MATHEMATICS
HIGH SCHOOL

sin θ =

cos θ =

Answer:

Answer:

Sin θ = and .

Step-by-step explanation:

Given : cot θ = -8/15.

To find : sin θ and cos θ.

Solution : We have given

cot θ = .

cot θ = .

= .

Hypotenuse =

Hypotenuse = .

Hypotenuse = .

Hypotenuse = .

Hypotenuse =17 .

Sin θ = .

Plugging the values.

Sin θ = .

Cos θ = .

Cos θ = .

Therefore, Sin θ = and .

Answer: Sin(θ)=−15/17

cos(θ)=8/17

cos(θ)=8/17

MIDDLE SCHOOL

What is the factored dorm of 1256x to the sixth power minus 8

Answer:

8(157x^6 - 1)

Step-by-step explanation:

1256x^6 - 8

Start by factoring out a common factor. 1256 and 8 are both divisible by 8.

1256x^6 - 8 = 8(157x^6 - 1)

157 is prime, so 157x^6 - 1 is not factorable.

Answer: 8(157x^6 - 1)

MIDDLE SCHOOL

Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Which of the following are true? Select all that apply. A. One pound of pistachios plus 1 pound of almonds cost $20.

B. The pistachios cost twice as much per pound as the almonds.

C. Reducing the number of pounds of almonds by one results in a total cost of $40. D. The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48. E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.

We want to find a system of equations, and by solving that system we will be able to see which statements are true.

We will see that options A, C, and E are true.

We know that:

Venetta buys 2lb of pistachios

Venetta buys 3 lb of almonds.

Let's define the variables:

x = price per pound of pistachios

y = price per pound of almonds.

Now we also know that:

"The pistachios cost $4 more per pound than the almonds."

This can be written as:

"She pays a total of $48"

This can be written as:

So a system of equations:

To solve this system, the first thing we need to do is isolate one of the variables in one of the equations, particularly we can see that x is already isolated in the first equation, so we can skip that step.

Now we can replace the isolated variable in the other equation to get:

now we can solve this for y:

now that we know this, we can use:

now that we know:

y = $8

x = $12

Let's see which statements are true:

A) One pound of pistachios plus 1 pound of almonds cost $20.

True, $8 + $12 = $20.

B) The pistachios cost twice as much per pound as the almonds.

False, $12 is not the double of $8.

C) Reducing the number of pounds of almonds by one results in a total cost of $40.

True, one pound less of almonds means $8 less in the price.

D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48

Simplifying the expression we get:

2*(a - 4) + 3a = -8 + a = 48

a = 48 + 8 = 52

This clearly does not model the price of one pound of almonds, this statement is false.

E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.

Solving the equation we get:

2*p + 3*p - 12 = 48

5*p = 48 + 12 = 60

p = 60/5 = 12

This is true.

If you want to learn more, you can read:

brainly.com/question/20067450

COLLEGE

Find S7 for the geometric series 2 + -6 + 18 + -54 +…

Answer:

1094

Step-by-step explanation:

The sum of terms of a geometric series is given by ...

Sn = a1·(r^n -1)/(r -1)

You want the sum for ...

a1 = 2, r = -3, n = 7

Filling in the numbers, we get ...

S7 = 2·((-3)^7 -1)/(-3-1) = 2(-2188)/(-4)

S7 = 1094

HIGH SCHOOL

How are codons and anticodons alike?

A codon is a group of three mRNA bases while an anticodon is a group of three tRNA bases. For example AUC is a codon and UAG is an anticodon that matches it.