Plz help will mark brainliest

Create a list of steps, in order, that will solve the following equation 1/4(x+5)^2-1=3

julia-pushkina [17]

Answer:

either x = -1, or x = - 9

Step-by-step explanation:

given $\frac{1}{4} (x+5)^{2} -1=3$

add one to both sides $\frac{1}{4} (x+5)^{2} =4$

im not sure which one comes first. either you multiply both the x and the 5 in the parenthesis by $\frac{1}{4}$ . or you square x and 5

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 1/4*(x+5)^2-(4)=0

Step by step solution :

Step 1 :

1 /4

Equation at the end of step 1 :

1

(— • (x + 5)2) - 4 = 0

4

Step 2 :

Equation at the end of step 2 :

(x + 5)2

———————— - 4 = 0

4

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 4 as the denominator :

4 4 • 4

4 = — = ———

1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5)2 - (4 • 4) x2 + 10x + 9

——————— ——————— = ——

4 4

Trying to factor by splitting the middle term

3.3 Factoring x2 + 10x + 9

The first term is, x2 its coefficient is 1 .

The middle term is, +10x its coefficient is 10 .

The last term, "the constant", is +9

Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9

Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 10 .

-9 + -1 = -10

-3 + -3 = -6

-1 + -9 = -10

1 + 9 = 10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 9

x2 + 1x + 9x + 9

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+1)

Add up the last 2 terms, pulling out common factors :

9 • (x+1)

Step-5 : Add up the four terms of step 4 :

(x+9) • (x+1)

Which is the desired factorization

Equation at the end of step 3 :

(x + 9) • (x + 1)

————————————————— = 0

4

Step 4 :

When a fraction equals zero :

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

(x+9)•(x+1)

——————————— • 4 = 0 • 4

4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

(x+9) • (x+1) = 0

Theory - Roots of a product :

4.2 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.3 Solve : x+9 = 0

Subtract 9 from both sides of the equation :

x = -9

Solving a Single Variable Equation :

4.4 Solve : x+1 = 0

Subtract 1 from both sides of the equation :

x = -1

Supplement : Solving Quadratic Equation Directly

Solving x2+10x+9 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

6 0

3 years ago

Three more than a number is 15

podryga [215]

Answer:

The number is 12

Step-by-step explanation:

If 15 is three more than the number is three less so you do, 15 - 3 which is 12.

I hope this helps

7 0

2 years ago

PLS HELP IF YOU CAN!THIS IS DUE IN 30 MINUTES :(

ExtremeBDS [4]

Answer:

Length: 20 or 40 feet

Width: 40 or 20 feet

Step-by-step explanation:

Area = 800 = length*width = x*(60-x)= 60x - x^2

- x^2 + 60x - 800 = 0

x = 20

Or x = 40

So length can be either 20 feet or 40 feet and width can be 40 (60-20) or 20 (60-40)

6 0

2 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

so

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

2 years ago

Solve for y:<br> y+5x=6;x= -1,0,1

AlekseyPX

When x = -1

y + 5x = 6

y = 6 - 5x

y = 6 - (5)(-1)

y = 6 - (-5)

y = 11

when x = 0

y = 6 - 5x

y = 6 - (5)(0)

y = 6 - 0

y = 6

when x = 1

y = 6 - 5x

y = 6 - (5)(1)

y = 6 - 5

y = 1

7 0

3 years ago

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