Find the general form of the equation of a hyperbola with vertices at (-2, 5) and (6, 5) and foci at (-3, 5) and (7, 5). A. 16x2 - 9y2 - 160x + 36y - 508 = 0 B. 9x2 - 16y2 - 36x + 160y - 508 = 0 C. none of these D. 3x2 - 16y2 - 12x + 160y - 532 = 0

Answer:

164

Step-by-step explanation:

c = number of caps

t = number of t-shirts

c + t = 278

8c + 7t = 2110

   -7c - 7t = -1946

+   8c + 7t = 2110

-------------------------

      c         = 164

Answer: 164

-2W + 6 is The opportunity cost of 1 coconut is ½ bundle of firewood.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

For Alice:

In the amount of time it takes to gather a bundle of firewood, Alice could have gathered (1/2) * 6 = 3 coconuts. Thus, the opportunity cost of one bundle of firewood is 3 coconuts.

The opportunity cost of 12 coconuts is 4 bundles of firewood.

Alice can gather 12 coconuts in 8 hours. If she were to gather firewood instead during these 8 hours then she would be able to gather 4 bundles of firewood

Therefore, when she chooses to gather 12 coconuts she is giving up 4 bundles of firewood.

Denoting coconuts through C and firewood through W, we are able to discover the equation for the PPF through graphing directly, or through noting that if all time is spent amassing wood, she will be able to accumulate four bundles of wood, so the W intercept is four.

Since the opportunity cost of a bundle of wood is 3 coconuts, the coefficient on C will be -1/3.

Therefore, we have W = (-1/3)C + 4, or equivalently C = -3W + 12.

(Alice’s PPF is plotted below in the solution to part (c).)

For Bob:

Since Each bundle of firewood takes as long as gathering 2 coconuts, the opportunity cost of one bundle of firewood is 2 coconuts.

The opportunity cost of 1 coconut is ½ bundle of firewood. Repeating the procedure from before, we find Bob’s PPF can be expressed by either W

= (-1/2)C + 3 or C = -2W + 6.

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Complete question:

Alice has found herself on a desert island and must gather supplies to survive. Alice has 8 hours of useful stamina that she can use towards gathering firewood or coconuts. She finds that she can gather 1 bundle of firewood every two hours, or 6 coconuts every 4 hours.

a. In terms of the number of coconuts, what is the opportunity cost of 1 bundle of wood? What is the opportunity cost of 12 coconuts in terms of bundles of wood?

b. Draw a plot of and give an algebraic expression for Alice’s production possibility frontier (PPF). Measure coconuts on the horizontal axis and bundles of wood on the vertical axis.

Bob just crash-landed on the island too. He doesn’t have quite the stamina that Alice does so he can only work 6 hours a day. He finds that he can gather a bundle of wood in 2 hours or 1 coconut per hour.

The number of animals left in the wild after 4 years is approximately 306.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

We are using the concept of compound interest to solve the given problem.

The formula to find the final amount in compound interest is,

A = P (1 + r) ^t

Here P = 400

r = -6.5% = -0.065 (negative sign because the rate is decreasing)

t = 4 years

Substituting the values,

A =400 (1 - 0.065)⁴

  = 305.71 ≈ 306

Hence there will be 306 animals left in the wild after 4 years.

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Answer:

Below

Step-by-step explanation:

Convert football field to inches

   100 yd  * 36 in/yd = 3600 inches

now multiply by the conversion factor:

    3600 inches  *  2.54 cm / in = 9144 cm

The modification that would have to  result in a net worth of $100,000 is: adding $1,000 in credit card debt. Option D

They currently have $101,000 in assets.

We have the value of the automobile plus the value of the recreational vehicle.

110000+27000 = 137000

When the medical expenses are subtracted from the net assets, we have

137000-8700 = 128300

When the loan sum is subtracted from net value, we have

128300-80000 = 48300

Savings and net wealth together provide us

48300+5000 = 53300

Retirement money added to net worth gives us

53000+50000 = 103300

After deducting the credit card debt from net value, we have

103300-2300 = 101000

We deduct $1,000 from this to create $100,000. Therefore, choice D is the best one.

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Answer:

  (x+4)/(3x-3)

Step-by-step explanation:

You want to simplify the compound fraction ((x²/(x-1))/((3x²/(x+4)).

As with numerical fractions division by a fraction is the same as multiplication by its inverse. Common factors in the numerator and denominator cancel.

  [tex]\dfrac{\left(\dfrac{x^2}{x-1}\right)}{\left(\dfrac{3x^2}{x+4}\right)}=\dfrac{x^2}{x-1}\times\dfrac{x+4}{3x^2}=\dfrac{x+4}{3(x-1)}=\boxed{\dfrac{x+4}{3x-3}}[/tex]

Third side of a triangle is, 14.4

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Two sides of triangle are 8 and 12.

Now, By using Pythagoras theorem we get;

Let third side = x

⇒ x² = 8² + 12²

⇒ x² = 64 + 144

⇒ x² = 208

⇒ x = √208

⇒ x = 14.4

Thus, The third side = 14.4

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The odds of drawing a 9 card or a black card from a standard 52- card deck is [tex]\frac{7}{13}[/tex]

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A regular deck of cards contains 4 nines, therefore P(A) = [tex]\frac{4}{52}[/tex]

In a typical deck of cards, there are 26 black cards, hence P(B) = [tex]\frac{26}{52}[/tex].

When a card is both a 9 and black, there is overlap between the two events. Since there are only two such cards in a typical deck of cards, P(A and B) = [tex]\frac{2}{52}[/tex].

Using the P-formula (A or B),

P(A or B) = P(A) + P(B) (A and B)

P(A or B) = [tex]\frac{4}{52}+ \frac{26}{52} -\frac{2}{52}[/tex]

P(A or B) = [tex]\frac{28}{52} =\frac{7}{13}[/tex]

Therefore, the odds of drawing a 9 or a black card is [tex]\frac{7}{13}[/tex]

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Answer:

Step-by-step explanation:

The expression (2x + 3y)² - 9 can be fully factorised as follows:

(2x + 3y)² - 9 = (2x + 3y + 3)(2x + 3y - 3)

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

The expression is now fully factorised.

(-2, 64), (-1, 49), (0, 36), (1, 25) and (2, 16) are the ordered pairs of given equation.

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=x²-12x+36

y equal to x square minus twelve times of x plus thirty six.

Now let us find some values of x and y.

If x=-2

y=64

If x=-1

y =49

If x=0

y=36

If x=1

y=25

If x=2

y=16

Hence, (-2, 64), (-1, 49), (0, 36), (1, 25) and (2, 16) are the ordered pairs of given equation.

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Answer:

x - 6,5,7,9,4

y - 0,1,1,9,4

Step-by-step explanation:

Answer: Anand's salary after 10 years working for the company can be calculated as follows:

$60000 + $2000 * 10 = $60000 + $20000 = $80000.

To determine Anand's salary after t years working for the company, we can use the following formula:

$60000 + $2000 * t

So, if t is the number of years he has worked for the company, his salary after t years would be:

$60000 + $2000 * t.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the green one no

the red ones yes

The distance between each pair of letters in the word is given by the equation A = 5 inches

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance between each pair of letters be A

Now , the equation will be

Let the total distance of the wide banner be = 61 inches

Now , the word is given by { E , A , G , L , E , S }

The number of letters in the word = 6 letters

The width of each letter = 6 inches

So , the total length of all the letters = 6 x 6 = 36 inches

The remaining distance in the wide banner = total distance of the wide banner - total length of all the letters

On simplifying the equation , we get

The remaining distance in the wide banner = 61 - 36

The remaining distance in the wide banner = 25 inches

Now ,

The distance between each pair of letters = remaining distance in the wide banner  / 5 spaces

On simplifying the equation , we get

The distance between each pair of letters A = 25 / 5

The distance between each pair of letters A = 5 inches

Hence , the equation is A = 5 inches

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The best buy is at the campus canteen. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

According to mathematicians, all real numbers may be described by the four basic operations, often known as "arithmetic operations." The phrases quotient, product, sum, and difference are produced by the four mathematical operations of division, multiplication, addition and subtraction, respectively.

We are given that a can of tab costs Rs. 7.20 at Timber City.

So, the cost of 6 packs will be

6 (7.20) = Rs. 43.20

But, on promotion, the cost is Rs. 39.60.

So, the discount is

D = Rs. 43.20 - Rs. 39.60

D = Rs. 3.60

Similarly,

A can of tab in the campus canteen costs Rs. 7.50.

So, the cost of 6 packs will be

6 (7.50) = Rs. 45

But, on promotion, the cost is Rs. 39.

So, the discount is

D = Rs. 45 - Rs. 39

D = Rs. 6

Hence, the best buy is at the campus canteen.

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Answer:

1) The math curriculum typically includes components such as number sense, arithmetic operations, algebra, geometry, data analysis and probability, among others. Problem solving and procedural fluency are emphasized as important skills to develop. Students may also receive instruction on missed mathematical concepts from previous grades to ensure they have a strong foundation for future learning.

2) Some specific types of mathematical instruction that are promoted include hands-on and concrete learning experiences, use of real-world problems, direct instruction, cooperative learning, and using technology to enhance learning. Additionally, promoting a growth mindset and a positive attitude towards mathematics is also emphasized.

3) Some specific procedures used to teach basic mathematical instruction include direct instruction, visual aids such as graphs and diagrams, manipulatives and hands-on activities, scaffolding, and systematic review and practice. Teachers may also use questioning techniques to encourage students to think critically and develop their problem-solving skills.

Step-by-step explanation:

The relationship between x and y is y = x + 2

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

(1, 3), (2, 4), (3, 5) and (5, 7)

See attachment for the line

Using the above as a guide, we have the following:

The three other points are (6, 8), (7, 9) and (8, 10)

From the ordered pairs, we can see that

y is the sum of x and 2

This means that

y = x + 2

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The solution to the subtraction and addition of the given expressions are;

- 2x² + 9x - 23

3x² - 2x - 1

5y² - 7y + 5

(5x² + 3x - 9) - (7x² - 6x + 14)

= 5x² + 3x - 9 - 7x² + 6x - 14

= - 2x² + 9x - 23

(8x² - 11x + 6) + (-5x² + 9x - 7)

open parenthesis

= 8x² - 11x + 6 - 5x² + 9x - 7

= 3x² - 2x - 1

(14y² - 4y + 3) - (9y² + 3y - 2)

= 14y² - 4y + 3 - 9y² - 3y + 2

combine like terms

= 14y² - 9y² - 4y - 3y + 3 + 2

= 5y² - 7y + 5

Hence, the solution to the expressions are - 2x² + 9x - 23; 3x² - 2x - 1; 5y² - 7y + 5.

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The slope of the line with the first two points (0, 1) and (-7, -3) is equal to 4.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-3 - (-7))/(1 - 0)

Slope, m = 4/1

Slope, m = 4.

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The given  function  [tex]f(x)\left\{ \begin{array} { l } { \frac{1}{2}\left(x+4\right)-5 }\\{\ \ \ \ \ \ 3 } \end{array} \right.[/tex] can plotted on graph as given in the attachment.

Any relation in which each input has exactly one output is referred to as a function. To put it another way, the function outputs one value exactly for each input value. Because one is mapped to two different values, the graph above depicts a relation rather than a function. But if one were instead mapped to a single value, the relation above would become a function. Furthermore, output values could be identical to input values.

The function machine receives the input of the x-values. Following that, the function machine runs its operations and produces the y-values. Any function could be the one inside.

The given  function

So the graph of the above function will be plotted.

Hence The graph of the given function is potted below.

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The area of the composite shapes found using the formula for the area of a rectangle and the perimeter of the figure indicates that the solution to the puzzle is; AGIH

The area of a rectangle = The length of the rectangle × The width of the rectangle

The area and perimeter of the shapes can be found by considering the shapes as composite figures as follows;

Area of shape 1 = Area of the 8 by 5 rectangle - Area of the 2 by 2 square at the top middle portion

Therefore;

The area of shape 2 = Area of the 13 by 4 rectangle - Area of the 2 by 3 rectangle at the top middle part of the shape.

(The width of the open part at the top of the rectangle is (13 cm - 2 × 5 cm) = 3 cm)

The four letter code is therefore;

AGIH

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Answer: 5 miles

if they go 10 miles in one hour, they would only go 5 miles in one half-hour.

Step-by-step explanation:

10 miles in 60 min, so you half that for the miles and minutes

half of 10 is 5 and half of 60 is 30

The difference between the two populations will be 38466.22.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Compare the January 2014 values of 5422.53 to the values of 43888.75 in 2010.

The population difference is calculated as:-

Differnce = 43888.75 - 5422.53

Difference = 38466.22

Therefore, the difference between the two populations will be 38466.22.

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The range of the cigarette tax (in cents) for 50 selected states is 62.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The range of a given set of data is the difference between the largest value and the smallest value.

Given the data shown represent the cigarette tax (in cents) for 50 selected states

70,12,42,45,50,51,60,69,8,40,18

Required; The range

This is calculated as:

Range = highest - lowest

Range = 70 - 8

Range = 62

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Answer:

Below

Step-by-step explanation:

From - 5/6  to zero on the line is  5/6

  then go another 23/12        now add them

      5/6 + 23/12     must have common denominator to add fractions

   5 / 6 = 10 /12

                10/12 + 23/12 = 33/12    = 2 9/12 = 2 3/4 units

On solving the provided question, we can say that the expression will be

an = a + (n-1)d => 20.75 = 5 + (n-1)1.75 => n = 10

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

Given that

a=5

d = 1.75

an = 20.75

the expression will be

an = a + (n-1)d

20.75 = 5 + (n-1)1.75

15.75 = (n- 1) 1.75

n-1 = 15.75/1.75

n- 1 = 9

n = 10

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The Simple Interest on Principal amount: $1,000 is $100.

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.

Given:

Principal amount: $1,000

Interest rate: 10%

Time: 12 months

So, the Simple Interest

= P x R x T/100

= 1000 x 10 x 1 / 100

= 10000/100

= $100

and, Amount = P + I

Amount = $1100

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Answer:

t + 40 = 59

Step-by-step explanation:

We know

She has 59 tests to grade. So, it will be the total of the equation.

She already grades 40 on the tests.

t is the number of tests she has left to grade.

So, the equation is

t + 40 = 59

The values of the expression following the collection of like terms, rearranging and factoring are presented as follows;

1.1 4·x + 5·a + 3·a + x - 6 = 5·x + 8·a - 6

1.2. 6·a·b + 2·b - 16·a - 2 = 2·(3·a·b + b - 8·a - 1)

1.3. 1024000 : 360000 : 180000 = 256 : 90 : 45

1.4. 150 min : 3 hours = 5 : 6

A mathematical expression comprises of mathematical symbols, numbers and variable, properly arranged to represent a value.

The simplification of the expressions can be presented as follows;

1.1. 4·x + 5·a + 3·a + (x - 6)

The terms in the above expression can be rearranged as follows;

4·x + 5·a + 3·a + (x - 6) = 4·x + x + 5·a + 3·a - 6

4·x + x + 5·a + 3·a - 6 = 5·x + 8·a - 6

Therefore, whereby the expression in the question is; 4·x + 5·a + 3·a + (x - 6), we get;

1.2. Whereby the possible expression in the question is; 6·a·b + 2·b - 16·a + (-2), we get;

The factor common to the terms of the expression 6·a·b + 2·b - 16·a + (-2) is 2. Therefore by factoring the expression, we get;

1.3. 1024000: 360,000 : 180,000

The expression is a ratio of the form a : b : c

Dividing each term in the ratio by 1,000, we get

1024000 ÷ 1000 : 360,000 ÷ 1000 : 180,000 ÷ 1000 = 1024 : 360 : 180

1024000: 360,000 : 180,000 = 1024 : 360 : 180

The common factors of 1024, 360 and 180 are; 1, 2, and 4

Therefore, the GCF of 1024, 360, and 180 is 4

Dividing the terms of the ratio 1024 : 360 : 180 by 4, we get;

1024 ÷ 4 : 360 ÷ 4 : 180 ÷ 4 = 256 : 90 : 45

Therefore;

1.4 150 min : 3 hours

The above ratio can be simplified by rewriting the ratio using unit conversion as follows;

3 hours = 180 minutes, therefore;

150 min : 3 hours = 150 min : 180 min

150 : 180 = 5 : 6

Therefore; 150 min : 180 min = 5 min : 6 min

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