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4 years ago

In the diagram, BC¯¯¯¯¯∥DE¯¯¯¯¯ . What is CE ? Enter your answer in the box. ft

Mathematics

1 answer:

Marizza181 [45]4 years ago

4 0

The segments AE, EC, AD and DB are in proportion.

Therefore we have the equation:

$\dfrac{CE}{BD}=\dfrac{AE}{AD}$

AE = 4ft, AD = 8ft and BD = 2ft. Substitute:

$\dfrac{CE}{2}=\dfrac{\not4^1}{\not8_2}$ multiply both sides by 2

$CE=\dfrac{1}{\not2_1}\cdot\not2^1\\\\\boxed{CE=1\ ft}$

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In the New Orleans metropolitan area in August 2005, the labor force was 634,512 and 35,222 people were unemployed. In Septem

Lisa [10]

Answer:

Unemployment (August) = 35'222/634'512 ≈ 0.0555 ≈ 5.55%

Employed (August) = 634'512-35'222 = 599'290

Labor force (September) = 634'512-156'518 = 477'994

Employed (September) = 599'290-206'024 = 393'266

Unemployed (September) = 477'994-393'266 = 84'728

Unemployment (September) = 84'728/477'994 ≈ 0.177 ≈ 17.7%

Step-by-step explanation:

8 0

3 years ago

SOMEONE HELP ???? Select steps that could be used to solve the equation 1+ 3x = -x+4

Alex

Answer:

a) add x , subtract 1 and divide by 4

The solution of given equation $x = \frac{3}{4}$

Step-by-step explanation:

Given equation 1+3 x = -x +4

Add 'x' on both sides , we get

1 + 3 x + x = - x + x +4

1 + 4 x = 4

Subtract '1' on both sides , we get

1+4 x -1 = 4 -1

4 x = 3

Dividing '4' on both sides, we get

$\frac{4x}{4} = \frac{3}{4}$

$x = \frac{3}{4}$

Final answer:-

The solution of given equation $x = \frac{3}{4}$

5 0

3 years ago

Rewrite the expression as a product of two factors. 72t+8

Aneli [31]

Step-by-step explanation:

The above given expression "72t+8 " have to be factorized by the following methods.

Step 1 :

First we must check both numbers in order to obtain common factor for both ,for this equation "8" is the common factor for both .

Step 2:

After obtaining the common factor for the equation equation, we must now take the factor as common outside the bracket and form the equation as follows,

⇒ 8 * ( 9*t + 1 )

Here there are the two factors for the equation " 72 t+ 8 " that are 8 and 9t+1.

Step 3 (optional) :

Now check weather the factors are correct or not by multiplying factors with each other.

Multiplying ,

⇒ 8 * ( 9*t + 1 )

Gives -

⇒ 72 t+ 8

5 0

4 years ago

I really need it to be sold in imaginary numbers

Yuliya22 [10]

Solving a 5th grade polynomial

We want to find the answer of the following polynomial:

$x^5+3x^4+3x^3+19x^2-54x-72=0$

We can see that the last term is -72

We want to find all the possible numbers that can divide it. Those are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

We want to factor this polynomial in order to find all the possible x-values. In order to factor it we will have to find some binomials that can divide it using the set of divisors of -72.

We know that if

(x - z) is a divisor of this polynomial then z might be a divisor of the last term -72.

We will verify which is a divisor using synthetic division. If it is a divisor then we can factor using it:

Let's begin with

(x-z) = (x - 1)

We want to divide

$\frac{(x^5+3x^4+3x^3+19x^2-54x-72)}{x-1}$

Using synthetic division we have that if the remainder is 0 it will be a factor

We can find the remainder by replacing x = z in the polynomial, when it is divided by (x - z). It is to say, that if we want to know if (x -1) is a factor of the polynomial we just need to replace x by 1, and see the result:

If the result is 0 it is a factor

If it is different to 0 it is not a factor

Replacing x = 1

If we replace x = 1, we will have that:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ 1^5+3\cdot1^4+3\cdot1^3+19\cdot1^2-54\cdot1-72 \\ =1+3+3+19-54-72 \\ =-100 \end{gathered}$

Then the remainder is not 0, then (x - 1) is not a factor.

Similarly we are going to apply this until we find factors:

(x - z) = (x + 1)

We replace x by -1:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ (-1)^5+3\cdot(-1)^4+3\cdot(-1)^3+19\cdot(-1)^2-54\cdot(-1)-72 \\ =-1+3-3+19+54-72 \\ =0 \end{gathered}$

Then, (x + 1) is a factor.

Using synthetic division we have that:

Then:

$x^5+3x^4+3x^3+19x^2-54x-72=(x+1)(x^4+2x^3+x^2+18x-72)$

Now, we want to factor the 4th grade polynomial.

Let's remember our possibilities:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

Since we verified ±1, let's try with ±2 as we did before.

(x - z) = (x - 2)

We want to divide:

$\frac{x^4+2x^3+x^2+18x-72}{x-2}$

We replace x by z = 2:

$\begin{gathered} x^4+2x^3+x^2+18x-72 \\ \downarrow \\ 2^4+2\cdot2^3+2^2+18\cdot2-72 \\ =16+16+4+36-72 \\ =0 \end{gathered}$

Then (x - 2) is a factor. Let's do the synthetic division:

Then,

$x^4+2x^3+x^2+18x-72=(x-2)(x^3+4x^2+9x+36)$

Then, our original polynomial is:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =\mleft(x+1\mright)\mleft(x^4+2x^3+x^2+18x-72\mright) \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \end{gathered}$

Now, let's prove if (x +2) is a factor, using the new 3th grade polynomial.

(x - z) = (x + 2)

We replace x by z = -2:

$\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-2)^3+4(-2)^2+9(-2)+36 \\ =-8+16-18+36 \\ =26 \end{gathered}$

Since the remainder is not 0, (x +2) is not a factor.

All the possible cases are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

let's prove with +4

(x - z) = (x + 4)

We want to divide:

$\frac{x^3+4x^2+9x+36}{x+4}$

Let's replace x by z = -4 in order to find the remainder:

$\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-4)^3+4(-4)^2+9(-4)+36 \\ =-64+64-36+36 \\ =0 \end{gathered}$

Then (x + 4) is a factor. Let's do the synthetic division:

Then,

$x^3+4x^2+9x+36=(x+4)(x^2+9)$

Since

x² + 9 cannot be factor, we have completed our factoring:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \\ =(x-1)(x-2)(x+4)(x^2+9) \end{gathered}$

Now, we have the following expression:

$(x-1)(x-2)(x+4)(x^2+9)=0$

Then, we have five posibilities:

(x - 1) = 0

or (x - 2) = 0

or (x + 4) = 0

or (x² + 9) = 0

Then, we have five solutions;

x - 1 = 0 → x₁ = 1

x - 2 = 0 → x₂ = 2

x + 4 = 0 → x₃ = -4

x² + 9 = 0 → x² = -9 → x = ±√-9 = ±√9√-1 = ±3i

→ x₄ = 3i

→ x₅ = -3i

<h2>Answer- the solutions of the polynomial are: x₁ = 1, x₂ = 2, x₃ = -4, x₄ = 3i and x₅ = -3i</h2>

7 0

1 year ago

Your uncle is currently four times as old as you are. In five years, your uncle will be three times as old as you. What is your

sertanlavr [38]

Answer:

your uncle will always be 4 times as old as you if he is currently 4 times as old as you

Step-by-step explanation:

kinda self explanatory so i think its a trick question haha

8 0

3 years ago