A hot air balloon rises 350 feet in 5 minutes

What is the balloon’s ascent rate in feet per minute?

How long did it take the balloon to rise 1470ft?

Estimate how high the balloon will ascend after 27 minutes.

You didn't specify which problems you needed and you are only allowed to submit three questions in one posting so I chose to solve 1, 3, and 5.

NOTES:

Inverse means to swap the x's and y's and solve for "y"

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1. Answer: y = [tex]\frac{2x+4}{3}[/tex]

Step-by-step explanation:

y = [tex]\frac{-4+3x}{2}[/tex]

swap: x = [tex]\frac{-4+3y}{2}[/tex]

         2x = -4 + 3y

   2x + 4 =        3y

   [tex]\frac{2x+4}{3}[/tex] =         y

3. Answer: y = -3(x - 1)

Step-by-step explanation:

y = [tex]-\frac{1}{3}x[/tex] + 1

swap: x = [tex]-\frac{1}{3}y[/tex] + 1

     x - 1 = [tex]-\frac{1}{3}y[/tex]

  -3(x - 1) = y

5. Answer: y = [tex]-\frac{4}{9}[/tex](x - 4)

Step-by-step explanation:

y = 4 - [tex]\frac{9}{4}x[/tex]

swap: x = 4 - [tex]\frac{9}{4}y[/tex]

    x - 4 =      [tex]-\frac{9}{4}y[/tex]

 [tex]-\frac{4}{9}[/tex](x - 4) =      y

Answer:

A

Step-by-step explanation: Scale Factor is defined as a ratio between the actual figure to that of the other figure.

And as it is clearly given in the question that 2 cm of length corresponds to 100 meters so the ratio comes out to be 1:50.

So the scale factor of the actual farm to the photo is A that is 1 to 50.

The scale factor of the actual farm to the photo is 1 to 50.

To determine the scale factor of the actual farm to the photo, we can use the given information that 2 centimeters in the photo corresponds to 100 meters in actual height. Since the scale factor relates the lengths in the photo to the actual heights, we need to find the ratio of the length in the photo to the corresponding actual height. In this case, the scale factor is 2 centimeters / 100 meters, which simplifies to 1 centimeter / 50 meters. Therefore, the scale factor of the actual farm to the photo is 1 to 50.

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The equation of line CD in standard form is;

B: 5x - 3y = 30

Formula for slope of line between two coordinates is;

m = (y2 - y1)/(x2 - x1)

Thus, slope of line CD is;

m = (0 - (-5))/(6 - 3)

m = 5/3

c is y - intercept which is when x = 0.

Point D gives us the x-intercept because y is zero.

Thus;

0 = (5/3)(6) + c

c = -10

Thus, the equation of the line CD is;

y = (5/3)x - 10

Multiply through by 3 to get;

3y = 5x - 30

>> 5x - 3y = 30

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Answer:

2 and 1/3

Step-by-step explanation:

1 hour = 5/5 so 2/3 + 5 = 8/3

= 2 and 2/3

Hope this helps :)

3 and 1/3

2/3 ÷ 1/5 = 10/3 = 3 and 1/3

1 hour =  1 × 3 and 1/3 = 3 and 1/3

Answer:

The variable having largest coefficient is solved first.

Step-by-step explanation:

The variable having greater coefficient is solved first because we can substitute the value of smaller coefficient variable easily as compared to the greater one.

Because in substitution method we first substitute the value of coefficient which has smallest coefficient and as a result the coefficient with greater coefficient is solved.

Final answer:

When solving a linear system by substitution, choose the variable that is already isolated in one of the equations. Substitute the value of that variable into the other equation.

Explanation:

When solving a linear system by substitution, it is important to decide which variable to solve for first. One strategy is to choose the variable that is already isolated in one of the equations. This makes it easier to substitute the value of that variable into the other equation.

For example, consider the system:

Equation 1: x + 2y = 5

Equation 2: 3x - y = 2

In this case, Equation 1 is already isolated for x, so it would be a good choice to solve for x first. By substituting the expression for x from Equation 1 into Equation 2, you can solve for the remaining variable y. Once you have the value of y, you can substitute it back into Equation 1 to find the value of x.

Answer:

It's simple Add the fractions, find the LCD and then combine

Exact form: 3/2

Decimal form: 1.5 Hope this helps have a nice day :)

Step-by-step explanation:

Answer:

4/6 + 5/6 = 9/6

Step-by-step explanation:

First find the least common denominator which is 6. Then add the fractions. Hope this helps.

Answer:

an=3n+14

Step-by-step explanation:

Use the formula  

an=a1+d(n−1)  to identify the arithmetic sequence.

an=3n+14

The standard form of the

An arithmetic sequence is formed by adding a constant value to each term. In this case, the first term is 17 and the common difference is 3 (since we add 3 to each term to get the next term).

The standard form of an arithmetic sequence is:

an = a1 + (n-1)d

Where:

Let's calculate the standard form for the given arithmetic sequence:

an = 17 + (n-1)3

So, the standard form of the arithmetic sequence 17, 20, 23, 26... is an = 17 + 3(n-1).

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Question

20% of miran’s allowance is 5$ how much is his total allowance?

Answer:

25 $

Step-by-step explanation:

you can solve with an equation

20 : 5 = 100 : x

x = 5 * 100 : 20

x = 25

or you can solve with an expression

5 : 20 * 100 =

25

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

check

25 * 20% = 5

the answer is good

The area of the section she wants to paint is 48 square feet.

In Euclidean Geometry, the area of a rectangle can be calculated by using this formula;

Area of rectangle  = length × width

Area of rectangle 1 = 4 × 9

Area of rectangle 1 = 36 square feet.

For the area of rectangle 2, we have;

Area of rectangle 2 = 4 × 3

Area of rectangle 2 = 12 square feet.

Now, we can find the area of the figure;

Area of figure = 36 + 12

Area of figure = 48 square feet.

Complete Question:

Mrs. Rios puts tape around the section of wall shown to indicate the area of the mural she will paint. What is the area of the section she wants to paint?

a. 14, 18, 22, 26.... It is +4

b. 2,430, 7,290, 21,870..... It is x3

c. So it is going -2, -4, -6, -8 so the next one would be -10 which is -13 then -12 which is -25 and so on.

Hope this helps!

Answer:

d

Step-by-step explanation:

There are 4 cards in a standard deck. So 52-4 is 48. 48 cards are not aces then.  So the ratio is 48 to 52. Which simplifies to 12 to 13. Otherwise known as 12/13

Answer:

#1 is -1

Step-by-step explanation:

The answer to Problem 1 is the number -1. You use PEMDAS to evaluate division first, then you subtract later.

For problem 2, we combine like terms to get this answer: -4a+b. You only add the 'a' terms together, same with the 'b' terms. Think of it like having 2 books and add on 3 more books. We can write that as 2b+3b = 5b. So we have 5 books total.

Problem 3) The answer here is 1.2n after adding n to 0.2n. Think of the first n as 1n or 1.0n

Problem 4) Divide both sides by 15 and you end up with the answer a = 2

Problem 5) Answer: 31.4 This answer is found by multiplying the diameter (10) by the approximate value for pi (3.14). The formula is C = pi*d

Answer:

6,561 = 3h

Step-by-step explanation:

The equation B) [tex]\( 6,561 = 3^h \)[/tex] determines the number of hours, c[tex]\( h \)[/tex], for the algae population to reach 6,561 blooms.

1. Identify the exponential growth formula:

[tex]\[ N = N_0 \cdot r^h \][/tex]

2. Define the given variables:

[tex]- \( N \):[/tex] Final number of algae blooms = 6,561

[tex]- \( N_0 \):[/tex] Initial number of algae blooms = 1

[tex]- \( r \):[/tex] Growth rate = 3 (since the population triples every hour)

[tex]- \( h \)[/tex]: Number of hours (this is what we need to find)

3. Substitute the given values into the formula:

[tex]\[ 6,561 = 1 \cdot 3^h \][/tex]

4. Simplify the equation:

[tex]\[ 6,561 = 3^h \][/tex]

5. Result:

  The equation B) [tex]\( 6,561 = 3^h \)[/tex] can be used to determine the number of hours, [tex]\( h \)[/tex], it will take for the algae population to reach 6,561 blooms.

Complete Question:

Answer:

17 + 6c +d

Step-by-step explanation:

To simplify the expression, we need to combine like terms

23+6c+8d−7d−6

I like to put like terms next to each other

23-6+6c+8d−7d

17 + 6c +d

23 + 6c + 8d - 7d - 6

combine like terms

=  6c + (8d - 7d) +(23 - 6)

Answer:

24 students

Step-by-step explanation:

If 60% equals 72, then 20% would be 1/3 of 72 which is 24.

Answer:

24 students selected milk

Step-by-step explanation:

Let x be the total number of students,

Since, 60% of students selected soda,

⇒ Number of students who selected soda = 60% of x = 0.6x

According to the question,

0.6x = 72

Divide both sides by 0.6,

⇒ x = 120

Now, 20% students selected milk

Hence, the number of student who selected milk = 20% of 120 = 0.20 × 120 = 24

Answer:

x = 7.25

Step-by-step explanation:

First you must try to get the x by itself with the 4, so, you have to subtract 5 from both sides so that the five is no longer on the side of the variable. Once you do this the equation becomes 4x = 29. Then you have to get x by itself so you then have to divide the 4 on both sides and the answer it then x = 7.25

Answer:

5 hours

Step-by-step explanation:

Let x be the number of hours.

18x=90

Divide by 18 on each side

x=5

Final answer:

Corey can rent the canoe for 5 hours with his $90 by setting up and solving the linear equation 18x = 90.

Explanation:

To determine how many hours Corey can rent a canoe, given that he has $90 to spend and the rental cost is $18 per hour, we can set up a linear equation. We let x represent the number of hours Corey can rent the canoe for.

The equation is simply 18x = 90, where 18 represents the hourly rental rate of the canoe and 90 represents the total amount Corey has to spend.

To solve for x, we divide both sides of the equation by 18:

18x / 18 = 90 / 18

x = 5

So, Corey can rent the canoe for 5 hours with his $90.

Answer:

Explicit formula

f(n) = 2*2⁽ⁿ⁻¹⁾

Recursive formula                  

f(n) = aₙ₋₁ * r

Step-by-step explanation:

Since, Nathan has two parents, four grandparents, and so on, it would form a Geometric Progression (GP) series for the number of Nathan's ancestors as below:-

2, 4, 8, 16, 32, ....

First term (a₁) = 2

Common Ratio (r) = [tex]\frac{a_{2} }{a_1}[/tex]

                             = [tex]\frac{4}{2}[/tex]

                             = 2

So,

Number of ancestors of Nathan if we go back n generations = a₁r⁽ⁿ⁻¹⁾

Plugging in the values of a₁ and r, we get

f(n) = 2*2⁽ⁿ⁻¹⁾                       [Explicit formula]

Now,

A geometric progression (GP) series is of the form,

a, ar, ar², ar³, ar⁴, ar⁵........  

in which the first term a₁=a and other the terms are obtained by multiplying with r.

Observe that each term is r times the previous term. So, to get the [tex]n_{th}[/tex] term, we multiply [tex](n-1)_{th}[/tex] term by r.

i.e. aₙ = aₙ₋₁ * r    

=> f(n) = aₙ₋₁ * r                     [Recursive formula]                                                                                      

Answer:

1:2

Step-by-step explanation:

Because 10/20 = 1/2

Answer: 10,20

Step-by-step explanation:

Answer:

The point ( 0,-1) is a solution.

Step-by-step explanation:

y<= (x+1) (x+5)

y>= (x-1)^2 -6

See attached graph.

To prove algebraically, put the point (0,-1) into both equations and see if it is true for both of them.

y<= (x+1) (x+5)

-1 <= (0+1) (0+5)

-1<= 1*5

-1 <=5

True

y>= (x-1)^2 -6

-1 >= (-1)^2 -6

-1 >= 1-6

-1 >=-5

True

The point is a solution

Answer: B

Step-by-step explanation:

1) First find the weight of the elephant: 1.1 * 10^4 = 11,000

2) Then find the weight of the giraffe: 2.1 * 10^3 = 2,100

3) Then subtract the weight of the giraffe from the weight of the elephant

11,000 - 2,100 = 8,900

4) And there is your answer 8.9 * 10^3 = 8,900

It is found that elephant weighs 9,000 more lb than the giraffe.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

Given that an elephant weighs 1.1  x 10⁴ and a giraffe weighs 2.1 x 10³. The weight will be estimated as below;

1.1  x 10⁴ = 11000 lb

2.1 x 10³ = 2100 lb

The difference in the weight of an elephant and the Giraffe ;

D = 11000 -2100= 9000 lb

Hence, an elephant weighs 9,000 more lb than the giraffe.

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Answer:

Look Below

Step-by-step explanation:

I'm not going to do any of these, i'll just set up the equation for you to find x.

9. 75+x=90

10. x+22=180

11. x=84

12. 82+78+x=180

13. (4x+3)+(x-8)=90

14. (8x+9)+(5x+15)=180 (This was hard to read, check to see if I typed it right.)

15. 2x+4+140=180

16. 4x-13=67+2x

17. 9x+7=115

18. 12x=60

19. 4x=x+21

20. 5x+12+73=180

Answer:

1st and last group represent similar figures.

Step-by-step explanation:

We have been given a graph. We are asked to find the similar figures.

We can see that triangles in the 1st group are similar triangles as the measure of their corresponding angles are equal.

We can see that rectangle in the last group are also similar as the sides of the yellow rectangle is 2 times the sides of smaller rectangle, therefore, last pair is also similar.

Therefore, 1st and last group represent similar figures.

Answer:

Greg is 67 years old.

Step-by-step explanation:

John = 2 * B

G = 7 + B

J - 4 + B - 4 + G - 4 = 55

J + B + G = 67

2B + B + 7 + B = 67

4B = 60

B = 15

J = 30

G = 22

30 + 15 + 22 = 67

67 = 67

- I.A -

The age of Greg is 31 years.

solving this we will get the valve of Y if x is given.

Calculation:-

⇒let the actual age of Bill is X years.

      four years ago the age Bill = X-4

⇒   then, the age of John is twice of Bill = 2X

           four years ago age John = 2X-4

⇒Greg is 7 years older than Bill

       Age of Greg =  2X+7

 four years ago age Gerg = 2X+7-4

Four years ago Sum of their ages = 55

                  ⇒ ( X-4)+(2X-4)+(2X+7-4)=55

                ⇒X-4+2x-4+2x+7-4=55

               ⇒5X=60

              ⇒X=12

∴age of Gerg is 2X+7

                      ⇒2(12)+7

                      ⇒31 years

age of bill=12 years

age of John 24 years.

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Answer:

(x+4,y+5)

Step-by-step explanation:

If you look at the differences in the x and y rows t=you can see that x is added 4 each time and y is add 5 each time.

In the trinagle 30 - 60 - 90 the sides are in proportion 1 : √3 : 2.

Look at the picture.

We have:

[tex]a=2\sqrt5[/tex]

Therefore

[tex]A=2a\to A=(2)(2\sqrt5)=4\sqrt5\\\\B=a\sqrt3\to B=(2\sqrt5)(\sqrt3)=2\sqrt{(5)(3)}=2\sqrt{15}[/tex]

Answer:

The ordered pair that is on the line is​ (−5,−6) ​

Step-by-step explanation: You have to substitute...

Soooo....

(1,-32):

3x − 4y = 9

3(1) - 4(-32) = 9

3 + 128 = 9

131 = 9

NO

(-1,3):

3x − 4y = 9

3(-1) - 4(3) = 9

-3 - 12 = 9

-15 = 9

NO

(-5, -6)

3x − 4y = 9

3(-5) - 4(-6) = 9

-15 + 24 = 9

9 = 9

YES

(23, -74)

3x − 4y = 9

3(23) - 4(-74) = 9

69 + 296 = 9

365 = 9

NO

By substituting the x and y values from the given ordered pairs into the equation, we find that the only ordered pair on the line represented by the equation 3x−4y=9 is (-5,-6).

The equation 3x−4y=9 represents a line on a coordinate plane, and ordered pairs (x, y) are points on this plane. To determine which given ordered pairs are on the line, we substitute each x and y value into the equation.

The only correct ordered pair on the line 3x−4y=9 is (-5,-6).

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Answer:

Four

Step-by-step explanatio

Materials + installation = $192.49

-Materials                       =   132.49

Installation                    = $ 60.00

Installation cost = 1 skateboard/$15

No. of skateboards = 60.00 × 1/15

No. of skateboards = 4

Four skateboards will be repaired.