What the sum of the first seven terms 4,12,36,108

Answers

Answer 1

Answer: 4,12,36,108,324,972,2916.

The pattern is each number is getting 3x bigger.

If you add all of the numbers, you will get 4372.

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The function g(x) = 3x2 − 12x + 7 written in vertex form is g(x) = 3(x − 2)2 − 5. What is the vertex of g(x)?(−6, −5) (−2, −5) (2, −5) (6, −5)

HELP! The average male Burns about 100 calories per mile and 140 calories per mile joggimg. using X to represent the miles walked and y to represent miles johged. Write a linear inequality modeling the number of miles a man should walk and jog in order to burn at least 500 calories

Answers

Answer:ididnt ask

Step-by-step explanation:

yes

Number with 1 decimal place is rounded to the nearest whole numberwhat the smallest number rounds up to 100?

Answers

Answer:

100.4

Step-by-step explanation:

100.4 will be smallest number with 1 decimal place and when rounded to the nearest whole number gives 100 as an answer

Which of the following is a rational number?

Answers

Answer:

A, B, D are the answers

Step-by-step explanation:

Polygon ABCDEFGH will be dilated by a scale factor of 3.4 with the origin as the center of dilation to produce polygon A′B′C′D′E′F′G′H′. What will the length of A'H'¯¯¯¯¯¯¯ be?

Answers

A'H'¯¯¯¯¯¯¯=2*3.4 = 6.8

Answer:

6.8 units

Step-by-step explanation:

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.Write the function in standard form. f(x) = 5x2 + 40x
Factor a out of the first two terms. f(x) = 5(x2 + 8x)
Form a perfect square trinomial. = 16
f(x) = 5(x2 + 8x + 16) – 5(16)
What is the function written in vertex form?

A.f(x) = 5(x + 4) – 80
B.f(x) = 5(x + 8) – 80
C.f(x) = 5(x + 4)2 – 80
D.f(x) = 5(x + 8)2 – 80

Answers

The right answer for the question that is being asked and shown above is that: "C.f(x) = 5(x + 4)2 – 80." Write the function in standard form. f(x) = 5x2 + 40x. Factor a out of the first two terms. f(x) = 5(x2 + 8x). Form a perfect square trinomial. = 16. f(x) = 5(x2 + 8x + 16) – 5(16). The vertex form is C.f(x) = 5(x + 4)2 – 80

Use the formula $(a+b)^2=a^2+2ab+b^2$ for quadratic trinomial. Then you can form from a quadratic trinomial perfect square:

$x^2 + 8x + 16=x^2+2\cdot x\cdot 4+4^2=(x+4)^2$ .

From the last given step you have that

$f(x) = 5(x^2 + 8x + 16)-5\cdot 16$ .

Since 5·16=80, you can substitute the previous expression for perfect square into function expression and get:

$f(x)=5(x+4)^2-80$ .

This means, when x=-4, f(-4)=-80 and vertex has coordinates (-4,-80).

Answer: correct choice is C.

how to solve 4n²-3n-7=0

Answers

$4n^2-3n-7=0\n \n a=4, \ \ b=-3 \ \ c=-7\n \n \Delta = b^(2)-4ac = (-3)^(2)-4*4* (-7)= 9+112=121$

$x_(1)=(-b-√(\Delta ))/(2a) =( 3-√( 121))/(2*4)=( 3-11)/(8)= (-8 )/( 8)=-1 \n \nx_(2)=(-b+√(\Delta ))/(2a) =( 3+√( 121))/(2*4)=( 3+11)/(8)= (14 )/( 8)= (7)/(4)=1(3)/(4)$

$4n^2-3n-7=0\n\n\underbrace{(2n)^2-2\cdot2n\cdot(3)/(4)+\left((3)/(4)\right)^2}_((*))-\left((3)/(4)\right)^2=7\n\n(2n-(3)/(4))^2-(9)/(16)=7\n\n(2n-(3)/(4))^2=7+(9)/(16)\n\n(2n-(3)/(4))^2=(112)/(16)+(9)/(16)\n\n(2n-(3)/(4))^2=(121)/(16)\to2n-(3)/(4)=\sqrt(121)/(16)\ \vee\ 2n-(3)/(4)=-\sqrt(121)/(16)$

$2n=(11)/(4)+(3)/(4)\ \vee\ 2n=-(11)/(4)+(3)/(4)\n\n2n=(14)/(4)\ \vee\ 2n=-(8)/(4)\n\n2n=(7)/(2)\ \vee\ 2n=-2\n\nn=(7)/(4)\ \vee\ n=-1$

$(a-b)^2=a^2-2ab+b^2$

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