What reference angle in the first quadrant corresponds to theta = -120? Answer in radians.

The discriminant of [tex]3x^2-10x=-2[/tex] is 76

To find the discriminant of [tex]3x^2-10x=-2[/tex], we have to recall the quadratic formula.

The formula of the quadratic equation can be expressed as [tex]ax^2+bx+c=0[/tex] and discriminant also expressed as [tex]D=b^2-4ac[/tex]

Using the quadratic formula, the given question can be expressed as:

[tex]3x^2-10x+2=0[/tex]

Where a = 3, b = -10, and c = 2

If we substitute the values, then the discriminant would be:

Recall the discriminant is [tex]D=b^2-4ac[/tex]

Therefore, we have

[tex]D=(-10)^2-4(3)(2)[/tex]

[tex]D=100-24[/tex]

[tex]D=76[/tex]

Thus, the discriminant of [tex]3x^2-10x=-2[/tex] is 76.

Discriminant is very helpful in quadratic equation as it helps reveals the number of real solutions to a given quadratic equation. In other words, it helps you to solve quadratic equation.  

While discriminant only tells only reveals the number of real solutions, it doesn’t reveal what the solutions are. The determinant would only give you hint as regards the number of real solution to look for.

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Factoring out the Greatest Common Factor (GCF) simplifies the expression, making further manipulation and factoring simpler. It reduces complexity, much like simplifying fractions in arithmetic, and aids in revealing patterns for easier factoring. This step also minimizes calculation errors and assists in proper unit analysis during problem-solving.

Factoring out the Greatest Common Factor (GCF) is a critical step in the process of factoring algebraic expressions. This is important because it simplifies the remaining expression, making it easier to manipulate and factor further if necessary. It is similar to simplifying fractions before performing operations with them; the process becomes cleaner and more straightforward.

For example, when you have an equation with multiple terms, each with a common factor, factoring out this GCF reduces the complexity of the terms, possibly revealing a more obvious pattern or structure that can then be factored more easily. Additionally, removing the GCF early in the process can prevent calculation errors and make other factoring techniques, like the difference of squares or trinomial factoring, more apparent and easier to apply.

In cryptography, algorithms rely on the principle that multiplying large numbers is computationally simple, whereas factoring a large number into its prime factors is difficult. Similarly, in algebra, starting by factoring out the GCF simplifies the entire problem, making the next steps more manageable. In physics equations, where units are involved, ensuring that all factors are in proper form before solving can prevent unit conversion errors, thus factoring out can play a useful role in unit analysis as well.

Answer:

9/4 on edg

Step-by-step explanation:

Final answer:

To form a perfect square trinomial from x² + 3x + c, we find c by taking half of 3, squaring it, which gives us 9/4. Hence, the value of c is 9/4, making x² + 3x + 9/4 a perfect square trinomial.

Explanation:

To form a perfect square trinomial in the process of completing the square, you need to find the value of c that completes the square for the given quadratic expression x² + 3x + c. The process involves taking half of the coefficient of x, squaring it, and adding it as the constant term c.

Given that the coefficient of x is 3, we take half of it, which is 3/2, and then square this value to get (3/2)² = 9/4. Therefore, the value of c that makes x² + 3x + c a perfect square trinomial is 9/4.

This method is very helpful in solving quadratic equations by completing the square, and it forms a basis for the derivation of the quadratic formula.

Answer:

Step-by-step explanation:

Answer:

3/2x+3

Step-by-step explanation:

Final answer:

In mathematics, the order of operations dictates that multiplication should be performed before addition. This is a fundamental principle to follow when dealing with expressions involving both addition and multiplication. The commutative property of addition means that the order of adding whole numbers does not affect the result.

Explanation:

In the subject of mathematics, when solving operations that involve both addition and multiplication, the principle to follow is the order of operations, commonly known as BIDMAS or PEMDAS. This stands for Brackets, Indices (or Powers), Division and Multiplication (left-to-right), and Addition and Subtraction (left-to-right). According to this rule, multiplication comes before addition. Therefore, when you see a mathematical expression that includes both addition and multiplication, you should perform the multiplication first.

When working with whole numbers in addition, you should pay attention to the commutative property which states that numbers can be added in any order and the result will be the same. For example, 2 + 3 is the same as 3 + 2. In multiplication, when we work with exponents, the rule is to multiply the digit terms normally and add the exponents for exponential terms. When multiplying fractions, the general rule is to multiply the numerators together and the denominators together.

To solve this problem, let us first remember that the formula for rate is:

rate = f (n) = A (r)^(n-1)

Where,

A = the 1st term

r = fractional rate of evaporation

n = number of terms

Now let us calculate for the fraction rate of evaporation, r. Since it is stated that the evaporation is happening at a fixed rate, therefore we can use any two given f (n) values to find for r. In this case, let us use when n=1 and 2.

r = 27 / 54

r = 0.5

The first term in the series is when n = 1 and that is:

A = 54

Therefore substituting all known values to the equation:

f (n) = 54 (0.5)^(n-1)                       (ANSWER)

We can solve this problem by first solving for the total volume of the cube. The formula for volume of cube is given as:

V cube = s^3

Where s is the length of one side which is equivalent to 2 inches. Therefore:

V cube = (2 inches)^3

V cube = 8 cubic inch

Assuming that all the pebble fills the cube without any spaces, then the total weight of the pebbles in the cube would simply be:

Total weight = 0.5 lb per cubic inch * 8 cubic inch

Total weight = 4 lb

Therefore, the total weight of the pebbles in the cube is 4 lbs.

The next step is to use the compass to find the perpendicular bisector for side DF. Option B

The steps include;

Thus, the next step is to use the compass to find the perpendicular bisector for side DF. Option B

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P(A|B) is the probability of event A happening given that B has occurred. It is calculated as P(A|B)=P(A∩B)/P(B). In this case, P(A|B) would be 1325/1320, assuming the provided values are correct.

In the given question, we have the probabilities P(A∩B) and P(B), and we need to find P(A|B). The conditional probability P(A|B) is given by the formula P(A∩B)/P(B). In this case, P(A∩B) is given to be 1325, which seems a bit high. Normally, probabilities are numbers between 0 and 1 where 1 means certainty and 0 means impossibility. So, the value 1325 might be a typo. Anyway, assuming that it's not a typo, calculating P(A|B) would still involve the step P(A∩B)/P(B), which in this case is 1325/1320. This shows that A is slightly more likely to happen given B has already occurred.

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The problem is about conditional probability P(A|B), which is calculated using the formula P(A ∩ B)/P(B). Given the provided values, the result exceeds the maximum limit for a probability, suggesting an error in the original values.

This problem asks us to determine the conditional probability of two events, specifically P(A|B). This represents the probability of event A occurring given that event B has occurred. According to the formula for conditional probability:

P(A|B) = P(A ∩ B) / P(B)

In your problem, we are given the values of P(B) and P(A∩B). Therefore we can substitute these into the formula: P(A|B) = 1325 / 1320. Please note the values seem to be incorrect because the probability of A and B (P(A ∩ B)) or A given B (P(A|B)) cannot be larger than P(B).

However, if we proceed with the given values, we get a result of P(A|B) = 1.0038, which is also unusual because probabilities range from 0 to 1.

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Answer:

It is still 3.

Step-by-step explanation:

We only translated it, so we just moved it over to the side. Translating cannot take away length.

The missing constant in the perfect square is 25

A quadratic equation is of the form:

[tex]ax^2+bx+c[/tex]

The giving perfect square is:

[tex]x^2+10x[/tex]

Comparing the two equations above:

a = 1, b = 10

The coefficients a, b, and c are related by the equation:

[tex]b^2=4ac[/tex]

Substitute a = 1, b = 10, and solve for c

[tex]10^2=4(1)c\\\\4c=100\\\\c=\frac{100}{4} \\\\c = 25[/tex]

Therefore, the missing constant in the perfect square is 25

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The only positive number that is the same as its reciprocal is 1. This is achieved by setting up the equation x = 1/x and solving it.

In mathematics, a number and its reciprocal are the same when the number is 1. If you denote the mysterious number we are looking for as 'x', then its reciprocal would be 1/x. Since the number and its reciprocal are the same, we can set up the equation x = 1/x. Solving this equation, we cross multiply to get x^2 = 1. The positive solution to this equation is x = 1, which confirms that the only positive number that is the same as its reciprocal is 1.

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Answer: 5.7

I just did the test and got it correct

Answer:

The produced parts average each day were 370.75.

Step-by-step explanation:

We have to find the average of parts produced by day, to calculate it we have sum all the parts produced by day and divide it by the number of days (4 days). In the equation we have:

[tex]Average=\frac{345+298+452+388}{4}=\frac{1483}{4}=370.75[/tex]

The produced parts average each day were 370.75.