1 Given F(x) = 1/2 (4 – x), what is the value of F(3)?

Answer:

A= 66.6667

B = 333.3333

Step-by-step explanation:

Initial value of A = $20

Initial value of B = $80

Initial total=$ 28000

A moves up 50%= 20+(0.5*20)

A moves up 50% = 20+10

A moves up 50% =$ 30

B double it values = $80*2

B double it values = $160

Now total value is = $54000

A20+B80= 28000... equation 1

A30+B160= 54000.... equation 2

Multiplying equation 1 * 2

Multiplying equation 2 * 1

A40 +B160 = 56000

A30+B160= 54000

A30 = 2000

A= 2000/30

A= 200/3

A= 66.6667

A20+B80= 28000

Substituting A

200/3 (20) +B80= 28000

B80= 28000-4000/3

B80= 80000/3

B= 80000/240

B = 333.3333

Answer:36mm

Step-by-step explanation:

6 times 6 equals 36

36 is the perimeter

Answer:

infinite number of solutions

Step-by-step explanation:

\(\frac{4}{5}\) (x + 9) - \(\frac{1}{5}\) x = \(\frac{3}{5}\) (x + 12)

multiply through by 5 to clear the fractions

4(x + 9) - x = 3(x + 12) ← distribute parenthesis on both sides

4x + 36 - x = 3x + 36

3x + 36 = 3x + 36

since both sides are the same then any value of x will make the equation true.

Thus there are an infinite number of solutions

The shorter distance he can take if directly from cabin to firepit that is 1.41x.

Trigonometry is a branch of mathematics that focuses on the study of the relationships between the sides and angles of triangles. It is based on the fact that the ratios of the lengths of the sides of a right-angled triangle are always constant, regardless of the size of the triangle. Trigonometry involves the use of several mathematical functions such as sine, cosine, and tangent, which are defined based on the ratios of the sides of a right triangle. For instance, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse, while the cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Here,

Let x be he distance from firepit to dock, y be the distance from dock to cabin and z be the distance from firepit to cabin.

tan 45=1

x/y=1

x=y

sin 45=1/√2

x/z=1/√2

z=x√2

Total distance:

Path 1: Patrick walks directly from his cabin to the firepit, so the distance he walks is z.

z=x√2

z=1.41x

Path 2: Patrick walks from his cabin to the dock, and then from the dock to the firepit. The distance he walks is y + z.

=x+y

=2x

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Answer:

Step-by-step explanation:

To solve this question, I have divided the shape into squares and rectangles. Then, I found out the area of each square and rectangle. Lastly, I added up all the areas and found the area of the shape. Please consider looking at the picture uploaded to understand better.

When looking at the picture, we can say that the area is 55 + 120 + 304.

Hence, the area of the shape is 479 yd².

9514 1404 393

Answer:

  4 1 5 3 6 2

Step-by-step explanation:

The general approach to this proof is to show the triangles created by the diagonal are congruent. Then, parts of those triangles (opposite sides) are congruent. The congruence of the triangles is shown by making use of the fact that alternate interior angles are congruent, and the diagonal is congruent to itself. Thus, you have two angles and the side between shown as congruent, and can invoke the ASA postulate.

The steps of the proof (1 to 6) are already in order. The task is to find the geometric relation the step is describing from the list on the left.

__

Statements A to F on the left match with numbered statements 1 to 6 on the right as follows:

A - 4 (reflexive prop)

B - 1 (given)

C - 5 (ASA)

D - 3 (alt int angle)

E - 6 (the end point of the proof)

F - 2 (definition)

Answer:

N = 3M

Step-by-step explanation:

Answer:c, the answer is c

Step-by-step explanation:

Answer:

see the work below

Step-by-step explanation:

20.)    x = √32²+32² = √2048 = 45.25

y = 32(sin60) = 27.7

z = 32(cos60) = 16

22.)   x = 7√3 / cos60 = 24.25 = 14√3

y = 14√3 / tan30 = 42

sin30 = 14√3 / (z+7√3)

z + 7√3 = 14√3 / sin30

z = 14√3/√sin30 - 7√3 = 36.37 = 21√3

24.) z = 18(tan30) = 10.4

h = √10.4² + 18² = √432 = 20.785

x = y

2x² = 20.785²

x = √20.785²/2 = 14.7

y = 14.7

Answer:

Question 20:

Question 22:

Question 24:

Step-by-step explanation:

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.  Therefore, the formula for the ratio of the sides is b : b : b√2 where:

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:

Side x is the hypotenuse of a 45-45-90 triangle with congruent legs measuring 32 units. Therefore b = 32.

\(\implies x=b\sqrt{2}=32\sqrt{2}\; \sf units\)

Side y is the side opposite the 60° angle in a 30-60-90 triangle with a hypotenuse of 32 units. Therefore, 2c = 32 so c = 16.

\(\implies y = c\sqrt{3}=16\sqrt{3}\; \sf units\)

Side y is the side opposite the 30° angle in the same 30-60-90 triangle.

\(\implies z=c = 16\; \sf units\)

Side x is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 7√3 units. Therefore c = 7√3.

\(\implies x=2c=2 \cdot 7 \sqrt{3}=14\sqrt{3}\; \sf units\)

Therefore, other leg of the same triangle (opposite the 60° angle) measures c√3 = 7√3 · √3 = 21 units.

Side y is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 21 units. Therefore c = 21.

\(\implies y=2c=2 \cdot 21 = 42\; \sf units\)

Side z is the leg of the same 30-60-90 triangle opposite the 60° angle.

\(\implies z=c\sqrt{3}=21\sqrt{3}\; \sf units\)

Side z is the side opposite the 30° angle in a 30-60-90 triangle with the other leg (opposite the 60° angle) measuring 18 units. Therefore, c√3 = 18, so c = 18/√3 = 6√3 units.

\(\implies z=c = 6\sqrt{3}\; \sf units\)

Therefore, the hypotenuse of the same triangle measures 2c = 12√3 units.

Sides x and y are the congruent legs of a 45-45-90 triangle with hypotenuse measuring 12√3 units. Therefore b√2 = 12√3, so b = 6√6.

\(\implies x=6 \sqrt{6}\; \sf units\)

\(\implies y=6 \sqrt{6}\; \sf units\)

Answer:

2x-3x=24____eqn 1

3x+4y=2____eqn 2

solve eqn 1 and 2 simultaneously using elimination method

eliminate x use the coefficients of x in the two equations to multiply each other i.e

3(2x-3y=24)

2(3x+4y=2)

6x-9y=72

6x+8y=4

eliminate x using the subtraction sign(-)

6x-6x-9y-(+8y)=72-4

-9y-8y=68

-17y=68

divide both side by the coefficient of y

y=68/-17

y=-4

put y=-4 in eqn 2

3x+4y=2

3x+4(-4)=2

3x-16=2

collect like term

3x=2+16

3x=18

divide both side by the coefficient of x

x=18/3

x=6

since we're asked to find x-y

6-(-4)

6+4=10

"In a relation r, for every instance of a, that value of a uniquely determines the value of b then a primary dependency exists in the relation.

Relation:

In math relation means the relationship between sets of values of ordered pairs.

Given,

Here we need to find if for every valid instance of a, that value of a uniquely determines the value of b in the relation.

As per the definition of relation, for every relation has two set of data ad each of the element in one set is uniquely refers the other one's element.

Here we have to identify the type of relation between a an b.

Here we have given that the relation a uniquely determines the value in b.

So, this type primarily refers the dependency of the relation.

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Answer:

8×18=144

4±15=19

144÷19

7.579 answer

Answer:

\(y=7x-26\)

Step-by-step explanation:

1) Write it in the slope-intercept form of \(y=mx+b\), where m is the slope and b is the y-intercept.

\(y=7x +c\)

2) Substitute the given coordinates into \(y=7x +b\), and then solve for c.

\(9=7(5) +b\\9=35+b\\9-35=b\\b= -26\)

3) Substitute c into \(y=7x +b\)

\(y=7x-26\)

Therefore, the answer is \(y=7x-26\).

The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.

At Mega Mart, a 5kg cake costs $2500.

Therefore, the price per kilogram for this cake is:

Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.

At the same time, a 2kg chocolate cake costs $1200.

So, the price per kilogram for this cake is:

Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.

Now, let's calculate the total price for 10kg of cake from each option:

Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.

Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.

Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.

Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.

Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.

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The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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Answer:

where are the expressions?

Step-by-step explanation:

The volume of A and B are 28m³ and 16m³ respectively.

For volume of A

The formula for volume of a cuboid is given as:

Volume = length × width × height

Substitute the values

Volume = 7 × 2 × 2

Volume = 28m³

For cuboid B

Volume = length× width × height

Substitute the values

Volume = 4 × 2 × 2

Volume = 16m³

Thus, the volume of A and B are 28m³ and 16m³ respectively.

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The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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Answer:

80 km/h

Step-by-step explanation:

2 h 30 min = 2.5 h

Average speed = distance/time= 200 km/2.5 h = 80 km/h

Answer:

ok

Step-by-step explanation:

Answer:

x is -1/b yw

Step-by-step explanation:

The distance at which the Benson family would be from home after 412 hours of driving according to the task content is; 18,640 miles.

It follows from the task content that the equation which models the distance of the Benson's family from home after a given time t is;

d = 45t +100

Hence, when t = 412 hours.

d = 45(412) + 100

d = 18540 +100

d = 18,640miles.

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Answer:

n = 14

Step-by-step explanation:

2 + n = 16

-2         -2

2 - 2 = 0

16 - 2 = 14

n = 14

SOLUTION

The transformation of the function

To give the graph in the question is as follows.

The graph is move to the left from the origin by 1 unit on the x-axis, which is to add 1 to x, we have

Also,

The graph is the move upward along the y-axis by 7 unit, which is addition of 7 to the function

Then, the equations becomes

Therefore

The function that produce the graph in the image is

y = (√x+1) + 7

Answer:

B and E

Step-by-step explanation:

15 divided by 12 is =1.25

1.25 ti.es 36 rooms =45 hours

Answer:

4

Step-by-step explanation:

in y=mx+b, the "b" is the y-intercept

Answer:

4

it's in y = mx + b form, where b is the y-intercept

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Both A and B are exclusive to each other because of P(A and B) = 0.

Therefore, Let A be the major in mathematics and B be the major in philosophy.

Each student is required to only have one major.

No student does have two significant students.

Therefore, the likelihood of both the major pupils being zero.

This is P(A and B) = zero

Therefore, The events are exclusive to each other.