.

as well as b=3a (alternative interior angles are equal) resulting in b=45

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Answer: hypotenuse-leg

Step-by-step explanation:

assuming you posted it on a math website

Answer:

a1 = 3

a2 = 3 + 2 = 5

a3 = 5 + 2 = 7

a4 = 7 + 2 = 9

The answer is x = 2, y = -1.

The solution by the method of elimination goes as follows:

3x + 10y = -4        ...(i)

2x + 2y = 2          ...(ii)

Multiplying eq.(ii) by 5, we get

10x + 10y = 10      ...(iii)

Subtracting eq.(iii) from eq(i), we get

-7x = -14

x = -14/-7 = 2

Thus, x=2

Putting the value of x in eq.(ii), we get

2×2 + 2y = 2

2y = 2-4

2y = -2

y = -1

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The missing term is "zero" for the given equation.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles. There are two types of supplementary angles.

As per the given figure, the required solution would be as:

8x - 3 + 4x + 3 = 180

Rearrange the likewise terms and apply the arithmetics operation,

12x + 0 = 180

We know that the sum of 3 and -3 is 0.

Compared to the given equation, we get the missing term as zero.

Thus, the required value is 0.

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The mathematical relationship between force and work is that Work = Force x Distance.

The mathematical relationship between force and work is that Work is equal to the Force multiplied by the Distance. In other words, the work done by a force is equal to the force multiplied by the distance over which the force is applied. This can be expressed as the equation W = F x D, where W is the work, F is the force and D is the distance. This equation means that the amount of work done is proportional to the force applied and the distance over which it is applied. Thus, if the force is doubled, the work done will also double, and if the distance is doubled, the work done will also double. This equation can also be used to calculate the force required to do a certain amount of work. For example, if it is known that a certain amount of work must be done, then the equation can be rearranged to calculate the force needed to do that work.

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Answer:

Step-by-step explanation:

blb

Answer:

Step-by-step explanation:

1/6 attended in the morning.

1/3 attended in the afternoon.

1/6 + 1/3

1/6 + 2/6 = 3/6

3/6, or 1/2 attended in the morning and afternoon combined.

a) If 1/2 attended in the morning and afternoon combined, then the other 1/2 attended in the evening.

b) 1/2 of 30 = 15, so 15 parents attended in the evening.

The number of downloads that make site A the better deal is 31 downloads

An equation shows the relationship between numbers and variables in an expression.

Let y represent the total cost of download for x downloads.

For site A, there is a flat rate of $29 per month plus $0.80 per download, hence:

y = 0.8x + 29

For site B, there is a flat rate of $17 per month plus $1.19 per download, hence:

y = 1.19x + 17

For site A to be better then the total cost should be lower:

0.8x + 29 < 1.19x + 17

-0.39x < -12

x > 30.8

It would take 31 downloads for site A to be the better deal

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