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Crazy boy [7]
2 years ago
11

For the geometric sequence x, (2x + 1), (4x + 10), ... the value of x, to the nearest

Mathematics
1 answer:
mel-nik [20]2 years ago
6 0

Answer:

x ≈ 0.17

Step-by-step explanation:

There is a common ratio r between consecutive terms in a geometric sequence, that is

r = \frac{a_{2} }{a_{1} } = \frac{a_{3} }{a_{2} } , substitute values

\frac{2x+1}{x} = \frac{4x+10}{2x+1} ( cross- multiply )

x(4x + 10) = (2x + 1)² ← expand using FOIL

4x² + 10x = 4x² + 4x + 1 ( subtract 4x² + 4x from both sides )

6x = 1 ( divide both sides by 6 )

x = \frac{1}{6} ≈ 0.17 ( to the nearest hundredth )

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Which table shows the function y = -2x + 4? A) x y 0 4 1 2 2 0 B) x y 1 25 2 26 3 27 C) x y 0 -4 1 -2 2 0 D) x y -1 6 -2 8 -3 12
Svet_ta [14]
The answer is A.

From looking at the A graph, you must plug in the x variable into<span> y = -2x + 4.

y = -2(0) + 4 = 4
y = -2(1) + 4 = 2
y = -2(2) + 4 = 0</span>
4 0
3 years ago
hey, can someone please double check these questions for me / or help me solve them if they are incorrect? thank you U-U ​
zzz [600]

Question 11

The directrix is a horizontal line, which means the parabola opens either upward or downward. In this case, it opens downward. This is because all answer choices have a negative leading coefficient. Also, it's because the focus is below the directrix.

For vertically opening parabolas, we use this form

4p(y-k) = (x-h)^2

where (h,k) is the vertex and p is the focal distance, aka the distance from the vertex the focus. To find (h,k), we start at the focus (0,-4) and move directly up until we reach the directrix y = 4. We'll arrive at (0,4). The midpoint of (0,-4) and (0,4) is (0,0) which is the vertex's location. So (h,k) = (0,0).

Note that in moving from (0,-4) to (0,4) is a span of 4 units. So this is the value of p.

Plug h = 0, k = 0, p = 4 into the equation mentioned and solve for y

4p(y-k) = (x-h)^2

4*4(y-0) = (x-0)^2

16y = x^2

y = (1/16)x^2

The only adjustment we need to make is to change the 1/16 to -1/16 so that the parabola opens downward.

<h3>Answer:  Choice D.  y = -(1/16)x^2</h3>

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

Question 3

The given equation is in the form y = ax^2+bx+c

In this case,

  • a = 2
  • b = 4
  • c = 3

Let's compute the x coordinate of the vertex h

h = -b/(2a)

h = -4/(2*2)

h = -1

This h value is plugged into the original function to find k

f(x) = 2x^2+4x+3

f(-1) = 2(-1)^2+4(-1)+3

f(-1) = 1

We find that h = -1 and k = 1 pair up together. In short, (h,k) = (-1,1) is the vertex.

<h3>Answer: Choice B.  (-1,1)</h3>
8 0
2 years ago
Evaluate x2/y + x2/z , if x = 10, y = -5, and z = -2.
ch4aika [34]
X^2/y + x^2/z =
10^2/(-5) + 10^2/(-2) =
100/(-5) + 100/(-2) =
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-70
6 0
3 years ago
Read 2 more answers
Solve for y: 2x+3y=21
stealth61 [152]

Answer:

y = 7 - 2x/3

Step-by-step explanation:

Make the y alone, so 3y = -2x+21

Divide everything else by 3, so y = -2x/3 +7

You end with the answer of y= 7-2x+3

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Cloud [144]
The answer is 12.6 for sure
6 0
3 years ago
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