A farmer fills his field proportionately with soybeans and corn. Last year he planted 200 acres of corn and 50 acres of soybeans. Answer these questions in the textbox or upload your work.

a) Are the number of acres of corn and the number of acres of soybeans directly proportional or inversely proportional? Explain your answer.

b) What is the constant of proportionality? Tell how you found it.

c) Let x equal the number of acres of corn and y equal the number of acres of soybeans. Write an equation to show this relationship.

d) How many acres of soybeans can the farmer plant this year if he plants 250 acres of corn? Show your work.

Answer:

Part a) The distance on a map between Joseph's house and the airport is 2.53 inches

Part b) The distance on a map between the airport and the restaurant is 1.68 inches and the total distance on a map between Joseph's house and the restaurant is 4.21 inches

Step-by-step explanation:

Part a) The actual distance between Joseph's house and the airport is 24 miles. How far apart are Joseph's house and the airport on the map?

we know that

The scale of a map is 1 inch : 9.5 miles

so

using proportion

Find the distance on a map if the  actual distance between Joseph's house and the airport is 24 miles

Let

x-----> the distance on a map

1/9.5=x/24

x=24/9.5=2.53 inches

Part b) Joseph traveled from his house to the airport. He then traveled another 16 miles past the airport to a restaurant. How many inches on the map represent this distance?

we know that

The scale of a map is 1 inch : 9.5 miles

so

using proportion

Find the distance on a map if the  actual distance between airport to the restaurant is 16 miles

Let

x-----> the distance on a map

1/9.5=x/16

x=16/9.5=1.68 inches

The total distance on a map between Joseph's house and the restaurant is equal to

2.53 inches+1.68 inches=4.21 inches

Answer:

Difference is 26 degrees f

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Since all 3 angles are congruent then the triangle is equilateral, thus all 3 sides are also congruent.

Equate any 2 of the sides and solve for x

5x - 22 = 3x + 2 ( subtract 3x from both sides )

2x - 22 = 2 ( add 22 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Answer:

The value of x is 12

Step-by-step explanation:

* Lets talk about the equilateral triangle

- The three sides of the triangle are equal in length

- The three angles of the triangle are equal in measure

- To find the measure of each one divide the sum of the measures

  of the angles of the triangle by 3

∵ The sum of the measure of the angles in any triangle = 180°

∴ The measure of each angle in the equilateral Δ = 180° ÷ 3 = 60°

* Now lets solve the problem

- From the figure the three angles have the same mark, that means

 the three angles are equal in measure

∵ m∠A = m∠B = m∠C

∴ Δ ABC is equilateral triangle

∴ AB = BC = AC

- WE can use any two sides of them to find the value of x

∵ AB = 4x - 10

∵ BC = 3x + 2

∵ AB = BC

∴ 4x - 10 = 3x + 2 ⇒ add 10 and subtract 3x from both sides

∴ 4x - 3x = 2 + 10 ⇒ add the like terms

∴ x = 12

- To check the answer substitute the value of x in the 3 sides to

 find the length of each side (they must have the same length)

∵ AB = 4x - 10

∴ AB = 4(12) - 10 = 48 - 10 = 38 units

∵ BC = 3x + 2

∴ AB = 3(12) + 2 = 36 + 2 = 38 units

∵ AC = 5x - 22

∴ AB = 5(12) - 22 = 60 - 22 = 38 units

- All the sides are equal, then the value of x is right

* The value of x is 12

Two large numbers are converted to words. The first is 'nine hundred sixty-five trillion, four hundred six billion, three hundred fifty-one thousand, six hundred eighty-two and sixty-two hundredths' and the second is 'eight billion, five hundred ninety-one million, eight hundred six and thirty-six hundredths'.

The number 965406000351682.62 in words is nine hundred sixty-five trillion, four hundred six billion, three hundred fifty-one thousand, six hundred eighty-two and sixty-two hundredths.

The number 8591000806.36 in words is eight billion, five hundred ninety-one million, eight hundred six and thirty-six hundredths.

ANSWER

C. is the correct answer

[tex] {y}^{2} = 32x[/tex]

EXPLANATION

The given parabola has a focus at (8,0) and directrix at x=-8.

The equation of this parabola is of the form:

[tex] {y}^{2}=4px[/tex]

Where p is the the distance from the vertex to the focus.

Since the vertex is at the origin,the distance from the vertex to the focus (8,0) is p=8.

[tex] {y}^{2} = 4(8)x[/tex]

[tex] {y}^{2} = 32x[/tex]

Answer:

C on edge

Step-by-step explanation:

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+4}{2}~~,~~\cfrac{y-3}{2} \right)=\stackrel{\textit{midpoint}}{(3,2)}\implies \begin{cases} \cfrac{x+4}{2}=3\\[1em] x+4=6\\ \boxed{x=2}\\ \cline{1-1} \cfrac{y-3}{2}=2\\[1em] y-3=4\\ \boxed{y=7} \end{cases}[/tex]

Answer:

[tex]\large\boxed{3\sqrt{16}-5=7}[/tex]

Step-by-step explanation:

[tex]3\sqrt{16}-5=3(4)-5=12-5=7\\\\\sqrt{16}=4\ \text{because}\ 4^2=16[/tex]

Answer:

5 sin 38 should be the length.

I’m pretty sure it’s the last answer. 5 sin 38

Answer:

x=1 or x=−9

Step-by-step explanation:

Let's solve your equation step-by-step.

x(x+8)=9

Step 1: Simplify both sides of the equation.

x2+8x=9

Step 2: Subtract 9 from both sides.

x2+8x−9=9−9

x2+8x−9=0

Step 3: Factor left side of equation.

(x−1)(x+9)=0

Step 4: Set factors equal to 0.

x−1=0 or x+9=0

x=1 or x=−9

Hey there!

(x + 8) = 9

➡️ x + 8 = 9

SUBTRACT 8 to BOTH SIDES

x + 8 - 8 = 9 - 8

CANCEL out: 8 - 8 because that gives you 0

KEEP: 9 - 8 because it helps solve for the x-value

x = 9 - 8

9 - 8 = x

9 - 8 = 1

Therefore your answer is: x = 1

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

-5y - 4 = -(x + 3)^2 - 1/2

Answer:

This is the answer

Answer:

12 cookies and 10 brownies

Step-by-step explanation:

Eder needs 15 cookies and 5 brownies.

Given in the question is Eder needs 6 cookies and 2 brownies for 4 plates.

We have to calculate the cookies and brownies required for 10 plates.

Let's first calculate the cookies by unitary method.

∵ 4 plates required cookies = 6 cookies

∴  1 plate will require cookies = 6/4

∴ 10 plates will require cookies = 6×10/4 = 15

Similarly we will calculate the brownies.

∵ 4 plates required number of brownies = 2

∴ 1 plate will require = 2/4 brownies

∴ 10 plates will require = 2×10/4 = 5 brownies

Therefore 15 cookies and 5 brownies will be required for 10 plates.

Answer:

1 2 3 1

Step-by-step explanation:

To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together. Bam!

Answer:

The GCF is [tex]u^3v^2[/tex]

Step-by-step explanation:

The given monomials are:

[tex]u^3v^6[/tex]

and

[tex]u^6v^2[/tex]

The greatest common factor is the product of the least powers of the common factors.

The least of the powers of the common factors are:

[tex]u^3[/tex] and [tex]v^2[/tex].

Their product is [tex]u^3v^2[/tex]

Therefore the Greatest Common Factors is [tex]u^3v^2[/tex]

Add the ratios together:

5 +4 = 9

Divide the total amount by t his number:

54 / 9 = 6

Now multiply each side of the ratio by 6:

Sam = 5 x 6 = £30

Bethan = 4 x 6 = £24

Answer:

15.00 once you add percent

Answer:

The increase from $3.50 to $8.50 was 243%.

Step-by-step explanation:

The increase from $3.50 to $12.00 was $8.50.

We need to compare this to the original $3.50 by writing the following ratio, evaluating it and converting the result to a percentage:

$8.50

--------- = 2.43

$3.50

Multiply this result by 100%:  (100%)(2.43) = 243%

The increase from $3.50 to $8.50 was 243%.

The graph of f(x) is shifted k units above the graph of g(x). Therefore, the option C is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x) = 2ˣ and f(x) = 2ˣ+k

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: g(x)=2x

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Vertical Compression or Stretch: None

So, from graph of g(x) to the graph of f(x), it shifted k units up.

Therefore, the option C is the correct answer.

To learn more about the function visit:

https://brainly.com/question/28303908.

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"Your question is incomplete, probably the complete question/missing part is:"

The function g(x) = 2ˣ. The f(x) = 2ˣ+k and k < 0. Which of the following statements is true?

A) The graph of f(x) is shifted k units to the left of the graph of g(x).

B) The graph of f(x) is shifted k units to the right of the graph of g(x).

C) The graph of f(x) is shifted k units above the graph of g(x).

D) The graph of f(x) is shifted k units below the graph of g(x).

Answer:

I want to say the answer is D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A filled in circle located on the number line indicates x can equal that value

If the circle is open then x cannot equal that value

An arrow pointing right from the circle indicates that x is greater

An arrow pointing left from the circle indicates that x is less

Since the number line has a filled in circle at x = 3 and the arrow is pointing to the right , thus

x ≥ 3 → D

Answer:

Josh won the race 5 seconds ahead of Rafael

Step-by-step explanation:

The winner of the race is the individual who completes the race in the shortest time. From the graph, Josh reaches the finish line at the 15 seconds mark while Rafael finishes at the 20 seconds mark.

The difference in the time is thus;

20 - 15 = 5 seconds.

Therefore, Josh won the race 5 seconds ahead of Rafael

Answer:

Divide 96/4 to get how many cars can be washed within a single hour. Cut that in half to get 12.

Step-by-step explanation:

96÷4=24 cars/hr

24÷2=12 Cars for every 30 minutes.

Which outcomes are in a or b is answer B

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \end{cases}\implies V=\pi r^2\cdot \cfrac{h}{3}~~ \begin{cases} \pi r^2=&area~of\\ &circular\\ &base\\ \cline{1-2} \stackrel{B}{\pi r^2}=&5\\ V=&45 \end{cases} \\\\\\ 45=5\cdot \cfrac{h}{3}\implies 135=5h\implies \cfrac{135}{5}=h\implies 27=h[/tex]

Answer:

The correct option is C) 27

Step-by-step explanation:

Consider the provided figure.  

Volume of a cone is: [tex]V=\frac{1}{3}\pi r^2h[/tex]

The area of base of the cone is = area of circle = [tex]\pi r^2[/tex]

Volume of the cone is 45 in³ and the area of base is given as 5 in²

Therefore, [tex]45=\frac{1}{3}\pi r^2h[/tex]

and [tex]5=\pi r^2[/tex]

Substitute the value of [tex]\pi r^2=5[/tex] in  [tex]45=\frac{1}{3}\pi r^2h[/tex]

[tex]45=\frac{1}{3}\times 5\times h[/tex]

[tex]45\times \frac{3}{5}=h[/tex]

[tex]h=27[/tex]

Hence, the height of the cone is 27 in.

Therefore, the correct option is C) 27

Answer:

B) 20

Step-by-step explanation:

Subtract  10  from both sides of the equation.

6 a = 130 - 10

Subtract  10  from  130 .

6a=120

Divide each term by  6  and simplify.

6 a/ 6  = 120 /6

Reduce the expression by cancelling the common factors.

a=120/6

Divide  120  by  6 .

a  =  20

Hope this helps.

The value of a is 20.

Parallelogram's characteristics

Given

6a + 10 = 130 [The opposing angles congruent.]

6a = 120

a = 20

Therefore, The value of a is 20.

To know more about parallelogram refer to :

https://brainly.com/question/970600

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Answer:

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

Step-by-step explanation:

The given function is

[tex]F(x)=x^{3}[/tex]

The transformations to this graph are  in the form;

[tex]G(x)=a(x-b)^3+c[/tex]

where [tex]a=\frac{1}{2}[/tex] is the vertical compression by a factor of [tex]\frac{1}{2}[/tex]

b=3 is a shift to the right by 3 units.

c=2 is an upward shift by 2 units.

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

Answer:

The equation is

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

Step-by-step explanation:

If the graph of the function [tex]G(x)=cf(x+h) +b[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <|c| <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

If [tex]b> 0[/tex] the graph moves vertically upwards.

If [tex]b <0[/tex] the graph moves vertically down

If [tex]h <0[/tex] the graph moves horizontally h units to the right

If [tex]h >0[/tex] the graph moves horizontally h units to the left

In this problem we have the function [tex]G(x)[/tex] and our parent function is [tex]f(x) = x^3[/tex]

We know that G(x) is equal to f(x) but reflected on the x-axis ([tex]c <0[/tex]), compressed vertically by a multiple of 1/2 ([tex]0 <|c| <1[/tex] and [tex]c = -\frac{1}{2}[/tex]), displaced 2 units upwards ([tex]b = 2>0[/tex]) and moved to the right 3 units ([tex]h = -3<0[/tex])

Then:

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

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

Answer:

A coordinate plane graph is shown. A line passes through the y-axis at 3 and through the point 2 comma 4. Which equation best represents the line?

y=6x+3

Step-by-step explanation:

You add each number by 6n - fourth choice. I am not sure if this is the right answer.

ANSWER

6n

EXPLANATION

The given sequence is

6,12,18,24,...

We can rewrite the terms of the sequence to observe some pattern.

The first term is 6(1)=6

The second term is 6(2)=12

The third term is 6(3)=18

The fourth term is 6(4)=24

Based on this pattern we can generalize that, the nth term of the sequence is 6(n).

Therefore the rule of the sequence is 6n

Answer:

4n²+2n as a factorial is given as:

[tex]= (2n+1)!/(2n-1)![/tex]

Step-by-step explanation:

We are given an expression which has to be converted into factorial form.

The expression is as follows:

[tex]4n^{2} + 2n\\ = 2n(2n+1)\\ = (2n+1)2n\\[/tex]

Now we know that 2n+1 and 2n differs by '1' and the next smaller term is '2n-1'.

Hence, multiplying and dividing by '(2n-1)!'; we get:

[tex]= ((2n+1)(2n)(2n-1)!)/(2n-1)![/tex]

we know that x(x-1)(x-2)! = x!, so:

[tex]= (2n+1)!/(2n-1)![/tex]

Hope this helps :)

Answer:

A = 340,000 square feet

B = 467,500 square feet

C = 361,250 square feet

D = 180,625 square feet

Answer:

If x and y are independent events;

[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]

If x and y are dependent events then;

[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]

Step-by-step explanation:

The expression;

P(x|y)  in probability represents the conditional probability of an event x occurring given that an event y has already occurred. An example of such would be; the probability that a student passes the examination given that he attempted all the assignments.

If x and y are independent events, that is the occurrence of y does not in any way influence the occurrence of x, then;

[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]

If x and y are dependent events then;

[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]

[tex]P(xny)[/tex] represents the probability of both x and y occurring together;

n denotes intersection

Answer:

Gabby received

7 nickels

10 dimes

3 quarters

Step-by-step explanation:

Let

x----> the number of dimes

y----> the number of nickels

z---> the number of quarters

Remember that

1 dime=$0.10

1 nickel=$0.05

1 quarter=$0.25

we know that

0.10x+0.05y+0.25z=2.10 ------> equation A

x=y+3-----> equation B

z=y-4 -----> equation C

substitute equation B and equation C in equation A and solve for y

0.10(y+3)+0.05y+0.25(y-4)=2.10

0.10y+0.30+0.05y+0.25y-1=2.10

0.40y=2.10-0.30+1

0.40y=2.80

y=7 nickels

Find the value of x

x=y+3 -----> x=7+3=10 dimes

Find the value of z

z=y-4 -----> z=7-4=3 quarters

therefore

Gabby received

7 nickels

10 dimes

3 quarters

Answer:

Step-by-step explanation:

1.5

Answer:

m = 3

because qrst is a parallelogram opp. sides are equal

Answer:

Step-by-step explanation:3