Rahul is deciding between two parking garages. Garage A charges an initial fee of $12 to park plus $4 per hour. Garage B charges an initial fee of $6 to park plus $5 per hour. Let AA represent the amount Garage A would charge if Rahul parks for tt hours, and let BB represent the amount Garage B would charge if Rahul parks for tt hours. Write an equation for each situation, in terms of t,t, and determine which garage would be cheaper if Rahul needs to park for 10 hours.

Answer:

the first 3 terms are 3 9 19

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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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 However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid.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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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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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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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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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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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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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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The business college wants to determine the proportion of business students who have extended time between classes. The p value for two tailored test was 0.0124

Let p represent the percentage of business students who own laptops.

As said, we must conduct the exam.

The test is a two-tailed test because the alternative hypothesis has two tails.

We presume that a normal distribution would apply in this situation.

We employ the z-test for proportion.

The two-tailed test's P-value is 2P(Z>|z|)=2P(Z>|2.5|).

=2P(Z>2.5)=2(1-P(Z<2.5)) P(Z>z)=1 - P(Zz)

=2(1-0.9938) Z-table, by

= 2(0.0062) (0.0062)

= 0.0124

Consequently, the two-tailed test's p-value was 0.0124.

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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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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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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

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 rational root theorem is the representation of the finding rational solution of the given polynomial function.

As given in the question,

Therefore, the rational root theorem is the representation of the finding rational solution of the given polynomial function.

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In order to understand all properties of an equilateral triangles we will take a traingle ΔABC and let the side length be a,b,c and angle measures be α, β and Ф.

1. All 3 side of an equilateral triangles have same length .

   so as mentioned a=b=c.

2. All 3 angles of an equilateral triangles have same measure.

   so α=β=Ф , which shows that all angles measures same.

3. Each angles of an equilateral triangles is [tex]60^0[/tex].

4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4}*a^2[/tex]

5 . Perimeter of an equilateral triangles = 3*a

6. Any two triangle sides can add up to a length that is longer than the third side.

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Answer: ruler

Step-by-step explanation:

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).

Answer:

Step-by-step explanation:

(5x )4 +(5x )3 = (10x)12

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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When a person registers for SSS membership in any capacity, he/she becomes a member for life. Thus, withdrawal of membership is not possible.

Once you become a covered SSS member, you become a member for life. The contributions that you remit become savings for the future that will serve as the basis for the granting of social security benefits in times of contingencies. Membership cannot be withdrawn and contributions paid cannot refund.

Workers in the private sector are covered by social security under the Social Security System (SSS). In the event of a worker's passing, disability, illness, pregnancy, or old age, social security provides replacement income. The Social Security Act of 1954 went into effect on September 1st, 1957.

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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?

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: Yes, you will make it on time

Step-by-step explanation:

The distance from San Antonio to Dallas is 274 miles

We take 274 divided by 65 = 4.2 hours or 4 hours and 12 minutes to get there at the speed of 65 mph

We have 4 1/2 hours to get there

4 1/2 hours = 4 hours 30 minutes

So, you will make it on time!

Let x be the speed of Santa's sleigh in still air and y be the speed of the wind. We can use the formula d = rt, where d is the distance traveled, r is the speed at which the sleigh is traveling, and t is the time elapsed, to find x and y.

For the first case, where Santa is flying with the wind, the distance traveled is 35 miles, the time elapsed is 5 minutes, and the speed of the sleigh is x + y. Since there are 60 minutes in an hour, the time elapsed in hours is 5 minutes / 60 minutes/hour = 1/12 hours. So, we can write the equation 35 miles = (x + y) * (1/12 hours). Solving for x + y, we get x + y = 35 miles / (1/12 hours) = 420 miles/hour.

For the second case, where Santa is flying against the wind, the distance traveled is 35 miles, the time elapsed is 7 minutes, and the speed of the sleigh is x - y. Since there are 60 minutes in an hour, the time elapsed in hours is 7 minutes / 60 minutes/hour = 7/60 hours. So, we can write the equation 35 miles = (x - y) * (7/60 hours). Solving for x - y, we get x - y = 35 miles / (7/60 hours) = 300 miles/hour.

We can solve for x and y by equating the expressions for x + y and x - y and then solving for x and y. Since x + y = 420 miles/hour and x - y = 300 miles/hour, we can add these equations together to get 2x = 720 miles/hour. Dividing both sides of the equation by 2, we get x = 360 miles/hour. We can then substitute this value for x into the equation x + y = 420 miles/hour to solve for y, giving us y = 420 miles/hour

Answer:

1.3

Step-by-step explanation:

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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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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