A ladder is leaning against a wall. The ladder is 5 metres long. The top of the ladder is 3 metres above the ground. The top of the ladder is sliding down at 8 metres/second. At what rate is the bottom of the ladder moving away from the wall?

Answer:

3m(1-2m)(1+2m+4m^2)

Step-by-step explanation:

Answer:

3m(1-2m)(4m²+2m+1)

Step-by-step explanation:

3m - 24m⁴   (factorize 3m)

=3m(1) - 3m(8m³)

= 3m (1-8m³)

=3m (1³ - 2³·m³)

=3m [ 1³ - (2m)³ ]

recall the cubic formula:

a³ + b³ = (a+b)(a² - ab + b²)

if we apply this to [ 1³ - (2m)³ ], we will eventually get

= 3m(1-2m)(4m²+2m+1)

edit: last step got cut off. fixed

edit 2: by request, i added more detail to the last 2 steps

Answer:

two feet cubed

Step-by-step explanation:

Hey there! I'm happy to help!

When working with percents, the word "is" means "equals". We can use this to make an equation. The decimal form of 40% is 0.4. Our number will be represented by the variable n.

22=0.4n

Flip equation around so n is on the left (you don't have to do this, but I like having the variable on the left)

0.4n=22

We divide both sides by 0.4

n=55

Therefore, your answer is B) 55.

Have a wonderful day! :D

Answer:

55 =x

Step-by-step explanation:

Is means equals and of means multiply

22 = 40% * x

Change to decimal form

22 = .40x

Divide each side by .40

22/.40 = .40x/.40

55 =x

Answer:

v is 9

Step-by-step explanation:

it is 9 because if you simplify it is 8v=72 or 9

Answer:

v = 9

Step-by-step explanation:

3v + 5v = 72

combine like terms

8v = 72

Divide by 8

8v/8 = 72/8

v =9

Answer:

Angle MON is equal to 130 degrees.

Step-by-step explanation:

We are told LON is 180 degrees.

Angles LOM and MON are supplementary meaning they add to 180 degrees.

Using this information we know 12x+120=180.

We can use the subtractive property of equality to subtract 120 from both sides.

Do thins we get 12x=60.

Using the division property of equality we can divide both sides by 12 to get x=5.

We can then use the substitution property of equality to get MNO=8(5)+90.

We can then simplify to get MNO=130.

Answer:

12 1/2 hours

Step-by-step explanation:

This is because (0*1) + (1/4*1) + (1/2*1) + (3/4*3) + (1*3) + (1 1/4*4) + (1 1/2*1) = 12 1/12.

Answer:

no

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The first one is not. Think money. Would you rather be 1 dollar in the hole or 6 dollars in the hole? b = - 1. It is larger than - 6.

The third one is not correct either. -c = - 5

- b = 1

1 is larger than -5

The answer is the middle one

-b becomes 1 which is greater than 0.

Answer:You cant get someone to do all of this try doing a few or getting help from someone older that's what I did

I asked help for one problem and the explanation and now I understand how they did it so the other problems I can do now

It's better to make an effort and try doing some of them instead of asking someone to do all of it

Because when the test comes it won't be that easy so next time just try putting a few so that way you can try understanding it and you can apply it to similar problems

Answer:

Don't ask someone to do this if your question is a test

Step-by-step explanation:

Answer:

I would say b

Step-by-step explanation:

3 x 10^-4

if you have 88 tablespoons and you convert them into cups you would have 5.5 then you would convert that into a fraction which would be 5 1/2

Answer:

5/9 is the simplest fraction for this ratio

Answer:

x=0, 2. y=-1, 5.

Step-by-step explanation:

y=(1/2)x^2+2x-1

3x-y=1

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

3x-y=1

y=3x-1

-----------

(1/2)x^2+2x-1=3x-1

(1/2)x^2+2x-3x-1-(-1)=0

(1/2)x^2-x-1+1=0

(1/2)x^2-x=0

factor out the x

x[(1/2)x-1]=0

zero property,

x=0, (1/2)x-1=0

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

(1/2)x-1=0

1/2x=0+1

1/2x=1

x=1/(1/2)=(1/1)(2/1)=2/1=2

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

x=0, x=2

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

y=(1/2)(0)^2+2(0)-1=0+0-1=-1

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

y=3(0)-1=0-1=-1

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

y=(1/2)(2)^2+2(2)-1=(1/2)(4)+4-1=4/2+4-1=2+4-1=6-1=5

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

y=3(2)-1=6-1=5

Answer:

The solutions are (0, -1) and (2, 5)

Step-by-step explanation:

y = (1/2)x^2 + 2x - 1 ------ eqn(I)

3x - y = 1

y = 3x - 1 ------------- eqn(II)

Equate eqn(I) & (II)

(1/2)x^2 + 2x - 1 = 3x - 1

Multiply each term by 2

x^2 + 4x - 2 = 6x - 2

x^2 + 4x - 6x = -2 + 2

x^2 - 2x = 0

x(x - 2) = 0

x = 0, 2

Substitute the values of x in eqn(II)

y = 3x - 1

When x = 0

y = 3(0) - 1 = 0 - 1 = -1

y = 3x - 1

When x = 2

y = 3(2) - 1 = 6 - 1 = 5

The solutions are (0, -1) and (2, 5)

Answer:

100 times

Step-by-step explanation:

5•1000000 has 2 more zeros than 5•10000 so that means the first number is 100 times larger than the second number! hope this helps and please mark as brainiest

ANSWER:

4d shape LOOKS LIKE THIS

Answer:

In 7, seven kids checked out 7. [tex]7*7=49[/tex] (Correct answer because 49 is the biggest number here)

In 1, only two kids checked out 1. [tex]1 *2=2[/tex] (Wrong answer because 2 is lower than 49)

In 4, only eight kids checked out 4. [tex]4*8=32[/tex] (Wrong answer because 32 is lower than 49)

In 12, only two kids checked out 12. [tex]12*2=24[/tex] (Wrong answer because 24 is lower than 49)

So 7 is the correct answer because [tex]7*7=49[/tex] is the greatest equation here.

The 0 and 11 number book is the typical book one student checked out.

Given, the dot plot shows the no. of book  each student checked out from the library last month.

Since each dot represent a different student, so clearly from the dot plot the 8 number book is checked out by the most of the students because it has most of the dots.

Since the number 0 and 11 has only one dot it represent that only 1 student checked out these books last month.

Hence the 0 and 11 number book is the typical book one student checked out.

For more details on dot plot follow the link:

https://brainly.com/question/4398979

Answer:

[tex]\boxed{\sf B}[/tex]

Step-by-step explanation:

-1 < y < 0

The value of y is negative.

Let’s take the number -0.5.

(-0.5)² = 0.25

1 - (-0.5) = 1.5

1 + (-0.5) = 0.5

2(-0.5) = -1

The greatest value is 1.5.

The answer is 1 - y.

Answer:

see the picture below

Step-by-step explanation:

There is 19, 13, 8, 4, 7, 14, 7, 9.

There is 1 number between 0 and 5.

and there's 4 on between 6 to 10.

and so far.

Step-by-step explanation:

Taller bars show that more data falls in that range.

19, 13, 8, 4, 7, 14, 7, 9 stay in order = 1,2,3,4,5,6,7,8

Add 2 more months to make 8 months

Then go vertical if using this histogram so that numbers of feathers above are vertical shaped bars.  |--------------| stacked on top of each other.

Or///

Copy the diagram and swap the names ie) months so they go at the bottom and feathers go along the side axis.

Answer:

A True

Step-by-step explanation:

B vertices would be the top of an isosceles

As any equal sides can form an isosceles, the measure of the base could be any size and isnt relevant to the triangle unless we are looking for a calculation for its height, which does not determine shape only equation.

Therefore with sides of triangles if they are equal we cna make the shape consist of any length base as long as it measures less than double than either side length.

Therefore a 1cm base does apply and can form a triangle of two equal sides 7cm and 7cm as the diagram asks.

Answer:

true

Step-by-step explanation:

THE reason it true is because on on the lines doesn't equal to the 2 other lines

Answer:

80°

Step-by-step explanation:

Answer:

20 and 1/4.

Step-by-step explanation:

9x^2 * y^(-2), for x = -3 and y = 2.

9(-3)^2 * 2^(-2)

= 9 * 9 * (1/4)

= 81 * 1/4

= 81 / 4

= 20.25

= 20 and 1/4.

Hope this helps!

Answer:

Step-by-step explanation:

Let's fill the values in.

9(-3)*2(2)*-2

Using PEMDAS, we would first multiply the two numbers where x and y used to be.

-27 * 4 * -2

Now we would finish multiplying this.

216.

Hope this helps!! <3

Answer:

Step-by-step explanation:

I think 3-y slope

Answer: [tex]\hat{p}=0.28[/tex]

Step-by-step explanation:

Given : Tonya interviews an SRS of 50 of the 175 students living in the dormitory.

i.e. Sample size : n= 50

Number of students think the dorm food is good: x = 14

Now , the numerical value of the sample proportion p from Tonya's sample:

[tex]\hat{p}=\dfrac{x}{n}[/tex]

[tex]=\dfrac{14}{50}=0.28[/tex]

Hence, the numerical value of the sample proportion p from Tonya's sample is 0.28.

Answer:

x = 2  ,  y = 3  ,   z = 1

Step-by-step explanation:

I believe is the answer correct me if wrong

Answer:

x-1

Step-by-step explanation:

|x-1| if x>1. the expression must be positive, therefore you can remove the absolute values without trouble so you get x-1

Answer:

D. g(x) is a reflection of f(x) over the x-axis.

Step-by-step explanation:

Given

f(x) = 2x²

g(x) = -2x²

Required

Determine the difference between f(x) and g(x)

Start by expanding g(x)

g(x) = -2x²

g(x) = -1 * 2x²

Substitute 2x² for f(x)

g(x) = -1 * f(x)

g(x) = -f(x)

Using the format (x,y):

Take for instance x = 2

f(x) = 2x² = 2 * 2² = 2 * 4 = 8

This means (x,y) = (2,8)

g(x) = -f(x)= -8

This means that (2,-8)

Notice that only the y value changed in both cases from 8 to -8

From the above expression, g(x) = -f(x) and illustration of when x = 2

This implies that g(x) is a reflection of f(x) along the x axis..

From the list of given options, the correct answer is D.

Answer:

First Answer: y= 64 and x=64

Second Answer: 1&4, 2&3, 6&7, 5&8

Step-by-step explanation:

First Answer: 63 and ∠y is the same measure since there are

Second answer: They are vertical angles, each of the pairs of opposite angles made by two intersecting lines.

Hope this helps:)

Answer:

[tex]x=\pm 7\text{ or } x=\pm i\sqrt{2}[/tex]

Step-by-step explanation:

We have the equation:

[tex]x^4-5x^2-14=0[/tex]

Since this is in quadratic form, we can consider using u-substitution. Thus, we will let:

[tex]u=x^2[/tex]

Then by substitution:

[tex]u^2-5x-14=0[/tex]

Now we can solve normally. Factor:

[tex](u-7)(u+2)=0[/tex]

Zero Product Property:

[tex]u=7\text{ or } u=-2[/tex]

Back-substitute:

[tex]x^2=7\text{ and } x^2=-2[/tex]

Take the square root of both sides. Since we are taking an even-root, we will need to add plus-minus:

[tex]x=\pm 7\text{ and }x=\sqrt{-2}[/tex]

Therefore, our solutions are:

[tex]x=\pm7\text{ and } x=\pm i\sqrt{2}[/tex]

Answer:

$60

Step-by-step explanation:

Represent the original price by p.  Then:  

1.00 p = original price

0.20 p = discount

0.80p = price after discount = $48

Solving for p, we divide both sides by 0.80:

        $48

p = ---------- = $60

        0.80

Answer:

36.

Step-by-step explanation:

The perimeter = 2 * length + 2 * width, so we have:

2(2x - 1) + 2(3x + 3) = 114

4x + 6x - 2 + 6 = 114

10x = 114+ 2 - 6 = 110

x = 11.

So the length = 3(11) + 3

= 36.