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3 years ago

Is the relationship shown by the data linear? If so, model the data with an equation. x= -7, -5, -3 ,-1 , y = 5, 9, 13, 17

1 answer:

4 0

The data is linear as the x and y are both increasing at a set amount.
X increases by 2 each time Y increases by 4.
Our slope would be 2x because every time x goes up 1 y goes up 2.
With that knowledge I can figure that if you increased the point -1,17 by the slope to get 0,21 that would be the y intercept.
Thus the equation should be y=2x+21

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A. [4 marks]

storchak [24]

The value of d is -2

Step-by-step explanation:

The nth term of the arithmetic sequence is $u_{n}=u_{1}+(n-1)d$ , where

$u_{1}$ is the first term
d is the common difference between each 2 consecutive terms

The nth term of the geometric sequence is $u_{n}=u_{1}r^{n-1}$ , where

$u_{1}$ is the first term
r is the common ratio between each two consecutive terms $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∵ $u_{1}$ of an arithmetic sequence is 1

∵ The common difference is d, where d ≠ 0

∵ $u_{2}$ , $u_{3}$ , $u_{6}$ are the first 3 terms of a geometric sequence

∵ $u_{2}$ = 1 + (2 - 1)d

∴ $u_{2}$ = 1 + d

∵ $u_{3}$ = 1 + (3 - 1)d

∴ $u_{2}$ = 1 + 2d

∵ $u_{6}$ = 1 + (6 - 1)d

∴ $u_{2}$ = 1 + 5d

∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,

(1 + 5d)

∵ The common ratio in the geometric sequence is $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∴ $r=\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

- Use cross multiplication with the equal fractions

∵ $\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)

∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²

- Add like terms in each side

∴ 1 + 4d + 4d² = 1 + 6d + 5d²

- Subtract 1 from both sides

∴ 4d + 4d² = 6d + 5d²

- Subtract 4d from both sides

∴ 4d² = 2d + 5d²

- Subtract 4d² from each side

∴ 0 = 2d + d²

- Take d as a common factor

∴ 0 = d(2 + d)

- Equate each factor by 0

∴ d = 0 but we will reject it because d ≠ 0

∴ 2 + d = 0

- Subtract 2 from both sides

∴ d = -2

The value of d is -2

Learn more:

You can learn more about the sequence in brainly.com/question/1522572

#LearnwithBrainly

7 0

3 years ago

Can you help me please!!!!

Alexeev081 [22]

Answer:

Step-by-step explanation:

(-10,0)(0,-4)

find slope

m=-2/5

b=-4

y=-2/5x-4

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3 years ago

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What is the perimeter of the rectangle?

UkoKoshka [18]

B. Because 5 t 5 t 4 t 4 equals 18

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3 years ago

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N76 [4]

Y=-1/3x+5
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3 years ago

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Find the value of X

olchik [2.2K]

<h3>Answer: 112</h3>

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

Explanation:

The angle adjacent to the 146 degree angle is 180-146 = 34 degrees.

In other words, the angles 34 and 146 combine to 180. These angles are supplementary.

The tickmarks on this triangle tell us it is isosceles. The angles opposite the congruent sides are congruent angles. So the unmarked interior angles (not marked x) are 34 degrees each.

Now use the fact that any triangle has its interior angles always add to 180

x+34+34 = 180

x+68 = 180

x = 180-68

x = 112

5 0

3 years ago