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2 years ago

If (-3, y) lies on the graph of y = (1/2)^x, then y =

1 answer:

6 0

$\text{If (-3, y) lies on the graph of}\ \ y = \left(\dfrac{1}{2}\right)^x, \text{then substitute x = -3}\\\text{ to the equation and calculate y}:\\\\y=\left(\dfrac{1}{2}\right)^{-3}=(2)^3=8\\\\Answer:\ \boxed{y=8}\\\\Used:\ a^{-n}=\dfrac{1}{a^n}$

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I just need no. a please help me to prove this.

OleMash [197]

Answer: see proof below

Step-by-step explanation:

Given: A + B + C = π and cos A = cos B · cos C

scratchwork:

A + B + C = π

A = π - (B + C)

cos A = cos [π - (B + C)] Apply cos

= - cos (B + C) Simplify

= -(cos B · cos C - sin B · sin C) Sum Identity

= sin B · sin C - cos B · cos C Simplify

cos B · cos C = sin B · sin C - cos B · cos C Substitution

2cos B · cos C = sin B · sin C Addition

$2=\dfrac{\sin B\cdot \sin C}{\cos B \cdot \cos C}$ Division

2 = tan B · tan C

$\text{Use the Sum Identity:}\quad \tan(B+C)=\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}$

Proof LHS → RHS

Given: A + B + C = π

Subtraction: A = π - (B + C)

Apply tan: tan A = tan(π - (B + C))

Simplify: = - tan (B + C)

$\text{Sum Identity:}\qquad \qquad \qquad =-\bigg(\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}\bigg)$

Substitution: = -(tan B + tan C)/(1 - 2)

Simplify: = -(tan B + tan C)/-1

= tan B + tan C

LHS = RHS: tan B + tan C = tan B + tan C $\checkmark$

5 0

2 years ago

The weight of people in a small town in missouri is known to be normally distributed with a mean of 188 pounds and a standard de

Radda [10]

29=0.29 0.29*188=54.52 i think this is right but i may be wrong

5 0

2 years ago

What is 0.80 as a fraction

UNO [17]

8/10 = 4/5 would be the answer

4 0

2 years ago

Read 2 more answers

Anna starts a fixed deposit with $178000, the bank offers 9.5% per year simple interest for 8 months. she has the option of rest

soldier1979 [14.2K]

Using simple interest, we have that:

A) The interest due after 8 months is $11,272.33.

B) The total value of the investment will be of $189,986.24.

The amount of interest earning using simple interest, after t years, with an yearly interest rate of i and an initial investment of P is given by:

$E = Pit$

In this problem:

Deposit of $178,000, hence $P = 178000$ .
Interest rate of 9.5% per year, hence $i = 0.095$ .
8 months, the time is in years, hence $t = \frac{8}{12} = \frac{2}{3}$

Item a:

$E = Pit$

$E = 178000(0.095)\frac{2}{3} = 11272.33$

The interest due after 8 months is $11,272.33.

Item b:

For the second interest, we consider $P = 11272.33$ , hence:

$E_2 = Pit$

$E_2 = 11272.33(0.095)\frac{2}{3} = 713.91$

The total value will be composed by:

The initial deposit of $178,000.
The first interest of $11,272.33.
The second interest of $713,91.

Hence, it will be:

$T = 178000 + 11272.33 + 713.91 = 189986.24$

The total value of the investment will be of $189,986.24.

A similar problem is given at brainly.com/question/13176347

3 0

2 years ago

a bike race is 6 miles long by noon tammy had ridden 3/4 of the distance. at this rate how long will it take her to finish the r

Tasya [4]

The racer take 4 hours (between 8:00 to 12:00) to race 3/4 of 6 miles

3/4 of 6 miles = 18/4 = 4.5 miles

4 hours ⇒ 4.5 miles
1 hour ⇒ 4.5 ÷ 4 = 1.125 miles

The time taken to complete 6 miles = 6 ÷ 1.125 = 16/3 hours = 5.3 hours

4 0

2 years ago