Write the decimal as a percent. 0.097

Svetllana [295]

The answer is x=2

Remember, first add/substract the like terms, in this case 6x-10x to get -4x. Then, add 8x to negative 8x to cancel it out and do the same thing to -4x. Do this with all your terms and you should get 4x=8. Then divide both sides by 4 to get x=2.

4 0

3 years ago

Car X weighs 136 pounds more than car Z. Car Y weighs 117 pounds more than car Z. The total weight of all three cars is 9439 pou

Aleksandr [31]

Let x, y and z denote the weighs of car X, car Y and car Z, respectively.

We know that car X weighs 136 more than car Z, this can be express by the equation:

$x=z+136$

We also know that Y weighs 117 pounds more than car Z, this can be express as:

$y=z+117$

Finally, we know that the total weight of all the cars is 9439, then we have:

$x+y+z=9439$

Hence, we have the system of the equations:

$\begin{gathered} x=z+136 \\ y=z+117 \\ z+y+z=9439 \end{gathered}$

To solve the system we can plug the values of x and y, given in the first two equations, in the last equation; then we have:

$\begin{gathered} z+136+z+117+z=9439 \\ 3z=9439-136-117 \\ 3z=9186 \\ z=\frac{9186}{3} \\ z=3062 \end{gathered}$

Now that we have the value of z we plug it in the first two equations to find x and y:

$\begin{gathered} x=3062+136=3198 \\ y=3062+117=3179 \end{gathered}$

Therefore, car X weighs 3198 pound, car Y weighs 3179 pounds and car Z weighs 3062 pounds.

4 0

1 year 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

Multiply -10(-7x² + 5x)

tatiyna

Answer: 70x^2 -50x

Step-by-step explanation:

^ means exponent

7 0

2 years ago

Read 2 more answers

Given a spinner with 9 equal-area sections, a trial of 100 spins resulted in an experimental probability of 13% for the spinner

defon

Answer:

b

Step-by-step explanation:

4 0

3 years ago