The question attached please.

Answer:

The average rate of change = -10

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Step-by-step explanation:

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function [tex]f(x) =-x^2 + 20x + 100[/tex] models the crops in pounds per acre over x years.

The average rate of change can be calculated using formula

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

In your case,

[tex]a=10\\ \\b=20,[/tex]

then

[tex]f(a)=-10^2+20\cdot 10+100=-100+200+100=200\\ \\f(b)=-20^2+20\cdot 20+100=-400+400+100=100[/tex]

and the average rate of change is

[tex]\dfrac{100-200}{20-10}=\dfrac{-100}{10}=-10[/tex]

This means the crop yield decreased by 10 pounds per acre (negative rate of change) from year 10 to year 20.

Answer:

'The crop yield decreased by 10 pounds per acre from year 10 to year 20.'

Step-by-step explanation:

i got it right on the test =)

Answer:

[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 6 and r = 30 ÷ 6 = 5, thus

[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]

The solution is x = 6

Step-by-step explanation:

Let us revise some rules of the exponents

∵ [tex]9^{(x+15)}=3^{7x}[/tex]

∵ 9 = 3 × 3

∴ 9 = 3²

- Substitute 9 by 3² in the equation above

∴ [tex](3^{2})^{(x+15)}=3^{7x}[/tex]

- Use the second rule above for the left hand side

∵ [tex](3^{2})^{(x+15)}=3^{2(x+15)}[/tex]

∴ [tex](3^{2})^{(x+15)}=3^{2x+30}[/tex]

∴ [tex]3^{2x+30}=3^{7x}[/tex]

- By using the first rule above

∴ 2x + 30 = 7x

- Subtract 2x from both sides

∴ 30 = 5x

- Divide both sides by 5

∴ 6 = x

The solution is x = 6

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Answer:

B.9

Step-by-step explanation:

9*1=9

Answer:

101/3 or 33 2/3

Step-by-step explanation:

7 2/15=107/15

9 13/15=138/15

107/15+52/3+138/15

107/15+138/15+52/3

245/15+52/3

245/15+260/15

505/15

simplify,

101/3

Answer:

[tex]x=0,x=-4,x=-3[/tex]

Step-by-step explanation:

The given equation is

[tex]x^3 + 7x^2 + 12x = 0[/tex]

Factoring by x:

[tex](x^2 + 7x + 12)x = 0[/tex]

One of the root is x=0. Let's solve the parentheses.

Expanding the trinomial

[tex]x^2 + 4x+3x + 12=0[/tex]

Factoring

[tex]x(x + 4)+3(x + 4)=0[/tex]

Factoring

[tex](x + 4)(x+3)=0[/tex]

This will give us the two remaining roots

[tex]x=-4,x=-3[/tex]

Answer:

4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold

Step-by-step explanation:

Given:

Tickets are sold at price [tex]\$28[/tex] and [tex]\$40[/tex].

Let Number of tickets sold at price [tex]\$28[/tex] be [tex]x[/tex].

Let Number of tickets sold at price [tex]\$40[/tex] be [tex]y[/tex].

Theater has maximum capacity of 6000 seat.

Hence,

[tex]x+y=6000 \ \ \ \ equation \ 1[/tex]

Total revenue to be generated is [tex]\$189600[/tex]

[tex]\therefore 28x + 40y= 189600 \ \ \ \ equation \  2[/tex]

Now Multiplying equation 1 by 40 we get,

[tex]x+y=6000\\40x+40y=240000\ \ \ \ equation \ 3[/tex]

Now Subtracting equation 2 by equation 3 we get,

[tex](40x+40y=240000)- (28x + 40y= 189600)\\12x=50400\\\\x=\frac{50400}{12}=4200[/tex]

Now substituting value of x in equation 1 we get,

[tex]x+y=6000\\4200+y=6000\\y=6000-4200= 1200[/tex]

Hence a total of 4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold

To generate a total revenue of $189,600, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40.

To find the number of tickets to be sold at each price, we can set up a system of equations. Let's assign variables:

       Let x be the number of tickets sold at $28.

The total revenue from selling x tickets at $28 is 28x, and the total revenue from selling y tickets at $40 is 40y. Since the total revenue is $189,600, we can write the equation:

28x + 40y = 189,600

We also know that the total number of tickets sold is x + y = 6000.

We can solve this system of equations to find the values of x and y. One way is to multiply the second equation by 28 and subtract it from the first equation:

28x + 40y - 28x - 28y = 189,600 - 28(6000)

12y = 189,600 - 168,000

12y = 21,600

y = 21,600 / 12 = 1800

Substituting the value of y in the equation x + y = 6000, we get:

x + 1800 = 6000
x = 6000 - 1800 = 4200

Therefore, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40 to generate a total revenue of $189,600.

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It would take 13 buses to get everyone to the zoo

It would take 26 vans to get everyone to the zoo

It would be cheaper to rent buses

Step-by-step explanation:

The given is:

We need to find how many buses it would take to get everyone to the zoo, how many vans it would take to get everyone to the zoo, and would it be cheaper to rent

∵ The number of students is 388

∵ Each bus can hold 30 students

- Divide the number of students by 30 to find the number of buses

∴ The number of buses = 388 ÷ 30 = 12.92

- They must to rent 13 bus to hold all the students

∴ The number of buses is 13

It would take 13 buses to get everyone to the zoo

∵ The number of students is 388

∵ Each van can hold 15 students

- Divide the number of students by 15 to find the number of vans

∴ The number of vans = 388 ÷ 15 = 25.87

- They must to rent 26 vans to hold all the students

∴ The number of vans is 26

It would take 26 vans to get everyone to the zoo

Let us find the cost of rent of the buses and vans to find which of them is cheaper

∵ The cost of rent of each bus = $895

∵ The number of buses = 13

∴ The cost of rent the buses = 13 × 895 = $11635

∵ The cost of rent of each van = $450

∵ The number of vans = 26

∴ The cost of rent the buses = 26 × 450 = $11700

∵ $11635 < $11700

∴ The cost of rent the buses < the cost of rent the vans

∴ The buses is cheaper than the vans

It would be cheaper to rent buses

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Answer:

1

Step-by-step explanation:

Using the rule of exponents

[tex]a^{0}[/tex] = 1

Thus

[tex](75x^2z^12)^{0}[/tex] = 1

Answer:

1

Step-by-step explanation:

any non-zero expression raised to the power of 0 equals 1

Answer: 53.2

Step-by-step explanation:

Answer:

0.01879

Step-by-step explanation:

Answer:

1260 words

Step-by-step explanation:

if you divide 840 by 2.4 you would get 350 then multiply by 3.6

With the same rate the number of words typed in 3.6 hour is 1260.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a typewriter types 840 words in 2.4 hours.

Now, number of words typed in 1 hour is

840/2.4

= 350

Now, the number of words typed in 3.6 hour is

350×3.6

= 1260

Therefore, with the same rate the number of words typed in 3.6 hour is 1260.

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Answer:

No, the correct answer of 4.9+0.03 would be 4.93

Good morning,

Answer:

No

Step-by-step explanation:

4.9+0.03=4.93

and 4,93≠4.093.

:)

The right answer is Option D.

Step-by-step explanation:

Given,

Food and Drinks = $200

Game tokens = $100

Other = $60

Total amount = 200+100+60 = 360

Deposit = 10%

Deposit amount = 10% of total amount

[tex]Deposit\ amount=\frac{10}{100}*360\\Deposit\ amount=\frac{3600}{100}\\Deposit\ amount= \$36[/tex]

Amount left to be paid = Total amount - deposit amount

Amount left to be paid = [tex]360-36=\$324[/tex]

$324 is still owed for Molly's party.

The right answer is Option D.

Keywords: Percentage, subtraction

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Answer: 6.65

Step-by-step explanation:

19-(19×.65)

Answer:

$ 6.65

Step-by-step explanation:

100% - 65% = 35%

Hence, $19 x 35% = $6.65

Answer:

The sum of the age of pupils is 81

Step-by-step explanation:

Let sum of age of 18pupils = x

Average ages = 4.5

Average = total/no. of pupil

4.5 = x/18

x = 81

Answer:

The sum of the age of pupils is 81

Answer:

6 papayas and 11 pineapples

Step-by-step explanation:

So, we need to find an answer of how many papayas and pineapples she bought, and we only spent $48.

So,  papayas are $2.50 each, and Pineapples are $3.00 each and we only bought 17 fruits total.

lets try 8 papayas, and 9 Pineapples.

$2.50 x 8 = $20.00 total on Papayas

$3.00 x 9 = $27.00 total on Pineapples.

That would only be $47 spent total.

Lets try 10 papayas and 7 pineapples.

$2.50 x 10 = $25.00

$3.00 x 7 = $21.00

That would only be a total of $26 spent.

Lets try 6 papayas and 11 pineapples.

$2.50 x 6 = $15.00

$3.00 x 11 = $33.00

This would be a total of $48 spent.

Step-by-step explanation:

You have the equation of a line in the point-slope form:

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

m - slope

(x₁, y₁) - point on a line

Convert the given equation to the slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept (0, b)

[tex]y+1=\dfrac{1}{3}(x-3)[/tex]         use the distributive property

[tex]y+1=\dfrac{1}{3}x-1[/tex]          subtract 1 from both sides

[tex]y=\dfrac{1}{3}x-2[/tex]

We only need two points to draw the line.

Choose two different x values. Put them in the line equation and calculate the y values:

for x = 0:

[tex]y=\dfrac{1}{3}(0)-2=0-2=-2\to(0,\ -2)[/tex]

for x = 3:

[tex]y=\dfrac{1}{3}(3)-2=1-2=-1\to(3,\ -1)[/tex]

Answer:

b=22

Step-by-step explanation:

11/4 divided by 1/4 equals 11. 11*2 =22

Answer:

The answer is actually 10

Step-by-step explanation:

b = 10

780 students prefer chocolate milk.

Step-by-step explanation:

Let,

the total percentage = 100%

Students who prefer plain white milk = 35%

Students who prefer chocolate milk = 100 - 35 = 65%

Number of students = 1200

No. of students who prefer chocolate milk = 65% of total students

No. of students who prefer chocolate milk = [tex]\frac{65}{100}*1200[/tex]

No. of students who prefer chocolate milk = [tex]\frac{78000}{100}\\[/tex]

No. of students who prefer chocolate milk = 780

780 students prefer chocolate milk.

Keywords: percentage, subtraction

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Answer:

x=-5, y=-5. (-5, -5).

Step-by-step explanation:

-x-5y=30

10x+5y=-75

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

9x=-45

x=-45/9

x=-5

-(-5)-5y=30

5-5y=30

5y=5-30

5y=-25

y=-25/5

y=-5

The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]

Step-by-step explanation:

Given

Length of box = l = ab

Width of box = w = a+5b

Height of box = h = 2b^2

The volume of a box is given by:

[tex]V = Length*Width*Height\\V = l*w*h[/tex]

Putting the values

[tex]V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4[/tex]

Hence,

The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]

Keywords: Volume, Polynomials

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The equation of the line in standard form is 3x - 5y = 26

Step-by-step explanation:

Let us revise the forms of the linear equation

∵ The line passes through point (2 , -4)

∵ The slope of the line is [tex]\frac{3}{5}[/tex]

- Let us using the point-slope form and then change it to the

  standard form

∵ [tex]x_{1}[/tex] = 2 and [tex]y_{1}[/tex] = -4

∵ m = [tex]\frac{3}{5}[/tex]

- Substitute these values in the form of the equation below

∵ [tex]y-y_{1}=m(x-x_{1})[/tex]

∴ [tex]y-(-4)=\frac{3}{5}(x - 2)[/tex]

∴ [tex]y+4=\frac{3}{5}(x - 2)[/tex]

Let us change it to standard form

- Multiply each side my 5 to cancel the denominator in the

   right hand side

∴ 5(y) + 5(4) = 3(x - 2)

- Simplify the two sides

∴ 5y + 20 = 3x - 6

- Add 6 to both sides

∴ 5y + 26 = 3x

- Subtract 5y from both sides

∴ 26 = 3x - 5y

- Switch the two sides

∴ 3x - 5y = 26

The equation of the line in standard form is 3x - 5y = 26

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Answer:

4.8, 135, 0.2822, 0.024

Step-by-step explanation:

4*1.2=4.8

7.5*18=135

0.34*0.83=0.2822

0.04*0.6=0.024

Answer:

[tex]a_{n}[/tex] = 2n - 3

Step-by-step explanation:

Note the difference in consecutive terms is constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2

This indicates that the terms are an arithmetic sequence with

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 2, thus

[tex]a_{n}[/tex] = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

Answer:

Step-by-step explanation:

$3.55 ÷ 5 = .71 each peach

To find out how much Tomas paid for each fruit, we set up the equation m = $3.55 / 5, which when solved gives m = $0.71. This means that Tomas paid $0.71 for each peach.

To find out how much Tomas paid for each peach, you can set up an equation. Because Tomas buys 5 peaches for $3.55 in total, you can express this as a simple division. To solve the equation, divide $3.55 (total cost) by 5 (total number of peaches).

So, the equation would be m = $3.55 / 5.

Solving this equation gives: m = $0.71. Therefore, Tomas paid $0.71 for each peach.

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Answer:

(0, 5 )

Step-by-step explanation:

The y- intercept is the value of the y- coordinate where the function crosses the y- axis. At this point the x- coordinate is zero.

From the table when x = 0, y = 5

Thus (0, 5) is the y- intercept

Answer:

6-pack for 3.12

Step-by-step explanation:

Find unit price

2.24/4=0.56

3.00/3=1

4.24/8=0.53

3.12/6=0.52

Answer:

80

Step-by-step explanation:

35/100X = 28

35X = 2800

2800/35=80

Answer: 80

Step-by-step explanation: To answer the question 28 is 35% off what number, we translate the question into an equation.

So we have "28 is" which means 28 = 35% which we need to write as a decimal. To write a percent as a decimal, we move the decimal point 2 places to the left so 35% can be written as the decimal .35. Next we have "of what number" which means times X.

Now we have the following equation.

28 = (.35) (x)

Now to solve for x since x is being multiplied by .35, we need to divide by .35 on both sides of the equation.

On the right side of the equation, the .35's cancel and we have x. On the left side of the equation, we have 28 ÷ .35 which is 80.

So 80 = x.

Therefore, 28 is 35% of 80.

Answer:

90°

Step-by-step explanation:

5, 12 and 13 are the sides of a right triangle ( Pythagorean triple )

13 is the measure of the hypotenuse whose opposite angle is 90°

Answer:

90°

Step-by-step explanation:

5^2+ 12^2 = 13^2

25 + 144 = 169

The Converse Pythagorean Theorem (Egyptian triangle) states that if the length of the sides of a triangle, say a, b, and c, satisfy a^2 + b^2 = c^2, then this is a right triangle with a right angle opposite to side c.

And since 5^2 + 12^2 = 13^2 satisfies the statement a^2 + b^2 = c^2, c (which is 13) is opposite to a 90° angle.