Pedro’s book weighs 19 4 pounds. Blanca’s book weighs 17 7 pounds. Use estimation to determine about how much more Pedro’s book weighs than Blanca’s. 1 lb 2 lbs 6 lbs 7 lbs

The probability that Paxon loses all four games is 16/81.

In the games played between the Rattlesnake and Paxon colleges, the probability of each team winning the game is 2/3 and 1/3 respectively.

We find the probability that Paxon loses all four games.

Firstly, we can find the probability of Paxon losing a single game as:

P(Paxon loses) = 1 - P(Paxon wins)

P(Paxon loses) = [tex]1-\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex]

To find the probability that Paxon loses all four games, we can assume that the events of losing a game are independent of each other.

This means that losing one game doesn't affect the probability of losing another game.

P(Paxon loses all 4 games) = P(Paxon loses game 1) × P(Paxon loses game 2) × P(Paxon loses game 3) × P(Paxon loses game 4)

P(Paxon loses all 4 games) = [tex](\frac{2}{3} )\times(\frac{2}{3} )\times(\frac{2}{3} )\times(\frac{2}{3} )[/tex]

P(Paxon loses all 4 games) = [tex]\frac{16}{81}[/tex]

Therefore, the probability that Paxon loses all four games is 16/81.

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The perimeter of the triangle is 52 units where x = 4.5

To find the perimeter we have to find x. To solve for both x and the perimeter we use the knowledge of tangents to a circle

The formula below exists due to relationship between tangents

2x = 9

x = 4.5

Also, QU = 4, and UR = 13

The perimeter is solved by adding all the sides

= (9 + 4) + (9 + 13) + (4 + 13)

= 13 + 22 + 17

= 52 units

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An inequality that represent the values of x that ensure triangle ABC exists is: A. 7/4 < x < 11/2.

In Mathematics, the Triangle Inequality Theorem is a type of theorem which states that the sum of any two side lengths of a triangle must be greater than the measure of the third side.

Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, we have:

2x + 4 + 6x > 18

8x > 18 - 4

x > 14/8

x > 7/4

6x - (2x + 4) > 18

4x > 18 + 4

x > 22/4

x > 11/2

Therefore, we have 7/4 < x < 11/2.

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Answer:

Ingredient | 4 servings | 2 servings | 8 servings

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

flour (c)      |        1          |       1/2       |        2          

sugar (c)    |       3/4       |       3/8      |       3/2                

butter (T)   |        1          |       1/2       |        2          

salt (t)        |        1/4       |       1/8       |        1/2  

Step-by-step explanation:

4 servings:

1 c flour

3/4 c sugar

1 T butter

1/4 t salt

2 serving = 4 servings / 2 =

1 c flour/2 = 1/2 c flour

3/4 c sugar/2 = 3/8 c sugar

1 T butter/2 = 1/2 T butter

1/4 t salt/2 = 1/8 t salt

8 servings = 4 servings * 2 =

1 c flour * 2 = 2 c flour

3/4 c sugar * 2 = (3*2)/4 = 3/2 c sugar

1 T butter * 2 = 2 T butter

1/4 t salt * 2 = 2/4 = 1/2 t salt

Table:

Ingredient | 4 servings | 2 servings | 8 servings

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

flour (c)      |        1          |       1/2       |        2          

sugar (c)    |       3/4       |       3/8      |       3/2                

butter (T)   |        1          |       1/2       |        2          

salt (t)        |        1/4       |       1/8       |        1/2          

The event definition that corresponds to exactly one outcome of the experiment is selecting a specific number on the die and drawing a specific card from the set. For example, if the event definition is "rolling a 3 on the die and drawing the card numbered 7," this corresponds to exactly one outcome in the experiment.

In this experiment, there are six possible outcomes for rolling the die (numbers 1 to 6) and ten possible outcomes for drawing a card (numbers 1 to 10).

When we specify a particular number on the die and a particular card from the set, we narrow down the possible outcomes to only one combination. This means that there is only one way this event can occur, making it a single outcome event.

For instance, if we define the event as "rolling a 4 on the die and drawing the card numbered 5," there is only one instance where this can happen.

If the die lands on 4 and the card drawn is number 5, then the event has occurred. Any other combination of numbers on the die or cards from the set would not satisfy this event definition.

Therefore, by specifying a particular number on the die and a specific card from the set, we create an event definition that corresponds to exactly one outcome in the experiment.

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sin ∠MQP = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{MQ}{MP}[/tex].

To determine the value of sin ∠MQP, we need to use the given information about the triangle.

Since we know the measures of angles MQP and MQN, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle QMP.

Let's calculate it:

Angle MQP + Angle MQN + Angle NQM = 180 degrees

56 degrees + 90 degrees + Angle NQM = 180 degrees

Simplifying the equation:

146 degrees + Angle NQM = 180 degrees

Subtracting 146 degrees from both sides:

Angle NQM = 180 degrees - 146 degrees

Angle NQM = 34 degrees

Now, we have all the angles needed to calculate sin ∠MQP.

The sine function relates the lengths of the sides of a right triangle to its angles.

In this case, we are interested in the side opposite to ∠MQP, which is side MQ, and the hypotenuse, which is side MP.

Therefore, sin ∠MQP = opposite/hypotenuse = MQ/MP.

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For the expression [tex]x^64 + ax^b + 25[/tex] to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = [tex]y^2.[/tex]

To determine the values of a and b such that the expression[tex]x^64 + ax^b[/tex] + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of[tex](x^n)^2,[/tex] where n is an even integer.

Let's examine the given expression: [tex]x^64 + ax^b[/tex] + 25

For it to be a perfect square, the quadratic term [tex]ax^b[/tex]must have the same exponent as the leading term[tex]x^6^4.[/tex] This means b must be equal to 64.

So we have:[tex]x^64 + ax^64 + 25[/tex]

Now, we can rewrite this as:[tex](x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2[/tex]

By comparing this with the standard form of a perfect square, ([tex]x^n +\sqrt{k} )^2[/tex], we can deduce that √a must be equal to x^32 and [tex]\sqrt{25}[/tex] must be equal to [tex]\sqrt{k.}[/tex]

Therefore, we have: [tex]\sqrt{a} = x^3^2[/tex]and[tex]\sqrt{25} = \sqrt{k}[/tex]

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: [tex]\sqrt{a} = x^3^2[/tex]

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =[tex]y^2[/tex], where y is an integer.

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The equation that represents the total cost of purchasing currency is 1.40x + 1.50y = 3400.00.

The equation that represents the relationship between the number of currency A and number of currency B is x = 5y.

x = 2000 and y = 400

There are 2000 of currency A and 400 of currency B

In order to write a system of linear equations to describe this situation, we would assign variables to the number of currency A and currency B, and then translate the word problem into an algebraic equation as follows:

Since she budgeted $3400.00 for spending money on an upcoming trip and currency A is trading at $1.40 per euro, and currency B is trading at $1.50 per pound, a system of linear equations to describe this situation is given by;

1.40x + 1.50y = 3400.00

x = 5y

1.40(5y) + 1.50y = 3400.00

8.5y = 3400

y = 3400/8.5

y = 400

x = 5y

x = 5(400)

x = 2000

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Mr. Williams takes (total number of questions) / 8 minutes to complete his homework, Miss Hymers takes (total number of questions) / 6 minutes to complete her homework, and the lowest number of questions they could have done is 24.

To find the number of minutes it takes for each of them to complete their homework, we can divide the total number of questions by the number of questions they complete per minute.

For Mr. Williams, he completes 8 questions per minute, so if we divide the total number of questions by 8, we will get the number of minutes it takes for him to complete his homework.

Similarly, for Miss Hymers, she completes 6 questions per minute, so if we divide the total number of questions by 6, we will get the number of minutes it takes for her to complete her homework.

To find the lowest number of questions they could have done if they both completed the same amount of questions and worked for an exact number of minutes, we need to find the least common multiple (LCM) of 8 and 6. The LCM of 8 and 6 is 24. Therefore, the lowest number of questions they could have done is 24.

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The quotient when (16x^4 + 40x^3 − 24x^2) is divided by 8x^2 is 2x^2 + 3x - 5.

To find the quotient when (16x^4 + 40x^3 − 24x^2) is divided by 8x^2, we perform polynomial long division.

We divide each term of the dividend by the divisor and simplify the result. The steps are as follows:

             2x^2

8x^2 | 16x^4 + 40x^3 - 24x^2

- (16x^4 + 0x^3)

40x^3 - 24x^2

- (40x^3 - 0x^2)

-24x^2

The division process ends here, as the degree of the remaining term (-24x^2) is less than the degree of the divisor (8x^2).

Therefore, the quotient is 2x^2.

Hence, the correct answer is option A: 2x^2 + 3x - 5.

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The reflected figure is labeled figure C is B: A is congruent to A, B is congruent to B, C is congruent to C. The correct answer is B: A is congruent to A, B is congruent to B, C is congruent to C.

To explain why figure A is congruent to figure C, we need to understand the transformations that were applied to create each figure.

In the given scenario, figure A was translated 3 units to the right and 2 units up to create figure B. This means that every point in figure A was shifted horizontally by 3 units to the right and vertically by 2 units up to obtain the corresponding points in figure B.

Next, figure B was reflected over the x-axis to create figure C. This reflection flips the figure vertically, so the y-coordinates of each point are negated while the x-coordinates remain the same.

Now, if we compare the coordinates of figure A and figure C, we can see that the x-coordinates of each point in figure C are the same as in figure A, while the y-coordinates are negated. This means that the two figures have the same shape and size, just positioned differently on the coordinate plane.

Therefore, we can conclude that figure A is congruent to figure C because they have the same shape and size, even though they are located in different positions on the coordinate plane.

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The Laplace transform of the given function is L{(2+6)te^((2+0)t)+(3+0)sin3t}. Simplifying the expression inside the Laplace transform, we get L{8te^(2t)+3sin3t}.

The Laplace transform of te^(at) is (s-a)^(-2) and the Laplace transform of sin(at) is a/(s^2+a^2). Substituting these values into the expression, we get:

L{8te^(2t)+3sin3t} = 8(s-2)^(-2) + 3(3/(s^2+9)) = 8/(s-2)^2 + 9/(s^2+9)

This is the simplified form of the Laplace transform of the given function.

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The ordered triple representing [tex]3u - 2v[/tex] is [tex](13, -8, 5)[/tex].

To find an ordered triple representing [tex]3u - 2v[/tex],

where [tex]u = (5, -2, 3)[/tex] and [tex]v = (1, 1, 2)[/tex],

we can perform the following operations:

[tex]3u = 3(5, -2, 3)[/tex]

[tex]3u = (15, -6, 9)[/tex]

[tex]2v = 2(1, 1, 2)[/tex]

[tex]2v = (2, 2, 4)[/tex]

Now, subtracting 2v from 3u gives:

[tex]3u - 2v = (15, -6, 9) - (2, 2, 4)[/tex]

[tex]3u - 2v = (15-2, -6-2, 9-4)[/tex]

[tex]3u - 2v = (13, -8, 5)[/tex]

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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Step-by-step explanation:

The equation of rectangular coordtion given polar coordinates are

[tex]x = r \cos( \alpha ) [/tex]

[tex]y = r \sin( \alpha ) [/tex]

R is 2, and alpha is 5pi/4

So

[tex]x = 2 \cos( \frac{5\pi}{4} ) = - \sqrt{2} [/tex]

[tex]y = 2 \sin( \frac{5\pi}{4} ) = - \sqrt{2} [/tex]

So our rectangular coordinates are

[tex]( - \sqrt{2} , - \sqrt{2} )[/tex]

To convert from rectangular coordinates to polar coordinates

[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

[tex] \alpha = \tan {}^{ - 1} ( \frac{y}{x} ) [/tex]

Since the point (3,-2), is in the fourth quadrant, our angle should be within (270 and 360 degrees)

[tex]r = \sqrt{ {3}^{2} + ( - 2) {}^{2} } = \sqrt{13} [/tex]

[tex] \alpha = \tan {}^{ - 1} ( - \frac{2}{3} ) [/tex]

We about about

[tex] \alpha = 326.31[/tex]

So our polar coordinates are

[tex]( \sqrt{13} ,326.31)[/tex]

The second entry is in degrees. If you need to convert to radians, let me know

The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.

To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.

Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.

Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).

Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).

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A careful examination of the residual plot is crucial in determining the goodness of fit for the linear model.To determine whether the linear model from the regression calculator is a good model, we need to analyze the residual plot.

A residual plot is a graphical representation of the differences between the observed values and the predicted values from the linear model.

If the residual plot exhibits random scatter around the horizontal line (y = 0) with no discernible pattern, it suggests that the linear model is a good fit for the data. This indicates that the model captures the underlying linear relationship between the variables adequately, and the residuals have no systematic bias or trend.

However, if the residual plot displays a distinct pattern, such as a curved shape, a funnel shape, or an increasing/decreasing trend, it indicates that the linear model may not be appropriate. In such cases, the model may not be capturing all the relevant information or may be missing higher-order relationships.

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The accurate description of the scatterplot would be: "Lower high school GPAs correlate to lower college GPAs, with one exception of a low high school GPA and high college GPA."

The correct answer is D.

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The given system of linear equations is represented by two lines on the coordinate plane. The first line passes through points (0,2) and (2,3), while the second line passes through points (0,-3) and (2,-2).

To determine the number of solutions the system has, we need to analyze the relationship between these lines.
1. If the lines intersect at a single point, the system has one solution.
2. If the lines are parallel and never intersect, the system has no solution.
3. If the lines coincide and overlap, the system has infinitely many solutions.

Let's find the slopes of both lines:

The slope of the first line is given by (change in y) / (change in x) = (3-2) / (2-0) = 1/2.

The slope of the second line is given by (change in y) / (change in x) = (-2-(-3)) / (2-0) = 1/2.

Since the slopes of the two lines are equal, we can determine that the lines are parallel. Therefore, the system has no solution, as parallel lines never intersect.

In conclusion, the system of linear equations represented by the given graph has no solutions.

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The system of linear equations shown in the graph has no solutions.

To determine the number of solutions, we need to analyze the relationship between the lines.
If the two lines intersect at a single point, the system has one solution. This means that the lines are not parallel and have different slopes.
If the two lines are parallel and do not intersect, the system has no solutions. This occurs when the slopes of the lines are equal but the y-intercepts are different.
If the two lines are the same, they are coincident and have infinitely many solutions. This happens when the slopes and y-intercepts of the lines are equal.
To find the slope of a line, we can use the formula: slope = (change in y)/(change in x). We can use the given points to calculate the slopes of the two lines.
Line 1: (0, 2) and (2, 3)
Slope = (3-2)/(2-0) = 1/2
Line 2: (0, -3) and (2, -2)
Slope = (-2-(-3))/(2-0) = 1/2
The slopes of the two lines are equal, which means they are parallel. However, the y-intercepts of the lines are different (2 for Line 1 and -3 for Line 2). Therefore, the system of linear equations has no solutions.

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Answer:

Measure of AC is 150°

Step-by-step explanation:

Given : ∠ABC = 75°

To Find : Arc AC

Solution :

Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of the intercepted arc.

So, using this theorem

ABC=1/2 arc (AC)

->75=1/2 arc (AC)

->75= * 2=arc(AC)

->150=arc(AC)

Arc AC = 150°

BAM, Measure of AC is 150°

your welcome :)

im probably wrong cause i needed like 50 people to help but i hope this helps </33333333

Answer: 6

Step-by-step explanation:

85-79=6

Answer:

6

Step-by-step explanation:

85-79=6

a) The operating costs can be computed using multiplication and addition as follows:

Depreciation costs = $590

Repairs & Maintenance = $230

Gas & Oil = $280

Insurance = $230

Federal and State Taxes and Levies = $110

Total operating costs = $1,440

b) The depreciation for this vehicle using method 2 will be $590.

The operating costs and depreciation are computed using the mathematical operations of multiplication and addition.

The depreciation cent per mile = 5.9 cents = 0.059 (5.9/100)

The miles driven = 10,000

Year driven = third

Depreciation costs = $590 ($0.059 x 10,000)

Repairs & Maintenance = $230 ($0.023 x 10,000)

Gas & Oil = $280 ($0.028 x 10,000)

Insurance = $230 ($0.023 x 10,000)

Federal and State Taxes and Levies = $110 ($0.011 x 10,000)

Total operating costs = $1,440 ($0.144 x 10,000)

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The distance along the ground between the building and the pilot is approximately 92.19 feet (rounded to the nearest tenth).

To find the distance along the ground between the building and the pilot, we can use trigonometry.

We have the following information:

Angle of elevation (θ) = 38°

Distance from the building to the pilot (opposite side) = 72 ft

We need to find the adjacent side, which represents the distance along the ground.

Using the trigonometric function tangent (tan), we can set up the following equation:

tan(θ) = opposite/adjacent

tan(38°) = 72/adjacent

To find the adjacent side, we rearrange the equation:

adjacent = 72 / tan(38°)

Using a calculator, we can evaluate this expression:

adjacent ≈ 72 / 0.7813 ≈ 92.19 ft

Therefore, the distance along the ground between the building and the pilot is approximately 92.19 feet (rounded to the nearest tenth).

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Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

Answer is [tex]2\sqrt{2}[/tex] mi

Given,

Kaylib’s eye-level height is 48 ft

Addison’s eye-level height is 85 and one-third ft above sea level.

From the formula d= [tex]\sqrt{3h/2}[/tex],

get the difference as:

[tex]d=\sqrt{(3*(85+1/3))/2} - \sqrt{(3*48)/2}[/tex]

=[tex]\sqrt{256/2} - \sqrt{3*24}[/tex]

=[tex]\sqrt{128} - 6\sqrt{2}[/tex]

=[tex]8\sqrt{2} - 6\sqrt{2}[/tex]

d=[tex]2\sqrt{2}[/tex]

Therefore, Addison sees [tex]2\sqrt{2}[/tex]mi to the horizon

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The velocity of the body is[tex]v = 108t + t^4[/tex], and the acceleration of the body is a = [tex]108 + 4t^3[/tex].

Given:S(t) = [tex]62.6 + 54t^2 + 0.2t^5[/tex]We are supposed to determine the velocity and acceleration of the body at a given distance.Solution:Velocity v is the derivative of displacement with respect to time, that is[tex],v = S'(t).[/tex]

Let us find the derivative of S(t)dS(t)/dt = [tex]d(62.6)/dt + d(54t^2)/dt + d(0.2t^5)/dt[/tex]We know that d/dt(C) = 0 (where C is a constant)The derivative of 62.6 is zero.[tex]d(54t^2)/dt = 108tandd(0.2t^5)/dt = t^4[/tex]Using the above derivations, the velocity of the body at any given time t is given by,[tex]v = dS(t)/dt = 108t + t^4.[/tex]

The acceleration of the body is the derivative of velocity with respect to time, that is,[tex]a = v'(t)[/tex]Again, let us differentiate[tex]v w.r.t t,dv/dt = d(108t)/dt + d(t^4)/dt = 108 + 4t^3[/tex]Using the above derivation, the acceleration of the body at any given time t is given by[tex],a = dv/dt = 108 + 4t^3.[/tex]

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Answer:

false

Step-by-step explanation:

A ⊆ B if every element in A is in B

For the question,

A = {4, 5, 6, 7}

B = {4, 5}

Since all the elements in A are not in B

A [tex]\nsubseteq[/tex] B

Therefore the statement is false

Answer:

The statement is false.

Step-by-step explanation:

The symbol ⊆ is used in set theory to represent the subset relationship.

The notation A ⊆ B signifies that set A is a subset of set B, indicating that every element of set A is also present in set B.

The given statement {4, 5, 6, 7} ⊆ {4, 5} states that the numbers in the first set are also present in the second set.

The statement is false, as the first set {4, 5, 6, 7} contains the numbers 6 and 7 that are not present in the second set {4, 5}. Therefore, {4, 5, 6, 7} is not a subset of {4, 5}, and the statement is false.

Answer:

x = 150 , y = 30 , z = 60

Step-by-step explanation:

x and 30° are same- side interior angles and sum to 180° , that is

x + 30 = 180 ( subtract 30 from both sides )

x = 150

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

x and y are a linear pair and sum to 180° , that is

x + y = 180

150 + y = 180 ( subtract 150 from both sides )

y = 30

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

since EF and EG are congruent then Δ EFG is isosceles with base angles congruent , then

2 = y = 30

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

z is an exterior angle of Δ EFG , then

z = ∠ 2 + ∠ y = 30 + 30 = 60

90% confident that the population mean falls within the range of $119.26 to $128.74 and the width of the 90% confidence interval is $9.48.

To construct a 90% confidence interval for the population mean, we can use the formula:
Confidence interval = sample mean ± (critical value * (population standard deviation / sqrt(sample size)))
Given that the sample mean is $124.00, the population standard deviation is $18.20, and the sample size is 40, we need to find the critical value for a 90% confidence level.
Using a table or a calculator, the critical value for a 90% confidence level is approximately 1.645.
Plugging in the values into the formula, we get:
Confidence interval = $124.00 ± (1.645 * ($18.20 / sqrt(40)))
Calculating the value inside the parentheses, we get:
Confidence interval = $124.00 ± (1.645 * ($18.20 / 6.324555))
Simplifying the expression inside the parentheses, we get:
Confidence interval = $124.00 ± (1.645 * $2.884)
Calculating the value inside the parentheses, we get:
Confidence interval = $124.00 ± $4.74298
Rounding the confidence interval to two decimal places, we get:
Confidence interval = ($119.26, $128.74)
This means that we can be 90% confident that the population mean falls within the range of $119.26 to $128.74.
To compare the widths of the confidence intervals, we can calculate the difference between the upper and lower limits of the confidence intervals.
For the 90% confidence interval, the width is calculated as:
Width = Upper limit - Lower limit
Width = $128.74 - $119.26
Width = $9.48

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The equivalent expression is [tex]X^5 * Y^{(-4)} - 2.[/tex]

The expression can be simplified as follows:

[tex]X^(-4) * Y / (X^{(-9)} * Y^5) - 2[/tex]

To simplify this expression, we can use the properties of exponents. When dividing terms with the same base, we subtract the exponents:

[tex]X^{(-4)} / X^{(-9)} = X^{(-4 - (-9))} = X^5[/tex]

Similarly, when dividing terms with the same base, we subtract the exponents:

[tex]Y^1 / Y^5 = Y^{(1 - 5)} = Y^{(-4)}[/tex]

Substituting these simplifications back into the expression:

[tex]X^5 * Y^{(-4)} - 2[/tex]

So, the equivalent expression is [tex]X^5 * Y^{(-4)} - 2.[/tex]

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The length of segment EA, considering the trigonometric ratios in this problem, is given as follows:

146 units.

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

As the tangent of 45º is of 1, on a triangle with an angle of 45º, the two sides have equal measure, hence the length of BA is given as follows:

BA = 64.

Applying the segment addition postulate, the length of AG is given as follows:

AG + 64 = 137

AG = 137 - 64

AG = 73.

73 is adjacent to the angle of 60º, while EA is the hypotenuse, hence the length of EA is given as follows:

cos(60º) = 73/EA

1/2 = 73/EA

EA = 2 x 73

EA = 146 units.

A similar problem, also about trigonometric ratios, is given at brainly.com/question/24349828

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