Determine 3rd term in the geometric sequence whose first term is -8 and whose common ratio is 6

Please help asap. due today

Ksivusya [100]

Answer:

ASA

Step-by-step explanation:

∠BAC ≈ ∠CAD

AC = AC

∠BCA ≈ ∠ACD

5 0

2 years ago

4 cos²x – 1=0 What is the solution?

andreev551 [17]

Answer:

$x=\frac{\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{5\pi }{3}+2\pi n, n \in \mathbb{Z}$

$x=\frac{2\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{4\pi }{3}+2\pi n, n \in \mathbb{Z}$

or

$x=\frac{\pi}{3}+\pi n, n \in \mathbb{Z}$

$x=\frac{2\pi }{3}+\pi n, n\in \mathbb{Z}$

Step-by-step explanation:

$4\text{cos}^2(x)-1=0\\4\text{cos}^2(x)=1\\$

$cos(x)=\pm\sqrt{\frac{1}{4} }$

$cos(x)=\pm\frac{1}{2}$

So, when cos(x) is equal to

$\frac{1}{2} \text{ and } -\frac{1}{2}$ ?

For

$cos(x)=\frac{1}{2}$

We are talking about x = 60º and x = 300º, Quadrant I and IV, respectively. In radians:

$x=\frac{\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{5\pi }{3}+2\pi n, n \in \mathbb{Z}$

or

$x=\frac{\pi}{3}+\pi n, n \in \mathbb{Z}$

For

$cos(x)=-\frac{1}{2}$

We are talking about x = 120º and x = 240º, Quadrant II and III, respectively. In radians:

$x=\frac{2\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{4\pi }{3}+2\pi n, n \in \mathbb{Z}$

or

$x=\frac{2\pi }{3}+\pi n, n\in \mathbb{Z}$

6 0

3 years ago

In supply (and demand) problems, y is the number of items the supplier will produce (or the public will buy) if the price of the

SSSSS [86.1K]

Answer:

A) (17 ; 550)

B) $17/item

C) 550

Step-by-step explanation:

First we must calculate the intersection point of the two lines. Since in that point y has the same value in both equations, we can obtain x by equalling the two equations and then using that value for obtaining y:

$5x+465=-6x+652\\5x+6x=652-465\\11x=187\\x=\frac{187}{11}\\x=17$

So the value of x in the intersection point is 17. We now use this value with either one of the equations to obtain y. Let's use the supply equation:

$y=5*17+465\\y=550$

So the intersection point is (17 ; 550)

Supply and demand are in equilibrium when the amount of items on supply are the same as the ones on demand. That is the point were the two lines intersect, which means the selling price is the x coordinate and the amount of items is the y coordinate, so that is a selling price of $17/item with a number of items of 550.

3 0

2 years ago

Solve by the elimination method

Usimov [2.4K]

There is one solution. The solution of the system is (9,-5)

Option A is correct.

Step-by-step explanation:

We need to solve the system of equations by elimination method

$6x= 64+2y\\2x= -7-5y$

Rearranging the equations:

$6x-2y=64\,\,\,eq(1)\\2x+5y=-7\,\,\,eq(2)$

Eliminating y to find value of x:

Multiply eq(1) by 5 and eq(2) by 2 and add both equations:

$30x-10y=320\,\,\,\\4x+10y=-14\\--------\\34x=306\\x=\frac{306}{34}\\ x=9$

So, value of x= 9

Eliminating x to find value of y:

Multiply eq(1) by 2 and eq(2) by 6 and subtract both equations:

$12x-4y=128\\12x+30y=-42\\-\,\,\,\,-\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\\---------\\-34y=170\\y=\frac{170}{-34}\\ y=-5$

So, value of y = -5

There is one solution. The solution of the system is (9,-5)

Option A is correct.

Keywords: Solving system of equations

Learn more about Solving system of equations at:

#learnwithBrainly

5 0

3 years ago

Find the domain and range of the function represented by the graph

lora16 [44]

Answer:

4(b) , 5(a)

Step-by-step explanation:

(4). (b) Domain is {0, 1, 2, 3} and Range is { - 3, - 2, - 1, 0}

(5). (a) Domain is [ - 4, 2] and Range is [ - 4, 4]

or

domain: - 4 ≤ x ≤ 2 , range: - 4 ≤ y ≤ 4

6 0

2 years ago