Find the exact value by using a sum or difference identity.
sin (185° -65°) please please help me :/

The solution of the given system is x = -5/2, y = 2, and z = 13/2.

To determine whether the given system is inconsistent, dependent, or neither, we need to solve the system using any of the methods, such as substitution or elimination.

The given system is:
4x + y + 4z = 4
5x - y + 3z = 5
x - 2y - z = 0

Let's use the elimination method to solve the system.

Multiply the first equation by 2 and subtract the second equation from it to eliminate the y variable.
8x + 2y + 8z = 8
5x - y + 3z = 5
-------------------
3x + 5z = 3

Multiply the third equation by 2 and subtract it from the second equation to eliminate the y variable.
5x - y + 3z = 5
2x - 4y - 2z = 0
-------------------
3x + y + 5z = 5

Subtract the equation obtained in step 1 from the equation obtained in step 2 to eliminate the x variable.
3x + y + 5z = 5
3x + 5z = 3
----------------
y = 2

Substitute the value of y in the third equation to find the value of z.
x - 2(2) - z = 0
x - 4 - z = 0
x + z = 4

Substitute the value of y in the second equation to find the value of x.
5x - (2) + 3z = 5
5x + 3z = 7

Substitute the value of x + z in the equation obtained in step 5.
5(4 - z) + 3z = 7
20 - 5z + 3z = 7
2z = 13
z = 13/2

Substitute the value of z in the equation obtained in step 4 to find the value of x.
x + (13/2) = 4
x = 4 - (13/2)
x = -5/2

Therefore, the solution of the given system is x = -5/2, y = 2, and z = 13/2. Since the system has a unique solution, it is neither inconsistent nor dependent. Hence, the given system is neither inconsistent, dependent, nor neither.

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To find out how much of each mixture Donny should combine to make 6 kg of a mixture of 33% almonds, we need to use a system of equations. Let x be the amount of the first mixture and y be the amount of the second mixture.

The first equation represents the total amount of the mixtures:

x + y = 6

The second equation represents the amount of almonds in the mixtures:

0.40x + 0.25y = 0.33(6)

Solving the system of equations, we get:

0.40x + 0.25y = 1.98

0.40x + 0.25(6 - x) = 1.98

0.40x + 1.50 - 0.25x = 1.98

0.15x = 0.48

x = 3.2

Substituting the value of x back into the first equation:

3.2 + y = 6

y = 2.8

So Donny should combine 3.2 kg of the first mixture and 2.8 kg of the second mixture to make 6 kg of a mixture of 33% almonds.

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Among Luc, Deborah, and Melanie, the ratio in which the profit was shared is 2:3:7.

Let us assume that the ratio in which the profit shared among the three partners is L:D:M,

We know that the total profit for the year is = R176496,

We also know that Luc received R29416 and

Melanie received R102956.

So, Deborah profit share is calculated as;

⇒ Deborah's share = Total profit - Luc's share - Melanie's share

⇒ Deborah's share = R176496 - R29416 - R102956

⇒ Deborah's share = R44124,

So, now we know that the ratio of the profit shared among the three partners is:

⇒ L:D:M = R29416 : R44124: R102956

To simplify this ratio, we can divide all the amounts by R14708,

We get,

⇒ L:D:M = 2:3:7

Therefore, the profit was shared in the ratio of 8:1:28 among Luc, Deborah, and Melanie.

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The given question is incomplete, the complete question is

Three partners Luc, Deborah and Melanie, share the profits of a business. The profit for the year is R176496. If Luc receives R29416 and Melanie receives R102956, determine the ratio in which the profit was shared.

The axis of symmetry of a quadratic function can be found by taking the negative of the coefficient of the x term, and then dividing it by 2. In this case, the coefficient of the x term is -2, so the axis of symmetry is located at x = -1.

The key features of the quadratic function are the vertex, the y-intercept, and the x-intercepts. To find the vertex, substitute the x-value for the axis of symmetry into the equation. In this case, the vertex is located at (x, y) = (-1, 27).

The y-intercept is found by setting x = 0 and solving for y. This gives us y = -24, so the y-intercept is located at (0, -24).

To find the x-intercepts, set y = 0 and solve for x. In this case, the x-intercepts are located at (2, 0) and (6, 0).

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The two lines are parallel because both have equal slope.

What area parallel lines?

If two lines do not cross one another anywhere on the plane, they are considered to be parallel. All parallel lines are spaced equally apart from one another.

Numerous forms have parallel lines running along their edges. In the rectangle below, the single and double arrow lines, as well as their junction points, are parallel to one another. Additionally, it is possible to create both horizontal and vertical shapes.

Given : line 1  : y=5x+1

          line 2 :  2y-10x+3=0

                       2y = 10x - 3

We know that, parallel lines always have equal slope.

The slope can be found by using formula :

     coefficient of y / coefficient of x

So, here, line 1 has slope = 2/10 = 1/5

and, line 2 has slope = 1/5

So, both have same slopes hence, both are parallel lines.

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Answer:

50%

Step-by-step explanation:

percent change = (new number - old number)/(old number) × 100%

Here, the new number is 2.

The old number is 4.

percent change = (2 - 4)/(4) × 100%

percent change = -2/4 × 100%

percent change = -50%

Since the percent change is negative, it's a percent decrease.

The percent decrease is 50%.

Answer:

B. (-2,2)

Step-by-step explanation:

The interval on which the temperature was over 100°F is (0.79, 1.26).

To find the interval on which the temperature was over 100°F, we need to solve the inequality T(t) > 100.
First, let's rearrange the equation to isolate t:
T(t) = [4t / (t²+1)] + 98.6 > 100
[4t / (t²+1)] > 1.4
4t > 1.4(t²+1)
0 > 1.4t² - 4t + 1.4
Now we can use the quadratic formula to find the values of t that make this inequality true:
t = [-(-4) ± √((-4)² - 4(1.4)(1.4))] / [2(1.4)]
t = (4 ± √(16 - 7.84)) / 2.8
t ≈ 1.26 or t ≈ 0.79
Therefore, the temperature was over 100°F between the interval (0.79, 1.26).

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After performing multiplication or division and simplify we get 2x2 − xy − 3y2 as the answer of this question.

The question is asking you to perform the multiplication or division and simplify:

x2 + 2xy + y2 ÷ x2 − y2 =

(x2 + 2xy + y2)(3x2 − xy − 2y2) ÷ (x2 − y2) =

3x4 − x3y − 2x2y2 − 3xy2 + 2xy3 + 2y4 ÷ (x2 − y2) =

3x4 − x3y − 2x2y2 − 2y4 ÷ (x2 − y2)

= 2x2 − xy − 3y2

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The solution to this system of linear equations is x = 11/3, y = -3/13, and z = 1/12.

The augmented matrix of a system of linear equations is [[1,0,5,-(11)/(3)],[-4,1,-23,(68)/(3)],[5,0,25,-(43)/(3)]]. To solve this system, we can use the process of elimination.

Step 1: Add 4 times row 1 to row 2.

[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[5,0,25,-(43)/(3)]]

Step 2: Subtract 5 times row 1 from row 3.

[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[0,0,15,-(32)/(3)]]

Step 3: Divide row 2 by -13.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,15,-(32)/(3)]]

Step 4: Add 3 times row 2 to row 3.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,12,-(1)/(13)]]

Step 5: Divide row 3 by 12.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,1,(1)/(12)]]

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By following the 6 steps explained, you can find the quotient of a multiple of 10 and any number.

To use place value to find the quotient of a multiple of 10 and a number, you can use the following steps:

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Answer: 3, 5, and 7

Step-by-step explanation:

Vertical angles, corresponding angles, and alt. ext. angles

The expected net gain (or loss) for playing one game is -$3.125, which rounds to -$3.25. The correct answer is d. -$3.25.

I am a question answering bot and do not have personal experiences to share. However, I can help you find the expected net gain (or loss) for playing one game in this scenario.

First, let's calculate the probability of each possible outcome:
- Probability of winning: 1/8
- Probability of placing 2nd or 3rd: 2/8
- Probability of placing 4th through 8th: 5/8

Next, let's calculate the net gain (or loss) for each possible outcome:
- Net gain for winning: $125 - $25 = $100
- Net gain for placing 2nd or 3rd: $0 (since you receive your money back)
- Net gain for placing 4th through 8th: -$25 (since you lose your money)

Finally, let's use these probabilities and net gains to calculate the expected net gain (or loss) for playing one game:
Expected net gain = (Probability of winning) x (Net gain for winning) + (Probability of placing 2nd or 3rd) x (Net gain for placing 2nd or 3rd) + (Probability of placing 4th through 8th) x (Net gain for placing 4th through 8th)
= (1/8) x ($100) + (2/8) x ($0) + (5/8) x (-$25)
= $12.50 + $0 - $15.625
= -$3.125

Therefore, the expected net gain (or loss) for playing one game is -$3.125, which rounds to -$3.25. The correct answer is d. -$3.25.

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The value of (g + f) (-1) is -6. The solution has been obtained by using operations on functions.

What are operations on functions?

The operations on functions allow us to add, subtract, multiply, and divide functions with overlapping domains in a manner akin to how we operate on the terms of the functions.

We are given f(x) = 3x²  and g(x) = x - 8

f(-1) = 3(-1)²

f(-1) = 3

g(-1) = -1 - 8

g(-1) = -9

(g + f) (-1)

⇒(g + f) (-1) = g(-1) + f(-1)

⇒(g + f) (-1) = -9 + 3

⇒(g + f) (-1) = -6

Hence, the value of (g + f) (-1) is -6.

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To prove that {f € C°([0,1]) ||. f()dx = 0} is a vector space, we need to verify the following properties:

Closure under addition: Let f,g be two functions in {f € C°([0,1]) ||. f()dx = 0}. Then, for any x € [0,1], we have:

(f+g)(x) = f(x) + g(x)

Now, we can calculate the integral of (f+g)(x) from 0 to 1 as follows:

∫0^1 (f+g)(x) dx = ∫0^1 f(x) dx + ∫0^1 g(x) dx

Since f and g are in the set {f € C°([0,1]) ||. f()dx = 0}, we know that ∫0^1 f(x) dx = 0 and ∫0^1 g(x) dx = 0. Therefore, we have:

∫0^1 (f+g)(x) dx = 0

This means that f+g is also in the set {f € C°([0,1]) ||. f()dx = 0}, and thus the set is closed under addition.

Closure under scalar multiplication: Let f be a function in {f € C°([0,1]) ||. f()dx = 0} and let r be a scalar. Then, for any x € [0,1], we have:

(rf)(x) = r*f(x)

Now, we can calculate the integral of (rf)(x) from 0 to 1 as follows:

∫0^1 (rf)(x) dx = r*∫0^1 f(x) dx

Since f is in the set {f € C°([0,1]) ||. f()dx = 0}, we know that ∫0^1 f(x) dx = 0. Therefore, we have:

∫0^1 (rf)(x) dx = 0

This means that rf is also in the set {f € C°([0,1]) ||. f()dx = 0}, and thus the set is closed under scalar multiplication.

Existence of zero vector: The zero vector is the function f(x) = 0 for all x € [0,1]. This function clearly satisfies the condition that ∫0^1 f(x) dx = 0, and thus it is in the set {f € C°([0,1]) ||. f()dx = 0}.

Existence of additive inverse: Let f be a function in {f € C°([0,1]) ||. f()dx = 0}. Then, the additive inverse of f is -f(x) for all x € [0,1]. This function clearly satisfies the condition that ∫0^1 -f(x) dx = -∫0^1 f(x) dx = 0, and thus it is also in the set {f € C°([0,1]) ||. f()dx = 0}.

Since all the four properties are satisfied, we can conclude that {f € C°([0,1]) ||. f()dx = 0} is a vector space under the usual addition and scalar multiplication of functions.

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The total cost price of the book in birr using the cost in USA and importing value is equal to  62.80 birr per copy.

Cost of book = 2.40 USD in USA.

Convert the cost of the book in USD to birr,

1 USD = 21 birr

⇒2.40 USD = 2.40 x 21 birr

⇒2.40 USD = 50.40 birr

⇒ Cost of the book in birr is equal to 50.40 birr.

Cost of importing a book = 12.40 birr per copy

Add the cost of importing the book,

Total cost price of the book, including importing is equal to,

= 50.40 birr + 12.40 birr

= 62.80 birr

Therefore, the cost price of the book in birr including the cost of importing is equal to 62.80 birr per copy.

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The possible numbers of hours Yolanda could rent the boat is 6 hours.

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

Here the given boat cost per hour = $7.

Offer he gets = $3.

Now writing a inequality then, t represent number of hours,

=> 7t-3[tex]\le[/tex]39

Now solving this inequality for t then,

=> 7t[tex]\le[/tex]39+3

=> 7t[tex]\le[/tex]42

=> t[tex]\le[/tex]42/7

=>t[tex]\le[/tex]6

Hence the possible numbers of hours Yolanda could rent the boat is 6 hours.

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The number from oldest to youngest is - 5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3 , the layer 5 is older than the layer 3 and line "B" represent - Fault .

How to do ordering of rock layers ?

Ordering of rock layers, also known as stratigraphy, is a process of arranging rock layers in a specific order based on their age and location. There are several principles that geologists use to determine the relative ages of rock layers:

Law of superposition: In an undisturbed sequence of rocks, the oldest rocks are at the bottom and the youngest rocks are at the top.

Principle of original horizontality: Layers of sediment are originally deposited horizontally, and any deformation of these layers must have occurred after deposition.

Principle of cross-cutting relationships: Any feature that cuts across a rock or rock layer is younger than the rock or layer that it cuts across.

Principle of inclusions: Any rock fragments included in another rock layer must be older than the rock layer that contains them.

Ordering of given rock layers :

The number from oldest to youngest is given below -

5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3

The age of layer 5 is older than the layer 3 .

The line "B" represent - Fault . A fault in rock is a fracture or break in the Earth's crust where rock on either side has moved relative to the other side.

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Answer: 52.5

Step-by-step explanation: I used a calculator.

The radical expressions' exponents should match, or you should be able to modify the expressions to make the exponents match.

A radical is a symbol used in mathematics to symbolise the root of a number or mathematical expression. The square root, denoted by the sign, is the most prevalent variety of radical. The result of multiplying the square root of a number by itself is the initial value. For instance, 3 is the square root of 9, as 3 3 Equals 9. Additional values for radicals include cube roots, fourth roots, and so forth. A value that, when raised to the power of n, yields the initial number is known as the nth root of a number.

given

You usually need an equation with a single radical expression or multiple radical expressions that can be combined into a single expression when solving with radical exponents.

The radical expressions' exponents should match, or you should be able to modify the expressions to make the exponents match.

As soon as you have one radical expression, you can separate the radical word and then raise both sides of the equation to the proper power to get rid of the radical.

The resulting solution for the variable can then be solved.

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Answer:

the account balance will be $15, 485.41

Step-by-step explanation:

Compound interest, can be calculated using the formula FV = P*(1+R/N)^(N*T), where FV is the future value of the loan or investment, P is the initial principal amount, R is the annual interest rate, N represents the number of times interest is compounded per year, and T represents time in years.

5890*(105.61/100)*17

=15485.41

Answer:

a) experimental : 4 ÷ 20 = 1/5 or 20%

Theoretical : 1/6

b) experimental: 18÷20= 9/10 or 90%

Theoretical : 5/6 or 83%

c) experimental: 2÷20 = 1/10 or 10%

Theoretical : 1/6

Using the conversion formula,

In Australia on the country roads the speed is 60mph and on the motorways is 66mph.

In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.

In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.

In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.

To translate the number to miles per hour, we must multiply it by the conversion factor of 0.6214. As an illustration, 50 km/h is equivalent to 31.07 mph.

In the question,

By multiplying each speed limits with the conversion factor = 0.6214,

we can get the speed limits in miles per hour.

Therefore,

In Australia on the country roads the speed is 60mph and on the motorways is 66mph.

In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.

In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.

In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.

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The complete question is:

The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to miles. What are these speed limits in miles per hour?

For a=7 the quadratic equation have no real roots. (4)

For a quadratic equation y=ax^(2)-6x+3 to have no real zeroes, the discriminant of the equation must be less than zero. The discriminant of a quadratic equation is given by the formula b^(2)-4ac, where a, b, and c are the coefficients of the equation. In this case, a=a, b=-6, and c=3.

Plugging these values into the formula for the discriminant, we get:

(-6)^(2)-4(a)(3)<0

36-12a<0

12a>36

a>3

Therefore, the values of a that will make the quadratic equation have no real zeroes are those that are greater than 3. This means that the correct answer is (4) a=7, since this is the only value of a that is greater than 3.

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the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.

why it is and what is multiple?

a) The number 5,364 can be written as the sum of multiples of powers of 10 as follows:

5,364 = 5 × 1,000 + 3 × 100 + 6 × 10 + 4 × 1

= 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰

(b) If x = 10, then we can write 5,364 as:

5,364 = 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰

= 5x³ + 3x² + 6x + 4

Therefore, the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.

A multiple is a product of a given number and any other whole number. In other words, if a number 'a' can be expressed as the product of another number 'b' and a whole number 'c', then 'a' is a multiple of 'b'. For example, 10 is a multiple of 5 because 10 can be expressed as 5 multiplied by 2. Similarly, 15 is a multiple of 3 because 15 can be expressed as 3 multiplied by 5.

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a. The variables are x (number of adult tickets sold) and y (number of children's tickets sold).

b. The system of equations are x + y = 140 and 20x + 10y = 2270.

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 ("=").

a. Variables are defined as -

Let x be the number of adult tickets sold.

Let y be the number of children's tickets sold.

b. System of equations is obtained as -

The total number of tickets sold is 140 -

x + y = 140

The total revenue earned is $2270 -

20x + 10y = 2270

Therefore, the variables and system of equations is obtained.

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The probability that a person who tests positive actually has the

the disease is, 10%.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Given, A certain disease has an incidence rate of 0.8%.

Therefore, The probability that a person who tests positive actually has the disease is,

= (8/0.8)%.

= 10%.

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Answer:

72*price of pig= 54*560

price of pig=54*560/72

= 420

Just multiplying the amount of possibilities in each category together will give us the total number of meals that can be made using the options provided.

This is known as the Fundamental Counting Principle. Using this principle, the total number of possible meals is:

6 main courses × 4 vegetables × 2 salads × 3 beverages = 144 possible meals

Therefore, there are 144 possible meals that can be made by choosing from the given options.

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