the smaller triangle has a perimeter of 31 ft and an area of 40 ft2. if the larger triangle has a perimeter of 62 ft, what will it's area be?

Answer:

Triangle UTS is congruent to Triangle RST.

Step-by-step explanation:

When stating congruence, the corresponding angles and sides must be listed in order. In triangle uts, based on the points, the angle is U, and the side is US. This means that for the other triangle, the first point needs to be the angle, and the last one needs to be the other point for the side. This gives us Triangle UTS is congruent to triangle RST. Hope this helps!

The dimensions of building lot are 396 feet width and 1980 feet length.

Let the width of building lot be x. So, the length of the same building lot will be 5x. According to the formula, the area will be length × width.

18 acre = x×5x

Keep the value of acre in the above mentioned relation

18 × 43,560 = 5x²

Performing multiplication on Left Hand Side of the equation

784,080 = 5x²

Performing division by 5

x² = 156,816

Now taking square root to find the value of x

x = ✓156,816

x = 396 ft

Thus, the width of building lot is 396 feet

The length of building lot = 5×396

Performing multiplication

The length of building lot = 1980 feet

Therefore, the length and width of building lot is 1980 feet and 396 feet respectively.

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\(~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan \theta = \dfrac{LN}{LM}\\\\\\\implies \theta = \tan^{-1} \left( \dfrac{LN}{LM} \right)\\\\\\\implies \theta = \tan^{-1} \left(\dfrac{12.81}{7.72} \right)\\\\\\\implies \theta =58.92^{\circ}\)

Answer:

The time take for the journey can be calculated by dividing the total distance by the distance travelled in an hour.

Which is 2171 (Total distance) / 520 (Distance travelled in a hour)

\(2171/520 = 4.175\)

Which can be rounded of to 4.2

It takes 4.2 hours for the flight between Los Angeles and Toronto

In general, the Divergence Test (nth term test) only allows us to determine whether a series diverges or not. It does not help us to determine the convergence of a series. Therefore, none of the other tests apply to this series.

The Divergence Test (nth term test) states that if the limit of the nth term of a series is not equal to zero, then the series diverges.

The series [infinity] 12 n n=1 is defined as follows:

[infinity] 12 n n=1 = 12¹ + 12² + 12³ + ...

The nth term of this series is given by:

aₙ = 12ⁿ As n → ∞, aₙ → ∞,

which means the limit of the nth term of the series does not exist.

Therefore, the series [infinity] 12 n n=1 diverges by the Divergence Test (nth term test).

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64 - 9 = 55  \sqrt{55}  =  7.4161984871

7.4161984871/2 ≈3.7

Answer:

  D(3.4, 20.8)

Step-by-step explanation:

Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.

The equation for the slope between two points is ...

  m = (y2 -y1)/(x2 -x1)

Using this formula and the given points, we can find D(x, y) to satisfy ...

  2 = (y -10)/(x +2)

  -3 = (y -7)/(x -8)

Putting each of these equations in general form, we have ...

  2(x +2) -(y -10) = 0

  2x -y +14 = 0

and

  -3(x -8) -(y -7) = 0

  3x +y -31 = 0

Adding the two equations eliminates the y-variable:

  (2x -y +14) +(3x +y -31) = 0

  5x -17 = 0 . . . . . . simplify

  x -3.4 = 0 . . . . . . divide by 5

  x = 3.4 . . . . . . . . . add 3.4

Substituting for x in the first equation gives ...

  2(3.4) -y +14 = 0

  y = 6.8 +14 = 20.8 . . . . add y

The point D has coordinates (3.4, 20.8).

__

Additional comment

The graph shows the equations of the lines written in point-slope form.

Answer:

t = 6 km/hour

And, J would be 4 km per hour

Step-by-step explanation:

Let us assume the speed of Tom be T

And, the Speed of Jim  be J

Given that  

T - J = 2 km /hr ...........(i)

After 3 hours distance between them  = 30 km

As they are walking in the opposite direction

Thus,  

Net speed =T + J

L ÷ (T+J) = 3

30 ÷ (T+J) = 3

T +J =10 ..............(2)

After solving these two equations

2T = 12

t = 6 km/hour

And, J would be 4 km per hour

Answer: the circles diameter is 14 meters

Step-by-step explanation:                                {Formula for circumference

2TUR = 43.96                                                      of a circle : L 27UR}

2x3 . 14r = 43.96

r=7

d=2r=2x7=14                                                         {d=2r}  

Answer:

The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.

To find the diameter of the circle, we can use the formula:

d = 2r

where d is the diameter and r is the radius.

Given that the circumference of the circle is 43.96 meters, we can use the formula for circumference to solve for the radius:

C = 2πr

43.96 = 2 × 3.14 × r

r = 43.96 / (2 × 3.14)

r = 6.998 meters

Now we can use the formula for diameter to find the diameter:

d = 2r

d = 2 × 6.998

d = 13.996 meters

Therefore, the diameter of the circle is approximately 13.996 meters.

Step-by-step explanation:

mag delete nito napaka bob0 nya promise

Answer:

abcdefghijklmnopqrstuvwxyz

Answer:

$21.60

Step-by-step explanation:

20% can be written as 0.2

0.2 · $18 = 3.6

Add 3.6 to $18

$18.00 + 3.60 = $21.60

So the answer is $21.60

Hope I helped :)

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By the ASA postulate, it can be said that the triangle ABC and triangle MRQ are congruent. Thus, option B is correct, Yes, they are congruent by either ASA or AAS.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Using Angle Sum Property, in ΔMRQ

<M + <R + <Q= 180

<M + 42 + 85 = 180

<M = 180 -42

<M= 53°

Now, In ΔMRQ and ΔABC  

<A= <R ,

<B = <M

AB = MR

Hence, By ASA criteria ΔMRQ ≅ ΔABC.

Thus, option B is correct, Yes, they are congruent by either ASA or AAS.

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Answer: Yes, they are congruent by either ASA or AAS.

Step-by-step explanation:

Given: After taking the first exam, 15 of the students dropped the class.

Required: To determine whether the given value is a statistic or a parameter.

Explanation: Parameter and statistic are very similar. The parameter is when the complete data of the population is presented. The statistic is when a particular data is used for fraction of the population.

Since it is given that among all the students in the class 15 students dropped out. Hence the given data is Parameter.

Final Answer: Parameter.

The dot plots are plotted and the heights are compared

Given data ,

The heights of the tennis and badminton teams are given

Tennis team’s height (in inches): 66, 67, 69, 70, 71, 73, 73, 74, 75, 75, 76

Range: 10

Mean: 71.73

Median: 73.00

Mode: [73,75]

Badminton team’s heights (in inches): 62, 62, 65, 66, 68, 71, 73

Range: 11

Mean: 66.71

Median: 66.00

Mode: [62]

Now , each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value.

So , the frequency of the plots are given

Hence , the dot plots are plotted and the graph is given

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Answer:

8673404

Step-by-step explanation:

Your commas are in the wrong spots. If the question is asking the profit then it would be 15,548,000 - 6,974,596 = 8,673,404

I am not sure what it means when asking how much money was saved. Is this the complete question and the exact wording?

The number of lollipops in a container is 206.

These are steps to find the number of lollipops in a container:

1. Let x be the number of lollipops in a packet and 2x be the number of lollipops in a container.

2. According to the given information, we have the equation: 2(2x) + 3x = 721

3. Simplify the equation: 4x + 3x = 721 7x = 721

4. Solve for x: x = 103

5. Substitute x back into the equation to find the number of lollipops in a container: 2x = 2(103) = 206 Therefore, the number of lollipops in a container is 206.

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The minimum number of masthead lights for the given vessel is 2.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
A towing vessel 35 meters in length, with a tow 100 meters astern,

Masthead lights = total length of the tow / total length of the vessel
                        = 100 / 35 = 2.85

So, the Number of Masthead lights for the given vessel is 2 ≤ x ≤ 3.
And a minimum number of masthead lights is 2.

Thus, the minimum number of masthead lights for the given vessel is 2.

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Evaluating this double integral will give us the surface area of the part of the paraboloid y = x^2 + z^2 that lies inside the cylinder x^2 + z^2 = 16.

To find the surface area of the part of the paraboloid y = x^2 + z^2 that lies inside the cylinder x^2 + z^2 = 16, we can use the concept of surface area integration.

The given paraboloid can be written in the form:

y = f(x, z) = x^2 + z^2

The surface area element can be expressed as:

dS = √(1 + (∂f/∂x)^2 + (∂f/∂z)^2) dA

Where (∂f/∂x) and (∂f/∂z) are the partial derivatives of f(x, z) with respect to x and z, respectively, and dA is the infinitesimal area element in the x-z plane.

Let's calculate the partial derivatives:

(∂f/∂x) = 2x

(∂f/∂z) = 2z

Substituting these values into the surface area element equation, we have:

dS = √(1 + (2x)^2 + (2z)^2) dA

= √(1 + 4x^2 + 4z^2) dA

Now, we need to determine the limits of integration for x and z.

Since the paraboloid lies inside the cylinder x^2 + z^2 = 16, we can rewrite the cylinder equation as:

z = √(16 - x^2)

The limits of integration for x will be from -4 to 4, and for z, it will be from -√(16 - x^2) to √(16 - x^2).

Now, we can integrate the surface area element over these limits to find the total surface area.

S = ∫∫√(1 + 4x^2 + 4z^2) dA

= ∫[-4,4]∫[-√(16 - x^2),√(16 - x^2)] √(1 + 4x^2 + 4z^2) dz dx

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Answer:

the answser is A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to 8.

Step-by-step explanation:

The explanation is i got it right

Answer:

Its A

Step-by-step explanation:

Cuz i got it right

The recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs.

A recursive definition of a function is when the definition of the function involves the function itself. This type of definition is used to express complex operations in a simpler form. It is an effective way to break down a complicated problem into simpler, manageable parts. It allows us to define a set of rules in terms of smaller versions of itself, which can then be worked out using a series of steps.

A recursive definition for the function f is a process by which the value of f for a given input can be defined in terms of the values of f for smaller inputs. In other words, a recursive definition for f is a definition that describes how f can be calculated from its inputs.

In this case, the recursive definition for the function f is given by:

f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3

This means that the value of f for a given x can be calculated by multiplying 500 (the value of f for x = 1) by 1/5 raised to the power of x-1. This is because f(1) = 500, f(2) = 100 (1/5 * 500), and f(3) = 20 (1/5 * 1/5 * 500).

This recursive definition can also be expressed in a more general form as:

f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3

Where a and b are constants. In this case, a is 500 and b is 1/5.

In conclusion, the recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs. This definition can also be expressed in the more general form of f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3.

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Answer:

x =98

Step-by-step explanation:

Extend the line in the upper part.

By Alternate interior angle theorem, the alternate interior angle would be 62°.

By Linear pair theorem the angle beside 144° is supplementary, and therefore is equal to 36°.

Finally, the line would create a triangle, which means that we can use that to solve for the linear pair of x°

Recall that the sum of the interior angle of a triangle is 180°  

Therefore that angle is

36° + 62° + third angle in triangle = 180°

98° + third angle in triangle = 180°

third angle in triangle = 180° - 98°

third angle in triangle = 82°

Now that we know the measurement of the linear pair of x°, we can conclude that

x° + 82° = 180°

x° = 180° - 82°

x° = 98°

Therefore, x° = 98°

(If you have any question please let me know)

Answer:

Step-by-step explanation:

so we can make a system of equations

y=hotdogs

x=hamburgers

you need a combination that sums to 23, so add the two and get 23:

y+x=23

and then you need to account for how much money you have and the cost.

1.50x+1.10y=32.10

still working on it, will edit in rest so that you can see what I did

Answer:

Answer:

52,000 to the nearest thousand

Answer:

52,000

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

3x + 9 = 25x + 14

-3x         -3x

9 = 22x + 14

-14         - 14

-5 = 22x

Answer:

9.30

Step-by-step explanation:

Using SOHCAHTOA

tan=opposite/adjacent

tan25°=x/20

tan 25°=0.4663

0.4663=x/20

cross multiply

x=0.4663*20

x=9.326

to the nearest tenth=9.30

1) 3,500 rounded to the nearest ten thousand is 0.

2) 462,183.5062749 rounded to the nearest tenth is 462,183.5.

3) 6 + (-3) - 5 is equal to -2.

QUESTION 1:The given number is 3,500. To round it to the nearest ten thousand, we need to see which ten thousand is closest to the number. In this case, 3,500 is between 0 and 10,000. Since 0 is closer, we round down to 0. So, 3,500 rounded to the nearest ten thousand is 0.

QUESTION 2: To round the given number, 462,183.5062749, to the nearest tenth, we need to look at the digit in the hundredths place (the second digit after the decimal point), which is 0. Since 0 is less than 5, we round down the digit in the tenths place to 3.

Therefore, 462,183.5062749 rounded to the nearest tenth is 462,183.5.

QUESTION 3:We have to evaluate 8 to the 8th power. That means we have to multiply 8 by itself 8 times. Using a calculator, we can find that 8^8 is equal to 16,777,216.

QUESTION 4:When solving the expression 6 + (-3) - 5, we should follow the order of operations, which is: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Since there are no parentheses or exponents in this expression, we can simply perform addition and subtraction from left to right.

6 + (-3) = 3, then 3 - 5 = -2.

Therefore, 6 + (-3) - 5 is equal to -2.

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