50 Points
What is the best approximation of the solution to the system to
the nearest integer values?
O(7, -2)
O(-2, 6)
O (6, -2)
O(-2,7)

Answer:

Step-by-step explanation: You want to figure out how much it costs per ounce. You’ll divide $4.50/18 ounces to get $0.25 per ounce for the 18 ounce bag and $8.80/40 ounces to get $0.22 per ounce for the 40 ounce bag. The 40 ounce bag is cheaper per ounce.

a. The equation that represents the given data is y = 700x + 2,000.

b. The average daily attendance at Disneyland on its 80th anniversary is 58,000.

We are given the data about average daily attendance at Disneyland's anniversary celebrations. At Disneyland's 40th anniversary, the average daily attendance was 30,000 people. On the 60th anniversary, the average daily attendance was 44,000 people. We need to create an equation that would represent y, the average daily attendance, based on x, the number of years after Disneyland opened.

We can write the data in the form of points on the coordinate axes. The coordinates of the points are (40, 30,000) and (60, 44,000). We can use the two-point form to write an equation.

(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)

(y - 30,000) = [(44,000 - 30,000)/(60 - 40)]*(x - 40)

(y - 30,000) = [(14,000)/(20)]*(x - 40)

(y - 30,000) = (700)*(x - 40)

y = 700x - 28,000 + 30,000

y = 700x + 2,000

Now, we need to find out the average daily attendance at Disneyland on its 80th anniversary.

y = 700*80 + 2,000

y = 56,000 + 2,000

y = 58,000

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If shipments increased by 7% (which is the same as 0.07) per year, then the shipment in a year can be found by multiplying the shipments in the previous year by 1.07.

Therefore, if [tex]x[/tex] represents the number of years since 2000 and [tex]f(x)[/tex] represents the number of shipments, then [tex]f(x)=3173000(1.07)^x[/tex].

1. Translation; y= f(x) + 2

2. Reflection; y= -f(x)

3. Stretch; y= 2f(x)

4. Shrink; y= 1/2 f(x)

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

Given:

When f(x) shifts 2 units up, we have

y= f(x) + 2; Translation

When the graph of f(x) to a symmetric position on the opposite side of the x-axis

y= -f(x); Reflection

When it stretches f(x) by a factor of 2

y= 2f(x); Stretch

When it reduces f(x) by a factor of 1/2

y=  1/2f(x); Shrink

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The value of the variable r in 6r+ r- 4 will be 4/7.

Given,

To solve the polynomial,

6r + r- 4,

and find the value of the variable r,

we have to convert the polynomial in to a quadratic equation by equating it with 0, or, in other words, making the polynomial equal to zero.

So, the quadratic equation will be,

6r + r- 4 = 0

=> (6r+ r) -4 =0

=> 7r -4 = 0

=> 7r = 4

=> r = 4/7.

Thus, the value of the variable r in the polynomial 6r + r -4 will be 4/7.

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The value of the missing interior angle is 25°

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

given angles of the triangle, 90° and 65°

Let, the unknown angle be x

so that,

x + 90 + 65 = 180 ( sum of angles in a triangle)

x + 155 = 180

x = 180 - 155

x = 25°

In conclusion, the unknown angle is 25°

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Answer:

(a) $2.40

(b) Chips: 4/7

Drink: 3/7

(c) $9.60

Step-by-step explanation:

Polly buys a drink at a convenience store for $1. 80. She also buys a bag of chips.

(a) The ratio of the cost of the chips to the cost of the water is 4:3. Find the cost of the chips.

chips : water = 4 : 3

chips/water = 4/3

c/1.8 = 4/3

3c = 1.8 × 4

c = 0.6 × 4

c = 2.4

$2.40

(b) Polly has $6 to spend. Work out the total amount she spends on a drink and chips as a fraction of the $6. Give your answer in its lowest terms.

4 + 3 = 7

Chips: 4/7

Drink: 3/7

(c) The $6 is 37. 5% less than the amount Polly had to spend last week. Calculate the amount she had last week.

Last week it was 100%.

This week it is 37.5% less.

100% - 37.5% = 62.5%

This week, it is 62.5% of last week.

Let x = last week's amount.

62.5% of (last week's amount) = $6

62.5% × x = 6

0.625x = 6

Divide both sides by 0.625

x = 6/0.625

x = 9.6

$9.60

The angle formed by 7th Avenue and Broadway at The Shake Hut's corner measures 126°.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

If we consider x to be the angle opposite the Pizza Palace, then x = 54°

Also:

The snake hut plus x equals 180

54 plus The Snake Hut = 180

126° is the snake hut.

The angle formed by 7th Avenue and Broadway at The Shake Hut's corner measures 126°.

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The distance of segment AX sis found to be 8.6 units using the distance formula.

Given: A(-4, 5), X (1, −2)

We need to find the distance of the segment AX.

Distance of AX is given as :

[tex]\sqrt{[1-(-4)]^{2} + [-2-5]^{2} } \\= \sqrt{25 + 49}\\ = \sqrt{74}\\ =8.6[/tex]

Therefore, the distance of segment AX sis found to be 8.6 units using the distance formula.

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Answer:

10.8 cm

Step-by-step explanation:

To solve this answer, we should use sine law.

[tex]\frac{SinA}{a}[/tex]=[tex]\frac{SinB}{b}[/tex]

[tex]\frac{Sin40}{7}[/tex]=[tex]\frac{Sin81}{x}[/tex]   (cross multiply)

xSin40 = 7Sin81

xSin = [tex]\frac{7Sin81}{40}[/tex]

x= [tex]\frac{7Sin81}{Sin40}[/tex]

x= 10.8 cm

By using function, it can be calculated that

The value of f(8, 9) is 73

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the function is

f(a, b) = ab - (a - b)

f(8, 9) = 8 [tex]\times[/tex] 9 - (8 - 9)

f(8, 9) = 72 + 1

f(8, 9) = 73

So the value of f(8, 9) is 73

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The expression that shows the distance you would drive from the library to the grocery store along this road is; |-5|+|7|

An absolute value inequality is defined as an expression that has absolute functions as well as inequality signs. For example, the expression |x + 5| > 1 is an absolute value inequality that contains a greater than symbol.

Now, from the inequality line graph attached, we see that the point of the library is at -5 on the line graph.

Similarly, we also see that the point of the grocery store which i will liken to the maths class is at the point 7.

Thus, the distance between both points when we take absolute values into consideration is; |-5|+|7|

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Answer:

x/2 = any number

Step-by-step explanation:

Answer:

Step-by-step explanation:

Put the value of a in equation 2. b² = 6² + a². b² = 36 + (81 / 4 ). b = √(225 / 4). b = 15 / 2. Therefore, the value of a and b will be 9.

Answer:

-18 + -5

Step-by-step explanation:

Because -18 - 5 is an inverse equation, that means that we are doing one equation that looks like something it usually doesn't. When subtracting a negative and a positive in that order, the result will be the sign of the greater value(-18), so the result will be negative. Subtracting a big number that's a negative by a smaller number that's a positive is the same as adding the same numbers together as if they are both negatives. E.g, -4 - 2 = -4 + -2.

Hope this helps!

Answer:8r squared -16

Step-by-step explanation:

A monomial function that has a minimum value is y = 5x^10

In this question, we have been given four monomial functions.

y = 5x^10

y = -4x^11

y = -x^12

y = 6x

we need  to find a monomial function that has a minimum value.

For function y = 5x^10, as x > 0 increases, f(x) increases. And as x < 0 decreases, f(x) increases.

We know that for even, positive monomial function if coefficient > 0 and exponent is even then a monomial has a minimum value.

Therefore, a monomial function that has a minimum value is y = 5x^10

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The tuition does not appear to have an association with graduation rate.

A scatter plot is a particular kind of plot or mathematical diagram that displays values for generally two variables for a collection of data. It uses Cartesian coordinates. A dot is used to symbolize each point on the scatter plot. It is used to demonstrate the link between the dots by illustrating how many of them would fall within the path of a straight line.

It is clear that there is no relation between tuition and graduation rate. Some selective colleges may have higher tuition and higher graduation rates but there may be some selective colleges with higher tuition but lower graduation rates.

Hence, the tuition does not appear to have an association with graduation rate. Option 2 is correct.

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Answer:

I think it's A- Higher tuition causes students to graduate at higher rates.

Step-by-step explanation:

tell me if I'm wrong...  forgive me if i am

The sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954

What is Pythagoras's theorem?

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle or in standard algebraic notation, a² + b² = c², is equal to the squares on the legs.

What is the sum of numbers?

The outcome or conclusion we arrive at when we add two or more integers is known as the sum. Addends are the numbers that are added.

Here, we calculate the sum of the given numbers

= (1³)^²⁰  +  (1³)²⁰  +  (2³)²⁰  +  (-2³)²⁰

= 2,305,843,009,213,693,954

Hence, the sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954.

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Answer:

Yes

Step-by-step explanation:

3:12 both have a common factor of 3 you divide both sides by 3 to get 1:4

If a coin is weighted so that the probability of heads is five times the probabily of tails, that means :

+) P(head) + P(tail) = 1
+) P(head) = 5P(tail)

Therefore, P(head) = 5/6 ; P(tail) = 1/6

For both head and tail to be flipped, the events must happen together.

Therefore, we have the probabilty that both head and tail is flipped = 5/6 x 1/6 = 5/36.

The three posts can be given in 4080 ways among 17 students.

It is given that the number of people available to choose the posts from is 17.

There are three posts here- president, vice president, and secretary.

Now, if we choose a candidate for President first, there are 17 students available.

Next, if we select a Vice-President, there are 16 ways to select the vice-president, since one student already is the president.

At, last there are 15 students available to choose the secretary from as two students already hold a post.

Hence, the number of ways to select the President, Vice-President, and Secretary are-

17 X 16 X 15 ways

Therefore we get

4080 ways.

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Perimeter of the parallelogram is 20 units.

According to question,

3 + x = 2a - 4

     x = 2a - 4 - 3

    x = 2a - 7

Diagonals in a parallelogram bisects each other.

Therefore, 2a - 7 = 3

                       2a = 3 + 7

                       2a = 10

                          a = 10/2

                          a = 5

a - 1 = 4b - 6

5 - 1 = 4b - 6

    4 = 4b - 6

  4b = 4 + 6

   4b = 10

     b = 10/4

     b = 5/2

Opposite sides of a parallelogram are equal.

Therefore, c - 2 = 2b

                  c - 2 = 2(5/2)

                  c - 2 = 5

                       c = 5 + 2

                       c = 7

Sides of parallelogram,

Side 1 = 12 - c

          = 12 - 7

          = 5

Side 2 = c - 2

           = 7 - 2

           = 5

Perimeter of parallelogram = 2(length of side 1 + length of side 2)

                                             = 2(5 + 5)

                                             = 2 * 10

                                             = 20

Hence, perimeter is 20 units.

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The correct multiplication of 1.8 and 2.4 will be 4.32.The product 0.432 calculated by Maura was incorrect.

For the given question-

Maura divide 1. 8 by 2. 4 and enter 0. 432 as the result.

Tom claims her product is unreliable.

Tom is able to make this deduction without the need for multiplication because the value 0.432 is less than even 1.8, which is not conceivable.

Thus,when multiplying by a number bigger than 1, the result will always be greater than the starting numbers.

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The exact values of the six trigonometric functions for the point (x, y) = (20, 21) are listed below:

sin θ = 21 / 29, cos θ = 20 / 29, tan θ = 21 / 20, cot θ = 20 / 21, sec θ = 29 / 20, csc θ = 29 / 21

Points in rectangular format are points of the form (x, y), where x and y represent the position of the point respect to the origin and along the respective orthogonal axis.

The line segment between the origin and that point represents the hypotenuse of a right triangle. Then, we can determine the six trigonometric functions by using the following formulae:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

If we know that x = 20 and y = 21, then the exact values of the trigonometric functions are:

sin θ = 21 / √(20² + 21²)

sin θ = 21 / 29

cos θ = 20 / √(20² + 21²)

cos θ = 20 / 29

tan θ = 21 / 20

cot θ = 20 / 21

sec θ = √(20² + 21²) / 20

sec θ = 29 / 20

csc θ = √(20² + 21²) / 21

csc θ = 29 / 21

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Answer:

1710 grams (not on the answer list)

Step-by-step explanation:

The total weight of the 4 packages is 3.8 pounds (lbs). The conversion factor is (0.45 kg/lb).

(3.8 lbs)*((0.45 kg/lb) = 1.71 kg or 1710 grams. Pease check the numbers provided.