In triangle ABC, what is the measure of angle C if A = 120°, a = 25, and b = 20? Round the answer to the nearest hundredth.

The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.

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Answer:

As a product of prime numbers:

420 = 2 × 2 × 3 × 5 × 7

Answer:

x,y [tex]( \frac{2}{61})(\frac{91}{61} )[/tex]

50 miles because of the miles

Answer:

surface area=2(lb+lh+bh)

surface area=2(9)(4)+(9)(12)+(4)(12)

surface area=384cm2

By using the concept of kinetic energy, it is obtained that

Kinetic energy of the  airplane when its velocity is 300 m/s is 20250 megajoule

What is Kinetic energy?

Kinetic energy is the energy possessed by the body by virtue of its motion

If m is the mass of the body and v is the velocity of the body, then kinetic energy is given by the formula

Kinetic energy = [tex]\frac{1}{2} \times m \times v^2[/tex]

Let the mass of the airplane be m kg

Velocity = 220 m/s

Kinetic energy = [tex]\frac{1}{2} \times m \times (220)^2[/tex]

By the problem,

[tex]\frac{1}{2} \times m \times (220)^2 = 10890\times 10^6[/tex]

[tex]m = \frac{10890\times 10^6\times 2}{220\times 220}[/tex]

m = [tex]0.45 \times 10^6[/tex] kg

Now,

Velocity = 300 m/s

Kinetic energy = [tex]\frac{1}{2} \times 0.45 \times 10^6 \times 300 \times 300[/tex]

                        = [tex]20250 \times 10^6[/tex] J

                        = 20250 mega joules

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Using the distributive property, the simplified form of the expression 1/4(12k-4) is 3k-1.

In the given question we have to simplify the given expression.

The given expression is 1/4(12k-4).

To simplify the given expression we use the distributive property.

According to property; a(b+c) = ab+bc

Now simplifying the expression;

1/4(12k-4) = 1/4*12k-1/4*4

1/4(12k-4) = 3k-1

Hence, the simplified form of the expression 1/4(12k-4) is 3k-1.

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The correlation coefficient of points is a negative correlation.

The given coordinates are (1, 9), (2, 7), (3, 6), (4, 1), (7, -2),(8, -5) and (10, -8).

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

• A scatter plot with increasing values of both variables can be said to have a positive correlation.

• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.

The given coordinate points are plotted on graph.

From the graph (scatter plot) we can see that, the points have a negative correlation.

Therefore, the correlation coefficient of points is a negative correlation.

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The shortest total length of fence this can be done with will be 440 m as the total area is 2000 m².

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The distance around an object is called the perimeter. For instance, the yard of your home is fenced in. The fence's length serves as the perimeter. Your fence is 200 feet long if the yard is 50 feet by 50 feet.

Here,

The area=2000 m²

xy=2000

x=2000/y

p=4x+2y

p=4*(2000/y)+2y

=8000/y+2y

p'=-8000/y²+2

-8000/y²+2=0

2y²-8000=0

y²-4000=

y²=4000

y= 20 m

p=8000/20+2*20

p=400+40=440 m

Given that the total area is 2000 m², the shortest total length of fence that can be used is 440 m.

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Answer: b

Step-by-step explanation:

Answer:

He will save 1 cent per pound if he buys the Sweet Sugar brand

The culture starts out with 39 members.

Given that;

After 20 minutes and 40 minutes, a bacteria culture had an 800 and 1700 count, respectively.

To get exponential growth;

We can get growth with an exponential function,

F(t) = A₀[tex]e^k^t[/tex]

Here, k is the growth constant and A₀ is the initial amount of bacteria.

Let;

800 = A₀[tex]e^2^0^k[/tex]  → (I)

1700 = A₀[tex]e^4^0^k[/tex] → (II)

From (I) and (II);

1700 / 800 =  A₀[tex]e^4^0^k[/tex] / A₀[tex]e^2^0^k[/tex]

17/8 = [tex]e^2^0^k[/tex]

For the above equation take the natural log on both sides;

ln(17/8) = ln [tex]e^2^0^k[/tex]

ln(17/8) = 20k

k = ln(17/8) / 20

To get the initial size of the culture;

From (I),

800 = A₀[tex]e^2^0^k[/tex]

800 = A₀e⁰°⁰³⁷⁶ ˣ ²⁰

A₀ = 800 / 20.76

A₀ = 38.53 ≅ 39

Therefore, the initial size of the culture is 39.

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Answer:

Step-by-step explanation: You want to figure out how much it costs per ounce. You’ll divide $4.50/18 ounces to get $0.25 per ounce for the 18 ounce bag and $8.80/40 ounces to get $0.22 per ounce for the 40 ounce bag. The 40 ounce bag is cheaper per ounce.

VZW=64

Step-by-step explanation:

Since the lines are straight the angles are equal. 2x+32=3x+16

Solve this for x.

32=x+16

16=x

Put the value for x (16) in to one of the angle equations

2(16) + 32 = 32 + 32 = 64

The sides of the triangle are 150m, 200m and 250m.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Given: The sides of a triangle are in the ratio of 3:4:5. A man jogged around it 5 times and cover a distance of 3000m.

As man jogged around triangle  5 times and cover a distance of 3000m.

So, the distance for one round is 3000/5 = 600m.

The covered distance is nothing but the perimeter of the triangle.

So, the perimeter of the triangle is 600m.

Let, 3x, 4x, 5x are the sides of the triangle.

⇒ 3x + 4x + 5x = 600

                 12 x = 600

                      x = 50

Therefore,

3x = 3(50) = 150

4x = 4(50) = 200

5x = 5(50) = 250

Hence, the sides of the triangle are, 150m, 200m and 250m.

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The maximum height covered is 32m and the time taken to reach maximum height is 1.25 seconds

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change = change in y / change in x. Rates of change can be positive or negative.

h(t) = -16[tex]t^{2}[/tex] +40t + 7

at maximum height the rate of change of h(t) with respect to t is zero.

so [tex]\frac{dh(t)}{dt}[/tex] = 0

but  [tex]\frac{dh(t)}{dt}[/tex] =  -32t + 40

so,

-32t + 40 = 0

32t = 40

t = 40/32

t = 1.25

to find h(t), we substitute t = 1.25 into the equation above

h(t) = -16[tex](1.25)^{2}[/tex] + 40(1.25) + 7

h(t) = 32m

In conclusion, the maximum height reached is 32m and the time taken to reach maximum height is 1.25 seconds

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The length CT of the line segment is 38 units

From the question, we have the following parameters

CJ = 9x + 1

JT = 2x + 15

Also, we understand that:

Point J is the midpoint of segment CT.

This means that

CJ = CT

So, we have

9x + 1 = 2x + 15

Evaluate the like terms

7x = 14

So, we have

x = 2

Length CT is calculated as

CT = 9x + 1 + 2x + 15

So, we have

CT = 9 x 2 + 1 + 2 x 2 + 15

Evaluate

CT = 38

Hence, the length is 38 units

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The total amount given the original price and tax rate is $33.59

From the question, we have the following parameters:

Original price = $31.69

Sales tax rate = 6%

In order to determine the total sales amount, we make use of the following total sales equation

Total sales = original price + original price * sales tax rate

Substitute the known values in the above equation

So, we have the following equation

Total sales = 31.69 + 31.69 * 6%

Evaluate

Total sales = 33.59

Hence, the total amount is $33.59

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Answer:

$24.50

Step-by-step explanation:

In order to predict the cost of an order with 6 boxes, x has to be equal to 6.

So we have to use the function 3.25x + 5 for [tex]x\geq 6[/tex].

Then, plug in 6 for x and solve.

3.25(6) + 5 = 19.50 + 5 = 24.50

The maximum number of people the lift can safely carry is 8 people.

Given that, the average mass of a man is 84 kg and of a woman is 70 kg.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Now, average = (84+72)/2

= 156/2

= 78

Let the number of people in the left be n.

So, 78n≤620

Divide 78 to both the sides of the inequality

78n/78≤620/78

⇒ n≤7.9

⇒ n≤8

Therefore, the maximum number of people the lift can safely carry is 8 people.

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For the given triangles the length of the missing side x is 56in.

As given in the question,

Two triangles are given ,

Let the triangle with measurement 40in. and 35in. be A and another is B.

In triangle A,

Let missing angle be α

Sum of all the angles in the interior of a triangle is equal to 180°

51°+ 74° + α = 180°

⇒α = 55°

In triangle B.

Let missing angle be β,

74° + 55° + β = 180°

⇒β= 51°

By AAA both the triangles are similar.

Length of corresponding sides are in proportion.

40: x = 35 : 49

⇒x = ( 40×49)/35

⇒x= 56in.

Therefore, for the given triangles the length of the missing side x=56in.

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Reflection in geometry means the type of transformation that flips a shape in a mirror line.

What is reflection ?

Reflection is a type of transformation that flips a shape in a mirror line so that each point is the same distance from the mirror line as its reflected point.

Let us suppose that the triangle with one coordinate  [tex](3,-5)[/tex] and the other two are unknown and we do not even want to know them but it would be better if we do know them:-

And we have a graph.

Let us draw a line [tex]y=-2[/tex] on the graph and draw the triangle

Now the coordinates [tex](3,-5)[/tex] are three boxes away from the line [tex]y=-2[/tex], so we plot this coordinate three boxes up from the line [tex]y=-2[/tex] and do the same for other coordinates so [tex](x,y)[/tex] is one box up from the line [tex]y=-2[/tex] so we plot the coordinates one box up from the line [tex]y=-2[/tex]

Hence, the image is located at [tex]G[/tex] is plotted above.

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Answer:

-7/5 or -1.4

Step-by-step explanation:

Answer:

Step-by-step explanation:

3.4.m+2.4.m.m

4m(3+2m)

Answer:

3 hours

Step-by-step explanation:

The robots are powered coffee alone. They use 2 bags of coffee each day. how long will 1/4 of a bag last them?

1/4 = 0.25

0.25 / 2 = 1/8 or 0.125

0.125 * 24 hours = 3 hours

Answer:

x = 36

The measure of the exterior angle is 114°

The remote interior angles are 24° and 90°.

Step-by-step explanation:

The angle marked 3x + 6 is the exterior angle. The other two marked angles are called "remote interior angles"

The two remote interior angles added together equals the exterior angle.

3x+6 = 24° + 2x + 18

Combine like terms.

3x + 6 = 2x + 42

Subtract 2x from both sides.

x + 6 = 42

Subtract 6 from both sides.

x = 36

If required, use the x=36 to find the measure of the exterior angle.

3(36) + 6

= 108 + 6

= 114°

Or find the measures of the remote interior angles.

2(36) + 18

= 72 + 18

= 90°

The remote interior angles are 24° and 90°.

The cycle in order is D, E, F, B, C then A.

Define life cycle.

An organism goes through a series of shape changes in a biological life cycle before reverting to its original state. The notion contrasts with those of life history, development, and ontogeny in that it emphasizes renewal. Life cycles are common to all animals and plants.

The stages, which frequently entail beginning as a seed, egg, or live birth, then growing up and reproducing, are best shown visually using diagrams. Life cycles keep repeating themselves.

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2(-x - 5) = 12

Step 1 : Expand the bracket.

=> -2x - 10 = 12

Step 2 :Add both side by 10.

=> -2x - 10 + 10 = 12 + 10
=> -2x = 22

Step 3 : Divide both side by -2.

=> -2x : (-2) = 22 : (-2)
=> x = -11

Therefore, x = -11.

Answer:

x = - 11

Step-by-step explanation:

2(- x - 5) = 12 ( divide both sides by 2 )

- x - 5 = 6 ( add 5 to both sides )

- x = 11 ( multiply both sides by - 1 )

x = - 11

The likelihood that the measured distance will be shorter than the actual distance is equal to 0.3085.

In this case, the chance that the measured distance will be less than the true distance will be determined using the z-score formula. The z score is a normal score that adheres to a normal distribution with a mean and standard deviation of 0 and 1, respectively.

Given that,

Mean, μ = 50

Standard deviation, σ = 100

Less than 0% of the time, the overestimation is likely.

Consequently, the necessary probability is P (X ≤ 0)

Now,

P (X ≤ 0) = P [(X − μ) / σ ≤ (0 − μ) / σ]

P (X ≤ 0) = P [Z ≤ (0 − 50) / 100]

P (X ≤ 0) = P [Z ≤ − 0.5]

Excel formula for the probability mentioned above:

=NORMDIST(-0.5,0,1,1)

P (X ≤ 0) = 0.3085

0.3085 is the likelihood that the measured distance will be shorter than the actual distance.

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Answer:

$470

Step-by-step explanation:

%30 of 470 = $141

Answer: $470

I hope it help