What is a segment that connects the midpoints of two sides of a triangle?

How many terms are there in a geometric series if the first term is 2, the common ratio is 4, and the sum of the series is 2,730

Furkat [3]

Answer:

n = 6

Step-by-step explanation:

Givens

r = 4

a = 2

Sum = 2730

Equation

Sum = a(1 - r^n)/(1 - r)

Solution

2730 = 2 (1 - 4^n) / (1 - 4) Reduce the denominator

2730 = 2(1 - 4^n)/-3 Multiply both sides by -3

2730*-3 = 2(1 - 4^n) Simplify the left

-8190 = 2(1 - 4^n) Divide by 2

-8190/2 = 1 - 4^n Simplify

-4095 = 1 - 4^n Subtract 1 from both sides.

-4096 = - 4^n Divide by - 1

4096 = 4^n This looks like n is fairly large. You could use logs. Try n = 6.

4^6 does equal 4096 So your answer is 6.

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

Let's try it with logs. Ignore this if you don't know how to do this.

log(4096) = log(4)^n

log(4096) = n*log(4) Divide by log 4

log(4096)/log(4) = n

3.6124 / 0.6021 = n

n = 6

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

The hint is very helpful. Make sure you can follow it through

6 0

3 years ago

- 2x - 66 = 84 + 4x<br> Solve please show your work

Mrac [35]

Answer:

Step-by-step explanation:

-2x-66=84+4x

collecting like terms

-2x-4x=84+66

-6x=150

divide both side by -6

-6x/-6=150/6

x=-25

4 0

3 years ago

GIVING BRAINLIEST TO WHOEVER ANSWERS FIRST!!!

kap26 [50]

I think it is the 4th answer I learned about this in 8th grade and had a A in that class so I am 90% sure it is correct

7 0

3 years ago

Read 2 more answers

Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

$\\$

⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$