2) you are comparing two investment options that each pay 6 percent interest, compounded annually. both options will provide you with $12,000 of income. option a pays $2,000 the first year followed by two annual payments of $5,000 each. option b pays three annual payments of $4,000 each. which one of the following statements is correct given these two investment options? assume a positive discount rate. (no calculations needed.) a) both options are of equal value since they both provide $12,000 of income. b) option a has the higher future value at the end of year 3. c) option b has a higher present value at time 0. d) option b is a perpetuity. e) option a is an annuity.

Answer: x < 9

Step-by-step explanation:

Move all terms not containing x to the right side of the inequality.

The dimensions of the region which enclose the maximum area is a side of 162 feet and vertical segment of 108 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the side parallel to the vertical segment and y represent the other side. If the farmer has 648 feet of fencing, hence:

x + x + y + y + x = 648

3x + 2y = 648

y = 324 - 1.5x

Area (A) = xy

A = xy

A = x(324 - 1.5x)

A = 324x - 1.5x²

The maximum area is at A' = 0, hence:

A' = 324 - 3x

324 - 3x = 0

3x = 324

x = 108 feet

y = 324 - 1.5(108) = 162 feet

x = 108 feet, y = 162 feet

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Answer:

a. Perpendicular

Make sure to read the step-by-step explanation to figure out how to do the other 2.

Step-by-step explanation:

I will not be providing answers to all three, but I will answer the first one (this is, so you don't depend on people to solve this for you).

Parallel lines have one thing in common, their slope. Two lines that have the same slope never intersect because they are both facing the same direction and moving the same distance. So, you can find the slope of two lines by using the slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{-6-(-3)}{-4-2}=\frac{-3}{-6}=\frac{1}{2}\\m_2=\frac{-8-2}{2-(-3)}=\frac{-10}{5}=-2[/tex]

This is evidence that the two lines are not parallel. But, by finding the slope, we can conclude that it is perpendicular.

This brings me to how to identify perpendicular lines. The slope of perpendicular lines is negative reciprocals. A reciprocal is just a fraction that is flipped, and it's negative. For example, [tex]\frac{-2}{3}[/tex]'s negative reciprocal would be [tex]\frac{3}{2}[/tex]. The negative of -2/3 is a positive, and the reciprocal of 2/3 is 3/2. So, the negative reciprocal is 3/2.

Well, [tex]-2[/tex] is the negative reciprocal of [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2, and the negative of 2 is -2. So, simply, lines 1 and 2 are perpendicular.

Use this method to solve the other questions. If they don't have the same slope and aren't negative reciprocals, then they are neither.

Answer:

Step-by-step explanation:

        To solve this problem, we use the following formula:

                        [tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

    a) (2,-3)  (-4,-6)

[tex]x_1=2\ \ \ \ x_2=-4\ \ \ \ y_1=-3\ \ \ \ y_2=-6[/tex]

[tex]\displaystyle\\\frac{x-2}{-4-2} =\frac{y-(-3)}{-6-(-3)} \\\\\frac{x-2}{-6}=\frac{y+3}{-6+3} \\\\\frac{x-2}{-6} =\frac{y+3}{-3}[/tex]

Multiply both parts of the equation by -3:

[tex]\displaystyle\\\frac{x-2}{2}=y+3\\\\0.5x-1=y+3\\\\0.5x-1-3=y+3-3\\\\0.5x-4=y\\[/tex]

⇔ Line 1: y=0.5x-4    m₁=0.5

   (-3,2)  (2,-8)

[tex]\displaystyle\\\frac{x-(-3)}{2-(-3)}=\frac{y-2}{-8-2} \\\\\frac{x+3}{2+3} =\frac{y-2}{-10} \\\\\frac{x+3}{5} =\frac{y-2}{-10} \\\\[/tex]

Multiply both parts of the equation by -10:

[tex]-2(x+3)=y-2\\-2x-6=y-2\\-2x-6+2=y-2+2\\-2x-4=y[/tex]

⇔ Line:y=-2x-4   m₂=-2

[tex]\displaystyle\\m_1=-\frac{1}{m_2}[/tex]

⇒ The given  lines are perpendicular

b)

(-4,-5)   (4,1)

[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+4}{4+4}=\frac{y+5}{1+5} \\\\\frac{x+4}{8} =\frac{y+5}{6} \\[/tex]

Multiply both parts of the equation by 6:

[tex]\displaystyle\\\frac{6(x+4)}{8} =y+5\\\\\frac{3}{4} x+3=y+5\\\\\frac{3}{4} x+3-5=y+5-5\\\\\frac{3}{4} x-2=y\\[/tex]

⇔ Line 1: y=(3/4)x-2     m=3/4

     (6,10)    (-3,-2)

[tex]\displaystyle\\\frac{x-6}{-3-6} =\frac{y-10}{-2-10} \\\\\frac{x-6}{-9} =\frac{y-10}{-12} \\\\[/tex]

Multiply both parts of the equation by -12:

[tex]\displaystyle\\\frac{-12(x-6)}{-9} =y-10\\\\\frac{4}{3}x-8=y-10 \\\\\frac{4}{3}x-8+10=y-10+10\\\\\frac{4}{3}x+2=y[/tex]

⇔ Line 2: y=(4/3)x+2    m=4/3

⇒  The given  lines are neither perpendicular and neither parallel

c)

  (0,-4)   (-2,-8)

[tex]\displaystyle\\\frac{x-0}{-2-0} =\frac{y-(-4)}{-8-(-4)} \\\frac{x}{-2}=\frac{y+4}{-8+4} \\\\\frac{x}{-2}=\frac{y+4}{-4}[/tex]

Multiply both parts of the equation by -4:

[tex]2x=y+4\\2x-4=y+4-4\\2x-4=y[/tex]

⇔ Line 1: y=2x-4     m₁=2

  (-1,5)   (1,9)

[tex]\displaystyle\\\frac{x-(-1)}{1-(-1)} =\frac{y-5}{9-5} \\\\\frac{x+1}{1+1} =\frac{y-5}{4}\\\\\frac{x+1}{2} } =\frac{y-5}{4} \\[/tex]

Multiply both parts of the equation by 4:

[tex]2(x+1)=y-5\\2x+2=y-5\\2x+2+5=y-5+5\\2x+7=y[/tex]

⇔ Line 2: y=2x+7    m₂=2

m₁=m₂  

⇒ The given  lines are parallel

Answer:

See below

Step-by-step explanation:

If there are no other forces on the body. the NET force is the result of the two forces acting to the left  and total  5 N  Left

Answer:  The correct answer is Net Force = 5, Direction = N

Step-by-step explanation:  Net force in the same direction is cumulative and simply added together, where opposing forces are subtracted. In this case, they are in the same direction or to the left.

Answer:

Below.

Step-by-step explanation:

1) Alternate exterior angles

2) Alternate interior angles

3) Alternate exterior angles

4) Alternate exterior angles

5) Alternate interior angles

6) Corresponding angles

7)Alternate exterior angles

8) Alternate interior angles

9) Corresponding angles

10) Corresponding angles

When two parallel lines are intersected by a transversal 8 angles are formed.

Alternate exterior angles: These angles are located outside the parallel lines but on the opposite side of the transversal.

Alternate interior angles:

These angles are located inside the parallel lines but on the opposite side of the transversal.

Corresponding angles: These angles are located at the same relative position on the same side of the transversal.

Answer:

The 5 students receive the larger amount.

100:5= 20 gram per student

100÷20= 5 gram per student

Step-by-step explanation:

prove me wrong

a shorter solution that probably will get full pts :

Because each group has the same mass of the chocolate bar, whichever group has less students will get a larger amount of chocolate per student (as there are less people receiving)

and here's if you think it is kinda not too detailed :

The first group has each student receiving 100 : 5 = 20 grams of chocolate per student
The second group has each student receiving 100 : 20 = 5 grams of chocolate per student

Both solutions give us a conclusion of : The group with 5 students have each of the receiving a larger amount of chocolate.

Grayce has 0.825 g of diamonds and Morgan has 0.824 g of diamonds. Grayce has more grams of diamonds

From the question, we are to determine the person that has more grams of diamonds

From the given information,

"Grayce has three diamonds that weigh 0.275 g each"

and

"Morgan has two diamonds that weigh 0.412 g each"

Thus,

The total mass of Grayce's diamonds is 3 × 0.275 g

3 × 0.275 g = 0.825 g

Also,

The total mass of Morgan's diamonds is 2 × 0.412 g

2 × 0.412 g = 0.824 g

Since 0.825 is greater than 0.824,

Then,

Grayce has more grams of diamonds.

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Answer:

5.48, 78.541 and 97

Step-by-step explanation:

A rational number by definition refers to a number that is in the form of k/m and in which k and m are integers and m is not equal to 0.

Let me give you some examples:

From our question,

Therefore 5.48, 78.541 and 97 are rational numbers

The range for the given domain D = {2, -3, 0} of the function f(x) = 2x² + 7 is; R = {7, 15, 25}

We are given the function as;

f(x) = 2x² + 7

We are given the domain set as;

D = {2, -3, 0}

Now, the range will simply be gotten by plugging in each domain value into the given function to get the output. Thus;

Range when x = 0 is;

y = 2(0)² + 7

y = 7

Range when x = 2 is;

y = 2(2)² + 7

y = 15

Range when x = -3 is;

y = 2(-3)² + 7

y = 25

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Answer:

24 wings

Step-by-step explanation:

Answer:

17 wings

Step-by-step explanation:

1. first we multiply 3 by 27.20 you get  81.6

2. then we divide 81.6 by 4.80 and we get 17

17 wings

1) (4, 8)

2) (4, 8)

The midpoints are already given to you.

Answers:

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

Explanation:

A = (9, -10)

B = (4,8)

C = (x,y)

A and C are the endpoints. B is the midpoint of segment AC.

The x coordinates of A and C are 9 and x respectively. Add them up and divide in half to get (9+x)/2. This is set equal to the x coordinate of point B and we solve for x.

(9+x)/2 = 4

9+x = 2*4

9+x = 8

x = 8-9

x = -1

The x coordinate of point C is -1.

Use the same idea for the y coordinates.

(-10+y)/2 = 8

-10+y = 2*8

-10+y = 16

y = 16+10

y = 26

Point C is located at (-1, 26)

The midpoint between (9, -10) and (-1, 26) is (4, 8)

Use the midpoint formula to confirm this.

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

The steps for the second problem are going to follow the same outline.

A = (-6,4)

B = (4,8)

C = (x,y)

(-6+x)/2 = 4 solves to x = 14

(4+y)/2 = 8 solves to y = 12

Point C is located at (14, 12)

The midpoint between (-6, 4) and (14, 12) is (4, 8)

Answer69

Step-by-step explanation:

Answer:

x = 22° (alternate angles, M//N)

Step-by-step explanation:

as the other answer said, if is the commutative property of multiplication (the same as for addition, as multiplication is just a shortcut form of special additions) :

a × b = b × a

you need a solution ? you mean, you need this multiplication done and simplified, right ?

you know that

a/b × c/d = (a×c)/(b×d)

so,

-33/57 × -7/28 = -33/57 × -7/(4×7) =

= -33/57 × -1/4 = (-33×-1)/(57×4) =

= 33/228

a) fractions; 15.3/3

b) yes, it is a rational number

John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.

In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent the slope; reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of equation for a straight line as "y = mx + b" and "y = mx + c," respectively.

He priced all items at a dime or a quarter. His sales totaled less than $5

Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25

Let x=x= the number of the items sold for a dime

Let y=y= the number of the items sold for a quarter

0.10x+0.25y<5

0.10x+0.25y<5

Inequality in the slope-intercept form

0.10x+0.25y Subtract 0.10x from both sides

0.25y<-0.10x+5 Divide both sides by 0.25

Subtract 0.10x from both sides

[tex]y= -\frac{2}{5}x+20\\[/tex]

The slope is, [tex]-\frac{2}{5}[/tex] and the y- intercept is 20

Since inequality sign is << so, draw a dashed line

Test point (0,0)(0,0)

Substituting the values 0 for x and 0 for y,

[tex]y < -\frac{2}{5}x+20\\\\0 < -\frac{2}{5}(0)+20\\\\0 < +20[/tex]

Since inequality is true

So, (0,0)(0,0) is solution of the inequality

Shade region containing (0,0)(0,0).

The graph below shows all possible solutions

Since boundary line is dashed and the number of items is always positive

The solution is shaded region in quadrant I

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Total charge for 1,920 squares feet is $160.

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including trigonometry, calculus, and coordinate geometry. 2x + 4 = 8 is a straightforward algebraic expression.In algebra, symbols are used, and operators are used to connect the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.

Given that :City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour.

City carpet can install 1,200 square feet of carpet in 2.5 hours

In 1 hour they can install [tex]\frac{1200}{2.5} =480 squares feet[/tex]

In 4 hour they can install 1920 squares feet carpet

They charge $40 per hour

So total charges for 1920 square feet will be 4 ×40

= $160

Total charge for 1,920 squares feet is $160.

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Answer:2x^2+3x-2

Step-by-step explanation:

2x-1*x+2=2x^2+3x-2

Answer:

2x+3

Step-by-step explanation:

so first you plug in g(x) in for x in f(x). this is how it will look like

2(x+2)-1

then you distribute the 2 in both terms in the parenthesis.

2(x)+2(2)-1

after that, you multiply them and you will get this

2x+4-1

subtract 4 and 1 and this is your answer

2x+3

total cost of metal in the pattern is £24.6

To compare two values is to use a ratio. A proportion is formed when two ratios have the same value. Choose whether the ratio is part-to-part or part-to-whole before you write it.

20 straight line cost £12

12 ÷ 20 = 0.6 per straight line

straight line : cost of one arc = 2:3

arc = 0.6 x (3/2) = 0.9

total = 12 + 14 x 0.9

         = 12 + 12.6

         = 24.6

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The minimum number of sets of knives Kaj should buy if the restaurant needs at least 736 knives is 48. 4 sets of knives

155 + 12x ≥ 736

12x ≥ 736 - 155

12x ≥ 581

x ≥ 581 / 12

x ≥ 48.41666666666666

Approximately,

x ≥ 48. 4 sets of knives

In conclusion, the sets of knives kaj needs to buy more is 48. 4 sets of knives

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a. Expression for length L in terms of x is  L = 1040 - 2x

b. Expression for the area of the pasture in terms of L and x, A = Lx

c. Expression for the area of the pasture in terms of x only = x (1040 - 2x)

d. The area of the pasture will enclose greater than or equal to 60 square feet

Given data

length of fence = 1040 ft

length if the pasture = L

width of the pasture = x

Expression for length L in terms of x

from the figure we can see that the fenced part is 3 sides which include 2 widths and 1 length. So we represent this with the expression below

L + x + x = 1040

L + 2x = 1040

L = 1040 - 2x

Expression for the area of the pasture in terms of L and x

Area of the pasture,  A = L * x

A = Lx

Expression for the area of the pasture in terms of x only

= L * x

and L = 1040 - 2x

= x (1040 - 2x)

A sentence that makes the area to enclose at least 60 000 square feet.

from A = Lx

we have

A = Lx ≥ 60

The area of the pasture will enclose greater than or equal to 60 square feet

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convert feet to miles;

10,560 = 2 miles

30 minutes to miles;

2; therefore,

in 1hr she walked 4 miles

4 miles/hour

Answer:

Step-by-step explanation:

Answer:

I think C. Correct me if I am wrong.

Step-by-step explanation:

Hope it helps! =D

Answer: The answer is C.

Step-by-step explanation: Because I use a graphing calculator

Semicircle is the best figure to use to estimate the volume of the punch bowl.

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Answer:

3

Step-by-step explanation:

m=y2-y1÷x2-x1

4-1÷1-0=3÷1=3

Answer:

5m+3 =3m

Step-by-step explanation:

−6(t − 8) = 12

-6((6) -8) =12

5m+3=3m

5m-3m=3

2m=3

2(6)≠3

t + 5 = 11

(6) + 5 = 11

9 = 2x − 3

2x = 9+3

2(6) = 12

The sum will be 46 which is the nearest combinational value that could be deduced from the digits 1, 2, 3, and 4.

Let's check all the combinations which can be possibly used,

34 + 21 = 46, which is 4 numbers less than 50 so far the nearest.

43 + 12 = 55, which is 5 numbers more than 50.

32 + 41 = 73, which is 23 numbers more than 50.

32 + 14 = 46, which is 4 numbers less than 50 so far the nearest.

23 + 41 = 64, which is 14 numbers more than 50.

So the two combinations are deduced after permutation and a combination of numbers that are 3 and 4 + 2 and 1 and another is 3 and 2 + 1 and 4.

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FOR THE GIVEN FUNCTION WE WILL HAVE TO CHECK DENOMINATOR PART BECAUSE IT IS THE ONE WITH THE GREATER EFFECT ON MAKING THE FUNCTION UNDEFINED.

THE FUNCTION WILL BE UNDEFINED ONLY IF x=0

THIS BRINGS US TO A CONCLUSION OF SAYING THE DOMAIN IS ALL REAL NUMBERS BUT X IS NOT EQUAL TO 0