Harper is getting ready to plant corn on his family's farm. The table shows the number of pounds of seed she needs to buy depending on the number of hectares she will plant. Hectares, h 10 15 25 50 Pounds of seed, p 200 300 500 1000 a. Write an equation that shows how to find the pounds of seed, p, needed for h hectares of land. b. Write an equation that shows how many hectares, h, Harper can plant with p pounds of seed.

Answer:

1. [tex](x-3)^2+(y+15)^2=13[/tex]

2. [tex](x+9)^2+(y+14)^2=5[/tex]

3. [tex](x+3)^2+(y+11)^2=\sqrt{51}[/tex]

4. [tex](x+3)^2+(y-0)^2=25[/tex]

Step 1: Formula

The standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex].

The h represents the x value of the coordinates of the circle's center and the k is the y value of the coordinates. The r is the radius.

So in the first problem h is going to be 3 and k is going to be -15. (In this problem the signs are flipped, so if you have a positive number it will be negative in the formula)

After inserting the values in the formula you have your answer of [tex](x-3)^2+(y+15)^2=r^2[/tex]. Now let us find the radius

Step 2: Find the radius

To find the radius of the first two problems what you can do is you can use the distance formula.

To use the distance formula you find have to identify the (x1, y1) and the (x2, y2)

In the first problem, the (x1, y1) would be the center of the circle. The reason for this is that on a graph you have to read it left to right (kinda like English) so to find the values you have to imagine what values would come first, in this case, the center point would come first.

So let us input the values in the formula. The formula is [tex]d = \sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]. This is the distance formula, this formula will be used in this problem.

Okay so the x1 is 3 and the y1 is -15. The x2 is 0 and the y2 is -13. So lets us input these values.

[tex]d = \sqrt{(0-3)^{2}+(-13--15)^2 } \\\\ = \sqrt{(-3)^{2}+(2)^2} \\\\=\sqrt{9+4}\\\\=\sqrt{13}\\\\= 3.605[/tex]

3.605 is our radius.

Now let us write our finished equation.

[tex](x-3)^2+(y+15)^2=\sqrt{13} ^2[/tex] or [tex](x-3)^2+(y+15)^2=13[/tex].

Doing these steps for the next problem gives us our second answer of [tex](x+9)^2+(y+14)^2=5[/tex]

Step 1: Midpoint Formula

To solve this problem you need to use the midpoint formula. The midpoint formula is [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex]. In the first problem, the x1 would be -10, the y1 would be -13. The x2, on the other hand, is 4 and the y2 is -9. Now find the center of the circle.

Step 2: Find the center

To find the center of the circle we need to insert the values of x and the values of y into the midpoint formula. We can do this because they gave us the diameter and the diameter goes through the middle of the circle. So we can do this.

[tex]\frac{-10 + 4}{2} ,\frac{-13+-9}{2}\\\\\frac{-6}{2} ,\frac{-22}{2}\\\\(-3,-11)[/tex]

So (-3, -11) is the center of the circle.

Step 3: Find the radius

Now that we have the center of the circle we can use the distance formula to find the radius. We already have two of the ends of the radius so we can simply use the distance formula with the center and the ends.

[tex]d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\\\\=\sqrt{(4--3)^2+(-9--11)^2 }\\\\= \sqrt{(7)^2+(2)^2 }\\\\=\sqrt{49+4 }\\\\=\sqrt{51}[/tex]

Step 4: Write your final equation

Know we can insert all the values we have into the standard form of a circle equation.

[tex](x-h)^2+(y-k)^2=r^2\\\\(x+3)^2+(y+11)^2=\sqrt{51} ^2[/tex] or [tex](x+3)^2+(y+11)^2=\sqrt{51}[/tex]. This is our answer.

Doing these steps for the next problem gives us our answer of  [tex](x+3)^2+(y-0)^2=25[/tex]

The answers are GBACGFI and when put in backward alphabetical order it becomes IGFDCBA.

The code is IGFDCBA.

The code is determined as follows:

1. 1/6 of students are trying out for a fall sport, then 5/6 are not.

The probability of selecting a student who is not trying out for a fall sport = 5/6.

Thus, the probability of students trying out for a spring sport = 5/6

To get 20 students who are trying out for a spring sport = 20 / (5/6)

To get 20 students who are trying out for a spring sport = 48 students.

Letter G

The smaller the mean absolute deviation the farther apart the data set is:  False; Letter B

Every part of the population has an equal chance of being selected when dealing with random sampling: True; Letter A

Rolling a number larger than one on a regular six-sided dice;

Likely; Letter C

The probability of pulling out a green marble and keeping it = 7/12.

The probability of pulling out another green marble = 6/11

Therefore, the probability of pulling out two consecutive green marbles = 7/12 * 6/11

The probability of pulling out two consecutive green marbles = 31.8%; Letter G

If an event is most likely to not happen then the probability gets close to 0; Letter F

B has a probability of 1/4 of being landed on

If you spin the spinner 500 times, you can land B 500 x 1/4 = 125 times.; Letter I

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Answer: A. an = 18 - 3.5

14.5, 11, 7.5, 4, 0.5

The first term (a₁) is 14.5

The difference (d) is -3.5

Step-by-step explanation:

The time required for the visit to the doctor should be more than 27 minutes.

It is given that the dose given by doctor is 14 mg radioactive dye. Dye remaining after 16 minutes is 4.25 mg.

Assuming the radioactive dye to decay exponentially then the amount present in body can be represented by the following expression

[tex]A(t) = A_0e^-^k^t[/tex] where, A(t) is the amount present after time t, k is a constant & t is the time elapsed

Initially,[tex]4.25=14e^-^1^6^k[/tex]

k=0.074/min

To calculate time such that 2mg of radioactive dye remains in the body substituting the values

[tex]2=14e^-^t^0^.^0^7^4[/tex]

t = 26.29 minutes.

Hence, the time required for doctor's visit must be more than 27 minutes to avoid the alarm.

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The value of x in the equation 9x In x + x = 0 is x = 0.895

From the question, we have the following parameters that can be used in our computation:

9x In x + x = 0

To calculate the value of x, we start by dividing through the equation by x

So, we have the following representation

9 In x + 1 = 0

Subtract 1 from both sides of the equation

This gives

9 ln x = -1

Divide both sides by 9

ln x = -1/9

So, we have

x = e^(-1/9)

Evaluate the exponent

x = 0.895

Hence, the solution to the equation is x = 0.895

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Answer:

C.

Step-by-step explanation:

We have five unshaded, 1 half of unshaded, and 1 shaded, Thus, It will be showed as [tex]\frac{1}{6}[/tex]  ➗ [tex]2[/tex]

Answer:

9

Step-by-step explanation:

1 · 3 = 3

3 · 3 = 9

9 · 3 = 27

27 · 3 = 81

81 · 3 = 243

Answer:

Step-by-step explanation:

Volume of a pentagonal prism = 1/4√(5(5 + 2√5))·a²h

a = length of a base edge

h = height

Realistic dimensions would be 8" base edge and 11" height for a decent size birdhouse.

V = 1/4√((5(5+2√5))·(8)²(11) = 1211.22 in³

Answer:

a. 830.380

Step-by-step explanation:

3 × [tex]\frac{1}{10}[/tex]  is [tex]\frac{3}{10}[/tex].  This is the same as .3 when it's written in decimal form.

The first place on the right side of the decimal is the 'tenths' place. The second spot on the right side of the decimal is the 'hundredths' place.

Like this:

hundreds   tens   ones   .  tenths   hundredths   thousandths

All of the answers have the 830 in them. The only difference between the answers is the .380, .308, .038, .083. Once you see you have 3/10 (which is said three-tenths, which is .3) you can eliminate the last two answers, c and d. Then check the hundredths place. You have 8/100 (which is said eight-hundredths, which is .08) then you can eliminate b and find your answer, a.

ΔBCD and ΔDAB are congreuent by SAS.

We have,

Side-Angle-Side (SAS) Congruence.

The two sides and the included angle of one triangle are equal to the corresponding two sides and included the angle of another triangle.

Now,

CB = AD (given)

CB || AD ( given )

∠CBD ≅ ∠ADB (alternate angles)

BD = BD  ( Common )

ΔBCD ≅ ΔDAB ( By SAS )

Thus,

ΔBCD and ΔDAB are congreuent by SAS.

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Check the picture below.

If a gasoline pump delivers 4 gallons of gas per minute, proportionately, it will take it 4 minutes to fill a gas tank that holds 16 gallons.

Proportion refers to the ratio of one unit or quantity compared to another unit or quantity.

Proportions are represented as fractional values using decimals, fractions, and percentages.

The time it takes the gasoline pump to deliver 4 gallons = 1 minute

Proportionately, to deliver 16 gallons, the time = 4 minutes (16 ÷ 4)

Thus, using proportional relationships, to deliver 16 gallons, the gasoline pump will take 4 minutes.

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Ryan drove 23 miles during the 27 minutes.

To discover the total distance Ryan drove during the 27 mins, we want to first calculate the distance he drove to reach every consumer and then add the ones distances collectively.

For the first customer, Ryan drove for 12 minutes at an average pace of 40 miles per hour:

For the second customer, Ryan drove for 15 mins at an average velocity of 60 miles consistent with hour:

therefore, the entire distance Ryan drove in the course of the 27 mins is:

So, Ryan drove 23 miles during the 27 minutes.

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Answer: x = - 5/19 , y = - 35/19

Answer :

Step-by-step explanation:

It's given that, Area of square is 595.36 square feet.

As we know that area of square is calculated by,

Substituting the values,

595.36 = side

side =√595.36

side = 24.4 feet

Hence, the side of the square is 24.4 feet.

Now,

Perimeter (square) = 4 × side

Perimeter = 4 × 24.4

Perimeter = 97.6 feet

Therefore, The perimeter of the square is 97.6 feet

Answer:

97.6 ft

Step-by-step explanation:

we know a square has 4 equal sides.
Area of a square = side X side or side squared

Plug in the value of area

595.36 square feet = side squared

24.4 ft = side ( do square root in both sides)

Perimeter of an square= side + side + side + side or 4 X side

That’s 4 X 24.4 ft = 97.6 ft.

When we say a tank is 284 cubic feet, we mean that the tank has a volume of 284 cubic feet.

We have,

When we say a tank is 284 cubic feet, we mean that the tank has a volume of 284 cubic feet.

When we measure the volume of a three-dimensional object like a tank, we typically use a unit of measures like cubic feet or cubic meters.

A cubic foot is the volume of a cube that measures 1 foot on each side.

So if we say a tank has a volume of 284 cubic feet, we mean that if we were to take a cube that measures 1 foot on each side and stack 284 of those cubes together, we would have a tank with the same volume as the resulting cube.

Thus,

When we say a tank is 284 cubic feet, we mean that the tank has a volume of 284 cubic feet.

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Answer: Given, sin θ = √2/6

We know that sin^2θ + cos^2θ = 1

Solving for cos θ, we get:

cos θ = ±√(1 - sin^2θ)

cos θ = ±√(1 - (2/6)^2)

cos θ = ±√(1 - 1/9)

cos θ = ±√(8/9)

Since θ is acute, cos θ is positive. Hence,

cos θ = √(8/9) = (2√2)/3

We know that tan θ = sin θ / cos θ

tan θ = (√2/6) / [(2√2)/3]

tan θ = √2/4

We know that cot θ = 1/tan θ

cot θ = 1/ (√2/4) = (2√2)/2 = √2

We know that csc θ = 1/ sin θ

csc θ = 1/ (√2/6) = (6√2)/2 = 3√2

We know that sec θ = 1/ cos θ

sec θ = 1/[(2√2)/3] = (3√2)/2

Hence, the exact values of the remaining trigonometric functions of the angle θ are:

cos θ = (2√2)/3

tan θ = √2/4

cot θ = √2

csc θ = 3√2

sec θ = (3√2)/2

The proportion of observations greater than 7 is 0.25 or 25%.

For this question, we need to identify the number of observations higher than 7.

After inspecting the dataset, 25 values can be seen that are greater than 7.

Then, the proportion of observations greater than 7 can be calculated as follows:

proportion = number of observations greater than 7 / total number of observations

proportion = 25 / 100

proportion = 0.25

Therefore, the proportion of observations greater than 7 is 0.25 or 25%.

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Suppose we have a dataset of 100 observations, where each observation is a continuous variable. What proportion of the observations in the dataset are greater than 7?

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Applying the inscribed angle theorem, the missing measures are:

measure of arc TR = 106°

measure of arc TL = 74°

m∠L = 50°

m∠R = 37°

m∠RTV = 37°

Here, we have,

The Inscribed Angle Theorem

Measure of an inscribed angle = half the measure of the arc it intercepts

Central angle = measure of intercepted arc

We are given the following:

LR and TV are diameters of the circle O.

m∠TOR = 106° (central angle)

Find measure of arc TR:

measure of arc TR = m∠TOR

measure of arc TR = 106°

Find measure of arc TL:

measure of arc TL = 180° - m∠TOR

measure of arc TL = 180° - 106°

measure of arc TL = 74°

Find m∠L:

m∠L = ½(measure of arc TR)

m∠L = ½(106°)

m∠L = 50°

Find m∠R:

m∠R = ½(measure of arc TL)

m∠R = ½(74°)

m∠R = 37°

Find m∠RTV:

m∠RTV = ½(measure of arc RV)

m∠RTV = ½(180 - 106)

m∠RTV = ½(74)

m∠RTV = 37°

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complete question:

Find the measure of the following: m arcTR = m arcTL = m ∠L = m ∠R = m ∠RTV =​

The identity of each of the hidden lines are:

A is a continuous thin single arrow head line.

B is a continuous thick short dashes line.

C is a long thin dashed and single dashed line.

D is a continuous thin double arrow head line.

E is a continuous thin zig-zag line.

A line is either a straight or curved path that joins to points of reference. Or it extends from one point to another point. There are various types of lines especially used in technical drawing, and each has its major purpose of use.

From the types of line given in the question, the identity of the hidden lines are;

i. A is a continuous thin single arrow head line.

ii. B is a continuous thick short dashes line.

iii. C is a long thin dashed and single dashed line.

iv. D is a continuous thin double arrow head line.

v. E is a continuous thin zig-zag line.

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The complete box table.

        2x        6

4x²    8x³    24x²

6x     12x²    36x

-3     -6x       -18

We have,

(4x² + 6x - 3) (2x + 6)

There are two factors.

We distribute one factor with the other factor.

Now,

Distributing the expression.

4x² (2x + 6) + 6x (2x + 6) - 3 (2x + 6)

8x³ + 24x² + 12x² + 36x - 6x - 18

We can combine like terms if we want to simplify.

8x³ + 36x² + 30x - 18

Thus,

The complete box table.

        2x        6

4x²    8x³    24x²

6x     12x²    36x

-3     -6x       -18

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Answer:

The son overtakes the father 3 hours after the father started driving which is 2 hours after the son started driving.

Step-by-step explanation:

Father:

speed = 48 km/h

distance = d

time = t

Son:

speed = 72 km/h

distance = d

time = t - 1

speed = distance/time

distance = speed × time

Father:

d = st

d = 48t

Son:

d = st

d = 72(t - 1)

d = 48t

d = 72(t - 1)

48t = 72(t - 1)

48t = 72t - 72

72 = 24t

t = 3

The son overtakes the father 3 hours after the father started driving which is 2 hours after the son started driving.

Analysis of Jake's free-throw data shows that it is positively skewed, indicating that he most frequently scores around 17-18 points per game, with fewer games with lower scores.

To visualize and understand Jake's free-throw data, we can create a histogram. First, we'll list the range of shots made per game. These are: 8, 9, 10, 11, 12, 15, 16, 17, 18, and 19. Then, for each number, count how many times it occurs in the data set. The distribution could look something like this:

Based on this distribution, the shape of the data is positively skewed, with most of the data clustered around 17-18 points per game, and fewer games with lower scores.

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The solution is:

Exponential model: ,horizontal asymptote

• Logarithmic model: ,vertical asymptote

Here, we have,

EXPLANATION

The exponential model has always a horizontal asymptote. In the parent function f(x) = aˣ, the asymptote is the x-axis because the function approaches 0 as x approaches infinity.

The logarithmic model has always a vertical asymptote. In the parent function f(x) = logₐ(x), the asymptote is the y-axis because the function approaches infinity as x approaches 0.

Hence, The solution is:

Exponential model: ,horizontal asymptote

• Logarithmic model: ,vertical asymptote

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