Given that 2x - 3y = 8 and 4x + 3y = -2, what is the product of x and y?

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Answer:

33.2

Step-by-step explanation:

Given that Coach King is holding a free-throw shooting contest for some students in his PE class. The students participating in the contest shoot 10 free throws each.

For finding mean we sum up all the entries and divide by total number here 10

Total

=[tex]26+34+42+40+38+35+20+34+45+18\\=332[/tex]

Mean =[tex]\frac{332}{10} \\=33.2[/tex]

Out of the four options given, we find that Option C is right

To prove the given trigonometric identity:

(sec 12A - 1)/(sec 6A -1) = tan 12A / tan 3A

We will proceed by transforming the left side of this identity and attempt to simplify it to the form of the right side. First, let's use the trigonometric identities.

Secant and tan identities are key to simplifying this expression. It's important to note that:

sec(x) = 1/cos(x)

tan(x) = sin(x)/cos(x)

Let's rewrite the left side of the equation using these identities:

((1/cos(12A)) - 1) / ((1/cos(6A)) -1)

Now bring each term over a common denominator:

((1 - cos(12A))/cos(12A)) / ((1 - cos(6A))/cos(6A))

By simplifying the complex fraction, we get:

(cos(6A) - cos(12A)) / (cos(12A) - 1)

Next, we can use the following identity to transform the numerator: sin(A+B) = sin A cos B + cos A sin B.

Applying a form of this identity to cos(6A - 12A), we get that the numerator is equivalent to -sin(6A)sin(12A).

Similarly, we can express tan 12A as sin(12A)/cos(12A) and tan 3A as sin(3A)/cos(3A).

Substituting these into our original equation, we obtain:

(-sin(6A) * sin(12A)) / sin(12A) * cos(3A) = tan 12A / tan 3A

After canceling out sin(12A) from the numerator and denominator, we are left with:

-sin(6A) / cos(3A) = tan 12A / tan 3A

Given that sin(6A) = 2sin(3A)cos(3A), the left-hand side simplifies to 2 * tan 3A, and since tan 3A is equivalent to sin(3A)/cos(3A), the expression simplifies to tan 12A / tan 3A, proving the identity.

The given polynomial is classified as a trinomial because it has three terms. The highest exponent is 5, making the degree of the polynomial 5. Therefore, the correct answer is D) trinomial; 5.

The given polynomial is 3y2 - y4 + y5. This polynomial consists of three terms, so it is a trinomial.

To find the degree of the polynomial, we look for the term with the highest exponent in the polynomial.

In this case, it is y5, so the degree of the polynomial is 5. Therefore, the correct classification and degree for the given polynomial is D) trinomial; 5.

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This question was asked almost 3 years ago, there is a very good chance that they're not even in school anymore, it's crazy to think about. 3 years ago, I was living in washington, and had joined online school for the first time, while this guy was here, begging people for answers to a question so he could pass highschool. Now, he's probably living his best life right now and doesn't even know what I'm typing right now, either that, or he's working at McDonald's. Honestly though, time flies by so fast though, it really is crazy.

The perimeter of the figure is 423.52 m

The area of Rectangle is length times of width.

From the figure the length of rectangle is 105m and width is 68m.

Perimeter of rectangle=2(length+width)

First the rectangle part with the length is 105m,

2(105)=210m

For the semicircle part, the circumference of the circle is 2πr

The circumference of the semicircle is 1/2(2πr)=πr

Diameter of semicircle=68

Radius is 34

circumference of the semicircle is 34(3.14)=106.76

As there are two semicircles=2(106.76)=213.52

The total perimeter of this figure is 213.52+210=423.52m

Hence, the perimeter of this figure is 423.52 m

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Total number of marbles in the bag =20

Number of blue marbles =4

Now we just want two blue marbles out of four.

Probability of taking out first marble which is blue =4/20

Now after we took out one blue marble , number of blue marbles left are 3.

Probability of taking out second marble which is blue =3/20

Total probability = 4/20 *3/20 = 12/400

So probability of taking out two blue marbles is 0.03 or 12/400.

Answer:

14m by 7m

Step-by-step explanation:

thats the answer

The dimensions that maximize the area is a length of 14m and a width of 7m.

For a rectangle of dimensions L and W, the area is:

A = L*W

In this case, we assume  L > W, and then one of the sides that measures L is the side where we will use the wall (so we save more of the fencing).

Then for the other 3 sides we use the 28 m of fencing, we will have:

28m = 2*W + L

Isolating L we get:

L = 28m - 2*W

And now we want to maximize the area, so first we can write:

A = L*W = (28m - 2*W)*W

A = 28m*W - 2*W^2

This is a quadratic function, where the vertex is the maximum, it happens at:

W = -28m/(2*-2) = 7m

So the width must be 7m, and the length is:

L = 28m - 2*7m = 14m

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Final answer:

Tripling the side lengths of a pentagon multiplies its perimeter by three, resulting in a new perimeter that is three times the original perimeter.

Explanation:

When we triple the side lengths of a pentagon, we essentially multiply the length of each side by three. Since a pentagon has five sides, if each side is tripled, the new perimeter will be three times the original perimeter. This is because the perimeter of any polygon is the sum of the lengths of its sides. In a more mathematical expression, if the original length of a side of the pentagon is s, the perimeter (P) of the original pentagon is 5s. When we triple the side length, each side becomes 3s, making the new perimeter P' to be 5(3s) = 3(5s) or simply three times the original perimeter, which is 15s.

The equation that represents the value of [x] is -

x + 4x - 85 = 90.

Given is a geometrical image as shown.

We can write the equation as -

x + 4x - 85 = 90

Therefore, the equation that represents the value of [x] is -

x + 4x - 85 = 90.

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The ball travels approximately 82.1 feet from corner A to corner B on the tennis court.

The ball travels along the diagonal of the rectangular court from corner A to corner B. We can find the distance using the Pythagorean theorem. The diagonal of the court is the hypotenuse of a right triangle with sides of 27 feet and 78 feet. Therefore, the distance the ball travels is approximately the square root of (27^2 + 78^2) feet, which is approximately 82.1 feet.

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replacing the values for x

 x = 2

2(2)^2 +3(2) +5 = 19

Answer:

Step-by-step explanation:

Answer:

The line passing through the origan (Graph 2 on Edu is correct.)

Step-by-step explanation:

The linear function described as a function with direct variation is the second graph .

Only those linear relationships where b = 0 relate to direct variation because the formula for a linear relationship between two variables is y = m x + b. A straight line that travels through the origin is the graph of direct variation (of a proportional relationship).

Given :

The four graphs of a line. Each graph represents a linear equation .

As, Direct variation equation does not have y intercept 'b'

and, Direct variation function crosses through origin .

First graph does not crosses through origin.

Second graph crosses through origin (0,0)

Also, Graphs with vertical and horizontal lines do not directly depict change.

Hence, second graph is the linear function.

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Answer:

The correct answers are -

Definition, Postulate, Corollary and Theorem.

Step-by-step explanation:

When we want to prove something, we already know that one thing is already there, proven and we have to prove the other part.

A definition is something that is absolutely true and valid. It can also be used to prove another statement.

A postulate is a statement that is assumed to be true, and is used to prove other statements.

A corollary is a direct consequence of an already proven fact, and can also be used used to prove other statements.

Theorems are already proven statements. These are used to prove other statements as well.