The true conditional statement, "If 1/2 (m∠ABC) = m∠ABD, then m∠ABC = 2(m∠ABD)," illustrates which property of equality?

(\tan ^(2)\theta \cos ^(2)\theta -1)/(1+\cos (2\theta ))=

Vitek1552 [10]

(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ))

Recall that

tan(θ) = sin(θ) / cos(θ)

so cos²(θ) cancels with the cos²(θ) in the tan²(θ) term:

(sin²(θ) - 1) / (1 + cos(2θ))

Recall the double angle identity for cosine,

cos(2θ) = 2 cos²(θ) - 1

so the 1 in the denominator also vanishes:

(sin²(θ) - 1) / (2 cos²(θ))

Recall the Pythagorean identity,

cos²(θ) + sin²(θ) = 1

which means

sin²(θ) - 1 = -cos²(θ):

-cos²(θ) / (2 cos²(θ))

Cancel the cos²(θ) terms to end up with

(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ)) = -1/2

7 0

3 years ago

What is the measure of angle FAB

antiseptic1488 [7]

It's an angle. That should work because it's obvious. Hope it helped.

7 0

3 years ago

FAST I NEED YOUR HELPPP

larisa [96]

Answer:

Function B has a greater slope than function A.

4 0

3 years ago

Y varies directly with X and has a constant rate of change of 6. When the value of Y is 11, then the value of X could be _____.

Bogdan [553]

Answer: The correct option is (B) less than 2.

Step-by-step explanation: Given that Y varies directly with X and has a constant rate of change of 6.

We are to find the possible value of X when the value of Y is 11.

Since Y varies directly with X, so we can write

$Y\propto X\\\\\Rightarrow Y=kx~~~~~~~~~~~~~~~(i),~~~~~~~~~\textup{[where 'k' is the constant of variation]}$

Since the rate of change is constant and is equal to 6, so we must have

$k=6.$

So, from equation (i), we have

$Y=kX\\\\\Rightarrow Y=6X~~~~~~~~~~~~~~~~~~~~~~(ii)$

Now, when Y = 11, then from equation (ii), we get

$Y=6X\\\\\Rightarrow 11=6X\\\\\Rightarrow X=\dfrac{11}{6}$

Thus, the value of X is less than 2 when Y = 11.

Option (B) is CORRECT.

8 0

3 years ago

What is the smallest value of y in the solution set to the system of equations below?

n200080 [17]

Answer:

The smallest value of y in the given two equations is 78

Step-by-step explanation:

Given as :

The two equation is given as :

y = x² + 6 x +23 ...........1

y = 18 x - 12. ..........2

Now, solving both equations

putting the value of y from eq 2 into eq 1

So, x² + 6 x +23 = 18 x - 12

Or, x² + 6 x +23 - 18 x + 12 = 0

Or, x² - 12 x + 35 = 0

Or, x² - 5 x - 7 x + 35 = 0

Or, x (x - 5) - 7(x - 5) = 0

Or, (x - 5) (x - 7) = 0

∴ x = 5 , 7

Now, for smallest value of y , take x = 5

∴ put the value of x in eq 2

So, y = 18 x - 12

I.e y = 18 × 5 - 12

Or, y = 90 - 12

∴ y = 78

Hence, The smallest value of y in the given two equations is 78 . answer

7 0

3 years ago