A square with an area of 4 in² is dilated by a factor of 7. What is the area of the dilated square?

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.

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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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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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:

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.

(-9, -6) (-5,1 ) (1,12) ordered pairs that could be used to show that this claim is incorrect.

A relation is a function if it has only One y-value for each x-value.

The given ordered pairs are {(–9, 1), (–5, 2), (0, 7), (1, 3), (6, –10)}

minus nine comma one,

minus five comma two

zero comma seven

one comma three

six comma minus ten

If Josiah claims that the ordered pair (6, –10) can be replaced with any ordered pair and the set will still represent a function.

Then we can replace with (-9, -6) (-5,1 ) (1,12) to make it incorrect. Two x values should not have same value.

Hence (-9, -6) (-5,1 ) (1,12) ordered pairs that could be used to show that this claim is incorrect.

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Answer: The answer is 232.5

Step-by-step explanation:First you to set up the proportion. If 80% equals to 12. You Would do 80 over hundred becuase percent is out of hundred (80/100) then you would do 12 over x or any other variable. FROM there on you would to the butter fly method. Cross multiply . ( 80 times variable, 12 times 100) now to isolate the variable you have to do inverse operation. So now do 1200 divided by 80 . And 80 divided by 80. Now you know.

X=15.

But were no done yet lol. Now do length times width times height to get the volume. 15 times 2 times 31/4 (7 3/4) . now we're done. Your welcome

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 average rate of change of the function h(x) = x² - 7x +7 over the interval 2 ≤ x ≤ 9 is 4.

The average rate of change for a function is determined by the difference in y values divided by the difference in x values over a specified interval. In this case, the function is h(x) = x² - 7x + 7, and the interval is 2 ≤ x ≤ 9. First, we calculate h(2) and h(9) for the y values.

h(2) = (2)² - 7(2) + 7 = 4 - 14 + 7 = -3

h(9) = (9)² - 7(9) + 7 = 81 - 63 + 7 = 25
Then, apply the formula for average rate of change which is (h(9) - h(2)) / (9 - 2).

(25 - (-3)) / (9 - 2) = 28 / 7 = 4

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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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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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replacing the values for x

 x = 2

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

Final answer:

The value of 'a' is found to be approximately 328.33 when b = 3 and c = 3, using the constant of proportionality obtained from the given values a = 197 when b = 5 and c = 5.

Explanation:

When a quantity varies directly as another quantity and inversely as the square of a third quantity, we can express this relationship with the following equation:

a = k x (b / c2)

where k is the constant of proportionality. Given that a = 197 when b = 5 and c = 5, we can solve for k:

197 = k x (5 / 52)

197 = k x (5 / 25)

197 = k / 5

k = 197 x 5

k = 985

Now we can use this value for k to find a when b = 3 and c = 3:

a = 985 x (3 / 32)

a = 985 x (3 / 9)

a = 985 x (1/3)

a = 328.333...

Hence, the value of a, when b = 3 and c = 3, is approximately 328.33.