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3 years ago

12

Connections between tan theta and tan(90 + theta)

1 answer:

Kaylis [27]3 years ago

7 0

Tan(90+ theta) = (tan90 + tantheta)/(1-tan90tantheta)

= ( sin90costheta + sintheta cos 90) / (cos90costheta - sin90sintheta))
= sin(90 + theta)/ cos(90+ theta) = costheta/-sintheta = - 1/tantheta

tan(90 + theta ) = -1/tantheta

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Explain how you would solve 16/c=8. Then solve the equation

Hoochie [10]

$\frac{16}{c} = 8$

16 = c8

c = $\frac{16}{8}$

c = 2

hope this helps!

7 0

3 years ago

Find the product.<br> (x+2)(x−2)=

kaheart [24]

Answer:

x² - 4

Step-by-step explanation:

Step 1: Write expression

(x + 2)(x - 2)

Step 2: FOIL

x² + 2x - 2x - 4

Step 3: Combine like terms

x² - 4

8 0

3 years ago

Read 2 more answers

Complete the square. Fill in the number that makes the polynomial a perfect-square

NeX [460]

Answer:

h² - 10h + <u>25</u>

Step-by-step explanation:

h² - 10h + _ → (h - 5)² = h² - 10h + 25

3 0

3 years ago

1. S(–4, –4), P(4, –2), A(6, 6) and Z(–2, 4) a) Apply the distance formula for each side to determine whether SPAZ is equilatera

Aleksandr [31]

Answer:

a) SPAZ is equilateral.

b) Diagonals SA and PZ are perpendicular to each other.

c) Diagonals SA and PZ bisect each other.

Step-by-step explanation:

At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.

a) If figure is equilateral, then SP = PA = AZ = ZS:

$SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}$

$SP \approx 8.246$

$PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}$

$PA \approx 8.246$

$AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}$

$AZ \approx 8.246$

$ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}$

$ZS \approx 8.246$

Therefore, SPAZ is equilateral.

b) We use the slope formula to determine the inclination of diagonals SA and PZ:

$m_{SA} = \frac{6-(-4)}{6-(-4)}$

$m_{SA} = 1$

$m_{PZ} = \frac{4-(-2)}{-2-4}$

$m_{PZ} = -1$

Since $m_{SA}\cdot m_{PZ} = -1$ , diagonals SA and PZ are perpendicular to each other.

c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:

$M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)$

$M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)$

$M_{SA} = (-2,-2)+(3,3)$

$M_{SA} = (1,1)$

$M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)$

$M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)$

$M_{PZ} = (2,-1)+(-1,2)$

$M_{PZ} = (1,1)$

Then, the diagonals SA and PZ bisect each other.

8 0

3 years ago

Find the discriminant and the number of real roots for this equation.

Margaret [11]

Our discriminant is 0 so, $4x^2 + 12x + 9 = 0$ has one real root.

Option C is correct.

Step-by-step explanation:

we need to find the discriminant and the number of real roots for the following equation:

$4x^2 + 12x + 9 = 0$

The discriminant is found by using square root part of quadratic formula:

$b^2-4ac$

where b =12, a=4 and c=9

Putting values:

$=b^2-4ac\\=(12)^2-4(4)(9)\\=144-144\\=0$

To find out the number of real roots using discriminant we have following rules:

if discriminant b^2-4ac >0 then 2 real roots
if discriminant b^2-4ac =0 then 1 real root
if discriminant b^2-4ac <0 then no real roots

Since our discriminant b^2-4ac is 0 so, $4x^2 + 12x + 9 = 0$ has one real root.

Option C is correct.

Keywords: discriminant

Learn more about discriminant at:

#learnwithBrainly

6 0

3 years ago