Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum of the given function for this region.

Answer:

To divide by a fraction, we can multiply by its reciprocal.

So,

4/9 /8 = 4/9 x 1/8 = 4/72 = 1/18

The answer of the given question based on  regular octagon ,the area of the regular octagon with center O is approximately 232.98 square units.

Area is  measure of  amount of space inside  2-dimensional figure or shape, usually measured in square units like square centimeters or square meters. It is calculated by multiplying  length and  width of the figure or a shape.

To find the area of a regular octagon, we need to use the following formula:

A = 2(1 + √2) × s²

Since O is the center of the octagon, we can draw lines from O to each vertex of the octagon. This will divide the octagon into 8 congruent isosceles triangles.

Let's call the length of each side of the octagon "s". Then the base of each triangle will also be "s". We can use the Pythagorean theorem to find the length of the other sides of the triangle:

s²+ s² = (2s)²/2

2s² = 4s² - 4s²/2

2s² = 2s²/2

s² = s²/2

s = √2s/2

Now we can substitute this value of s into the formula for the area of the octagon:

A = 2(1 + √2) × s²

A = 2(1 + √2) × (√2s/2)²

A = 2(1 + √2) × 2s²/4

A = (1 + √2) × s²/2

A = (1 + √2) × (17/2)²/2

A ≈ 232.98 square units

Therefore, the area of the regular octagon with centre O is approximately 232.98 square units.

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The vertex of the function is,

⇒ Vertex = (1, - 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = -x² + 2x - 5

Now,

We can change the quadratic function in the form,

⇒ f (x) = a (x - h)² + k

Hence, We get;

⇒ f (x) = - x² + 2x - 5

⇒ f (x) = - (x² - 2x + 1 - 1) - 5

⇒ f (x) = - (x - 1)² + 1 - 5

⇒ f (x) = - (x - 1)² - 4

Thus, The vertex of the function is,

⇒ Vertex = (1, - 4)

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Answer: 48

Step-by-step explanation: 9p p=4 9*4=36 +18 = 48

The value of x, given the sides in the right - angled triangle, would be 31. 8 °.

We are given side that is opposite the angle, and we are also given the hypotenuse.

This means that we can use the operation of Sin which is :

Sin ( angle ) = Opposite / Hypotenuse

Opposite = 10 units

Hypotenuse = 19 units

The value of x is :

Sin ( x ) = 10 / 19

Sin ( x ) = 0. 5263

x = Sin ⁻ ⁵ ( 0. 5663 )

x = 31. 8 °

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Answer:

Shirt = $20
Sweater = 30

Step-by-step explanation:

3sh + 2sw = 120

2sh + 4sw = 160

Multiply (3sh + 2sw = 120) by -2
-6sh + -4sw = -240  -> -6sh -4sw = -240
Add the two equations -6sh -4sw = -240 and 2sh + 4sw = 160 together. -4sh = -80
Shirt = 20
Substitude in 20
3 x 20 = 60 120 - 60 = 60 60/2=30

The value of n for the equation (1/36)n= 216 is -1.5.

The following equation is solved by the use of exponent power rule.

The step by step explanation is given below:

convert the fraction into negative exponential form,

(36∧-1)n=216

simplify using the exponent power rule,

(a∧n)∧m = a∧n×m

Covert both sides of the equation in terms with the same base,

(6 ∧2)∧-n = 6 ∧3

Simplify the equation ,

6∧2.-n = 6∧3

Corresponding exponents are equal to ,

-2n = 3

Divide both side of the equation by 2 ,

-n= 3/2

n= - 3/2.

Therefore n = -1.5.

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The equations that gives true value for x = -2 and x = 2 are option A: x² - 4 = 0 and option D: 4x² = 16.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equations that are true for x = -2 and x = 2 are -

x² - 4 = 0 (when x = -2, this becomes 4 - 4 = 0; when x = 2, this becomes 4 - 4 = 0)

4x² = 16 (when x = -2, this becomes 4(4) = 16; when x = 2, this becomes 4(4) = 16)

The other options are not true for x = -2 and x = 2.

Specifically -

x² = -4 is not true for any real value of x, since the square of any real number is always non-negative.

3x² + 12 = 0 is not true for x = -2 or x = 2, since plugging in these values gives 12 ≠ 0.

2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since plugging in x = -2 gives 2(16) ≠ 0.

Therefore, the options x² - 4 = 0 and 4x² = 16 are the correct ones.

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The length and width of the rectangle are 14 cm and 11 cm respectively

Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.

The perimeter of a rectangle = l+l+w+w = 2(l+w)

represent the length by x and width by y

x = 3+y

p = 2(x+y)

represent 3+y for x

50 = 2( 3+y+y)

50 = 2( 3+2y)

50 = 6 +4y

4y = 50-6

4y = 44

divide both sides by 4

y = 44/4

y = 11 cm

x = 3+y

x = 3+11

x = 14

therefore the length and width in cm of the rectangle are 14 and 11 respectively

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The number of hours till Ed and Julie were 875 miles apart was 7 hours.

Since Ed and Julie are traveling in opposite directions, we can think of their distances from Good Life City as two separate distances that are adding up to their total distance apart.

For Ed, his distance from Good Life City is:

= 60 t

For Julie :

=  65t

We want to know how many hours it took for their total distance to be 875 miles. So we can set up the equation:

875 = 60t + 65t

Simplifying, we get:

875 = 125t

t = 875 /  125

t = 7 hours

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The scale factor of the dilation for the rectangle ABCD is found as 3.

The ratio of the scale of an original thing to a new object that is a representation of it but of a varying design is known as a scale factor (bigger or smaller).

The rectangle A'B'C'D' is created by dilation of rectangle ABCD.

We shall calculate the ratio of the rectangle's lengths in order to get the scale factor.

A:(1,5) and B:(4,5).

Length of side AB = 4 - 1 = 3

And,

A':(3,15) and B': (12,15).

Length of the side A'B' = 12-3 = 9

Ratio of the sides

AB : A'B' = 3 : 9

AB : A'B' = 1 : 3.

Thus, the scale factor of the dilation for the rectangle ABCD is found as 3.

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Answer: 3

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

60>30 since pi is 180 ........

1. The finance charge on the loan is $9,920.

2. The total deferred payment price of the airplane is $39,120.

To find the finance charge on the loan, we need to first determine the amount financed. George Bell made a 15% down payment on the airplane, so the amount financed is:

= $29,200 - (0.15)($29,200)

= $29,200 - $4,380

= $24,820

The total amount of payments made over the life of the loan is:

= $579/month x 60 months

= $34,740

The finance charge on the loan is:

= $34,740 - $24,820

= $9,920.

The total deferred payment price of the airplane is the sum of the down payment and the total amount of payments made over the life of the loan. The down payment is 15% of the purchase price which is:

= 0.15 * $29,200

= $4,380

The total amount of payments made over the life of the loan is:

= $579/month * 60 months

= $34,740

The total deferred payment price of the airplane is:

= $4,380 + $34,740

= $39,120.

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Answer:

64%

Step-by-step explanation:

Convert a fraction to a decimal and move the decimal point to make a percent

hi

here is the answer

i hope it helps

good luck:))

To determine whether the function f(x) = (x^2-2x-3)/(x^2+3x+2) has any holes, we can factor the numerator and denominator and simplify the expression. The numerator can be factored as:

x^2 - 2x - 3 = (x - 3)(x + 1)

And the denominator can be factored as:

x^2 + 3x + 2 = (x + 1)(x + 2)

Therefore, we can simplify the function as:

f(x) = [(x - 3)(x + 1)]/[(x + 1)(x + 2)]

The factor of (x + 1) appears in both the numerator and denominator, so we can simplify further by canceling it out:

f(x) = (x - 3)/(x + 2)

Since (x + 1) was canceled out, we have a hole in the graph of the original function at x = -1. To find the coordinates of the hole, we can evaluate the simplified function at x = -1:

f(-1) = (-1 - 3)/(-1 + 2) = -4

Therefore, the hole in the graph of the original function is located at the point (-1, -4).

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

A linear function is a polynomial of degree 1, or a mathematical expression that describes a relation between two variables. It is often written in the form y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept.

The factored form of a linear equation is the same as the standard form of the equation, with the exception that the coefficients of the variables are each expressed as a product of their prime factors. In the case of y=3x+12, the factored form is (3x+12). The zero of the function (also known as the root of the equation) is the value of the variable that will result in a value of 0 for the equation. To find the zero of the function, we need to set the equation equal to 0 and solve for the value of x. When we set y=0, we get 3x+12=0, which can be solved to get x=-4. Therefore, the zero of the function is -4.

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

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-2x - 4 is not greater than 14

Step-by-step explanation:

I don't understand the question but I hope this helps

(-2 × X) + (-2 × 2)

10 3/8. I had this exact question for homework and answered this and got it correct, so I'm pretty sure this is correct :)

Answer: To find the monthly payment for each option, we can use the following formula:

Monthly Payment = Total Cost * (Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

For the option to finance at the store for 2 years at 14% interest:

Total Cost = $2,000

Monthly Interest Rate = 14% / 12 = 0.011667

Number of Months = 2 years x 12 months/year = 24 months

Substituting these values into the formula, we get:

Monthly Payment = $2,000 * 0.011667 / (1 - (1 + 0.011667)^(-24)) = $95.13

Therefore, the monthly payment for financing at the store for 2 years at 14% interest is $95.13.

For the option to use his credit card at 21% interest for 1 year:

Total Cost = $2,000

Monthly Interest Rate = 21% / 12 = 0.0175

Number of Months = 1 year x 12 months/year = 12 months

Substituting these values into the formula, we get:

Monthly Payment = $2,000 * 0.0175 / (1 - (1 + 0.0175)^(-12)) = $185.44

Therefore, the monthly payment for using his credit card at 21% interest for 1 year is $185.44.

To find the total repayment for each option, we can multiply the monthly payment by the number of months:

For the option to finance at the store for 2 years at 14% interest:

Total Repayment = $95.13/month x 24 months = $2,283.12

Therefore, the total repayment for financing at the store for 2 years at 14% interest is $2,283.12.

For the option to use his credit card at 21% interest for 1 year:

Total Repayment = $185.44/month x 12 months = $2,225.28

Therefore, the total repayment for using his credit card at 21% interest for 1 year is $2,225.28.

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

27+4*5+8-7-2=

27+20+8-7-2=

47+8-7-2=

55-7-2=

48-2=

46

By answering the above question, we may infer that As a result, (x, y) = is the answer to the system of equation (3, 0).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The equations in the system are:

x + 2y = 3 ... (1)

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

We may use equation (2) to solve for x in terms of y:

x = 3 + 3y

If this value of x is substituted into equation (1), the result is:

(3 + 3y) + 2y = 3

If we simplify this equation, we get:

5y = 0

Hence, y = 0. Inputting y = 0 into the equation we found for x results in:

x = 3 + 3(0) = 3

As a result, (x, y) = is the answer to the system of equations (3, 0).

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Olivia will need at least 11 months to reach her savings goal.

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent values and quantities in mathematical equations and formulas. Algebra is used to solve problems that involve unknown quantities by using rules and operations to manipulate the symbols representing those quantities.

Let's use algebra to solve this problem. Let "m" be the number of months it will take for Olivia to reach her goal of saving at least $7,500.

In one month, Olivia will deposit $650, so after "m" months, she will have deposited:

650m

In addition to this, Olivia already has a balance of $400, so her total savings after "m" months will be:

650m + 400

We want to find how many months "m" it will take for Olivia to save at least $7,500. So we can set up the following inequality:

650m + 400 >= 7,500

Subtracting 400 from both sides:

650m >= 7,100

Dividing both sides by 650:

m >= 10.92

Since we can't have a fraction of a month, we'll round up to the next whole number. Therefore, Olivia will need at least 11 months to save at least $7,500.

Therefore, Olivia will need at least 11 months to reach her savings goal.

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Where the above conditions exist:

(a) To find the weight of each type of coffee in 800g of X, we can use the ratio of P coffee to Q coffee in the blend, which is 3:13.

Let the weight of P coffee in 800g of X be 3x, then the weight of Q coffee in 800g of X is 13x.

The total weight of X is 800g, so we have:

3x + 13x = 800

16x = 800

x = 50

Therefore, the weight of P coffee in 800g of X is:

3x = 3(50) = 150g

And the weight of Q coffee in 800g of X is:

13x = 13(50) = 650g

(b) To find the weights of type P coffee and type R coffee in 800g of Y, we can use the ratio of the three types of coffee in the blend, which is 1:7:12 by weight.

Let the weight of P coffee in 800g of Y be x, then the weight of Q coffee in 800g of Y is 7x and the weight of R coffee in 800g of Y is 12x.

The total weight of Y is 800g, so we have:

x + 7x + 12x = 800

20x = 800

x = 40

Therefore, the weight of P coffee in 800g of Y is:

x = 40g

And the weight of R coffee in 800g of Y is:

12x = 12(40)

= 480g

(c) To find the ratio of the three types of coffee in a third standard blend Z, formed by mixing equal weights of X and Y, we first need to find the total weight of X and Y that will be used to make Z. Since we are mixing equal weights of X and Y, the total weight of X and Y in Z will be:

800g + 800g = 1600g

The ratio of P coffee to Q coffee in Z can be found by adding the weights of P coffee in X and Y, and then dividing by the total weight of X and Y:

(150g + 40g) / 1600g = 0.1125

Similarly, the ratio of Q coffee to the total weight in Z can be found by adding the weights of Q coffee in X and Y, and then dividing by the total weight of X and Y:

(650g + 7(40g)) / 1600g = 0.5063

The ratio of R coffee to the total weight in Z can be found by adding the weights of R coffee in Y, and then dividing by the total weight of X and Y:

(12(40g)) / 1600g = 0.3

Therefore, the ratio of the three types of coffee in Z is approximate:

P : Q : R = 0.1125 : 0.5063 : 0.3

(d) To find the weight of type P coffee in 800g of Z, we can use the ratio of P coffee to the total weight in Z, which is 0.1125.

Therefore, the weight of P coffee in 800g of Z is:

0.1125 * 800g = 90g

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Full Question:

Two types of coffee, P and Q, are blended in the ratio 3:13 by weight to form a standard blend X. A second standard blend, Y, is formed by blending type P coffee, type Q coffee, and type R coffee in the ratio 1:7:12 by weight. Find:

a) The weight of each type of coffee in 800 g of X

b) The weights of type P coffee and type R coffee in 800 g of Y

c) The ratio of the three types of coffee in a third standard blend Z, formed by mixing equal weights of X and Y

d) The weight of type P coffee in 800 g of Z.

Therefore , the solution of the given problem of ratio comes out to be 1:3 is the decreased loss-to-games-played ratio.

A collection of integers "a" as well as "b" that seem to be equal can be defined using the straightforward fraction calculation "a / b," at which "b" may be larger than zero. A ratio is created by combining two ratios. The ration would be 1:1 if there were just one male and three women. There are 1/4 guys and 3/4 women in the group. Portions can be a divide between different things, a number, or a specific portion of the volume of a component.

Here,

In events played, win:

Out of the 12 games contested, 8 were victories. We can split the numerator and denominator by 4 to decrease the ratio:

=> 8/12 = 2/3

The decreased win-to-games-played ratio is 2:3.

win to loss ratio

If a squad has 8 victories, they have 4 defeats (since they have played 12 games in total). As a result, the winning/losing split is as follows:

8:4, which is further diminished by multiplying the number and denominator by 4:

=> 2:1

The decreased win-to-loss ratio is 2:1.

Played events lost:

If a squad has 4 losses and has played a total of 12 games, the ratio of losses to games played is as follows:

=> 4/12 = 1/3

=> 1:3 is the decreased loss-to-games-played ratio.

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a) The finance charge for the financing of the company airplane priced at $250,000 with 15% down payment is $66,308.

b) The monthly payments Vista's aircraft loan are $4,646.80.

The finance charge and the monthly payments can be determined using an online finance calculator as follows:

The finance charge represents the total interest and other fees that the financier charges for the loan.

The monthly payments are the periodic payments that must be made to settle the loan and compounded interest with the installment period of 60 months.

Company Airplane Price = $250,000

Down Payment = 15%

Loan Term = 60 months (5 years x 12)

Interest Rate = 11.25%

Results:  

Monthly Payment (PMT):  $4,646.80

House Price = $250,000

Down Payment = $37,500 ($250,000 X 15%)

Loan Amount = $212,500 ($250,000 - $37,500)

Total of 60 Mortgage Payments = $278,808

Total Interest (Finance Charge) = $66,308 ($278,808 - $212,500)

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Answer:

3.3.1 Approximations for trigonometric functions. 3.3.2 ... 7.2.1 Consistency for three simultaneous linear equations in two unknowns ... x : y : z =5:4:3;.

The diagram shows the quantity x is 13.

A tape diagram, also known as a bar model or a strip diagram, is a visual representation of a problem or situation that helps students to organize and solve mathematical problems. It involves drawing a rectangular strip or bar to represent a quantity or a value, and then dividing or labeling the strip to represent different parts of the problem.

The full completed question is related to an equation as shown in the below diagram (Check it).

Given equation is x+4 = 17

If we select part 'a' the diagram is shown in the below diagram, see it.

For part 'b' the quantity x can be represent by:

x+4 = 17

x = 17 - 4

x = 13

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According to the graphs, the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia (option A).

To select an appropriate conclusion that matches the information in the graphs we must carefully analyze the information in the graphs. Additionally, we can read each of the options and check them with the trends shown in the graphs.

In accordance with the above procedure, we can infer that the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia because the Residential real estate graph shows that In 2010 housing was more expensive in Australia than in Spain.

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