Henry needs a 16 ft. table for his family dinner. He is going to put two tables together. He has an 8ft table. How long does the other need to be?

Step-by-step explanation:

The factor of the polynomial is (x-2)

We know that dividing a third degree polynomial by a first degree factor will yield a quadratic of the form ax²+bx+c and possibly a remainder r,except that in this case r=0 since x-2 is a factor

We therefore equate

x³-4x²+3x+2=(x-2)(ax²+bx+c)+r

x³-4x²+3x+2=ax³+bx²+cx-2ax²-2bx-2c+r

We group terms on the RHS

x³-4x²+3x+2=ax³+x²(b-2a)+x(c-2b)-2c+r

By equating the terms on both sides,

ax³=x³,a=1

Next,

b-2a=-4

b-2(1)=-4

b-2=-4

b=-4+2

b=-2

Next,

c-2b=3

c-2(-2)=3

c+4=3

c=-1

Now we piece together our quotient quadratic using a=1,b=-2,c=-1 to obtain x²-2x-1

We now find the zeros of x²-2x-1

which are 1+√2 and 1-√2

The values of x are therefore 2,1+√2, and 1-√2

Note that I used this method in lieu of the famous polynomial division approach to teach someone also ;)

Answer:

2, 1 +/- sqrt2

or 2, 2.414, -0.414 (correct to the nearest thousandth).

Step-by-step explanation:

Let x = 2: then

f(2) = 8 - 16 + 6 + 2 = 0

So x = 2 is one  of the zeros.

So one factor of the function is x-2.

If we divide  the function by  (x - 2) we get:

x-2)X^3-4x^2+3x+2(x^2-2x-1

     x^3- 2x^2

            -2x^2+3x

            -2x^2+4x

                       -x+2

                       -x+2

                        .......

So x^2-2x-1= 0

x = [-(-2 +/- sqrt(4 - 4*-1)] / 2

x = (2 +/- sqrt8) / 2

= 1 +/-sqrt8/2

= 1 +/- sqrt2

Answer:

x can be divided by 2,3,4,5,6

2 can be divided by 4, so is 3 to 6

so simply x can be divided by 4,5,6

4*5*6=120

Step-by-step explanation:

Answer:

Step-by-step explanation:

Is there another part to the question? Maybe the original function?

Answer:

labeled is the answer your looking for

Answer:

There are 625 trees in the park.

Step-by-step explanation:

Assume that there are x trees in the park

∵ The number of trees in the park = x

∵ 27% of them are oaks

∵ 16% are pins

∵ 33% of them are banyans

∵ The remaining are willows

→ The percentage of the total number of trees is 100%

∴ The percent of the remaining = 100% - (27 + 16 + 33)%

∴ The percent of the remaining = 100% - 76%

∴ The percent of the remaining = 24%

∵ The number of willows trees = 150

∴ 24% of x = 150

∴ 24% × x = 150

→ Change the percent to a decimal by divide it by 100

∵ 24% = [tex]\frac{24}{100}[/tex] = 0.24

∴ 0.24 × x = 150

∴ 0.24x = 150

→ Divide both sides by 0.24

∴ x = 625

∴ There are 625 trees at the park.

Complete Question:

Let x and y be positive integers and x be greater than y.

11x/11y = ?

Answer:

11x/11y = x/y

Step-by-step explanation:

Given

x > y

Required

11x/11y

From the question, we understand that x is greater than y (i.e. x > y)

Also, we'll assume that y ≠ 0, in other not to result in an undefined result.

So,

11x/11y

Divide the numerator and denominator by 11

(11x ÷ 11)/(11y ÷ 11)

The result of the division is:

(x)/(y)

x/y

Hence,

11x/11y = x/y for x > y and y ≠ 0

k-6:5 + 4-k:6= 6k-36+20-5k:30 =

k-16:30

Answer:i used a calculator 12000

Step-by-step explanation:12 × 10 × 10 × 10 = 12000

and have a nice Day :)

Answer:

12000

Step-by-step explanation:

If you multiply 12 by 10 its 120, if you add 2 more 0's to the end of the number, it will be 12000, so, basically, any time you multiply a number by 10, you add a 0 to the end of the number your multiplying 10 by, hope this helps:)

Answer:

£530

Step-by-step explanation:

Answer:

£530

I hope this helps!

Answer:

Option "A" is correct answer to the following question.

Step-by-step explanation:

We know that, in triangle sum of two smaller lines ≥ largest side

So,

3 cm + 3 cm < 6 cm   [Not correct to the given situation.]

3 cm + 4 cm > 5 cm [Correct]

3 cm + 5 cm > 7 cm [Correct]

3 cm + 6 cm > 6 cm [Correct]

Answer:

A  The one that says 3 cm, 3 cm, 6 cm.

Step-by-step explanation:

Answer:

x = -17

Step-by-step explanation:

y - y1 = m(x - x1)

y - 3 = 1/5(x - (-2))

y - 3 = 1/5(x + 2)

y - 3 = 1/5x + 0.4

y = 1/5x + 0.4 + 3

y = 1/5x + 3.4

Now we plug in y as 0 to find x

y = 1/5x + 3.4

(0) = 1/5x + 3.4

-3.4 = 1/5x + 3.4 - 3.4

-3.4 = 1/5x times 5

-3.4 times 5 = x

-17 = x

Answer:

Step-by-step explanation:

If we know the slope, we can solve for an unknown coordinate. First, let's review how to calculate slope.

Slope = Rise/Run (Change in y/Change in x)

In this case, we know the slope, so we will write out the slope formula. We will use the substitution method to solve this.

m = rise/run

rise = y2- y1 substituting ----> 3 - 0 = 3

run = x2 - x1 substituting ----> -2 - x = run

Now, we can return to the slope formula, as we now have enough information to solve.

1/5 = 3/R

To solve, we simply need to find the equivalent fraction of 1/5. We will use a proportion.

1R = 5 x 3

R = 15

Now that we know R, we can substitute it into the equation for run.

So, we now have:

15 = -2 - x

Subtracting -2 from both sides, gives us x = -17.

Finally, we must check our answer to make sure we are getting the correct slope when we calculate.

m = (3 - 0)/(-2 - -17)

m = 3/15 OR 1/5

Since. this matches the original slope we were given, we can be sure the answer is correct.

Answer:

33 minutes

Step-by-step explanation:

It would tale her 1.5 min for each page

Answer:

y = 69

Step-by-step explanation:

start with the distributive property:

5/9 * y and 5/9 * 3

and now you have: 5/9y + 15/9 = 40

and we have to isolate y so subtract 15/9 from both sides:

5/9y + 15/9 = 40

        - 15/9     -15/9

and now you have 5/9y = 345/9

and now divide both sides by 5/9 so: 5/9y divided by 5/9 = y

and 345/9 divided by 5/9 = 345/5 and lets simplify....

y= 69

hope this helps luv

Answer:

45°

Step-by-step explanation:

First, find the measure of each interior angle of the octagon.

Measure of each interior angle of the octagon = [tex] \frac{(n - 2)180}{n} [/tex]

Where, n = 8.

Plug in the value of n into the formula

[tex] = \frac{(8 - 2)180}{8} [/tex]

[tex] = \frac{(6)180}{8} [/tex]

[tex] = \frac{1,080}{8} = 135 [/tex]

x = 180 - 135 (straight line theorem.)

x = 45°

Answer:

Step-by-step explanation:

Given equation

Solving for b:

Answer:

b = ±√(c² - a²)

Step-by-step explanation:

We have to get the value of B.

Step 1: (b squared = c squared - a squared)

b² = c² - a²

Step 2: (cube root of b squared = cube root of c squared and a squared)

√b² = √(c² - a²)

We get the answer as:

b = ±√(c² - a²)

Answer:

13 1/3. have a great day!! :D

Step-by-step explanation:

To solve the equation, you first need to multiply 8 by 3/5's reciprocal, which is 5/3. Reciprocal basically means to flip the fraction. By multiplying 8 by 5/3 you'll get 40/3, which you can simplify to 13 1/3.

Answer:

[tex]y = 14x + 3400[/tex]

Step-by-step explanation:

Represent

- number of jackets with x

- costs of jackets with y

So, we have:

[tex](x_1,y_1) = (150,5500)[/tex]

[tex](x_2,y_2) = (370,8580)[/tex]

Required

Write an equation in form of y = mx + b

First, we need to determine the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{8580 - 5500}{370 - 150}[/tex]

[tex]m = \frac{3080}{220}[/tex]

[tex]m = 14\\[/tex]

The equation is calculated using:

[tex]y-y_1 = m(x - x_1)[/tex]

Where

[tex]m = 14\\[/tex]

[tex](x_1,y_1) = (150,5500)[/tex]

So, we have:

[tex]y - 5500 = 14(x - 150)[/tex]

[tex]y - 5500 = 14x - 2100[/tex]

Make y the subject

[tex]y = 14x - 2100 + 5500[/tex]

[tex]y = 14x + 3400[/tex]

Answer:

e

Step-by-step explanation:

Answer:

315

Step-by-step explanation:

The sum of -265 and -156:

-265 + (-156)

= -265-156

= -421

The sum of 356 and -250:

356 + (-250)

= 356-250

= 106

The sum of both:

-421 + 106

= -315

Hope this helped!

Answer:

Y= -1x - 4

Step-by-step explanation:

Answer:

17.6 minutes

Step-by-step explanation:

[tex]\frac{4}{5} = \frac{x}{22}[/tex]

[tex]5x=22[/tex]

[tex]x=\frac{22}{5}[/tex]

[tex]4(\frac{22}{5} ) = \frac{88}{5} = 17.6[/tex]

Answer:[tex] \huge{ \boxed{ \bold{ \tt{ x = - 2}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 6x + 13 = - 5(7 + 6x) }[/tex]

Distribute -5 through the parentheses

[tex]\longrightarrow{ \sf{ - 6x + 13 =  - 5 \times 7  + ( - 5 )\times 6x}}[/tex]

[tex]\longrightarrow{ \sf{ - 6x  + 13 =  - 35 + ( - 30x)}}[/tex]

[tex] \text{Remember} : \sf{( + ) \times ( - ) = ( - )}[/tex]

[tex]\longrightarrow{ \sf{ - 6x + 13 =  - 35 - 30x}}[/tex]

Move 30x to left hand side and change it's sign

[tex] \longrightarrow{ \sf{ - 6x + 30x + 13 = - 35}}[/tex]

Move 13 to R.H.S ( Right Hand Side ) and change it's sign[tex] \longrightarrow{ \sf{ - 6x + 30x= - 35 - 13}}[/tex]

Combine like terms

[tex] \longrightarrow{ \sf{24x = - 35 - 13}}[/tex]

The negative integers are always added but posses the negative ( - ) sign.[tex] \longrightarrow{ \sf{24x = - 48 }}[/tex]

Divide both sides by 24

[tex] \longrightarrow{ \sf{ \frac{24x}{24} = \frac{ - 48}{24}}} [/tex]

Dividing a negative integer by a positive integers gives a negative integer.

[tex]\longrightarrow{\sf{x = -2 }}[/tex]

-----------------------------------------------------

L.H.S = -6x + 13

Plug the value of x and simplify

[tex] \longrightarrow{ \sf{ - 6 \times ( - 2) + 13}}[/tex]

Multiplying negative integers by a negative integer gives a positive integer.

[tex] \longrightarrow{ \sf{ 12 + 13}}[/tex]

Add the numbers : 12 and 13

[tex] \longrightarrow{ \sf{25}}[/tex]

R.H.S = -5 ( 7 + 6x )

plug the value of x and simplify

[tex] \longrightarrow{ \sf{ - 5(7 + 6 \times ( - 2)}})[/tex]

Multiplying a positive integer by any negative integer gives a negative integer.

[tex] \longrightarrow{ \sf - 5(7 + ( - 12)}[/tex]

[tex]\longrightarrow{\sf{-5(7 - 12)}}[/tex]

Subtract 12 from 7

[tex] \longrightarrow{ \sf{ - 5 \times ( - 5)}}[/tex]

[tex]\longrightarrow{\sf{25}}[/tex]

L.H.S = R.H.S

The value of x is -2 .

Hope I helped!

Best regards!

~TheAnimeGirl

Answer:

The family will need to purchase 187 square ft carpeting.

Step-by-step explanation:

Area of Rectangles

Given a rectangle with width W and length H, the area is calculated as follows:

A = W * H

The new carpet of the family has the shape provided in the figure. We have completed the shape to add some missing dimensions by adding and subtracting the given lengths. Please refer to the attached image.

The total area of the carpet is the sum of the areas of three rectangles.

The rectangle at the bottom has dimensions 3 ft x 20 ft, thus its area is:

A1 = 3 ft * 20 ft = 60 square ft

The rectangle at the middle has dimensions 3 ft x 17 ft, thus its area is:

A2 = 3 ft * 17 ft = 51 square ft

The rectangle at the top has dimensions 4 ft x 19 ft, thus its area is:

A3 = 4 ft * 19 ft = 76 square ft

The total area of the carpet is:

A = 60 square ft + 51 square ft + 76 square ft

A = 187 square ft

The family will need to purchase 187 square ft carpeting.

Answer:

40 baskets

Step-by-step explanation:

Find out how many baskets she can make in an hour. Since she makes 4 in 1/2 an hour, multiply 4 by 2 to find out how much she makes in an hour. She makes 8 baskets an hour, so multiply 8 by 5. 8 x 5 = 40.

Answer:

40 Baskets

Step-by-step explanation:

4 x half an hour = 8 baskets an hour. 8 x 5 = 40

Answer:

The answer and explanation  is located in the screenshot.

Step-by-step explanation:

Hope this helped! And have a wonderful day!

Answer:

0.85

Step-by-step explanation:

1.37-0.52=0.85

Answer:

-13ºC

Step-by-step explanation:

The temperature has fallen, so you subtract.