What is the measure of angle RST? a. 87 b. 131 c. 93 d. 90

Let <img src="https://tex.z-dn.net/?f=%5Csf%20a%2Bb%2Ca-b%2Cab%2C%5Cdfrac%7Ba%7D%7Bb%7D" id="TexFormula1" title="\sf a+b,a-b,ab,

Black_prince [1.1K]

Answer:

171/40 or 4 11/40

Step-by-step explanation:

<h3>AP given</h3>

a + b, a - b, ab, a/b

6th term

<h3>Solution</h3>

Common difference

Difference of first two

d = (a -b) - (a + b) = -2b

Difference of second two

d= ab - (a - b)

Difference of last two

d = a/b - ab

Now comparing d:

-2b = ab - (a - b)
ab - a = - 3b
a(1 - b) = 3b
a = 3b/(1 - b)

and

a/b - ab = -2b
a(1/b - b) = -2b
a = 2b²/(b² - 1)

Eliminating a:

2b²/(b² - 1) = 3b/(1 - b)
2b/(b+1) = -3
2b = -3b - 3
5b = - 3
b = -3/5

Finding a:

a = 3b/(1 - b) =
3*(-3/5) *1/(1 - (-3/5)) =
-9/5*5/8 =
-9/8

So the first term is:

a + b = -3/5 - 9/8 = -24/40 - 45/40 = - 69/40

Common difference:

d = -2b = -2(-3/5) = 6/5

The 6th term:

a₆ = a₁ + 5d =
-69/40 + 5*6/5 =
-69/40 + 240/40 =
171/40 = 4 11/40

8 0

3 years ago

ANSWERRRR QUICKKKK PLEASEEEE

Brums [2.3K]

Answer: sqrt(2)/2 which is choice D

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

Explanation

(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).

The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle

180-135 = 45

Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2

sine is positive in quadrant 2

------------

Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2

Recall that y = sin(theta).

6 0

3 years ago

The average value of two positive numbers is 30% less than one of the two numbers. By which percentage is average value bigger t

Viefleur [7K]

Answer:

75% bigger

Step-by-step explanation:

Let the first number be x and the second be y.

So:

$Average = \frac{x + y}{2}$

And:

$Average = (1 - 30\%) * x$ -----30% less than x

Substitute $Average = (1 - 30\%) * x$ in $Average = \frac{x + y}{2}$

$\frac{x + y}{2} = (1 - 30\%) * x$

$\frac{x + y}{2} = (1 - 0.30) * x$

$\frac{x + y}{2} = 0.70 * x$

$\frac{x + y}{2} = 0.70x$

Cross multiply

$x + y = 0.70x * 2$

$x + y = 1.40x$

Collect like terms

$1.40x - x = y$

$0.40x = y$

Make x the subject

$x = \frac{y}{0.40}$

$x = 2.50y$

So, the average is:

$Average = (1 - 30\%) * x$

$Average = (1 - 30\%) * 2.50y$

$Average =0.70 * 2.50y$

$Average =1.75y$

Rewrite as:

$Average =(1 + 0.75)y$

Express as percentage

$Average =(1 + 75\%)y$

This means that the average is 75% bigger than the second number

6 0

3 years ago

Please help me with this question!

BigorU [14]

The answer is 8.8

You have to use SohCahToa to figure out the length of AB

3 0

3 years ago

1 + 1 . . . . . . . . Free answer

Gnom [1K]

its FISH... jk 2 LOL

5 0

3 years ago

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