How many terms in 2-8+22 A. 1 B. 2 C. 3 D. 26

Thomas is 4 years older than his brother william. in five years the sum of their age will be 24. how old is each boy?

Rasek [7]

Let William be x years old.

Thomas = (4 + x) years

In five years,

William = (x + 5) years

Thomas = 4 + x + 5 = (9 + x) years

Given, in five years sum of their ages is 24.

x + 5 + 9 + x = 24

2x + 14 = 24

2x = 24 - 14

2x = 10

x = $\frac{10}{2}$

x = 5

Hence, William is 5 years old and Thomas is 9 years old.

5 0

3 years ago

Solve 2(b − 3) ≥ 3(3 − b) and describe the graph of the solution. Show all your work.

solong [7]

Answer:

$\large\boxed{b\geq3\to b\in[3,\ \infty)}$

Step-by-step explanation:

$2(b-3)\geq3(3-b)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(2)(b)+(2)(-3)\geq(3)(3)+(3)(-b)\\\\2b-6\geq9-3b\qquad\text{add 6 to both sides}\\\\2b-6+6\geq9+6-3b\\\\2b\geq15-3b\qquad\text{add}\ 3b\ \text{to both sides}\\\\2b+3b\geq15-3b+3b\\\\5b\geq15\qquad\text{divide both sides by 5}\\\\\dfrac{5b}{5}\geq\dfrac{15}{5}\\\\b\geq3$

$,\ \geq-\text{line to the right}\\-\text{o}\text{pen circle}\\\leq,\ \geq-\text{closed circle}$

4 0

3 years ago

On Monday, Duncan’s skateboard shop received its first shipment of skateboards. Duncan sold 12 skateboards that day. On Thursday

dlinn [17]

Answer:

28

Step-by-step explanation:

8 0

2 years ago

The recursive function LaTeX: f\left(0\right)=1,\:f\left(n\right)=f\left(n-1\right)+2nf ( 0 ) = 1 , f ( n ) = f ( n − 1 ) + 2 n

m_a_m_a [10]

Question:

The recursive function $f(0) = 1$ , $f(n) = f(n-1) + 2n$ represents the nth term of a sequence. Determine the explicit function

Answer:

$f(n) = n^2 + n+1$

Step-by-step explanation:

Given

$f(0) = 1$

$f(n) = f(n-1) + 2n$

Required

Write an explicit formula

Let n = 1

$f(1) = f(1-1) + 2*1$

$f(1) = f(0) + 2$

$f(1) = 1 + 2 = 3$

Let n = 2

$f(2) = f(2-1) + 2*2$

$f(2) = f(1) + 4$

$f(2) = 3 + 4 = 7$

Let n =3

$f(3)=f(3-1) + 2 * 3$

$f(3)=f(2) + 6$

$f(3)=7+ 6 = 13$

Let n = 4

$f(4) = f(4 - 1) + 2 * 4$

$f(4) = f(3) + 8$

$f(4) = 13+ 8 = 21$

So, we have:

$f(1) = 3= 1 + 2 * 1=1+0*1*2*1$

$f(2) = 7= 3 + 2 * 2=1+1*2+2*2$

$f(3) = 13= 7 + 2 * 3= 1+2*3+2*3$

$f(4) = 21 = 13 + 2 * 4= 1+3*4 +2 *4$

Following the above pattern:

$f(n) = 1 + (n - 1) * n + 2 * n$

$f(n) = 1 + n(n - 1) + 2n$

Open bracket

$f(n) = 1 + n^2 - n + 2n$

$f(n) = 1 + n^2 + n$

$f(n) = n^2 + n+1$

3 0

2 years ago

Find y. Round to the nearest tenth: 31° у х 400 ft y = [ ? ]ft

hram777 [196]

Y equals 240.3 ft. This is because the bottom angle of the triangle is an alternate interior angle to 31 degrees, so it is also 31 degrees. You can then create the equation tan31=y/400. To find y multiply each side by 400 and you’ll get 240.344

4 0

3 years ago