The group of points {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function, but the group of points {(1, 4), (2, 7), (3, 1), (5, 7)} is a function. What do you notice about the two groups of points? What do you think it means to be a function?

Answer:

a. Average yield per tree will be 50 apples. Total yield in that case will be 10,000 apples per acre.

b. 25 more trees are to be planted per acre to maximize the total yield.

Step-by-step explanation:

If the no. of trees per acre is doubled then it will be equal to,

[tex]100 \times 2[/tex]

= 200

So, the no. of trees per acre is increased by (200 - 100) = 100

hence, the average yield per tree will be,

(150 - 100) = 50 in that case.

Hence, the total yield will be,

[tex]50 \times 200[/tex]

= 10,000 apples per acre

Now , if x trees are planted, the total no. of apples produced per acre will be,

[tex](150 - x) \times (100 + x)[/tex]

= [tex]15000 + 50x - x^{2}[/tex]

= f(x) [say]

So. [tex]\dfrac {df(x)}{dx}[/tex] = f'(x)

= 50 - 2x---(1)

taking f'(x) = 0 , we get,

50 - 2x = 0

⇒ x = 25 --------------(2)

Again,

[tex]\dfrac {d^{2}f(x)}{dx^{2}}[/tex] at x = 25

=  -2 (<0)

So, f(x) attains it's maximum value at x = 25

Hence,

25 more trees are to be planted per acre to maximize the total yield.

Answer:

HL

Step-by-step explanation:

HL is used for right triangles that are congruent. These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

Here, we have,

A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.

Types of triangles are isosceles, scalene and equilateral triangles.

Two angles are said to be complementary if their sum is 90 degrees.

Two triangles are said to be congruent if all their corresponding sides and angles are congruent.

This means that the triangles have equal angles and equal sides.

here, we have,

HL is used for right triangles that are congruent.

These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

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Answer:

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ ||\ k\iff m_1=m_2\\\\\text{We have}\ k:y=4x-1\to m_1=4.\\\\\text{Therefore}\ m_2=4.\\\\l:y=4x+b\\\\\text{Put the coordinates of the point (-3, 7) to the equation of a line:}\\\\7=4(-3)+b\\7=-12+b\qquad\text{add 12 to both sides}\\19=b\to b=19\\\\\text{Finally:}\\\\y=4x+19[/tex]

Answer:

f(x) = -|x| + 1

Step-by-step explanation:

f(x) = |xl when reflected over the x-axis is f(x) = -|x|.

When reflected over x-axis a graph becomes negative in y value.

f(x) = -|x| then translate 1 unit to the right is f(x) = -|x| + 1. Adding 1 translates the graph towards the right because the positive x-axis is on the right.

The function through the points (10, 18), (14, 24), and (18, 30) is a direct variation function with a constant of variation of 1.8.

In this case, we have a linear function. We can determine this by checking if the changes between the x-values and the y-values are consistent. For the change in x-values: (14-10 is 4) and (18-14 is also 4), the change is constant. Similarly, check the change in y-values: (24-18 is 6) and (30-24 is also 6), thus the change is constant. Hence, the function is linear.

More so, this function is a direct variation function because it passes through the origin. In direct variation functions, the ratio of y to x remains constant. In this case, the y divided by x at each point [(18/10=1.8), (24/14=1.71), (30/18=1.67)] is approximately 1.8, which is almost constant.

So, the best description of this function is: 'The function is a direct variation function with a constant of variation of 1.8'.

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Answer:

The function is linear but not a direct variation function.

Step-by-step explanation:

Answer:

D. 18 : 1

Step-by-step explanation:

Students : teachers and aides

450 : 25

Treat it like a fraction. 450 over 25 simplifies to 18 over 1 because 450/25=18 and 25/25=1.

Therefore, the ratio is 18 : 1

Answer: 18:1

Step-by-step explanation:

450 students : 25 teachers

18 students : 1 teachers

450/25= 18

Answer:

The answer should round up to 40 minutes. Do it to make sure the answer is 4 which in this case = 40

Step-by-step explanation:

[tex]22 - 7 \div 3.50[/tex]

Answer:

Computer can be rented for  42.85 minutes using $22

Step-by-step explanation:

Given:

Setup charge =  ​$ 7

Additional charge for every 10 minutes = ​$ 3.50

To find:

The time for which the computer can be rented for  ​$ 22

Solution:

Let the additional time be x

for  additional charge for 10 minutes =3.50

for 1 minute , additional charge = [tex]\frac{3.50}{10}[/tex]= $0.35

According to the question

setup cahrge + additional charge= $22

[tex]7+(0.35\times x)=22[/tex]

[tex](0.35\times x)=22-7[/tex]

[tex](0.35\times x)=15[/tex]

[tex]x=\frac{15}{035}[/tex]

x=42.85

After converting all measurements to the same format (decimals), we can see that the shortest piece of wood Jimmy measured is 4.02 ft.

To find the shortest piece of wood, we first need to convert all the lengths to the same format, preferably in decimals for easier comparison. The lengths of the wood pieces given are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft.

Let's break it down:

So, we have pieces of wood that are 4.2 ft, 4.5 ft, 4.02 ft, and 4.22ft. Looking at these numbers, it is clear that the piece of wood that measures 4.02 ft is the shortest.

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Answer:

Step-by-step explanation:

If [tex]y[/tex] is inversely propotional to the square of [tex]x[/tex], then the relation would be like

[tex]y=\frac{K}{x^{2} }[/tex]

Where [tex]K[/tex] is the constant of propotionality.

Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use [tex](1,4)[/tex]

[tex]y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4[/tex]

Replacing this constant, the expression between variables is

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

Which is the answer to a).

Now, if [tex]y=25[/tex] the value of [tex]x[/tex] would be

[tex]y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}[/tex]

Therefore, the answer to b) is [tex]x=\frac{2}{5}[/tex]

In an inverse variation, y is inversely proportional to the square of x. To express y in terms of x, the equation is y = k/(x^2). To find the positive value of x when y = 25, the equation is 25 = k/(x^2), and x = sqrt(k/25) is the solution.

In an inverse variation, a variable is inversely proportional to another variable if their product is a constant. In this case, y is inversely proportional to the square of x. We can write this relationship as y = k/x^2, where k is the constant of variation.

To express y in terms of x, we can rearrange the equation as y = k/(x^2).

To find the positive value of x when y = 25, we can substitute these values into the equation and solve for x. We have 25 = k/(x^2). Rearranging the equation gives us k = 25x^2. Since we want to find the positive value of x, we can take the square root of both sides to get x = sqrt(k/25).

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Answer:

Step-by-step explanation: If you add 19 and 17 together you get 36.

Hope this helps! :)

Answer:

a = - 10

Step-by-step explanation:

Given

[tex]\frac{a}{5}[/tex] = - 2

a is divided by 2. The inverse operation to division is multiplication, thus

Multiply both sides by 5 to clear the fraction

a = 5 × - 2 = - 10

Answer:44 cents

Step-by-step explanation:

7/16 = .4375

Answer:

Step-by-step explanation: To find the unit price you could divide 7 by 16

Answer:

4/3*100^3*π

Step-by-step explanation:

V = 4/3*π*r^3

= 4/3*π*100^3

≈ 4.18879*10^6

Equivalent expressions to given expression are:

A : -8+19-3x

C : -11x+19

Step-by-step explanation:

Given

[tex]-5+4(-2x+6)-3x[/tex]

We will simplify the given expression to find the equivalent expressions

[tex]-5+4(-2x+6)-3x\\= -5-8x+24-3x\\= -8x+19-3x\\=-11x+19[/tex]

by observing the simplification we can see that the equivalent expressions are:

A : -8+19-3x

C : -11x+19

Keywords: Polynomials, Expressions

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Answer:

10s^2-15s+20

Step-by-step explanation:

because 5(2s^2)=10s^2, 5(-3s)=-15s, and 5(4)=20

hope it helps:)

Answer:102−15+20

Step-by-step explanation:that’s that answer because I just did the question on imagine math

Answer:

y = -2x + 3

Step-by-step explanation:

Slope-intercept equation of a line is:

y = mx + b

where m is the slope and b is the y intercept.

Here, m = -2 and b = 3.

y = -2x + 3

Answer:

Yes, it's an arithmetic sequence.

Step-by-step explanation:

Each term in this sequence is 4 more than the previous term.  Therefore we have an arithmetic sequence.

Answer:

4

Step-by-step explanation:

Gave a picture to explain

Answer: I can confirm x=4

Step-by-step explanation:

The two equations that can be used to relate the distance from the focus and the directrix to any point on the parabola are x² = 4py and y = (x-k)² + h.

To correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola, we can use the following two equations:

Where p is the distance from the focus to the directrix, (h,k) is the vertex of the parabola, and the equation x² = 4py represents a parabola with its axis parallel to the y-axis, and y = (x-k)² + h represents a parabola with its axis parallel to the x-axis.

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Answer:

The answer is option A. 117

Step-by-step explanation:

The general solution of the quadratic equation is:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

The given equation is x2 + 9x − 9 is expressed as minus 9 plus or minus the square root of r, all over 2

Comparing to the general solution

∴ r = determinant = b² - 4 a c  

From the given equation: a = 1 , b = 9 and c = -9

∴ r = 9² - 4 * 1 * (-9) = 81 + 36 = 117

The answer is option A. 117

Answer:

117

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

-5 2/5=-27/5

9 8/11=107/11

-3 5/6=-23/6

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

-27/5+107/11-23/6

-27/5-23/6+107/11

-162/30-115/30+107/11

-277/30+107/11

-3047/330+3210/330=163/330=0.493=0.5

Answer:

4.213

Step-by-step explanation:

The Fendley family is planning a vacation, and they are trying to choose which resort they will stay in. Mrs. Fendley has created the table below showing their four options. They want to spend no more than $250 per night for the resort. Which resorts will fit into their budget? Select two that apply.

Resort Amount Charged

A $550 for 2 nights

B $694 for 3 nights

C $1028 for 4 nights

D $1153 for 5 nights

A no

Resort A $275 per night

B maybe

Resort B $231.33 per night

C no

Resort C $257 per night

D maybe

Resort D $230.60 per night

the answer is b or d you choose which one you would like to choose

Answer:

x = -12

Step-by-step explanation:

Remember that ax + bx = (a+b)x

-10x + 9x = 12

Add -10x and 9x together

(-10 + 9)x = 12

-x = 12  (-1x is written as -x, just as 1x is written as x)

÷ -1 both sides

x = -12

I hope this helps. Happy studying. :)

-10x+9x= -1x

-1x=12 -1 divided by 12 equals -12 Therefore x = -12

Answer:

Yes

Step-by-step explanation:

Another way of stating the question:  Does the Pythagorean Theorem apply here?  Does 6^2 + 8^2 = 10^2?

           Does 36   + 64   = 100?   YES

Yes, this is a right triangle.

Answer: Yes. That is because it fits the requirements of the Pythagoream Therom:

6^2+8^2    10^2

36+64        100

100      =    100  :)

Answer:

The fraction of Megan's blue stickers are 1/6.

Step-by-step explanation:

Given:

Megan has 12 star sticker. 1/2 of her stickers are yellow, 1/3 are green, and the rest are blue.

Now, to find the fraction of stickers which are blue.

Total number of stickers  =  12.

Number of red stickers are = [tex]12\times \frac{1}{2}[/tex]

                                              = [tex]6 stickers[/tex]

Number of green stickers are = [tex]12\times \frac{1}{3}[/tex]

                                                  = [tex]4 stickers[/tex]    

Number of blue stickers are = [tex]12-(6+4)[/tex]

                                               = [tex]12-10=2 stickers[/tex]

Now, to get the fraction of stickers we divide the number of blue stickers by the total number of stickers:

Fraction of blue stickers = [tex]2\div 12[/tex]

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

Therefore, the fraction of Megan's blue stickers are 1/6.

Answer:

30 Oranges!

Step-by-step explanation:

Given that for every 2 apples there are 3 oranges.

How many oranges would be there in a basket of 20 apples?

Since for every couple of apples we have 3 oranges we will calculate how many couples of apples are there in the basket.

Given there are 20 apples. This means that there are [tex]$ \frac{20}{2} $[/tex] = 10 pairs of apples.

Since for one pair we have three oranges, for 10 pairs we would have 3 X 10 = 30 oranges.

Therefore, we can conclude that the number of oranges in the bigger basket would be 30.

Answer:

B)

Step-by-step explanation:

16.24/14=1.16

33.3/30=1.11

1.16-1.11=0.05

The correct statement is The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.

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:

14 pound bag cost = 16.24

cost of 1 pound bag = 16.24/14

                                  = $1.16

and,

another bag which is of  30 pound costs = 33.30

                                                                    = 33.30 / 30

                                                                    = $1.11

Hence, The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.

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