At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys.

r + f ≥ 16

4r + 2f ≤ 40

A graph shows r on the x-axis, from 0 to 18, and f on the y-axis, from 0 to 20. Two solid lines are shown. The first line has a negative slope and goes through (0, 20) and (10, 0). Everything to the left of the line is shaded. The second line has a negative slope and goes through (0, 16) and (16, 0). Everything above the line is shaded.
What is the maximum number of ride tickets she can buy?

4
6
10
12

Answer:

a. 0, -6, -18, -21, -90

b. 3, 0, -6, -18, -42

c. A starting point of any number ≥ 6 will result in a sequence of positive values

Step-by-step explanation:

Here the sequence is governed by the rule:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
[tex]\textsf {where $a_n$ is the nth term and $a_{n-1}$ is the previous term}}[/tex]

1) Starting with a₁ = 0 we get
a₂ = 2(a₁ - 3) = 2(0 - 3) = -6
a₃ = 2(a₂ - 3) = 2(-6 -3) = 2(-9) = -18
a₄ = 2(a3 - 3) = 2(-18 - 3) = 2(-21) = -42
a₅ = 2(a₄ - 3) = 2(-42- 3) = 2(-45) = -90

So the first 5 numbers in the sequence starting with 0 are:
0, -6, -18, -21, -90

2) I will approach this slightly differently

We have the relationship:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]

Expanding the brackets we get
[tex]\sf a_{n} = 2a_{n-1} - 6[/tex]

We have a₁ = 3
a₂ = 2(a₁) - 6 = 2(3) - 6 = 6 - 6 = 0
a₃ = 2(a₂) - 6 = 2(0) - 6 = -6
a₄ = 2(a₃) - 6 = 2(-6) - 6 = -18
a₅ = 2(a₄ ) - 6 = 2(-18) - 6 = -42

The sequence starting with 3 is:
3, 0, -6, -18, -42

Both methods work exactly the same, some students find expanding the brackets easier to deal with

c. We can see that as a₁ increases, the number of negative numbers decreases by 2. So, in order for all numbers to be positive (> 0) we should start with a sufficiently large number so that all numbers are positive

The smallest such number is 6.
When a₁ = 6, the sequence is all 6s because
a₂ = 2(6) - 6 = 12 - 6 = 6

So the next number is a₃ = 12(6) - 6 = 6 and so on

So any starting point ≥ 6 will yield positive values. At 5 the sequence would be: 5, 4, 2, -2, -10 so starting point of 5 will not work

Answer:

Step-by-step explanation:

Both cyclist are moving apart at a speed of 9.434 mi/hr.

Velocity is the direction at which an item is moving and serves as a measure of the rate at which its location is changing as seen from a certain point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a basic idea. A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI (metric system).

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Answer:

C. [tex] \frac{ - 15x - 53}{ {x}^{2} + 8x + 15 }≥ 0[/tex]

Step-by-step explanation:

See attached image for explanation

The bat colony will cover an area of 80,000 square miles in 1.612 hours.

A circle is the collection of all the points together in plane that are equally distant from the a given point known as the circle's center. A circle is represented by the symbol. A radius of a circle is a line segment that connects the center of a circle toward any point on the circle.

Now, as per the given question;

The area covered (A) by the colony, evaluated in square miles, is depicted by the mentioned geometrical formula as the bat colony emerges from a cave & spreads out in a circular pattern:

A = π R²

R = the bat's distance from the cave, calculated in miles.

Furthermore, each bat moves at a constant speed, and distance is depicted by the following kinematic formula:

R = r₀ + rΔt

r₀ = The bat's initial distance from the cave, estimated in miles.

r = Bat speed, estimated in miles per hour.

Δt = Time, expressed in hours.

Substitute the value of R in the formula of area.

A = π (r₀ + rΔt)²

(r₀ + rΔt)² = A/ π

(r₀ + rΔt) = √(A/ π)

rΔt = √(A/ π) - r₀

Δt = (√(A/ π) - r₀)/r

r =  99 miles per hour

The distance between the bat and the cave has now been substituted, and time has been cleared:

A = area of 80,000 square miles

π = 3.14

r₀ = 0 miles per hour

Substituting all the values in the A we calculate the time.

Δt = (√( 80,000/3.14) - 0)/99

On solving;

Δt = 1.612 (approx)

Thus, It will take 1.612 hours for the bat colony to cover an area of 80,000 square miles.

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The complete question is-

The Brazilian free-tailed bat can travel 99 miles per hour. after sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. how long before these bats cover an area of 80,000 square miles? use pi = 3.14.

By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.

According to the statement, we have the equation of a fraction and we need to find the expression by simplify the former expression. In this situation we must use factor decomposition and algebra properties to make simplification effective:

42 / 49                           Given

(2 × 3 × 7) / (7 × 7)          Factor decomposition

(2 × 3) / 7 × (7 / 7)           Commutative and associative properties / Multiplication of fractions

6 / 7 × 1                           Definition of division / Existence of the multiplicative inverse

6 / 7                                 Modulative property / Result

By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.

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Answer:

he uses 2.33333333333 amount of walnuts in each muffin

Step-by-step explanation:

14 divided by 6 = 2.33333333333

Have a nice day!

The first five term of the sequence are 42, 35, 28, 21 and 14.

According to the given question.

We have a rule for finding the terms of a sequence i.e. [tex]a_{n} = a_{n-1} -7[/tex].

Also, the first term of the sequence is a1 = 42

Therefore,

The second term of the sequence is given by

Second term [tex]a_{2}[/tex] = [tex]a_{1}[/tex] - 7

⇒ Second term = 42 - 7 = 35

Similarly,

The third term of the sequence, [tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 7 = 35 - 7 = 28

Fourth term of the sequence = 28 - 7 = 21

Fifth term of the sequence = 21 - 7 = 14

Hence, the first five term of the sequence are 42, 35, 28, 21 and 14.

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Answer:

answer is ((1 × 2) + 3) × 4 × 5 + 6 - 7 - 8 + 9 = 100

The numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.

The largest factor of the two numbers which divides both the numbers is called as greatest common factor or GCF. In other words, the greatest common factor is the largest positive number which can be divided into given numbers evenly.

Given the number is 7 the pair of numbers having the greatest common factor is calculated below:-

For pairs 7 and 14. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 14.

Similarly for pairs 7 and 28. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 28.

Therefore, the numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.

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By definition of vertical angles, the value of the variable x behind the geometric system is equal to 12. The measure of the labeled angle is 48°.

The image shows a geometric system generated by two non-parallel lines that intersect each other and consequently two pairs of vertical angles are therefore created. In geometry, two vertical angles are opposite to each other and have the same measure. Then, the following mathematical relationship is found:

4 · x = 48

In addition, we must clear the variable x within the equation:

4 · x = 48                                   Given

x = 48 / 4                                   Compatibility with multiplication / Commutative, associative and modulative properties / Existence of multiplication

x = 12                                         Definition of division / Result

The value of the variable x behind the geometric system is equal to 12.

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An unreliable study can occur if the test administration is inconsistent

Consistency is the key to success in anything and it implies to the studies and surveys as well. If you want the results of the study to be reliable, then you must be consistent in test administration.

Inconsistency can lead to various issues like improper representation of the feedback which may alter the results. This can lead to various problems.

For example, test performed at certain time may have a different set of people and absence of periodic tests can accommodate feedback from irrelevant people.

Therefore, a proper set schedule must be followed for the tests with consistency.

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We get the age of Jack is 29 years and the age of Jill is 16 years.

We are given that the sum of Jack's age and Jill's age is 45 years.

Let Jack's age be x.

Let Jill's age be y.

x + y = 45

x = 45 - y

Now, we are also given that jack's age next year will be twice Jill's age last year.

Jack's age next year = x + 1

Jill's age last year = y - 1

ATQ, We get the equation as:

x + 1 = 2( y - 1)

x + 1 = 2 y - 2

x = 2 y - 2 - 1

x = 2 y - 3

We get that:

45 - y = 2 y - 3

2 y + y = 45 + 3

3 y = 48

y = 48 / 3

y = 16 years.

x + y = 45

x + 16 = 45

x = 45 - 16

x = 29 years.

Therefore, we get the age of Jack is 29 years and the age of Jill is 16 years.

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Answer: 24

Step-by-step explanation: first we can rewrite the expression as 170%*x=40.8 (x is your answer). By solving and simplifying it, you should get 24.

the variable(s) x have a value of 13.

A variable is any property, amount, or number that can be measured or counted. A data item is another name for a variable. Age, sex, business income and expenses, place of birth, capital expenditures, class grades, eye color, and car kind are only a few examples of variables.

A variable is a value that could change based on the details of an experiment or the parameters of a mathematical problem. A variable is typically identified by a single letter. The letters x, y, and z are the universal symbols for variables that are most frequently employed.

According to given value ;

4x+(7x+37)=180

sum of three angle equal to 180

4x+7x+37=180

4x+7x=180-37

11x=143

x=143/11

x=13

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Answer: B

Step-by-step explanation:

Answer:

23200

Step-by-step explanation:

After you depart jblm you will be the closest to mt. rainier after 4 minutes 35.5 seconds

The distance from JBLM to Mt. Rainier is found using the Pythagorean theorem:

 d = √((56 km)² +(40 km)²) = 8√74 km

The bearing from JBLM to Mt. Rainier is ...

 arctan(40/56) ≈ 35.538°  . . . . .  south of east

The heading of the airplane to its destination is ...

 arctan(289/218) ≈ 8.393°  . . . . .  south of east

Then the difference between these angles is ...

8.393° - 35.538° ≈ -27.145°

and the distance to the point of closest approach is ...

 8√74×cos(-27.145°) ≈ 61.238 . . . . km

The relation between time, speed, and distance is ...

 time = distance / speed

Then the time from JBLM to the point of closest approach is ...

 time = (61.238 km)/(800 km/h) ≈ 0.07654819 h ≈ 4.5928 minutes

≈ 4 minutes 35.5 seconds

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i think the answer is 3/10

The number is 5, the equation used is [tex]x^{2}[/tex] - x - 20 = 0

Let x be the number which is between 1 to 10.

From the question we get to know the equation:

(x-3)(x +2) = 14

x(x+2) -3(x+2) =14

[tex]x^{2}[/tex] +2x -3x - 6 =14

[tex]x^{2}[/tex] - x - 6 =14

[tex]x^{2}[/tex] - x - 20 = 0

This is the equation used to solve for Kevin's number.

Now we have to find the value of x.

[tex]x^{2}[/tex] - 5x + 4x -20=0

x(x-5) + 4(x-5) = 0

(x-5)(x+4) = 0

x = 5, -4

Hence we get two values of x which is 5, -4. But we have to find the number between 1 and 10.

Hence from the value of 5 and -4 , the number is 5 which is between 1 and 10 as -4 is not in the range of 1 to 10.

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The complete question is:

a number from 1 to 10. the product of 3 less than this number and 2 more than this number is equal to 14. which equation could be used to solve for kevin's number, x?

a) [tex]x^{2}[/tex]- x - 6 =0

b) [tex]x^{2}[/tex] - x - 20 = 0

c) [tex]x^{2}[/tex]- 6x + 14 =0

d) [tex]x^{2}[/tex] - x + 8 = 0

Answer:

5 miles

Step-by-step explanation:

distance = rate times time

distance = (10 miles per hour)( 30 minutes)  30 minutes is equal to 1/2 hour

distance = [tex]\frac{10 miles}{hour}[/tex] [tex](\frac{1 hour}{2} )[/tex]  You can cancel words, like like cancelling numbers  The hours cancel out and you are left with [tex]\frac{10 miles}{2}[/tex]  which is equal to 5 miles.

Answer: 5 miles

Step-by-step explanation:

Jim runs 10 miles per hour, and 30 minutes is half an hour, so divide 10 by 2.

Using a linear function, it is found that:

A linear function is modeled by the following rule:

y = mx + b

In which:

From the table, we have that:

Hence, we have that when x = 0, y = 45, meaning that:

The y-intercept is of 45.

When x increases by 5, y decays by 8, hence the slope is given as follows:

m = -8/5 = -1.6.

Then the function is:

y = -1.6x + 45.

The x-intercept is found as follows:

-1.6x + 45 = 0

1.6x = 45

x = 45/1.6

x = 28.125.

The x-intercept is of 28.125.

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Answer:

-11x + 30

Step-by-step explanation:

distribute the 5 into the parenthesis

= 4x -15x + 30

combine like terms

= -11x + 30

Answer:

-11x + 30

Step-by-step explanation:

4x + 5(-3x + 6)  Distribute the 5

4x + (5)-3x + (5)6

4x -15x + 30 Combine the x's

-11x + 30

When Point Q is on line segment PR, if PQ=x,QR=6, and PR =2x-10, then the length of PR is 18 units

Given,

That point Q is on line segment PR

The length of PQ = x

The length of QR = 6

The length of PR = 2x-10

We know,

Point Q is on line segment PR

So, the length of the PR = Length of PQ + Length of QR

Substitute the values in the equation

2x-10 = x+6

2x-x=6+10

x=14

Substitute the value of x in the equation of the length of line PR

PR= 2x-10

=2×14-10

=28-10

=18 units

Hence, when Point Q is on line segment PR, if PQ=x,QR=6, and PR =2x-10, then the length of PR is 18 units

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Answer 5795

Step-by-step explanation:

A line segment has the endpoints as K and L that are (0,2) and (0,6).The  midpoint M is (0,4).

Given that,

The line segment has the endpoints as K and L that are (0,2) and (0,6).

The Formula for the Midpoint of a Line Segment

Let the line segment's termination point be ([tex]a_{1}[/tex], [tex]b_{1}[/tex]) and ([tex]a_{2}[/tex], [tex]b_{2}[/tex]) respectively. The following is the midpoint formula for a line segment connecting these two points:

(a,b)=[tex](\frac{a_{1} -a_{2} }{2}, \frac{b_{1} -b_{2} }{2} )[/tex]

Where

[tex]a_{1} =0,b_{1} =2 \\and \\a_{2} =0,b_{2} =6[/tex]

[tex](a,b)=(\frac{0+0}{2},\frac{2+6}{2}) \\(a,b)=(0,4)[/tex]

Therefore, When the line segment with the endpoints k and L the midpoint M is (0,4).

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Answer: 28 feet

Step-by-step explanation: The ratio of length to width is 2:1. Add the 2 numbers and it will give you 3. Then, divide 84 by 3 and it will give you 28. Times this by 1 (as the ratio of the width is 1). This will give you 28.