A plane traveled 1092 miles to Riyadh and back. The trip there was with the wind. It took 6
hours. The trip back was into the wind. The trip back took 7 hours. Find the speed of the plane
in still air and the speed of the wind.

The equation of the ellipse with foci at ​(39​,0) and ​(-39​,0) and a constant difference of 30 is given as follows:

x²/39² + y²/9² = 1.

The equation of an ellipse of center (h,k) is given by the rule presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

In which:

The coordinates of the foci are given as follows:

​(39​,0) and ​(-39​,0).

The center is the midpoint of these two coordinates, hence:

The coefficient a is given as follows:

a = |39 - 0| = |0 - 39| = 0.

Considering the constant difference of 30, the constant b is given as follows:

b = a - 30 = 39 - 30 = 9.

Thus the equation of the ellipse is given as follows:

x²/39² + y²/9² = 1.

The problem asks for the equation of the ellipse with the given features.

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Negative infinity is an abstract concept used to describe a value that is lower than any other real number. It is not a direction, but rather an idea of an unlimited amount of negative numbers.

Negative infinity is an abstract concept used to describe a value that is lower than any other real number. It is not a direction, but rather an idea of an unlimited amount of negative numbers. Although it does not have a physical direction, it can be thought of as a direction that is always negative and decreasing without bound. This concept is often used in mathematics to compare values and calculate limits. For example, when graphing a function, negative infinity is often used as the lower bound on the x-axis. Negative infinity is also used to describe the behavior of certain equations when a variable approaches a certain value or when a denominator approaches zero. In these cases, the equation would approach negative infinity. Negative infinity is not a real number and cannot be used in calculations, but it can be used to compare values and describe the behavior of certain equations.

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After covering a distance of 160-mile rental cost of both company will become same.

Mathematical expressions with the symbols >,<, ≥ and ≤  are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. Inequalities are resolved using graphs and algebra. It is imperative that you practice the techniques described here a lot so they become second nature if you want to master them.

An inequality still exists if the same amount is added to both sides. The inequality still holds true if the same amount is subtracted from each side. An inequality still holds true if both sides are multiplied or divided by the same positive value. However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid. In actuality, the inequity is turned around.

Solving according to ques,

Let us represent distance covered be X miles.

$100+($0.30) X = $20 + ($0.80) X

subtracting $20 and ($0.30) X from both sides, we get

$80 = ($0.50) X

X = 160 mile.

So, rental costs for company will be same when bot the trucks will cover a distance of 160 mile.

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Inverse proportion is expressed by the equation x y = k or x = k/y. As a result, you can utilize the known values to get the constant k's value before applying this formula to determine all the other values.

Inverse Proportional Method Solutions

As one pair is always given, we may employ the equation to discover the unknown terms and so solve the problem.

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Tool dividing beats into two, three or four parts is called a simple meter.

A simple meter is a tool in music which divides beats into a number of two, three or four parts. A simple meter is of three types :

1. Duple - a meter which helps to divide a beat into 2 (i.e. into two parts).
2. Triple - a meter which helps to divide beats into 3(i.e. into three parts)

3. Quadruple - a meter which helps to divide beats into 4(i.e. into four parts).
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Duple - a meter which helps to divide a beat into 2 (i.e. into two parts).

Triple - a meter which helps to divide beats into 3(i.e. into three parts)

Quadruple - a meter which helps to divide beats into 4(i.e. into four parts).

If three angles of one triangle are congruent to three angles of another triangle then by the AAA similarity theorem, the two triangles are similar. Actually, you need only two angles of one triangle being congruent to two angle of the second triangle.

How to prove AAA Theorem?

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle automatically gives the third since the sum of angles in a triangle sums to 180 degrees (pi radians), i.e.,

C = π - A - B .

Prove:

Triangles ABC and DEF such that ∠A = ∠D; ∠B = ∠E; ∠C = ∠F

Δ ABC ~ ΔDEF

Construction : We mark point P on the line DE and Q on the line DF such that AB = DP and AC = DQ, we join PQ.

There are three cases :

Case ( i ) : AB = DE, thus P coincides with E.

⇒ AB = DE, BC = EF and AC = DF

Consequently, Q coincides with F.

AB BC CA

---- = ------ = ------

DE EF FA

Since the corresponding angles are equal, we conclude that Δ ABC ~ Δ DEF.

Case( ii ) : AB < DE. Then P lies in DE

In triangles ABC and DPQ,

Statements ------ Reasons

1) AB = DP- 1) By construction

2) ∠A = ∠D -2) Given

3) AC = DQ -3) By construction

4) ΔABC ≅ ΔDPQ -4) By SAS postulate

5) ∠B = ∠DPQ 5) CPCTC

6) ∠B = ∠E- 6) Given

7) ∠E = ∠DPQ- 7) By transitive property

( from above)

8) PQ || EF -8) If two corresponding angles are congruent then the lines are parallel

9) DP/DE = DQ/DF -9) By basic proportionality theorem

10) AB/DE = BC/EF- 10) By construction

11) AB/DE = AC/DF- 11) By substitution property

12) Δ ABC ~ Δ DEF - 12) By SAS postulate

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Out of 82, 58 tickets were sold to students and 24 tickets were sold to the adults for the musical.

How to solve an equation for x?

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

According to the given question:

Let the tickets sold to students be x.

Since total number of sold tickets are 82, the number of tickets sold to families will be 82 - x (that is 82 minus number of tickets sold to students)

Cost for one ticket for students is $3

So, the amount after selling tickets to students = 3x ---- 1)

Similarly, cost of one ticket for an adult is $5

Hence the amount after selling tickets to adults = 5(82 - x) ----- 2)

Total sales from selling tickets is $294

From equation 1) and 2)

3x + 5(82 - x) = 294

Solving for the value of x

3x + 410 - 5x = 294

2x = 410 - 294

2x = 116

x = 58

Therefore, out of 82, 58 tickets were sold to students and (82 - 58) = 24 tickets were sold to adults.

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Using the provided function and finding the values of input for which it will provide valid output values we can find the domain.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Yes. For instance, the set of all real numbers is the domain and range of the cube root function.

Choose the input values.

Exclude any real numbers that produce a negative value in the radicand because there is an even root. Solve for x by setting the radicand to be greater than or equal to zero.

The domain of the function is the solution(s). If at all possible, format your response as an interval.

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The required function obtained after solving f(g(x)) will be equal to 15x³ + 16. Hence, option C is correct.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the functions given in the question,

f(x) = 3x² + 16

g(x) = √5x³

Now, find the function f(g(x)).

f(g(x)) = f(√5x³),                     [g(x) = √5x³]

f(g(x)) = 3( √5x³)² + 16           [f(x) = 3x² + 16]

So,

f(g(x)) = 3(5x³) + 16

f(g(x)) = 15x³ + 16

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Answer:

f(g(x)) = 15x^3 + 16 dollars / hour

I answered the quiz and it's correct

Answer:

D. x=2, -2

Step-by-step explanation:

I think you're asking for the correct answer to the problem because all of the values for x won't work for the equation.

So all we have to do is simplify the equation to isolate x.

[tex]2x^2-8=0[/tex] (original problem)

[tex]2x^2=8[/tex] (add 8 to both sides)

[tex]x^2=4[/tex] (divide both sides by 2)

[tex]x=2, x=-2[/tex] (find the square root of both sides)

Note that x = ±2 and note just 2 because both [tex]2^2[/tex] and [tex](-2)^2[/tex] [tex]=4[/tex].

Hope this helped :D

Answer:

this answer can't be solved because there are two variables we need at least value of at least one variable

Answer:

y/x=2-x/y+2

Step-by-step explanation:

The solution of simultaneous equations 5x-3y=8 and 3x+Y=2 is (1,-1)

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form y=mx+c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

The given equations are:

5x-3y=8  ------(1)

3x+y=2   -------(2)

By solving the equations we get the points

Multiply equation(1) by 3 and equation (2) by 5 then we get

15x-9y=24

15x+5y=10

By solving the above equations we get x and y values.

-14y=14

y=-1

substitute y=-1 in equation(1) we get x value.

5x-3(-1)=8

5x=5

x=1

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1 Indexed means that the array elements are numbered starting at 0.

Array can be defined as a collection of elements of the same type placed in contiguous memory locations that can be individually referenced by using an index to a unique identifier also An array is a user defined data type consisting of an ordered set of elements of a single data type

Therefore add 1 to the array suppose an array contain elements  of 1, 2, 3, 4 then the array represents decimal number 1234 and hence adding 1 to this would result 1235.

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Answer: ruler

Step-by-step explanation:

According to the Angle-Angle-Side Postulate (AAS), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle. AAS congruence can be demonstrated with a few simple methods.

Triangles can be proved to be congruent using the methods SSS, SAS, ASA, and AAS, but SSA and AAA are invalid and cannot be utilized. The angle-angle-side theorem, or AAS, was discussed here. According to this theorem, triangles are congruent if two angles and any side of one triangle are congruent with two angles and any side of another triangle. An extension of angle-side-angle, or ASA, is this theorem.

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Answer:

x^2 + 4x - 2

Step-by-step explanation:

x - 4 = 0

x = 4

Use synthetic division:

4    |    1    0    -18    8   ==> 1=x^3,     0=0x^2,     -18=-18x

              +4   +16   -8

          1    4     -2,    0  ==> x^2 + 4x - 2 with no remainder

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The equation with values that will result in infinitely many solutions is 7x + 2(x + 5) = 7x + 2(x + 6)

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

7x+2(x+5)=

Rewrite properly

So, we have

7x + 2(x + 5) =

For the equation to have infinitely many solutions, then the variable part must be the same, while the constant part  must be different

So, we have

7x + 2(x + 5) = 7x + 2(x + k)

By comparison, we have

k = 5

This means that the value of k can be any real number except 5

So, we can make use of 7x + 2(x + 5) = 7x + 2(x + 6)

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Answer:

  at least 5

Step-by-step explanation:

You want to know the number of cups needed to contain 7/8 pitcher of water when each cup holds 3/16 pitcher.

The number of cups can be found by dividing the water quantity by the amount each cup holds:

  (7/8 pitcher)/(3/16 pitcher/cup) = 14/3 cups = 4 2/3 cups

Eve needs at least 5 cups to hold the amount of water in the bottle.

__

Additional comment

If every cup is filled to capacity, then the 5th cup will be 2/3 full. The number of cups can be any number greater than or equal to 5.

If you want, you can write an inequality relating the capacity of the cups to the amount of water:

  n(3/16) ≥ 7/8

  n ≥ 4 2/3 . . . . . . . . . where n is a counting number

  n ∈ {5, 6, 7, ...}

This more clearly shows that the number is not restricted to 5.

Answer:

Step-by-step explanation:

To rectify the errors using a suspense account, the following journal entries can be made:

i. Rs 3,000 received from a customer as an advance against order was credited to sales account.

To correct this error, we can make the following journal entry:

Debit Suspense Account 3,000

Credit Sales Account 3,000

ii. A sum of Rs 800 written-off as depreciation on machinery, were not posted to depreciation account.

To correct this error, we can make the following journal entry:

Debit Depreciation Account 800

Credit Suspense Account 800

iii. Purchase of a scooter was debited to conveyance account Rs 16,000. Firm charges 10% depreciation on vehicles.

To correct this error, we can make the following journal entries:

Debit Suspense Account 1,600

Credit Conveyance Account 1,600

Debit Depreciation Account 1,600

Credit Suspense Account 1,600

iv. Payment of Rs 500 to Mohan and Rs 600 to Sohan was made but Mohan was debited with Rs 600 and Sohan with Rs 500.

To correct this error, we can make the following journal entries:

Debit Suspense Account 100

Credit Mohan 600

Debit Sohan 500

Credit Suspense Account 100

v. Sales to X Rs 500 were posted to Y’s account

To correct this error, we can make the following journal entries:

Debit Y 500

Credit Suspense Account 500

Debit Suspense Account 500

Credit X 500

The leading coefficient is positive. So, the parabola is downward. Then the maximum value of vertex form will be negative 4.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = − x² + 2x − 5

Convert the equation into a vertex form. Then we have

y = − x² + 2x − 5

y = − x² + 2x − 1 − 4

y = − (x² − 2x + 1) − 4

y = − (x − 1)² − 4

The leading coefficient is positive. So, the parabola is downward. Then the maximum value of vertex form will be negative 4.

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The complete question is given below.

How do you find the maximum value of vertex form?

y = − x² + 2x − 5?

Answer:

1/13

Step-by-step explanation:

There are 4 cards that are a "3" in a deck of cards

3 of hearts, 3 of spades, 3 of clubs, 3 of diamonds

P( 3) = number of cards that are a "3" / total number of cards

P(3) = 4/52 = 1/13

Answer:

[tex]\frac{1}{13}[/tex] (one thirteenth)

1/13

Step-by-step explanation:

There's 4 of the card 3 in a deck. (3 of hearts, 3 of diamonds, 3 of clubs, 3 of spades.)

This means 4 of 52 cards are a 3, which makes the fraction [tex]\frac{4}{52}[/tex]. This is the probability.

This fraction can be simplified to [tex]\frac{1}{13}[/tex] by dividing the top and bottom by four. This is the final answer, since it is in the simplest form.

The expression in scientific notation expressed as 10³ is equivalent to the whole number 1000

Scientific notation is the mathematical representation of a number, based on a product of a number by another base 10, raised to an exponent that indicates where is the comma or what amount of zero has this, its form is:

a×10ⁿ

To know the value of the expression 10³, we will only add the number of zeros to the one as much as the exponent has

1 0 0 0

10³ = 1000

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Answer:

f(x)= √(x-a) +b

Step-by-step explanation:

parent function is y=√x. This has a domain and range of [0, ∞). The question asks what function transformations will move the domain to [a, ∞) and the range to [b, ∞).

Function transformations

To move the domain from [0, ∞) to [a, ∞) requires the function be translated 'a' units to the right. That transformation is accomplished by replacing x with (x-a) in the function definition.

To move the range from [0, ∞) to [b, ∞) requires the function be translated upward by 'b' units. This is accomplished by adding 'b' to every function value.

The net effect of these transformations is ...

  f(x) = √x   ⇒   f(x) = √(x -a) +b

If the angle is the opposite of the shorter of the two sides, there are two potential triangles. The perpendicular angle to the shortest side is the smallest angle.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The Latin word "angulus," which means "corner," is where the term "angle" originates.

When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °.

Acute, right, obtuse, and reflex angles are the other three significant types of angles.

360 degrees make up a circle.

A 720° angle indicates that the object has completed two full rotations.

There are two possible triangles if the angle is the opposite of the shorter of the two sides. The smallest angle is that which is perpendicular to the shortest side.

Therefore, if the angle is the opposite of the shorter of the two sides, there are two potential triangles. The perpendicular angle to the shortest side is the smallest angle.

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The  probability is 102.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Moderate Success     0.3 102.0 120 208.0

Failure                        0.4 102.0 10.0 100

Now, the probability

E(x) = [tex]\sum^3_i[/tex]= [tex]S_iP_i[/tex]

      = 102 x 0.3 + 102 x 0.3 + 102 x 0.4

      = 30.6 + 30.6 + 40.8

      = 102

Hence, the probability is 102.

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One pair of vertical angle are ∠1 and ∠4 ; ∠2 and  ∠3

One pair of adjacent angles are ∠1 and ∠2; ∠3 and ∠4; ∠1 and ∠3; ∠2 and ∠4.

One pair of supplementary angles are ∠1 and ∠2; ∠3 and ∠4.

What are vertical angles?

When two lines intersect, there are two vertical angles.

The vertical opposite angle of ∠1 is ∠4.

The vertical opposite angle of ∠2 is ∠3.

The vertical angles are ∠1 and ∠4; ∠2 and ∠3.

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end.

∠1 and ∠2 have similar vertex and side. ∠2 and ∠3 have similar vertex and side. ∠3 and ∠4 have similar vertex and side. ∠3 and ∠4 have similar vertex and side.

Angles that add up to 180 degrees are referred to as supplementary angles.

∠1 and ∠2 is linear pair, it supplementary angles.

∠2 and ∠4 is linear pair, it supplementary angles.

∠3 and ∠4 is linear pair, it supplementary angles.

∠1 and ∠3 is linear pair, it supplementary angles.

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A right circular cylinder's curved surface area is determined using the formula 2πrh square units.

a cylinder having two circular bases and a perpendicular line connecting the centers of the two bases.

The area with solely curved surfaces, omitting the top and bottom of the circle, is known as the curved surface area. The area of a 3D figure's solely curved portion is referred to as the curved surface area. In general, the meaning of the terms lateral surface area and curved surface area is the same. As an illustration, the lateral surface area of a cuboid is used, whereas the curved surface area of a cylinder is used when the top and base surfaces are left out.

A right circular cylinder's curved surface area is determined using the formula 2πrh square units.

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Answer:

the first 3 terms are 3 9 19

The percentage of children allergic to peanuts is 17.5%

The term 'per cent' means 'out of a hundred'. In mathematics, percentages are used like fractions and decimals, as ways to describe parts of a whole. When you are using percentages, the whole is considered to be made up of a hundred equal parts.

Given here, 200 children out of which 35 are allergic thus in percentage terms we have (35/200)×100 =17.5%

Hence, The percentage of children allergic to peanuts is 17.5%

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