All categories

3 years ago

Which property is used in the first step to solve this equation?

Mathematics

2 answers:

SOVA2 [1]3 years ago

6 0

Answer:

distributive

Step-by-step explanation:

Nat2105 [25]3 years ago

4 0

Answer:

distributive property

You might be interested in

(-8, 4), (4, -4) Write in standard form

Serjik [45]

Answer written in standard form:

2x + 3y = -4

7 0

3 years ago

Read 2 more answers

Find the general term of sequence defined by these conditions.

disa [49]

Answer:

$\displaystyle a_{n} = (2)^{2n -1} - (3) ^{n-1 }$

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

$\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0 \: \: where : \: \:a_1 = 1 \: ,a_2 = 5,$

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

${x}^{n} = c_{1} {x}^{n - 1} + c_{2} {x}^{n - 2} + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}$

the steps for solving a linear homogeneous recurrence relation are as follows:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

${x}^{2} - 7x+ 12= 0$

Step-2:Solve the polynomial by factoring

factor the quadratic:

$( {x}^{} - 4)(x - 3) = 0$

solve for x:

$x = \rm 4 \:and \: 3$

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

$\displaystyle a_{n} = c_{1} {x} _{1} ^{n } + c_{2} {x} _{2} ^{n }$

so substitute the roots we got:

$\displaystyle a_{n} = c_{1} (4)^{n } + c_{2} (3) ^{n }$

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

$\begin{cases}\displaystyle 4c_{1} +3 c_{2} = 1 \\ 16c_{1} + 9c_{2} = 5\end{cases}$

solve the system of equation which yields:

$\displaystyle c_{1} = \frac{1}{2} \\ c_{2} = - \frac{1}{3}$

finally substitute:

$\displaystyle a_{n} = \frac{1}{2} (4)^{n } - \frac{1}{3} (3) ^{n }$

$\displaystyle \boxed{ a_{n} = (2)^{2n-1 } - (3) ^{n -1}}$

and we're done!

7 0

3 years ago

The cost of every college is expected to increase 3.5%

lions [1.4K]

Answer:

$18,630

Step-by-step explanation:

The cost of every college is expected to increase 3.5% next year.

The cost to attend Westish College is currently $18000.

What is the expected cost to attend Westish College next year?

The increase in the cost for next year is calculated as:

3.5 % × Current cost

= 3.5% × $18,000

= $630.

The expected cost to attend Westish college next year=

$18,000 + $630

= $18,630

8 0

2 years ago

3) The graph of the equation y = x2 + 1 is shown. Which equation will shift the graph up 7 units? A) y = x2 + 7 B) y = x2 - 8 C)

Elina [12.6K]

Your answer is C. (1+7=8)

6 0

3 years ago

Read 2 more answers

Chicken strips at a restaurant sell for the following prices: 4 pieces for $2.40 6 pieces for $3.00 How much do customers save p

const2013 [10]

Answer:

10 cents

Step-by-step explanation:

In order to answer this question we have to find how much each chicken strip costs individually.

Let's start with the 4 piece.

To find how much each piece costs we have to divide $2.40 by 4. Like this:

$\frac{2.40}{4} = .60$

In the 4 piece, every chicken strip costs .60 cents.

Now, let's do the 6 piece.

Like before we are going to divide $3.00 by 6.

$\frac{3.00}{6} = .50$

In the 6 piece, every chicken strip costs .50 cents.

Therefore, customers save 10 cents when they buy the larger quantity.

I hope this helps!

If you have any questions let me know!

- Kay :)

7 0

3 years ago