Identify the type of transformation given the rule H(x, y) = (x – 2, y).

Mathematics

1 answer:

Nonamiya [84]3 years ago

6 0

Answer:

x is transformed 2 units to the right.

Step-by-step explanation:

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Find 10 partial sums of the series. (round your answers to five decimal places.) ∞ 15 (−4)n n = 1

nikklg [1K]

Given

$\Sigma_{n=1}^\infty15(-4)^n$

The first 10 partial sums are as follows:

$S_1=\Sigma_{n=1}^{1}15(-4)^n=15(-4)=\bold{-60} \\ \\ S_2=\Sigma_{n=1}^{2}15(-4)^n=\Sigma_{n=1}^{1}15(-4)^n+15(-4)^2 \\ =-60+15(16)=-60+240=\bold{180} \\ \\ S_3=\Sigma_{n=1}^{3}15(-4)^n=\Sigma_{n=1}^{2}15(-4)^n+15(-4)^3 \\ =180+15(-64)=180-960=\bold{-780} \\ \\ S_4=\Sigma_{n=1}^{4}15(-4)^n=\Sigma_{n=1}^{3}15(-4)^n+15(-4)^4 \\ =-780+15(256)=-780+3,840=\bold{3,060} \\ \\ S_5=\Sigma_{n=1}^{5}15(-4)^n=\Sigma_{n=1}^{4}15(-4)^n+15(-4)^5 \\ =3,060+15(-1,024)=3,060-15,360=\bold{-12,300}$

$S_6=\Sigma_{n=1}^{6}15(-4)^n=\Sigma_{n=1}^{5}15(-4)^n+15(-4)^6 \\ =-12,300+15(4,096)=-12,300+61,440=\bold{49,140}$

The rest of the partial sums can be obtained in similar way.

7 0

3 years ago

A graph of average resting heart rates is shown below. The average resting heart

kolbaska11 [484]

Step-by-step explanation:

its A 10-year-old has the same average resting heart rate as a 20-year-old

hope it helps!

5 0

2 years ago

The table shows the blood pressures of 16 clinic patients. What is the interquartile range of the data?

Alex73 [517]

I’ve attached my work below....
I ran out of space so the step 5 the last step is subtract q1 and q3 which step 3 and 4
So 90.9-81.8=9.1

5 0

2 years ago

For what value of xis the square of the binomial 3x+1 is 9 times greater than the square of the binomial x–2?

Zanzabum

X = 5/6.

The square of 3x+1 is written as (3x+1)². The square of x-2 is (x-2)². Using the information given to us, we want to solve the equation

(3x+1)²=9(x-2)²
(3x+1)(3x+1)=9(x-2)(x-2)

Multiplying the first two binomials, we have:
3x*3x + 1*3x + 1*3x + 1*1 = 9(x-2)(x-2)
9x²+3x+3x+1 = 9(x-2)(x-2)
9x²+6x+1 = 9(x-2)(x-2)

Multiplying the second two binomials, we have:
9x²+6x+1 = 9(x*x-2*x-2*x-2(-2))
9x²+6x+1 = 9(x²-2x-2x+4)
9x²+6x+1 = 9(x²-4x+4)

Using the distributive property gives us
9x²+6x+1 = 9*x²-9*4x+9*4
9x²+6x+1 = 9x²-36x+36

Subtracting 9x² from both sides leaves us
6x+1 = -36x + 36

Adding 36x to both sides we get
42x+1 = 36

Subtracting 1 from both sides we have
42x = 35

Divide both sides by 42:
42x/42 = 35/42
x = 35/42 = 5/6

3 0

3 years ago

X^2+16x=13<br><img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2016x%20%3D%2013" id="TexFormula1" title=" {x}^{2}

sesenic [268]

Solve by completing the square:

x² + 16x + 64 = 13 + 64
(x + 8)² = 77
x + 8 = +/- √77

x = - 8 +/- √77

OR

x = - 8 - √77, - 8 + √77

3 0

3 years ago