The sum of the first 7 terms of a geometric sequence is 16383.

Find the x-intercepts of the parabola with vertex (1,-108) and y-intercept (0,-105). Write your answer in this form: (X1,y1), (x

Stolb23 [73]

Answer:

(7, 0) and (-5, 0)

Step-by-step explanation:

Vertex form

$y=a(x-h)^2+k$

(where (h, k) is the vertex)

Given:

vertex = (1, -108)

$\implies y=a(x-1)^2-108$

Given:

y-intercept = (0, -105)

$\implies a(0-1)^2-108=-105$

$\implies a(-1)^2=-105+108$

$\implies a=3$

Therefore:

$\implies y=3(x-1)^2-108$

The x-intercepts are when y = 0

$\implies 3(x-1)^2-108=0$

$\implies 3(x-1)^2=108$

$\implies (x-1)^2=36$

$\implies x-1=\pm \sqrt{36}$

$\implies x=1\pm 6$

$\implies x=7, x=-5$

Therefore, the x-intercepts are (7, 0) and (-5, 0)

7 0

2 years ago

1/4, 32%, and 0.4 in least to greatest

lapo4ka [179]

Put them all in to decimals so dived 1 by 5 and 32 by 100 then they will all be decimals and you can more essay compare them

3 0

2 years ago

Read 2 more answers

HELP!!! HELP!!! WILL GIVE BRAINLIEST

Nesterboy [21]

Answer:

(a) Two x plus eight is greater than negative four

(b) x > -6; number line would be an open circle at -6 and the line pointing in the positive direction to be shaded

Step-by-step explanation:

(a)

Note first that the inequality sign ">" means "greater than", so 2x + 8 > -4 in written language is:

Two x plus eight is greater than negative four

(b)

We solve this just like how we'd solve it if it were 2x + 8 = -4: isolate the variable first.

Subtract 8 from both sides:

2x + 8 - 8 > -4 - 8

2x > -12

Divide by 2:

x > -12/2

x > -6

So, the solution set is all numbers greater than -6.

Drawn on a number line, we would first place an open circle at -6 (because we are using > rather than ≥, which would include the -6 in the solution set). Then, because our solution set includes all numbers greater than -6, we shade in the part of the line that points in the positive direction, so it should include numbers like -5, -4, -3, -2, -1, 0, 1, 2, ... and so on.

3 0

2 years ago

Read 2 more answers

A bank offers a money market account paying 4.9% interest compounded semiannually. A competing bank offers a money market accoun

soldier1979 [14.2K]

Assume $1000 at 4.9% semi-annually = $1,049.60
Assume $1000 at 4.8% daily = $1,049.17

Let's try a bigger number $50'000 4.9% semi-annually $52,480.01
 $50,000 4.8% daily = $52,458.37
It's a wash, the question is how long will you be investing, that might make a difference. I calculated 12 Millions over 6 years and bank A would be the better choice. Semi-annual compounded at 4.9%

4 0

2 years ago

What value makes 3(a+1.5)= -1.5 true

Reika [66]

First, write the equation:
3(a+1.5) = -1.5
Next, you can distribute 3 into the parentheses by multiplying 3 by a and 1.5. It should look like this:
3a + 4.5 = -1.5
When trying to find the value of a variable, you want to get the variable to one side of the equation by itself. Subtract 4.5 from both sides of the equation to get:
3a = -6
Now, divide both sides by 3 to get your final answer:
a= -2
The value that makes the equation true is -2
Hope this helped!

3 0

2 years ago