Can someone help me with this math homework (8th grade algebra)

The work done in pulling the rope up 20 ft is 101.43 ft-lbs.

To find the work done in pulling the rope up 20 ft, we need to first determine the initial potential energy of the rope before it is lifted up. We can do this using the formula:

Potential Energy = weight * height

where weight is the weight of the rope and height is the distance the rope is hanging from.

Given:

Length of the rope (L) = 70 ft

Weight of the rope (Wt) = 49 lbs

Height of the building (H) = 100 ft

Height to which the rope is lifted (h) = 20 ft

Using the Pythagorean theorem, we can find the distance (d) the rope is hanging from the building:

d^2 = H^2 + L^2

d^2 = 100^2 + 70^2

d^2 = 10000 + 4900

d^2 = 14900

d = \(\sqrt{14900}\)

d = 122.07 ft

Now we can find the initial potential energy of the rope:

Potential Energy = Wt * d

Potential Energy = 49 * 122.02

Potential Energy = 5981.43 ft-lbs

Next, we need to find the final potential energy of the rope after it is lifted up 20 ft. The height to which the rope is lifted is (H + h) = 100 + 20 = 120 ft. Using the same formula as before, we get:

Final Potential Energy = Wt * (H + h)

Final Potential Energy = 49 * 120

Final Potential Energy = 5880 ft-lbs

Finally, we can find the work done in lifting the rope up 20 ft:

Work Done = Initial Potential Energy - Final Potential Energy

Work Done = 5981.43 - 5880

Work Done = 101.43 ft-lbs

Therefore, the work done in pulling the rope up 20 ft is 101.43 ft-lbs.

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The perimeter of the triangle will be 41ft

The perimeter of a triangle is the sum of all the sides of the triangle

From the given triangle, we need to get the third sidee firse as shown:

h² = 12² + 12²

h² = 144 + 144

h² = 288

h = 17ft

Perimeter = 12 + 12 + 17

Perimeter = 41ft

Hence the perimeter of the triangle will be 41ft

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Answer: 41 ft

Step-by-step explanation:

Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...

To use the chain rule and find the derivative of the given expression, we need the functions g(u) = sin(u) and h(x) = 4x^2 + 3x.

To use the chain rule, we need to identify two functions within the given expression, one serving as the outer function and the other as the inner function.

Let's rewrite the expression in the required form:

f(x) = g(h(x))

In this case, we can choose the functions as follows:

g(u) = sin(u)

h(x) = 4x^2 + 3x

Now, we can rewrite the original expression using these functions:

f(x) = g(h(x)) = sin(4x^2 + 3x)

Here, g(u) represents the outer function, which is the sine function, and h(x) represents the inner function, which is the polynomial 4x^2 + 3x.

By using the chain rule, we can differentiate the composite function f(x) by taking the derivative of the outer function with respect to the inner function multiplied by the derivative of the inner function with respect to x:

f'(x) = g'(h(x)) * h'(x)

In this case, g'(u) represents the derivative of the sine function, which is cos(u), and h'(x) represents the derivative of the polynomial 4x^2 + 3x.

Therefore, to use the chain rule and find the derivative of the given expression, we need the functions g(u) = sin(u) and h(x) = 4x^2 + 3x.

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Answer:

c. equally likely events

Answer:

Step-by-step explanation: Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.

The solution of the expression is,

⇒ 0 + (7/11)√5

We have to given that;

Expression is,

⇒ (7 + √5) / (7 - √5) - (7 - √5) / (7 + √5)

Take LCM we get;

⇒ (7 + √5)² - (7 - √5)² / (7 - √5) (7 + √5)

⇒ (49 + 5 + 14√5) - (49 + 5 - 14√5) / (7² - √5²)

⇒ (28√5) / (49 - 5)

⇒ 28√5 / 44

⇒ 7√5 / 11

⇒ 0 + (7/11)√5

Thus, The solution of the expression is,

⇒ 0 + (7/11)√5

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Answer:

8x+8

Step-by-step explanation:

x+4+3x+x+4+3x

8x+8

hope it helps :)

Answer:

Should be 8x+8.

Step-by-step explanation:

(non simplified) 3x+3x+(x+4)+(x+4)

6x+(2x+8)

8x+8

Hope this could help

Answer:

£31.72

Step-by-step explanation:

This is a multiplication problem.

1 ticket costs £7.93; 4 tickets cost 4 times £7.93.

4 × £7.93 = £31.72

Answer:

7.93×4=31.72.if answer is correct pls follow me

Step-by-step explanation:

the reason is because, if one train ticket cost 7.93 then 4 ticket is going to be multiplied

Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.

If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:

Volume (V) = length × breadth × height

where;

the base = length × breadth = 16ft²

∴ the volume of the rectangular bathtub = 16h ---  (1)

Using differentiation to differentiate 16h with respect to t implicitly, then:

dV/ dT = 16 dH /dT

When the rate of rising of the volume is 0.5 ft³/min

Then:

0.5 = 16 dH /dT

dH /dT = 1 / 16 * 0.5

dH /dT = 0.3125.

Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.

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The higher price represents the cost burden of a significant barrier to entry.

What is the cost price?

The cost price in retail systems represents the particular value that corresponds to the unit price paid. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

Here, we have

Given: Customers of monopolistically competitive businesses will shell out more money for goods than they would if the identical goods were priced higher and supplied in a fully competitive market.

In contrast to perfectly competitive markets, monopolies have significant entry barriers and a single producer who serves as the price market.

As a result, costs are generally greater because there is only one vendor and numerous consumers.

Hence, the higher price represents the cost burden of a significant barrier to entry.

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Answer:

You can only solve this using BODMAS

Step-by-step explanation:

You solve them in this order

B=Brackets

O=Orders

D=Division

M=Multiplication

A=Addition

S=Subtraction

Answer:

5 + 2i

We were given the complex numbers;

a = - 2 - 5i

and

b = - i

We want to find the product;

ab^3                            ^ = Exponent

We substitute the complex numbers into the expression and simplify

( - 2 - 5i ) (i)^3                     ^ = Exponent            

This is rewritten as:

( - 2 - 5i) (i)^2     x  i                           ^ = Exponent

Note that

i^2 = - 1                                            ^ = Exponent

We substitute to obtain:

( - 2 - 5i )  x  - i                

Let us expand to get:  

- 2 x - i + 5i  x  - i

This simplifies to:

2i - 5i^2                           ^ = Exponent

This gives:

2i - 5 ( - 1 ) = 2i + 5

Hope This Helps

DOH! My Brian Hurts

The value of ab³ in simplified form is;  -250(i + 1).

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

From the given values in the question we have;

a = -2 + 2i

b = -5i

Thus

ab³ = (-2 + 2i) × (-5 i)³

=  (-2 + 2i) (-125 i³)

=  (-2 + 2i) (-125 (-i))

=  (-2 + 2i) (+125 i)

= 125 i(-2) + 125 i(2i)

= -250 i + 250 i²

= -250 i -250 or,

ab³ = -250 (i+1)

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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if KNML is indeed a rectangle per se, then if that's true NK = ML, or namely 3y +21 = 5y + 11.

And likewise if it's indeed true, is also true that all interior angles it has are all 90°, or namely 2x - 10 = 90.

\(3y+21=5y+11\implies 21=2y+11\implies 10=2y\implies \cfrac{10}{2}=y\implies \boxed{5=y} \\\\\\ 2x-10=90\implies 2x=100\implies x=\cfrac{100}{2}\implies \boxed{x=50}\)

Answer: D

Step-by-step explanation:

Answer:$22.50

Step-by-step explanation:

The three friends already paid the entrance fee. The question asks how much MORE will they pay for 5 MORE rides (8-3 rides). Since tickets are $1.50 each, and we have 3 people:

($1.50/ticket)*(5 tickets/person)*(3 persons) = $22.50 more.

[Note how the units cancel, leaving just $]

Answer:

Domain: \((-\infty,\infty)\)

Range: \([164.493,\infty)\)

Step-by-step explanation:

The domain is all x-values. Since it doesn't matter what you put in for x, all real numbers work.

The range is all y-values. Since the leading coefficient of 0.345 is positive, this means we need to find the absolute minimum by using the formula \(x=-\frac{b}{2a}\) and then determining what C is given the value of x:

\(x=-\frac{b}{2a}\)

\(x=-\frac{-7}{2(0.345)}\)

\(x\approx10.145\)

Therefore:

\(C=200-7x+0.345x^2\)

\(C=200-7(10.145)+0.345(10.145)^2\)

\(C\approx164.493\) is the absolute minimum

Answer:

Explanation:

From vertex form of quadratic function g(x)=a(x-h)²+k  the h and k are coordinates of vertex transformed from point (0,0) which is the vertex of parental function f(x)=ax²

It means the h determines how many units we moved parental graph horizontaly (to the left  if h<0, to the right if h>0) and the k determines how many units we moved parental graph verticaly  (down if h<0, up if  h>0)

g(x) = (x - 8)² + 5  ⇒  h = 8,  k = 5

So if h and k are >0 it means the parental graph was moved to the right and up.

The distance between the rock and the surface is 827.20 cm.

Given data,

There is a robot on Mars' surface. 13.33 degrees of depression can be seen between a camera in the robot and a boulder on the surface of Mars. 196.0 cm is how high the camera is from the ground.

How far is the rock from the camera?

From the given data,

tan c = AB/BC

tan 13.33° = 196/BC

BC = 196/tan 13.33°

BC = 827.20 cm

Hence, the distance between the rock and the surface is 827.20 cm.

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Katie is currently 17 years old.

Let's use substitution to solve for k. We can rearrange the second equation to solve for k:

k = e + 4

Now we can substitute that expression for k into the first equation:

k - 9 = 2(e - 9)

(e + 4) - 9 = 2(e - 9)

Simplifying, we get:

e - 5 = 2e - 18

Subtracting e from both sides, we get:

-5 = e - 18

Adding 18 to both sides, we get:

13 = e

So Elena is currently 13 years old. Now we can use the second equation to find Katie's age:

k = e + 4

k = 13 + 4

k = 17

Therefore, Katie is currently 17 years old.

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The balance in the account at the end of two years is $864.

The interest earned by Suki during that time is $64.

The initial principal amount "P" is $800.

The interest rate "R" is 4%.

The interest is compounded quarterly.

This means the value of "n" is 4.

The time period for which the interest is earned is 2 years.

The formula for compound interest is :

A = P*[1 + (R/n)]^(n*t)

A = 800*[1 + (0.04/4)]^(4*2)

A = 800*[1 + 0.01]^(4*2)

A = 800*[1.01]^(8)

A = 800*1.08

A = 864

The total interest earned is the final amount minus the principal amount.

The total interest earned is $864 - $800.

The total interest earned is $64.

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Answer:

4(3x+17)

Step-by-step explanation:

move the 96 to the other side and make it negative. then combine similar terms, and finally factor out 4

12x+164=96

12x+164-96

12x+68

4(3x+17)

y=4(3x+17)

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Answer:

c. 7x+11x=90

Step-by-step explanation:

right angle triangle sum up to 90

Answer:

7x+11x=90

Step-by-step explanation:

The 90 degree angle is made of 7x and 11x so you solve like a multi step equation after this.

Answer:

15a^3 -5y -10

Step-by-step explanation:

Use PEMDAS to simplify and combine like terms

Answer:

3(1−10x)43(1-10x)4

Step-by-step explanation:

34−4x+12x−212x34-4x+12x-212x

Simplify each term.

Combine 1212 and xx.

34−4x+x2−212x34-4x+x2-212x

Multiply the numerator by the reciprocal of the denominator.

34−4x+x2−(2(2x))34-4x+x2-(2(2x))

Multiply 22 by 22.

34−4x+x2−(4x)34-4x+x2-(4x)

Multiply 44 by −1-1.

34−4x+x2−4x34-4x+x2-4x

Find the common denominator.

Write −4x-4x as a fraction with denominator 11.

34+−4x1+x2−4x34+-4x1+x2-4x

Multiply −4x1-4x1 by 4444.

34+−4x1⋅44+x2−4x34+-4x1⋅44+x2-4x

Multiply −4x1-4x1 and 4444.

34+

Answer:

-3x + ¼

Step-by-step explanation:

Follow Me Please ...

Answer:

x = 2.5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 26 = 1.2 /x

x tan 26 = 1.2

x = 1.2/ tan 26

x=2.46036

Rounding to the nearest tenth

x = 2.5

Answer:

See below

Step-by-step explanation:

From the graph :

y = -x         -inf < x <=0

y = x             0<= x <= 2

y = 3            x > 2

The question mentions Rogawski/Adams and asks about critical points on a given interval. In calculus, critical points are where the derivative of a function is either zero or undefined.

To determine the number of critical points of the function on the interval [4,8], we need to find the derivative of the function and set it equal to zero to find any potential critical points. Without the actual function given, it is impossible to determine the number of critical points on the interval [4,8]. However, we can use the methods discussed in section 4.2.1 of Rogawski/Adams to solve for critical points and determine their number.

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Answer:

C) -38

Step-by-step explanation:

\(-5=y-7/9\\-5+7/9=y-7/9+7/9\\-38/9=y\)

I guess closest answer is C