Oliver is watching a farmer plant a vegetable garden. He notices two hours after they began that the farmer had planted seven rows of the garden. Three hours later, he noticed that the farmer had now planted seventeen and a half rows of the garden. Assume that the farmer works at a constant rate.

Part B)Create an equation to represent the rate at which the farmer plants his vegetables, where x equals the hours worked and y equals the number of rows planted.

Final answer:

The expression 6x²/5 is greater than 2/5 if x is a positive integer greater than 1. If x equals 1, the expression is still greater than 2/5. However, if x is zero or negative, the expression will be equal to or less than 2/5.

Explanation:

To determine whether 6x²/5 is greater or less than 2/5, we need to consider the value of x.

As long as x is a positive integer greater than 1, the expression 6x²/5 will indeed be greater than 2/5. If x equals 1, then 6x²/5 simplifies to 6/5, which is greater than 2/5.

However, if x is zero or negative, then 6x²/5 will be equal to or less than 2/5. For example, when x is 2, 6x²/5 becomes 6 × (2²)/5 = 24/5, which is clearly greater than 2/5.

This logic is similar to instances where combining certain quantities doesn't always lead to a straightforward sum, such as mixing volumes of liquids or combining probabilities of events.

Answer:

if a polygon is square,then it is also a rectangle is correct

Step-by-step explanation:

1)if a polygon has 4 right angles,then it is a square is wrong since in the statement a square has all its angles as right angles but it need not imply that it is a square as it could also be a rectangle

2) polygon need not have four right angles eg:rhombous with angles 60°,60°,120°,120° is also a polygon

3)every polygon need not be a rectangle as it could be square

4)if a polygon is square, then all its angles are right angles and if all its angles are right then it is rectangle.

hence option 4 is true.

Answer:

156 players

Step-by-step explanation:

The 9 players for baseball and 11 players for football are added. 9 + 11 = 20.

Once you have 20, you can multiply it by the 6 schools. Which gets you 120 players so far.

After you multiply the 4 schools by the 9 players for baseball. You’ll get 36. Add the 120 players to 36 players and you’ll get 156 players for the 10 schools in total

Answers are attached in the pictures. Solutions are in RED.

Answer:

12. 7.5

13. 0.224

14. 193.5

15. 2/3

16.  5/7

17. -10

18. 2:1

19. 16

20. 150

21. 46,200

22. 4

23. 18

24. 5.29

25. 7.07

26. 19.80

27. 15.87

28. 9.80

29. 6.71

30. 1.26

Step-by-step explanation:

12. 5/8 = x/12

  8x = 60

   x = 7.5

13. x/1.11 = 1/5

  5x = 1.12

   x = 0.224

14. 6x /27 = 43

      6x = 1161

         x = 193.5

15. x+2)/3 = 8/9

   9x + 18 = 24

   9x = 6

  x = 2/3

16. (3x -5)/4 = -5/7

     21x - 35 = -20

     21x = 15

     x = 5/7

17. (x-2)/4 = (x+4)/2

    2x - 4 = 4x + 16

    -2x = 20

     x = -10

18.  9 grams of fat.

      6 grams are saturated.

     9-6 = 3 grams are cheese.

  ratio of saturated to cheese = 6:3

                                                   = 2:1

19. goats to sheep = 4:7

     7/11 x = 28

     x = 28 × 11/7

     x = 44

   goats = 44-28 = 16

20. 280:4 = 10,500:x

   280/4 = 10,500/x

  280x = 42000

     x = 150

21. 42:2 = x:2200

   42/2 = x/2200

   92,400 = 2x

    x = 46,200

22. √(2×8) = √16 = 4

23. √(9×36) = √324 = 18

24. √(4×7) = √28 = 5.29

25. √(5×10) = √50 = 7.07

26. √(28×14) = √392 = 19.80

27. √(7×36) = √252 = 15.87

28. √(8×12) = √96  = 9.80

29. √(3×15) = √45 = 6.71

30. √4/5 × 2) = √8/5 = 1.26

Answer:

Yes, there is a similarity transformation that maps triangle ABC to Triangle DEF.

Step-by-step explanation:

Similarity transformation;

Triangle DEF has been transformed(dilated) by a factor of 2.

Since each dimension is twice that of the triangle ABC.

Two triangles are similar if their corresponding sides are congruent and corresponding angles are congruent.

Similarity statement:

ΔABC [tex]\sim[/tex] ΔDEF

these two triangles are similar because;

[tex]\frac{AB}{DE}= \frac{4}{8} = \frac{1}{2}[/tex]

[tex]\frac{AC}{DF}= \frac{4}{8} = \frac{1}{2}[/tex]

[tex]\frac{BC}{EF}= \frac{3}{6} = \frac{1}{2}[/tex]

⇒ [tex]\frac{AB}{DE}=\frac{AC}{DF} =\frac{BC}{EF}[/tex]

Yes, there is a similarity transformation that maps Triangle ABC to Triangle DEF.

To determine if two triangles are similar, one must check if they have the same shape, which means their corresponding angles are equal and their corresponding sides are in proportion.

Let's denote the angles of Triangle ABC  [tex]\(A\), \(B\), and \(C\),[/tex] and the angles of Triangle DEF as [tex]\(D\), \(E\), and \(F\),[/tex] respectively. Similarly, let's denote the sides opposite these angles as [tex]\(a\), \(b\), and \(c\)[/tex] for Triangle ABC, and [tex]\(d\), \(e\), and \(f\)[/tex] Triangle DEF.

For Triangle ABC and Triangle DEF to be similar, the following conditions must be met:

1. [tex]\(A = D\), \(B = E\), and \(C = F\)[/tex] (AA postulate for similarity).

2. [tex]\(\frac{a}{d} = \frac{b}{e} = \frac{c}{f}\)[/tex] (corresponding sides are in proportion).

If these conditions are satisfied, then there exists a similarity transformation that maps one triangle to the other. This transformation can be broken down into the following steps:

1. Dilation: To make the sides of Triangle ABC proportional to the sides of Triangle DEF, we perform a dilation. The scale factor k can be determined by the ratio of any pair of corresponding sides. For example, [tex]\(k = \frac{d}{a} = \frac{e}{b} = \frac{f}{c}\)[/tex]. This single scale factor should work for all three sides if the triangles are similar.

2. Rotation/Reflection (optional): If Triangle DEF is not oriented in the same direction as Triangle ABC, we may need to rotate or reflect Triangle ABC to align it with Triangle DEF. This does not affect the similarity.

3. Translation (optional): Finally, if Triangle DEF is not in the same position as Triangle ABC (but has the same orientation and size after the dilation), we perform a translation to move Triangle ABC to the position of Triangle DEF.

Since the angles are preserved under dilation, rotation, and translation, and the sides are made proportional by the dilation, the similarity transformation is complete.

If the corresponding angles are equal and the corresponding sides are in proportion, then the two triangles are similar, and a similarity transformation exists that maps one to the other. The similarity statement captures this relationship, indicating that the triangles are similar to the AA postulate and the sides are in proportion.

Answer:

Triangle A has one right angle

Step-by-step explanation:

Answer: h = -4

Step-by-step explanation:

-9h-6+12h+40=22

-9h+12h=22+6-40 "collect all unknown values in a side and collect numbers in other side "

"Don't forget to Change signs"

3h= -12

3h/3 = -12/3 "dividing by 3 in both sides"

h= -4

[tex]-9h-6+12h+40=22\qquad\text{combine like terms}\\\\(-9h+12h)+(-6+40)=22\\\\3h+34=22\qquad\text{subtract 34 from both sides}\\\\3h=-12\qquad\text{divide both sides by 3}\\\\\boxed{h=-4}[/tex]

Answer:

100;200

There are 200 total flips and to find probability we would have to divide it by two. Doing so, should give you something like this 100;200.

Answer:

D

Step-by-step explanation:

Answer:

D) 67  

Step-by-step explanation:

 j = 4N + 11

N = 14           Insert the value of N

j = 4×14 + 11    

j = 56 + 11

j = 67

Jupiter has 67 moons.

Answer:1 and a half

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

There are one in 1/2

Answer:

1.301 × 10⁴ ft  

Step-by-step explanation:

Difference = h₂ - h₁

Difference = 20 320 - 7310

Difference = 13 010 ft

To convert the number to scientific notation, we move the decimal point four places to the left and make the exponent of 10 equal to +4.

Difference = 1.301 × 10⁴ ft

You can use same operations on both sides such that both sides' x value come on one side and rest of the values go on other side so that you get what is equal to x.

The value of x is 6

It is because [tex]a^x[/tex] where x is a variable and "a" is a constant, is a function. A function only outputs single value to each input.

If for x = p and x = q, we get same value, then we will have  [tex]a^x[/tex]  not being a function. Thus, for that to be a function, we need those inputs same too for output to be same.

Thus,  [tex]a^p = a^q \implies p = q[/tex]

Remember that we need base to be same(here a is base and p and q are exponents)

We can use the fact that 64 is cube of 3 and can use the above stated fact.

Thus, we have:

[tex]4^{(x+30)} = 64^{(2x)}\\4^{x+30} = 4^{3^{2x}} \\\\\text{since power of power will multiply, thus,}\\\\4^{x + 30} = 4^{6x}\\\\or\\\\x+30 = 6x\\\\\text{Subtracting x on both sides}\\\\30 = 5x\\\\\text{Dividing by 5 on both sides}\\\\6 = x\\x = 6[/tex]

Thus, The value of x is 6

Learn more about base and exponent here:

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Meg can trade her tickets in for 20 small toys.

Answer:

A = 53.34 [tex]units ^ 2[/tex]

Step-by-step explanation:

To find the length of the rectangle we solve the PLA triangle

Using the Pythagorean theorem we find the PL side.

[tex]PL = \sqrt{4^2+12^2}\\PL = \sqrt{16+144}\\PL = 12.65[/tex]

Then the length of the rectangle is 12.65

Now we solve the MALU triangle. Where MU = PL

We use the Pythagorean theorem:

[tex]MU^2+LU^2 = (MA + AL)^2\\12.65^2+LU^2 = (MA+12)^2[/tex]

Where LU and MA are unknown.

Finally we solve the triangle MPA

[tex]MA^2 + PA^2 = PM ^2[/tex]

Where PM = LU

So:

[tex]MA^2 + 4^2 = LU^2[/tex]

Now we have two equations and two unknowns. So we solve the system.[tex]12.65^2 + LU^2 = (MA + 12) ^2[/tex]  (i)

[tex]MA^2+4^2 = LU^2[/tex]  (ii)

We introduce (ii) in (i)

[tex]12.65^2 + MA^2+16=MA^2+24MA+144[/tex]

Now we clear MA

[tex]160.02+16-1 44 = 24MA[/tex]

[tex]32.02 = 24MA[/tex]

[tex]MA = \frac{32.02}{24}[/tex]

MA = 1.3342 (iii)

Now we introduce (iii) in (ii)

1.3342^2 + 4^2 = LU^2

LU = 4.2166

Now we have the length of the rectangle and also its width.

The area A of a rectangle is:

A = l*w

Where

 l = length

w = width

A = 4.2166*12.65

A = 53.34 [tex]units^2[/tex]

Answer:The answer is 4

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

3 times 6

Answer:

13 y^2 - 9 x y + 3 x^2

Step-by-step explanation:

Simplify the following:

6 x^2 - 7 x y + 8 y^2 - (x^2 - 3 x y - y^2) - (2 x^2 + 5 x y - 4 y^2)

-(x^2 - 3 x y - y^2) = -x^2 + 3 x y + y^2:

6 x^2 - 7 x y + 8 y^2 + -x^2 + 3 x y + y^2 - (2 x^2 + 5 x y - 4 y^2)

-(2 x^2 + 5 x y - 4 y^2) = -2 x^2 - 5 x y + 4 y^2:

6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 + -2 x^2 - 5 x y + 4 y^2

Grouping like terms, 6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 - 2 x^2 - 5 x y + 4 y^2 = (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2):

(8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

8 y^2 + y^2 + 4 y^2 = 13 y^2:

13 y^2 + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

x y (-7) + x y 3 + x y (-5) = -9 x y:

13 y^2 + -9 x y + (6 x^2 - x^2 - 2 x^2)

6 x^2 - x^2 - 2 x^2 = 3 x^2:

Answer:  13 y^2 - 9 x y + 3 x^2

Answer:

$150   PLEASE GIVE BRAINLIEST

Step-by-step explanation:

The minimum you can earn would be $150.  This would be your base salary and you selling 0 cell phones.

The number of decimal places that the quotient has will be 3.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The numbers are given below.

7.7 and 700

The quotient of the numbers 7.7 and 700 will be

⇒ 7.7 ÷ 700

⇒ 0.011

Then the number of decimal places that the quotient has will be 3.

More about the Algebra link is given below.

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Answer:

D

Step-by-step explanation:

Answer: We can say that (a/b)^2 is a rational number

================================================

Proof:

Rational means the number is a ratio of two whole numbers

If 'a' is rational, then a = p/q for some whole numbers p,q (eg: p = 2, q = 3 so p/q = 2/3)

The same applies for b, which I'll let b = r/s, with r & s being whole numbers.

To avoid division by zero, I'm going to make p,q,r,s nonzero which leads to 'a' and 'b' being nonzero.

Now let's divide 'a' over b to get

a/b = (p/q) divided by (r/s)

a/b = (p/q) * (s/r)  .... flip the second fraction; multiply

a/b = (ps)/(qr)

The new numerator is p*s which is a whole number (because the product of two whole numbers is also a whole number). The same goes for q*r in the denominator. So a/b is rational if both 'a' and 'b' are rational together.

We can extend this to (a/b)^2 as well

(a/b)^2 = [ (ps)/(qr) ] ^2

(a/b)^2 = [ (ps)^2 ]/[ (qr)^2 ]

(a/b)^2 = (p^2*s^2)/(q^2*r^2)

p is a whole number, and so is p^2. Same for s and s^2. Overall, the final numerator p^2*s^2 is also a whole number. Similarly, q^2*r^2 is a whole number.

So we have yet another ratio of two whole numbers proving that (a/b)^2 is a rational number.

Answer:

C. 9x^2 − 6x

Step-by-step explanation:

3(x + 6x^2 − 3x − 3x^2)

According to PEMDAS, we need to simplify inside the parentheses first

3(x -3x+ 6x^2 − 3x^2)

3(-2x+3x^2)  

Now we can distribute the 3 to both terms inside the parentheses

3 * -2x + 3* 3x^2

-6x + 9x^2

We normally write them in decreasing powers of x

9x^2 -6x

Answer:

B

Step-by-step explanation:

using the cofunction identity

• sin (90 - x) = cosx / cos(90 - x) = sinx, hence

cos 19° = sin(90 - 19)° = sin 71°

Answer:

B

Step-by-step explanation:

using the cofunction identity

• sin (90 - x) = cosx / cos(90 - x) = sinx, hence

cos 19° = sin(90 - 19)° = sin 71°

If it's a graph: Solutions are points of intersection

The same line means infinitely many solutions

Parallel lines = never intersects = no solution

1 point of intersection = 1 solution

If it's a system of equations:

If you get _*x = _(a number), 1 solution (divide by the coefficient, and get only 1 possible value)

If you get x = x, infinitely many solutions (x can be anything and still equal itself)

If you get two different constants equaling (such as 1 = 2), there is no solution because no value of x can make those two values equal.

Answer:

136 ounces

Step-by-step explanation:

So you take 8.5 lbs and multiple it by the second number in the ratio this only works if the first number is 1 and it represents what you are starting with  

8.5*16=136

To convert pounds to ounces, multiply the number of pounds by 16. An 8.5 pound baby weighs 136 ounces.

To convert pounds to ounces, you need to multiply the number of pounds by 16 because there are 16 ounces in 1 pound.

In this case, an 8.5 pound baby would be equivalent to:

8.5 pounds x 16 ounces/pound = 136 ounces

Therefore, an 8.5 pound baby weighs 136 ounces.

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Answer:

$120.96

Step-by-step explanation:

So the area of the room is 14*12. So the area of the room is 168ft^2. So now we multiply it by .72 because it costs .72 per square foot. So the cost is 120.96

To calculate the cost of installing wallpaper around a rectangular room measuring 14 feet by 12 feet, you first find the perimeter, which is 52 feet, then multiply by the cost per foot, $0.72, leading to a total cost of $37.44.

The formula for the perimeter P of a rectangle is P = 2(length + width). In this case, the length is 14 feet and the width is 12 feet.

P = 2(14 feet + 12 feet) = 2(26 feet) = 52 feet.

Now that we have the perimeter, we multiply it by the cost per foot of the wallpaper to find the total cost. The wallpaper costs $0.72 per foot.

Total cost = Perimeter × Cost per foot = 52 feet × $0.72/foot = $37.44.

Hence, it will cost $37.44 to install the wallpaper around the rectangular room that measures 14 feet by 12 feet.

Answer: I am pretty sure your answer is 208 cm. Whenever you see a percentage immediately change it to a decimal like in this case 0.070 and multiply it by 400. 400x0.070 is equal to 280. Hope this helps :)

To find the total loudness of three earphones with a given ratio is 1176 decibels.

The ratio of loudness of the earphones is 6:5:3. Given that Polina's earphones have a loudness of 420 decibels, we can find the loudness of Lala's and Goffy's earphones. Let the loudness of Lala's earphones be 6x, Polina's is 5x, and Goffy's is 3x.

Adding the loudness of all three earphones, we have: Lala's (6x) + Polina's (420) + Goffy's (3x). Substituting 5x = 420 and solving gives 5x = 420, x = 84. Therefore, the total loudness of all three earphones is 6(84) + 420 + 3(84) = 504 dB + 420 dB + 252 dB = 1176 decibels.