What is the 42rd term in the arithmetic sequence 15,11,7 (give solution)

For each value of u determine it is a solution to 36=47-u u=9 u=11 u =8 u=38

OlgaM077 [116]

Answer:

u=11

Step-by-step explanation:

1. 36=47-9

36≠38

2. 36=47-11

36=36

3. 36=47-8

36≠39

4. 36=47-38

36≠9

3 0

2 years ago

Read 2 more answers

Which of the following shows the factors of 5x2 + 17x + 6? A. (5x + 1)(x + 6) B. (5x + 2)(x + 3) C. (5x + 3)(x + 2) D. (5x + 6)(

zysi [14]

Answer:

B. $(x+3)(5x+2)$

Step-by-step explanation:

The given quadratic trinomial is;

$5x^2+17x+6$

Comparing this to $ax^2+bx+c$ , we have a=5,b=17,c=6.

$ac=5\times6=30$

Two factors of 30 that add up to 17 is 15 and 2.

We split the middle term to obtain;

$5x^2+15x+2x+6$

We factor by grouping;

$5x(x+3)+2(x+3)$

Factor further

$(x+3)(5x+2)$

The correct answer is B.

5 0

3 years ago

Read 2 more answers

The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f

Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

$h(t)=-16t^{2}+25t+5$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

$h(t)=-16(t^{2}-\frac{25}{16}t)+5$

Complete the square

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}$

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

$h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

The vertex is the point $(\frac{25}{32},\frac{945}{64})$

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

$0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

$16(t-\frac{25}{32})^{2}=\frac{945}{64}$

$(t-\frac{25}{32})^{2}=\frac{945}{1,024}$

square root both sides

$(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}$

$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

the positive value is

$t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec$

8 0

3 years ago

A sum of $4000 is invested at 5.5% interest per year. Find the amount of time needed to double the money if it’s compounded mont

musickatia [10]

9514 1404 393

Answer:

C) 12y 8m

Step-by-step explanation:

The amount of principal P at compound monthly at interest rate r per year is given by ...

A = P(1 +r/12)^(12t) . . . . after t years

Here, we want to find t, so ...

A/P = (1 +r/12)^(12t)

log(A/P) = (12t)·log(1 +r/12)

t = log(A/P)/(12·log(1 +r/12))

Filling in the given values, we find t to be ...

t = log(8000/4000)/(12·log(1 +0.055/12)) ≈ 12.6315 ≈ 12 years 7.6 months

It will take about 12 years 8 months to double the money.

8 0

3 years ago

Which statement is true regarding the functions on the graph

Scilla [17]

Answer:

second one

Step-by-step explanation:

f(3)=g(3)=6

4 0

3 years ago