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3 years ago

8

What is the explicit formula for this sequence -7, -4, -1, 2, 5

1 answer:

Nataliya [291]3 years ago

6 0

Answer:

$\large\boxed{a_n=3n-10}$

Step-by-step explanation:

It's an arithmetic sequence.

$-4-(-7)=-4+7=3\\-1-(-4)=-1+4=3\\2-(-1)=2+1=3\\5-2=3$

The difference is constant.

The explicit formula of an arithmetic sequence:

$a_n=a_1+(n-1)d$

Substitute:

$a_1=-7,\ d=3$

$a_n=-7+(n-1)(3)$ <em>use distributive property</em>

$a_n=-7+3n-3\\\\a_n=3n+(-7-3)\\\\a_n=3n-10$

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Evaluate the function <br><br> f(x) = 3x^2 + 4x + 19<br><br> Find f(-7)

yanalaym [24]

Answer:

Step-by-step explanation:

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1 year ago

Please help me in this question.Tell me if it is good. And if it is not good then do it for me please.

Orlov [11]

Answer:

Y = 170, Z = 64.

Step-by-step explanation:

Since y is the external angle to x, which you got right, it is in fact, 180-10, = 170 degrees. And since z is the external to our unknown angle, that means it is equal to the sum of the other two angles in the triangle. That means z is 54 + 10, which is 64.

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3 years ago

In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the<br> function with its graph

MA_775_DIABLO [31]

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

$f(x)=(x-2)^{2}+1$

45)

The function g(x) is given by:

$g(x)=f(x-1)$

using f(x) we can find f(x-1)

$g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1$

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

$g(x)'=2(x-3)$

$2(x-3)=0$

$x=3$

Puting it on g(x) we will get y value.

$y=g(3)=(3-3)^{2}+1$

$y=g(3)=1$

<u>Then, the minimum point of this function is (3,1) and it corresponds to (A)</u>

46)

Let's use the same method here.

$g(x)=f(x+2)$

$g(x)=((x+2)-2)^{2}+1$

$g(x)=(x)^{2}+1$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2x$

$0=2x$

$x=0$

Evaluatinf g(x) at this value of x we have:

$g(0)=(x)^{2}+1$

$g(0)=1$

<u>Then, the minimum point of this function is (0,1) and it corresponds to (C)</u>

47)

Let's use the same method here.

$g(x)=f(x)+2$

$g(x)=(x-2)^{2}+1+2$

$g(x)=(x-2)^{2}+3$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}+3$

$g(2)=3$

<u>Then, the minimum point of this function is (2,3) and it corresponds to (B)</u>

48)

Let's use the same method here.

$g(x)=f(x)-3$

$g(x)=(x-2)^{2}+1-3$

$g(x)=(x-2)^{2}-2$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}-2$

$g(2)=-2$

<u>Then, the minimum point of this function is (2,-2) and it corresponds to (D)</u>

<u />

I hope it helps you!

<u />

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3 years ago

If you needed to triple a recipe, would the ratio change? Explain.

sveticcg [70]

Yes the ratio would change because it needs 3 times more than the original amount so you would multiply it by 3

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3 years ago

Find the distance between points (-3,-4) and (1,-2)

Ludmilka [50]

Answer:

√20 or 4.47 ish

Step-by-step explanation:

√(1--3)²+(-2--4)²

√(1+3)²+(-2+4)²

√(4)²+(2)²

√16+4

√20

4.47 ish

(Hopefully this is correct, have a nice day!)

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3 years ago