What is 938/6 and 762/4

10. The sum of two numbers is 102. One number is three less than twice the other.

netineya [11]

Answer:

(2n -3) + n = 102

2n - 3 + n = 102

3n - 3 = 102

3n = 105

n = 35 (the first number)

SO...

The other number is (2 x 35) - 3 =

70 - 3 = 67 (the second number)

The numbers are 35 and 67.

35 + 67 = 102 CHECK!

7 0

3 years ago

State whether each sequence is arithmetic and justify your answer. If the sequence is arithmetic, write a recursive and an expli

nasty-shy [4]

Answer:

Part A

$f(n)=52-12(n-1)$

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$ Geometric Sequence

Part C

1/4,3/4,5/4,7/4,9/4

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)\\f(n)=\left\{\begin{matrix}1/4if \: \:n=1 & \\ f(n+1)+2/4& if\: n\geq 2 \end{matrix}\right$

Part D:

$h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right$

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

$(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12$

Explicit Formula

To write an explicit formula is to write it as function.

$f(n)=52-12(n-1)$

Recursive Formula

To write it as recursive formula, is to write it as recurrence given to some restrictions:

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$

Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24

Part C

$(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\$

Arithmetic Sequence, difference

$d=\frac{2}{4}$

Explicit Formula:

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)$

Recursive Formula

$g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.$

Part D

(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4

Explicit formula

$h(n)=1.1+0.4(n-1)\\$

Recursive Formula

$h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.$

6 0

3 years ago

Please help!! answer choices and question below

puteri [66]

Answer:

3 because 3 times 4 is 12 and 18 divided by 6 is 3

Step-by-step explanation:

3 0

3 years ago

Write the equation of the line in fully simplified slope-intercept form.

fiasKO [112]

$y = -\frac{1}{2}x - 1$

Step-by-step explanation:

Let's pick two points on the line: $P_1(-4, 1)$ and $P_2(2, -2).$ Let's calculate the slope of this line using these points:

$m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-2 - 1}{2 - (-4)} = -\dfrac{1}{2}$

With this value of the slope, we can write the general slope-intercept form of the equation as

$y = -\frac{1}{2}x + b$

To solve for the y-intercept b, let's use either P1 or P2. I'm going to use P2:

$-2 = -\frac{1}{2}(2) + b \Rightarrow b = -1$

Therefore, the slope-intercept form of the equation is

$y = -\frac{1}{2}x - 1$

6 0

2 years ago

Find an equation for the line with the given properties. Express your answer using the general form or the slope-intercept form

Damm [24]

Answer:

$y=-3x+4$

Step-by-step explanation:

To get the equation in the slope-intercept form first, put the equation in slope-point form using the information given. The slope-point form is $y-(-2)=-3(x-2)$ . Then solve for y.

Distribute -3 to $(x-2)$ ,

$y-(-2)=-3x+6$

Then, add -2 to both sides,

$y=-3x+4$

This is your final answer; the slope is -3 and the y-intercept is 4. There are also a few other ways to solve but I find this the easiest.

3 0

3 years ago