An object’s weight on Earth varies directly to its weight on the Moon. If a man weighs 180 kg on Earth, then he will weigh 30 kg on the Moon. Set up an algebraic equation that expresses the weight on Earth in terms of the weight on the Moon and use it to determine the weight of a woman on the Moon if she weighs 120 kg on Earth.

Answer:

The maximum revenue is $25,000

Step-by-step explanation:

The model equation is;

R = -2.5p^2 + 500p

To find the maximum value, we differentiate this and set result = 0

The first differential of this model equation is -5p + 500

we set this to zero to get the maximum price

5p = 500

p= 500/5

p = 100

Now to get the maximum revenue, we simply substitute the value of the maximum price

That would be -2.5(100)^2 + 500(100)

= -2.5(10,000) + 50,000

= 25,000 + 50,000

= 25,000

Answer:

135, 137, 139

Step-by-step explanation: My bad, I did not see that it said consecutive odd integers

x+x+2+x+4=411

3x+6=411

3x=405

x=135

x+2+137

x+4=139

Represent 3 consecutive odd integers as follows.

X ⇒ first odd integer

X + 2 ⇒ second odd integer

X + 4 ⇒ third odd integer

Since their sum in this problem is 411, x + (x + 2) + (x + 4) = 411.

Now combine like terms to get 3x + 6 = 411.

No subtract 6 from both sides to get 3x = 405.

Now divide both sides by 3 and x = 135.

So x + 2 would be 137 and x + 4 would be 139.

So our consecutive odd integers are 135, 137, and 139.

Answer:

x = 37 y = 12

Step-by-step explanation:

Let x be one number

Let y = other number

x+y = 49

x-y = 25

Add the equations together

x+y = 49

x-y = 25

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

2x = 74

Divide by 2

2x/2 = 74/2

x =37

x+y = 49

37+y = 49

Subtract 37 from each side

37+y-37 = 49-37

y = 12

Answer:  The answers are in the steps but you have to look closely because i wasn't able to create the table  so I just did something that looks like the table and put in the answers. Hopes it helps.

Step-by-step explanation:  

d)                                       Empire State Building

Original Image   actual Height      1450       1450          1450

Reduced Image    Model Height       145            58           28    

                               Scale Factor         [tex]\frac{1}{10}[/tex]              1/25         1/50

e) Yes  is correct because a dilation makes the  Original shape bigger or smaller and that depends on the scale factor.The greater the scale factor is, the bigger the shape gets and the small the scale factor is the  less the shape gets in size. So sally is totally right because if the number is less than one it is probably going to be a decimal less than one so and that makes the original shape smaller.

Answer:

Step-by-step explanation:

Given

  Fantasy uses 4 lb of nuts, 3 lb of chocolate, for a profit of $50

  Ecstasy uses 4 lb of nuts, 1 lb of chocolate, for a profit of $40

  In stock are 16 lb of nuts, 10 lb of chocolate

Find

 amount of each to maximize profit

Solution

Let x and y represent barrels of Fantasy and Ecstasy, respectively. Then the limitations on production are ...

  4x +4y ≤ 16 . . . lb of nuts

  3x +y ≤ 10 . . . . lb of chocolate

We want to maximize

  50x +40y

The graph shows the feasible region. Its vertices are ...

  (0, 4), (3, 1), (3.33, 0)

Profit is maximized at $190 when production is 3 barrels of Fantasy and 1 barrel of Ecstasy.

Answer:

you should be able to use them

Step-by-step explanation:

Answer:

f(x)=(x)^(-2)

f(-3)=(-3)^(-2)

f(-3)=(9)^(-1)

f(-3)=(1/9)

Given

an 18 ft square with a uniform border of width x

the area of the border is 400 ft²

Find

x

Solution

The outside dimension of the square with the border added is 18+2x, so the total area of square and border is (18+2x)². Subtracting the area of the original square gives the area of the border.

... (18+2x)² -18² = 400

... 4x² +72x = 400 . . . . . simplify

... x² + 18x = 100 . . . . . . .divid by 4

... x² +18x +9² = 100 +9² . . . . complete the square

... (x +9)² = 181 . . . . . . . . .simplify

... x = √181 -9 . . . . . . . . . take the square root, subtract 9

... x ≈ 4.4536 . . . . . . . . . evaluate

The appropriate choice is ...

... c. 4.45 ft

The width should be 4.45 ft

Since there is uniform wi-dth  with 18-foot ed-ges. And, the surface is 400 feet

Also here we assume the width be x

Now the equation should be

[tex](18+2x)^2 -18^2 = 400\\\\ 4x^2 +72x = 400 \\\\ x^2 + 18x = 100 \\\\ x^2 +18x +9^2 = 100 +9^2 \\\\ (x +9)^2 = 181 \\\\ x = \sqrt181 -9 \\\\[/tex]

.x ≈ 4.4536

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Answer:

the third one

Step-by-step explanation:

a linear function is information that is increasing or decreasing at a steady rate, in that specific set of data their decreasing at a rate of 2

Answer:

65/9

Step-by-step explanation:

3 1/3=(3*3+1)/3=10/3

2  1/6=(2*6+1)/6=13/6

10/3*13/6=130/18=65/9

Answer:

[tex]7\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]3 \frac{1}{3} = \frac{10}{3}[/tex]

[tex]2\frac{1}{6} = \frac{13}{6}[/tex]

10 × 13 = 130

3 × 6 = 18

[tex]\frac{130}{18} = 7\frac{2}{9}[/tex]

Answer:

B

Step-by-step explanation:

The sample space is a set of any and all possible outcomes.

Answer:

[tex]m\widehat {EB}[/tex] = 96°

Step-by-step explanation:

From the figure attached,

m∠ECB = 25°

[tex]m\widehat {EB}={(4x+16)}[/tex] degrees

[tex]m\widehat{DB}=(7x+6)[/tex] degrees

From the theorem of secants intersecting outside the circle,

m∠ECB = [tex]\frac{1}{2}[m\widehat {DB}-m\widehat{EB}][/tex]

25° = [tex]\frac{1}{2}[(7x + 6) - (4x + 16)][/tex]

25° = [tex]\frac{1}{2}(3x-10)[/tex]

50 = 3x - 10

3x = 60

x = [tex]\frac{60}{3}[/tex]

x = 20

[tex]m\widehat {EB}[/tex] = (4 × 20 + 16)°

        = (80 + 16)°

        = 96°

Therefore, measure of arc EB is 96°.

Answer:

96°

Step-by-step explanation:

Got it right on the test

Answer:

F(x) = (x + 3)^2 -87

Step-by-step explanation:

Here, we want to rewrite the function by completing the square.

Firstly, we move the c term(-78) to the right hand side of the equation and that becomes

x^2 + 6x = 78

Then, we can complete the square on the right hand side here, to be

Let’s add 9 to both sides

That would be;

x^2 + 6x + 9 = 78 + 9

x^2 + 6x + 9 = 87

(x+3)^2 = 87

or simply

(x+3)^2 -87 = 0

So our F(x) becomes

F(x) = (x + 3)^2 -87

Answer:

The expression after completing the square is:

[tex]f(x) = (x+3)^{2} -87[/tex]

Step-by-step explanation:

The function is rewritten after making algebraic manipulation:

[tex]f(x) = x^{2} + 6\cdot x +9 - 9 - 78[/tex]

The expression after completing the square is:

[tex]f(x) = (x+3)^{2} -87[/tex]

Answer:

85 units^2 = Area of Blue Square

and

x = 5 units

Step-by-step explanation:

To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.

Since we know the area of a square is the side length multiplied by itself (or the side length squared), [tex]\sqrt{35}[/tex] is the side length of the pink square and [tex]\sqrt{50}[/tex] is the side length of the green square.

That means a = [tex]\sqrt{35}[/tex] and b = [tex]\sqrt{50}[/tex] , so...

[tex](\sqrt{35} )^{2} + (\sqrt{50})^{2} = c^{2}[/tex]

35 + 50 = c^2

85 = c^2

[tex]\sqrt{85} = c[/tex]

Now we need to square the square root of 85 to find the area of the blue square.

[tex](\sqrt{85})^{2} = Area of blue square[/tex]

85 units^2 = Area of Blue Square

To solve the other question we use the same formula again.

[tex]x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=\sqrt{25} \\x=5[/tex]

x = 5 units

Answer:

C. The y-intercept is (0, 4).

Step-by-step explanation:

The graph of f(x) = 4 is a straight line parallel to the x-axis passing through the point (0, 4).

Answer:C

Step-by-step explanation:

BIG BRAIN

Answer:

the answer is B thats wat equals to g(x)

Answer:

2x or h(x)

Step-by-step explanation:

Answer: There will be 8 balloons left over.

Step-by-step explanation: A total of 580 balloons to be distributed equally among 26 students means 580 ÷ 26.

The division is not exact, since 580 are not divisible by 26, it will result in a rest, so

580 ÷ 26 = 22 and has rest 8

Therefore, there will be 8 balloons left over.

Answer:

c

Step-by-step explanation:

Answer:

if a matrix and another are inverse of each other, then they will form something known as the identity matrix. The identity matrix is the one I posted in the picture above. So your answer would be B

Question :

Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a 20%, percent chance of winning each game and that Cam has a 50%, percent chance of winning each game. What is the probability that Ben will win the board game?

Answer: 30%

Step-by-step explanation:

Given the following :

Justin's chance of winning each game = 20%

Cam's chance of winning each game = 50%

Therefore, probability of :

Justin winning = 20/100 = 0.2

Cam winning = 50/100 = 0.5

Overall probability = 100% = 1

Therefore,

P(Justin winning) + P(Cam winning) + P(Ben winning) = 1

0.2 + 0.5 + P(Ben winning) = 1

P(Ben winning) = 1 - 0.7

P(Ben winning) = 0.3

0.3 = 30%

Answer:22.5

Step-by-step explanation:

multiply by 1.5

Answer:

22.5 cm

Step-by-step explanation:

Since the triangles are similar, we can use ratios to solve

AC          BC

-------- = ---------

FH             GH

12            15

-------- = ---------

18             x

Using cross products

12x = 15*18

Divide each side by 12

12x/12 = 15*18/12

x =22.5

Answer:

189.3cm2

Step-by-step explanation:

Divide the whole figure into 2 parts. One part as a rectangle and the other as a semicircle  ( half a circle). First find the area of the rectangle, 10 times 15 which will get you 150cm2. Next to find the area of the semicircle do [tex]\pi[/tex] times 5 times 5 times half. You will get an amount like 39.26990817 but do not worry for now. Just keep it like that. Then add this amount with 150 and you will get an amount like 189.2699082

Then round it of to one decimal place and you will get 189.3cm2

Answer:

For real

Step-by-step explanation:

Answer: 333.2ft

Step-by-step explanation:

We can draw a triangle rectangle, where the distance between the base of the building and the car is one cathetus (300ft)

The height of the building is the other cathetus.

Now, we know that the angle of depression from the top of the building to the car is 42°

This angle is measured from a perpendicular line in from the building, so the "top angle" of the triangle rectangle will be:

90° - 42° = 48°

if we steep on this angle, the 300ft cathetus is the opposite cathetus and the height of the building is the adjacent cathetus.

Here we can use the relation:

Tan(A) = Opposite cathetus/adjacent cathetus:

Then:

Tan(48°) = H/300ft

Tan(48°)*300ft = H = 333.2ft

Answer:

270 ft

Step-by-step explanation:

The angle of depression from the top of the building to the car = 42° and the distance from the car to the building is 300 ft.

This can be represented by a right triangle with:

Adjacent side to the angle = distance from the car to the building = 300 ft, opposite side to angle = height of building = x and angle (θ) = 42°

From trigonometry:

[tex]tan(\theta)=\frac{opposite}{adjacent} \\Therefore:\\tan(42)=\frac{x}{300}\\ x = 300*tan(42)= 300*0.9\\x=270ft[/tex]

The height of the building is 270 ft

Answer:

c = 14 * t

Step-by-step explanation:

we have to calculate the average to make the equation, the first thing is to calculate the calories burned per minute in the two days:

the first day:

280/20 = 14

second day:

490/35 = 14

that is, how it does not change from day to day, the average is 14 calories per minute, therefore, the equation would be:

c = 14 * t

The equation represents this relationship is [tex]c = 14 \times t[/tex]

Since Sarah burned 280 calories running 20 minutes. The next day, Sarah burned 490 calories running for 35 minutes. Let c represent the number of calories. Let t represent time, in minutes, spent running.

So, here we need to determine the burned per minute for 2 days

So,

the first day

[tex]= 280\div 20[/tex]

= 14

And, the second day:

[tex]= 490\div 35[/tex]

= 14

Therefore, The equation represents this relationship is [tex]c = 14 \times t[/tex]

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Answer:

The loose candy is less per gram

Step-by-step explanation:

First find the cost of the bags

1.49 /120 grams = .012416667 per gram

Then the cost of the loose candy

.89/100 grams = .0089 per gram

The loose candy is less per gram

Answer:

$9$

Step-by-step explanation:

Given: Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again such that the calculator displays final number as $243$.

To find: number that Thea originally entered

Solution:

The final number is $243$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $243$ must be $324$.

As previously the number was squared, so the number before $324$ must be $18$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $18$ must be $81$

As previously the number was squared, so the number before $81$ must be $9$.

Answer:

it will be: n =  5 d =  20 p = 5

Hope it helped!

Answer:

on edge

Step-by-step explanation:

The tree increased in height each month until the time period between month 9 and month 11

The statement that can be supported by the given information is, "The height of the tree increased in height each month until the time period between month 9 and month 11".

Given a table that shows the height of the tree that Margo planted over an 11-month period.

When the months are 1, 3, 5, 7, 9, and 11, the height of the tree is 1.4, 1.5, 2.1, 2.7, 3, and 1.8 respectively.

It is clear that the height of the tree increases during the months from 1 to 9.

During the time period between 9 and 11, the height of the tree decreases to 1.8 from 3.

So, the height of the tree increased in height each month until the time period between month 9 and month 11.

Hence the correct option is c.

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