Consider the following quadratic equation:
10x2 = -15x

i need help asap!! using standard form ax^2+bx+c=0

Given:

(12, 8) and (X, -4 )

Required:

To calculate the value of x

Explanation:

Determine the parameter through distance formula

Required answer:

x=7 or x=17

The possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3,  cos θ = √3/3, sec θ = √3

The law of sines, also known as the sine rule, is a mathematical principle that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.

Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Each function represents a different ratio of two sides of a right triangle and can be used to solve problems in geometry, physics, engineering, and other fields that involve angles and triangles.

According to the given information,

Given that tan θ = -√(1/3) and 0 < θ < 180°, we can use the trigonometric identities to find the values of the other trigonometric functions of θ.

First, we can use the definition of the tangent function:

tan θ = opposite/adjacent

Since tan θ = -√(1/3), we can assign opposite = -1 and adjacent = √3 as their ratio equals -√(1/3). This means that the terminal side of the angle θ will lie in the fourth quadrant of the unit circle since the opposite is negative and the adjacent is positive.

Next, we can use the Pythagorean identity:

sin²θ + cos²θ = 1

to find the value of sin θ. Since we know that θ is in the fourth quadrant, we can assign sin θ = -1/√3, since sin θ is negative in the fourth quadrant and the ratio of opposite/hypotenuse of a 30-60-90 triangle is √3/2, which means the ratio of hypotenuse/opposite is 2/√3 = √3/3.

Then, we can use the definition of the cosine function:

cos θ = adjacent/hypotenuse

to find the value of cos θ. We know that adjacent = √3 and the hypotenuse is positive (since it is a length), so we can assign cos θ = √3/3.

Finally, we can use the reciprocal identity:

sec θ = 1/cos θ

to find the value of sec θ. We know that cos θ = √3/3, so we can assign sec θ = √3.

Therefore, the possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3

cos θ = √3/3

tan θ = -√(1/3)

sec θ = √3

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Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

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Answer:

The value of the discriminant tells you whether the quadratic has 2 solutions, 1 solution, or no real solutions. If b2 – 4ac simplifies into a positive number, then the quadratic has 2 solutions. If b2 – 4ac simplifies into a 0, then the quadratic has 1 solution.

Step-by-step explanation:

Answer:

  y = 1/2x +4

Step-by-step explanation:

The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line. The hint suggests a useful approach to answering the question.

The equation of the given line is ...

  y = -2x +5

Comparing this to the slope-intercept form of the equation for a line ...

  y = mx +b

we see that the slope (m) is -2, and the y-intercept (b) is +5. Only the slope is of interest in this problem.

The slopes of perpendicular lines are opposite reciprocals of each other. That means the slope (m') of the perpendicular line will be ...

  m' = -1/m

  m' = -1/(-2) = 1/2

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

For the perpendicular line, the slope is m=1/2, and the point is (h, k) = (-4, 2). Using these values, we find the point-slope equation of the perpendicular line to be ...

  y -2 = (1/2)(x -(-4))

Adding 2 and simplifying the point-slope equation, we find ...

  y = 1/2x +1/2(4) +2

  \(\boxed{y=\dfrac{1}{2}x+4}\)

__

Additional comment

We have used m' for the slope of the perpendicular line in order to avoid confusion with the slope m of the given line it is perpendicular to. That value (m'=1/2) becomes the slope m in the point-slope equation for the perpendicular line. At that last step in the solution process, the original given line's slope of -2 is no longer of interest and can be forgotten. (In short, the variable "m" in the last step means something different from its original use in the first step of the solution process. We expect you will understand and not be confused by this.)

Answer:

24

Step-by-step explanation:

The required problem is (−1)×(−2)×(3)×4

=2×(12)

Hence the result is =24

Answer:

y=8

Step-by-step explanation:

because 3×8 is 24

and 8 would be the missing number

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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Answer:

5.25

Step-by-step explanation:

Answer:

∠ Y = 124°

Step-by-step explanation:

given the triangles are congruent , then corresponding angles are congruent, that is

∠ Y = ∠ N = 124°

The Julián has 0.84 euros left after making these purchases.

Given that Julián spends 2/5 of his savings on a school trip, and 25% of his savings on skates. The question is asking us to find out how much the skates cost and how much money he has left after making these purchases. Let's solve this problem step-by-step.

Part (a) is already solved as we know that Julián spends 2/5 of his savings on a school trip and 25% of his savings on skates.

Part (b) To determine how much the skates cost, we need to first find out what percentage of his savings he spent on skates. Since he already spent 2/5 of his savings, that means he has 3/5 left.

And since he spent 25% of his total savings on skates, we can set up an equation as follows:

0.25(x) = 3/5where x is his total savings.

Cross-multiplying: 0.25(x) * 5 = 3x1.25x = 3x = 3/1.25x ≈ 2.4So, his total savings would be around 2.4 euros.

Therefore, the cost of the skates is 0.25(2.4) = 0.6 euros.Part (c) To find out how much money he has left, we subtract the cost of the school trip and the skates from his total savings:

Total savings - School trip - Skates

= Money left2.4 - (2/5)(2.4) - 0.6

= Money left2.4 - 0.96 - 0.6

= Money left0.84 euros

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I'm tentatively changing my answer to say this kind of relies on practical knowledge of how stores tend to operate. If 20 coupons are given out, the store has sold all 500 shirts, arguably at a loss to the retailer. They have to have more shirts in stock to be sold at full price because, well, that's how they make money. It's more likely that such a store would carry more than just 500 shirts at the start of each day, so A is (probably) wrong.

Answer:

The answer f (x^2) = 3x^2 + 5

Step-by-step explanation:

hmm... i don't really know how to explain how I did it but that's the answer

Answer:

The area of the rectangle is;

Explanation:

Given the rectangle LKMN with the coordinates;

Recall that the area of a rectangle is the product of length and width;

From the given coordinates, the length and width of the rectangle are;

Substituting the values of the length and width, we have;

Therefore, the area of the rectangle is;

D

(It contradicts)

!!!!!!!

Any exception to a generalization is referred to as a counterexample. The correct option is D.

Any exception to a generalization is referred to as a counterexample. A counterexample disproves a generalization in logic, and it does so rigorously in mathematics and philosophy.

An example that contradicts a statement (shows that it is false). For instance, the assertion "all dogs are hairy" may be shown wrong by locating a single hairless dog (the counterexample), as seen below.

To demonstrate, you must discover an integer n such that n² is divisible by 4, but n is not divisible by 4 — the "if" portion must be true, but the "then" part must be false. Consider the number n = 6. Then n2 = 36 is divisible by 4, although n = 6 is not. As a result, n = 6 is a contradiction to the assertion.

Since a counterexample is an example that makes the statement false. Therefore, the best definition of a counterexample is An example that shows a statement is not true.

Hence, the correct option is "An example that shows a statement is not true".

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Answer:

Step by step explanation:

well this is simble you just do it

Answer:

C. Associative property of multiplication

Step-by-step explanation:

The associative property of multiplication states that the way in which factors are grouped in a multiplication problem does not change the product.

Answer:

C 1.1 mph

Step-by-step explanation:

Divide 2 3/4 by 2 1/2 to get 1.1

The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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Answer:

Step-by-step explanation:

This problem could keep you going for quite a while. My suggestion is that you go get a cup of coffee and sip it slowly as you read this.

Equation One

Sqrt(x - 1)^3 = 8

(x - 1)^(3/2) = 8

Square both sides to get rid of the 2.

(x - 1)^3 = 8^2  

(x - 1)^3 = 64

Now take the cube root of both sides to get rid of the 3 on the left

x - 1 = cuberoot(64)

x - 1 = 4                     Add 1 to both sides

x - 1+1 = 4 + 1

x  =  5

==============================

Second Equation

4th root (x - 3)^5 = 32

Take the 5th root of both sides.

4th root(x - 3) = 2

This can be written as (x - 3)^(1/4) = 2

Now take the 4th power of both sides.

(x - 3) = 2^4

x - 3 =  16

add 3 to both sides.

x = 16 + 3

x = 19

============================

Equation 3

(x - 4)^(3/2) = 125

Take the cube root of both sides

(x - 4)^(1/2) = 125^(1/3)     1/3 is the cube root of something

(x - 4)^(1/2) = 5    

square both sides to get rid of the 2    

(x - 4) = 5^2

x - 4 = 25

Add 4 to both sides.

x = 25 + 4

x = 29

============================

Fourth Equation

(x + 2)^(4/3) = 16        

take the 4th root of both sides

(x + 2) ^(1/3) = 16^(1/4)

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

Cube both sides

(x + 2) = 2^3

x + 2 = 8  

Subtract 2 from both sides

x + 2 - 2 = 8-2

x = 6

##########################

The first step is the most critical. You must look at what you are going to take the root of. When you do, for this question, it must come out even.

Answer:

536

Step-by-step explanation:

Answer:

536

Step-by-step explanation:

just add all of then together 232 + 181=413 413+68+55

Answer:

3

Step-by-step explanation:

1/5 / 1/15 = 3

Answer:

3750

Step-by-step explanation:

average of 25 salaries = 2500

average of 25 = total payroll of 25/number of employees

2500 = total payroll of 25/25

total payroll of 25 = 2500 × 25

total payroll of 25 = 62500

total payroll of all 26 = total payroll of 25 plus manager

total payroll of all 26 = 62500 + 35000 = 97500

overall average = 97500/26

overall average = 3750

Systematic random sampling is used when selecting every nth item from a list of items. In this example, every 49th student starting with the 3rd student is selected.

In systematic random sampling, a list of items is created and every nth item is selected for the sample. This technique is useful when selecting a representative sample from a large population of items. In the example given, 496 students were listed and every 49th student starting from the 3rd student was selected. This is a systematic random sampling technique because the items were selected in a systematic and random fashion. The selection of every 49th student starting from the 3rd student ensures that the sample is representative of the population while also randomizing it so that all students have an equal chance of being selected.

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Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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Answer:

1. convert mixed fractions into improper fractions

2 1/3 ÷ 8 1/2

7/3 ÷ 17/2

2. flip second fraction and change the sign

7/3 × 2/17

3. solve by multiplying

14/51

I don't know if this can be simplified further