15 POINTS


A store has 250 bottles of water. Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments. Which recursive function best represents the number of bottles of water in the store, given that f(0) = 250?

What even is this ???

The inverse function is [tex]\( f^{-1}(x) = \frac{x + 7}{4} \)[/tex].

To find the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex], we follow these steps:

1. Replace [tex]\( f(x) \) with \( y \): \( y = 4x - 7 \)[/tex].

2. Swap[tex]\( x \) and \( y \): \( x = 4y - 7 \)[/tex].

3. Solve this equation for [tex]\( y \)[/tex].

So, let's solve for [tex]\( y \)[/tex]:

[tex]\[ x = 4y - 7 \][/tex]

Add 7 to both sides:

[tex]\[ x + 7 = 4y \][/tex]

Divide both sides by 4:

[tex]\[ \frac{x + 7}{4} = y \][/tex]

Thus, the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex] is:

[tex]\[ f^{-1}(x) = \frac{x + 7}{4} \][/tex]

16)

15x + 7y = -5    ⇒  -10(15x + 7y = -5)   ⇒   -150x - 70y =   50

11x + 10y = -28 ⇒    7(11x + 10y = -28)  ⇒     77x + 70y = -196

                                                                    -73x           = -146

                                                                                   x = 2

11x + 10y = -28

11(2) + 10y = -28

 22 + 10y = -28

         10y = -50

             y = -5

Answer: x = 2, y = -5

18)

7x - 4y =  1     ⇒   1(7x - 4y =  1)   ⇒    7x  -  4y =  1

5x + 2y = -9   ⇒ 2(5x + 2y = -9)  ⇒ 10x  + 4y = -18

                                                          17x          = -17

                                                                      x = -1

 7x - 4y =  1

7(-1) - 4y =  1

 -7  - 4y = 1

       -4y = 8

          y = -2

Answer: x = -1, y = -2

Answer:

a. $36

b. $336

Step-by-step explanation:

The simple interest on a amount is:

A=P(1+rt)

A is the amount after interest, P is the amount before interest, r is the rate of interest and t is the time in years.

a.

We can use the formula:

The interest earned is the amount after interest minus the original amount before interest:

$36 of interest was earned

b.

The balance of the account is $336 worked out in a

Answer:

5000 square feet of lawn would provide the daily supplies of oxygen for 8 organisms.

Explanation:

 The daily supply of oxygen for a particular multi cellular organism is provided by 625 square feet of lawn

Total area of lawn provided = 5,000 square feet

Number of organism for which provided lawn area supplies oxygen = Total area of lawn provided/ Daily requirement of lawn area for 1 organism.

Number of organism for which provided lawn area supplies oxygen = 5000/625 = 8 organisms.

So 5000 square feet of lawn would provide the daily supplies of oxygen for 8 organisms.

A total of 5,000 square feet of lawn would provide the daily supplies of oxygen for 8 organisms based on the ratio given.

The question can be solved using the concept of ratios. The ratio of lawn to organisms is 625 square feet to 1 multicellular organism. So, if we have 5,000 square feet lawn area, we can find how many organisms it can support by setting up a proportion and solving for the unknown number of organisms.

Let's denote the unknown number of organisms as X. The proportion would then be: 625/1 = 5000/X.

To solve this equation for X, we can cross-multiply and divide. So, X = 5000 / 625 = 8 multicellular organisms.

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*(The first order pair)*

[tex]y=-9(0)+3[/tex]                   Substitute [tex]0[/tex] to [tex]y=-9(0)+3[/tex]

[tex]y=0+3[/tex]                        Multiply [tex]-9[/tex] to [tex]0[/tex]

[tex]y=3[/tex]                            Add [tex]3[/tex] to [tex]0[/tex]

*(Answer)*= [tex](0, 3)[/tex]

*(The second order pair)*

[tex]y=-9(3)+3[/tex]                   Substitute [tex]3[/tex] to [tex]y=-9(3)+3[/tex]

[tex]y=-27+3[/tex]                        Multiply [tex]-9[/tex] to [tex]3[/tex]

[tex]y=-24[/tex]                            Subtract [tex]3[/tex] to [tex]-27[/tex]

*(Answer)*= [tex](3, -24)[/tex]

*(The third order pair)*

[tex]30=-9x+3[/tex]                   Substitute [tex]30[/tex] to [tex]30=-9x+3[/tex]

[tex]27=-9x[/tex]                        Subtract [tex]3[/tex] to [tex]30[/tex]

[tex]x=-3[/tex]                           Divide [tex]-9[/tex] to [tex]27[/tex]

*(Answer)*= [tex](-3, 30)[/tex]

Hope this helps

The person who answer: BangtanBoyScouts

a 1.25L Coca Cola that cost $1.29

Unit rate means we need to find the rate of 1 liter of Coca Cola

1.25 L Coca Cola =  $1.29

1 L of Coca Cola = ?

To find 1 liter of Coca cola divide the cost by liter, so we divide 1.29 by 1.25

[tex]\frac{1.29}{1.25}[/tex]

1.032

So the cost of 1 liter of Coco Cola = $1.032

Answer:

A. 5

Step-by-step explanation:

Let n = number

(3n)+6 = 5n-4

Subtract 3n from each side

(3n)-3n+6 = 5n-3n-4

6 = 2n-4

Add 4 to each side

6+4 = 2n -4+4

10 = 2n

Divide by 2

10/2 = 2n/2

5 =n

Solution: The function that represents the Grace earning each week is defined as [tex]e(h)=9h[/tex], where [tex]e(h)[/tex] is in dollar and [tex]h[/tex] is the time in hours. domain of the function [tex]e(h)=9h[/tex] is [10,20].

Explanation:

Let, Grace works for h hours per week.

For one hour she get $9.

For h hours she get [tex]\$(9\times h)=\$9h[/tex].

So, the function that represents the Grace earning each week is defined as [tex]e(h)=9h[/tex].

It is given that she works from 10 to 20 hours per week, therefore the value of h lies between 10 to 20. Hence the Grace's earnings for each week is defined as [tex]e(h)=9h[/tex] and the domain of the function [tex]e(h)=9h[/tex] is [10,20].

We are given that

a line is perpendicular bisector on line between point (4,1) and (2,-5)

So, line intersect at mid-point between (4,1) and (2,-5)

so, firstly we will find mid-point

[tex](a,b)=(\frac{4+2}{2},\frac{1-5}{2})[/tex]

[tex](a,b)=(3,-2)[/tex]

now, we will find slope between (4,1) and (2,-5)

x1=4 , y1=1

x2=2 , y2=-5

slope is

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

now, we can plug values

[tex]m=\frac{-5-1}{2-4}[/tex]

[tex]m=3[/tex]

now, our required line is perpendicular to this line

so, slope of required line is -1/m

so, we get slope

[tex]m'=\frac{-1}{3}[/tex]

we have a point as (3 ,-2)

we can use point slope form of line

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

we can plug values

[tex]y+2=-\frac{1}{3}(x-3)[/tex]

now, we can solve for y

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

Answer:

PAST

Step-by-step explanation:

the words "taught" and "yesterday" are in the past tense.

Answer:

The number of melon was 3 and the number of apples was 45.

Step-by-step explanation:

1. Melons cost $20 per crate and apples cost $8 per create. If the total was 48 crates for $420, you can make the following system of equations, where [tex]x[/tex] is the number of melons and [tex]y[/tex] is the number of apples:

[tex]\left \{ {{x+y=48} \atop {20x+8y=420}} \right.[/tex]

2. By applying the Method of substitution, you can solve for [tex]y[/tex] in the first equation and substitute it into the second one to find [tex]x[/tex]. Then, you can substitute the value of [tex]x[/tex] into the first equation to find [tex]y[/tex]:

[tex]y=48-x[/tex]

[tex]20x+8(48-x)=420\\20x+384-8x=420\\12x=36\\x=3[/tex]

[tex]3+y=48\\y=45[/tex]

Final answer:

The order consisted of 3 crates of melons and 45 crates of apples.

Explanation:

To solve the problem of determining the number of crates of melons and apples based on the total cost and quantity, we can use a system of linear equations.

Given that melons cost $20 per crate and apples cost $8 per crate, with a total order of 48 crates for $420, we can set up the following equations:

Solving this system of equations:

Thus, the order consisted of 3 crates of melons and 45 crates of apples.

Answer-

The abs. minimum value of the given function was found to be 3.

Solution-

Here, the given function is,

[tex]f(x)=x^4-x^2-2x+5[/tex]

Then, calculating its first derivative,

[tex]{f}'(x)=4x^3-2x-2[/tex]

Then, calculating its second derivative,

[tex]{f}''(x)=12x^2-2[/tex]

Then, calculating all the critical values of the given function by equating the first derivative to 0,

[tex]\Rightarrow {f}'(x)=0[/tex]

[tex]\Rightarrow 4x^3-2x-2=0[/tex]

[tex]\Rightarrow 2x^3-x-1=0[/tex]

[tex]\Rightarrow 2x^3-x-1=0[/tex]

[tex]\Rightarrow 2x^3-2x+x-1=0[/tex]

[tex]\Rightarrow 2x(x^2-1)+(x-1)=0[/tex]

[tex]\Rightarrow 2x(x+1)(x-1)+(x-1)=0[/tex]

[tex]\Rightarrow (x-1)(2x(x+1)+1)=0[/tex]

[tex]\Rightarrow (x-1)(2x^2+2x+1)=0[/tex]

[tex]\Rightarrow (x-1)=0[/tex]    ( ∵ ignoring the imaginary roots)

[tex]\Rightarrow x=1[/tex]

Putting the value of x, in the second derivative,

[tex]{f}''(1)=12(1)^2-2=10[/tex]

As, the value of f"(x) is positive, the function attains its minimum value at x=1.

So, f(1) will give the absolute minimum value of the function,

[tex]f(1)=(1)^4-(1)^2-2(1)+5=3[/tex]

∴ The abs. minimum value of the given function is 3.

The product of -2 1/2 and -3 1/3 is 8 1/3. This is calculated by converting mixed numbers into improper fractions and then multiplying. Multiplying two negative numbers gives a positive result.

To compute the product of -2 1/2 and -3 1/3, first convert these mixed numbers into improper fractions.  -2 1/2 can be converted to -5/2 and -3 1/3 is -10/3.  Then, simply multiply these two fractions:

(-5/2) x (-10/3) = 50/6 = 25/3 or 8 1/3 .So the product of -2 1/2 and -3 1/3 is positive 8 1/3. Remember, multiplying two negative numbers results in a positive product.

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Answer:

21

Step-by-step explanation:

There are two parallel lines given.

Two transversals cut them.

Here m and n are parallel.

Two transversals cut them so that a triangle is formed.

Let us use the property that sum of angles of a triangle = 180

Bottom angle of triangle = 39 (vertically opposite angles)

Top left angle = 4x+3 (vertically opposite angles)

Top right angle = 180-6x (linear pair property)

Now add these 3 and equate to 180

39+4x+3+180-6x = 180

2x = 42

Or x = 21

Transformations of the graph y = x^3 to y=2x^3, y=(2x)^3, and y=(0.2x)^3 include a vertical stretch by a factor of 2, a horizontal compression by a factor of 2, and a horizontal stretch by a factor of 5 respectively.

The transformation of the graph of y = x^3 to the graphs of the equations: 1) y=2x^3, 2) y=(2x)^3, and 3) y=(0.2x)^3, is based on changes in scaling and stretching.

These transformations are characterized as vertically stretched, horizontally compressed, and horizontally stretched respectively.

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The answer you are looking for would be 63.

63 is greater than 60, but less than 70, and the tens place (6) is double the ones place (3). Thus meaning 63 is the answer.

I hope this helps!

[tex]3\frac{3}{8} = \frac{8(3) + 3}{8} = \frac{27}{8}[/tex]

[tex]5\frac{1}{4} = \frac{4(5) + 1}{4} = \frac{21}{4}[/tex]

[tex]\frac{21 (miles)}{4}[/tex] ÷ [tex]\frac{27 (miles)}{8 (hour)}[/tex]

= [tex]\frac{21 (miles)}{4} * \frac{8 (hours)}{27 (miles)} = \frac{21(8)hours}{4(27)} = \frac{42}{27}hours[/tex]

[tex]\frac{42}{27} hours[/tex] = [tex]\frac{14}{9}= 1\frac{14-9}{9} hours = 1\frac{5}{9}hours[/tex]

Answer:  [tex]1\frac{5}{9}hours[/tex]

First open the bracket by multiplying with -2

-2x - 26 +9x = 4

Solving like terms

7x - 26 = 4

Adding 26 to both sides

7x - 26 +26 = 4+26

7x = 30

X = 30/7

[tex]-2(x+13)+9x=4\\\\-2x-26+9x=4\\\\7x=30\\\\x=\dfrac{30}{7}[/tex]

Answer:

The second gear will complete 75 complete revolutions

Step-by-step explanation:

- There are two connected gears

- One has 60 teeth and the other has 40 teeth

- The two gears have different revolutions depends on the number of

  their teethes

- They do the same job

- The relation between them is

   [tex]n_{1}*c_{1}=n_{2}*c_{2}[/tex], where n is the number of the complete

   revolutions and c is the number of the teeth

- The gear which has less teethes makes more complete revolutions

∵ [tex]n_{1}[/tex] = 50

∵ [tex]c_{1}[/tex] = 60

∵ [tex]c_{2}[/tex] = 40

- Substitute these values in the rule below

∵ [tex]n_{1}[/tex] × [tex]c_{1}[/tex] = [tex]n_{2}[/tex] × [tex]c_{2}[/tex]

∴ 50 × 60 = [tex]n_{2}[/tex] × 40

∴ 3000 = 40 [tex]n_{2}[/tex]

- Divide both sides by 40

∴ [tex]n_{2}[/tex] = 75 complete revolutions

The second gear will complete 75 complete revolutions

12/4=x/20

x=60

60 people are needed

4x3=12 right. Then 20x3=60.

[tex]\dfrac{1}{2}x+2=1\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{2}x=-1\qquad\text{multiply both sides by 2}\\\\\boxed{x=-2}[/tex]

Step 1. Factor out the common term 2

n - 2 = 2(5n + 2)/2

Step 2. Cancel 2

n - 2 = 5n + 2

Step 3. Subtract n from both sides

-2 = 5n + 2 - n

Step 4. Simplify 5n + 2 - n to 4n + 2

-2 = 4n + 2

Step 5. Subtract 2 from both sides

-2 - 2 = 4n

Step 6. Simplify -2 - 2 to -4

-4 = 4n

Step 7. Divide both sides by 4

-1 = n

Step 8. Switch sides

n = -1

To find the value of n, rearrange the equation and simplify to solve for n.

To find the value of n, we need to solve the given equation. First, distribute the 2 on the right side:

n - 2 = 10n + 4

Next, subtract 10n from both sides:

n - 10n - 2 = 4

Combine like terms:

-9n - 2 = 4

Then, add 2 to both sides:

-9n = 6

Finally, divide both sides by -9 to solve for n:

n = -6/9 which simplifies to n = -2/3.

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The series is A.P. with first term = 44 and common difference = 39-44=-5 = 34- 39

Sum of A.P. is S = n/2(2a+ (n-1)d)

Where a is first term ,d is common difference and n no. Of terms

Here a = 44 ,d= -5 and n = 23

S = 23 /2(2×44+ (23-1)(-5))

S=23/2(88-110)

S = 23/ 2(-22)

S = 23×-11

S = -253

Okay so fiquring out 1/2 of 1/4 is simple got to the third diagram since it has been cut to match the 1/2.  1/3 of 3/8 would be the first diagram since the squares have been sliced in half.

[tex]\{0,1,5,7\}\cap\{0,5,7,9\}=\{5,7\}[/tex]

B. This is because falling represents negatives, or subtracting. 3-5 is -2.

11

11.06

11.56

11.6

is what you are looking for

The order would go 11; 11:06; 11.56; 11.6

The first integer (x) is equal to the consecutive even integers, x+2, x+4.

x = (x+2) + (x+4)

x = 2x + 6

x - 6 = 2x

x = -6 (First integer)

+2

-4 (Second integer)

+4

-2 (Third integer)

Integers: -6, -4, -2

Equation: x = (x+2) + (x+4)

Answer:

2x+2=x+4

Step-by-step explanation: