In Exercises 3-6, find the indicated measure. Explain your reasoning. Show your work

The equation that has no solution is 2x+1=5x-3.

To find out which equation has no solution, we can use the process of elimination. First, let's look at the equation 2(x-7)=2x-14. If we simplify this equation, we get:
2x-14=2x-14
This equation is true for all values of x, so it has infinitely many solutions.

Next, let's look at the equation 15x-30=0. If we simplify this equation, we get:
15x=30
x=2
This equation has one solution, x=2.

Now, let's look at the equation 2x+1=5x-3. If we simplify this equation, we get:
-3x=-4
x=4/3
This equation has one solution, x=4/3.

Finally, let's look at the equation 3(2x+1)=6x+1. If we simplify this equation, we get:
6x+3=6x+1
3=1

This equation is never true, so it has no solution.

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The state income tax owed on a $40,000 per year salary is $1,500.

What is income tax?

A tax levied against people or organizations (taxpayers) in relation to their income or profits is known as an income tax. (commonly called taxable income). Tax rates multiplied by taxable income are typically used to calculate income taxes. Tax rates might change depending on the taxpayer's attributes and source of income.

To calculate the state income tax owed on a $40,000 per year salary, we need to determine which progressive tax range it falls into and apply the corresponding tax rate.

Since $40,000 falls within the range of $10,001 - $50,000, we will use the tax rate of 5% for this portion of the income.

First, we need to calculate the amount of income within this range -

$40,000 - $10,000 = $30,000

Next, we calculate the amount of tax owed on this portion of the income -

$30,000 x 0.05 = $1,500

Therefore, the value is obtained as $1,500.

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On dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -

h(x) = x² + 3x - 3 + 7/(x + 4).

Division algorithm states that -

Dividend = (Divisor x Quotient) + Remainder

Given is to find the remainder when -

(x³ + 7x² + 9x - 5) ÷ (x + 4)

We can write -

f(x) = (x³ + 7x² + 9x - 5)

g(x) = (x + 4)

So -

h(x) = f(x) ÷ g(x)

h(x) = (x³ + 7x² + 9x - 5) ÷ (x + 4)

h(x) = (x³ + 4x² + 3x² + 9x - 5)/(x + 4)

h(x) = x² + (3x² + 9x - 5)/(x + 4)

h(x) = x² + 3x + (-3x - 5)/(x + 4)

h(x) = x² + 3x - 3 + 7/(x + 4)

Therefore, on dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -

h(x) = x² + 3x - 3 + 7/(x + 4).

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In the word problem, the time (in seconds) the ball was in the air is D)0.50 seconds.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here expression which describes height is,

h(t)= [tex]-18t^2+3t+2[/tex]

Now h(t)=0 then,

=> [tex]-18t^2+3t+2=0[/tex]

=> [tex]18t^2-3t-2=0[/tex]

=> [tex]18t^2-3t=2[/tex]

=> 3t(6t-1)=2

=> 3t=2 , 6t-1=2

=> t=2/3 , 6t=3

=> t=2/3 , t=1/2

=> t= 0.5 seconds.

Hence  the time (in seconds) the ball was in the air is D)0.50 seconds.

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Lucky duck probabilities include:

A duck with a number:

Every duck has a number, so the probability of choosing a duck with a number is certain (1/1 or 100%).

A duck with a number greater than 10:

is 2/12 or 1/6, since there are 2 ducks with numbers greater than 10 out of a total of 12 ducks.

Duck number 4:

There is only one duck with the number 4, so the probability of choosing this duck is 1/12.

A duck with sunglasses:

There are no ducks with sunglasses so the probability is impossible.

A duck with a hat:

We don't know how many ducks wear hats, so we cannot determine the probability.

An even-numbered duck:

There are 6 even-numbered ducks (2, 4, 6, 8, 10, 12) out of 12 ducks in total, so the probability of choosing an even-numbered duck is 6/12, which simplifies to 1/2.

A duck with a number less than 7:

There are 6 ducks with a number less than 7 (1, 2, 3, 4, 5, 6) out of 12 ducks in total, so the probability of choosing a duck with a number less than 7 is 6/12, which simplifies to 1/2.

A duck with a mustache:

There are no ducks with mustaches, so the probability of getting a duck with a mustache is impossible, 0.

A duck with a bow tie:

Ducks with bowties are 8, so the probability of choosing a duck with bowtie is likely 8/12, 2/3

A duck with a number lower than 25:

All ducks have a number lower than 25, so the probability of choosing a duck with a number lower than 25 is certain (1).

A duck with a number greater than 5:

There are 7 ducks with a number greater than 5 (6, 7, 8, 9, 10, 11, 12) out of 12 ducks in total, so the probability of choosing a duck with a number greater than 5 is 7/12.

A duck with number that's a multiple of 3:

There are 4 ducks with a number that's a multiple of 3 (3, 6, 9, 12) out of 12 ducks in total, so the probability of choosing a duck with a number that's a multiple of 3 is 4/12, which simplifies to 1/3.

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Answer:

x = 5

Step-by-step explanation:

 5x - 7 = 3x + 3

- 3x        -3x

2x - 7 =         3

      +7           +7

 2x =              10

Divide 2 from both sides

x = 5

Answer: 10

Step-by-step explanation:

2x - 7 = 3

add 7 to both sides = 2x = 10

now to solve:

once u have 2x = 10

divide both sides by 2

x=5

The lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years is $25,447.09.

To find the lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years, we can use the formula for compound interest;

A = P(1 + r/n)^(nt)

Where:
- A is the final amount
- P is the initial principal amount
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the number of years

Plugging in the given values, we get:

61,000 = P(1 + 0.07/12)^(12*13)

Solving for P, we get:

P = 61,000 / (1 + 0.07/12)^(12*13)

P = 61,000 / (1.00583)^156

P = 61,000 / 2.39717

P = 25,447.09

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Given the box and whiskers plot with the given data, the five number summary would be :

Arrange the numbers in order from smallest to largest:

2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15

The minimum number is therefore 2.

First Quartile Q1 = 4 :

= ( 15 + 1 ) / 4

= 4 th position

Median :

= ( 15 + 1 ) / 2

= 8 th position which is 8

Third quartile :

= ( 15 + 1 ) x 3 / 4

= 12 th position which is 13.

Maximum value is 15.

Move the box plot to correspond with these figures.

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Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.

To find the standard deviation of BMI for the 9 patients in the study, we need to follow these steps:
Find the mean of the BMI scores: (25 + 27 + 31 + 33 + 26 + 28 + 38 + 41 + 24) / 9 = 29.67
Subtract the mean from each BMI score to find the deviation: -4.67, -2.67, 1.33, 3.33, -3.67, -1.67, 8.33, 11.33, -5.67
Square each deviation: 21.81, 7.13, 1.77, 11.09, 13.45, 2.79, 69.43, 128.51, 32.15
Find the mean of the squared deviations: (21.81 + 7.13 + 1.77 + 11.09 + 13.45 + 2.79 + 69.43 + 128.51 + 32.15) / 9 = 32.12
Take the square root of the mean of the squared deviations to find the standard deviation: √32.12 = 5.67

Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.

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The measure of the height of the triangle measured by Manuel is given as follows:

5 feet.

The height of a triangle is the perpendicular distance from the base to the vertex opposite the base, and is used to calculate the area of the triangle.

Hence, the height is measured as the distance from the top vertex of the triangle to it's base.

In this problem, it is stated that:

"Manuel measured the distance from the top vertex of the triangle shown to its base".

He found the distance to be of 5 ft, hence the height of the triangle is of:

5 ft.

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The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,

tan (360° / (2 × 8)) = (n/2) ÷ 4

tan 22.5° = n / 8

n = 3.3137

Then the perimeter is given as,

P = 8 x 3.3137

P = 26.51 units

The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

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The variable that satisfies the condition that the trinomial a^2 + 7a + 6 and the binomial a + 1 have the same value is a = -5 or a = -1.

Setting the trinomial and binomial equal to one another and then solving for the variable will help us identify the variable that satisfies the stated criteria. Which is:

a^2 + 7a + 6 = a + 1

By putting all the terms to one side and grouping like terms, we may make this equation simpler:

a^2 + 6a + 5 = 0

The quadratic expression on the left-hand side can now be factored:

(a + 5)(a + 1) = 0

To make each factor equal to zero, we can use the zero product property:

a + 5 = 0 or a + 1 = 0

In each equation, we can solve for a to obtain:

a = -5 or a = -1

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Answer: A

Step-by-step explanation:

(3x ^ 2 + 4x - 7) (2x + 9)

2x (3x ^ 2 + 4x - 7) + 9 (3x ^ 2 + 4x - 7)

6x ^ 3 + 8x ^ 2 - 14x + 27x ^ 2 + 36x - 63

6x ^ 3 + 35x ^ 2 + 22x - 63

The solution is, the measure of the, inscribed angle: 30°, and,

central angle: 60°.

The solution are,

the measure of angle C is 52°

the measure of angle B is 52°

the measure of angle BSD is 71°

the measure of angle CSE is 71°

the measure of angle E is 57°

the measure of arc BC 57°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given figure, we get,

The central angle is double the inscribed angle for the same intercepted arc.

Since doubling the angle adds 30° to it,

the original inscribed angle must be 30°.

so, we get,

Then the central angle is 30°+30° = 2·30° = 60°.

The solution are,

the measure of angle C is 52°

the measure of angle B is 52°

the measure of angle BSD is 71°

the measure of angle CSE is 71°

the measure of angle E is 57°

the measure of arc BC 57°.

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Answer:

The volume of a rectangular solid is given by the formula V = LWH, where L is the length, W is the width, and H is the height.

In this case, we have:

W = x + 3

L = x + 2

H = x

So the volume is:

V = (x + 2)(x + 3)(x)

V = x(x + 2)(x + 3)

V = x(x^2 + 5x + 6)

V = x^3 + 5x^2 + 6x

Therefore, the volume of the rectangular solid is given by the polynomial expression x^3 + 5x^2 + 6x.

Answer:

41.9 cubic feet

Step-by-step explanation:

V = 1/3πr^2h,

r=radius

h=height.

V = 1/3πr^2h

  = 1/3π4^2 * 2.5

  = 40π/3 cubic feet

so the answer would be 41.9 cubic feet

One leg of a right triangle measures 7 feet. If the other leg is 1 foot shorter than the hypotenuse, the dimensions of the right triangle will be 7 feet, 24 feet, and 25 feet.

To find the dimensions of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs. The formula for the Pythagorean Theorem is a² + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.

We are given that one leg of the triangle measures 7 feet, and the other leg is 1 foot shorter than the hypotenuse. Let's call the length of the other leg x and the length of the hypotenuse x + 1. We can plug these values into the Pythagorean Theorem to find the dimensions of the triangle:

72 + x2 = (x + 1)2

49 + x2 = x2 + 2x + 1

48 = 2x

x = 24

So the other leg of the triangle measures 24 feet, and the hypotenuse measures 24 + 1 = 25 feet. The dimensions of the right triangle are 7 feet, 24 feet, and 25 feet.

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The area of the hexagon is given by A = 585 units²

Six equilateral triangles make create a regular hexagon, which has six congruent sides and angles. The following is the formula to get the area of a regular hexagon.

Area of a hexagon A = 3 (√3)/ 2 ) a²

where, a represent the length of a side of the regular hexagon

Given data ,

Let the area of the hexagon be represented as A

Now , the value of A is

Let the side length of the hexagon be a = 15

Now , area of a hexagon A = 3 (√3)/ 2 ) a²

On simplifying , we get

The area of hexagon A = 3 (√3)/ 2 ) ( 15 )²

The area of hexagon A = 584.56715 units²

The area of hexagon A = 585 units²

Therefore , the value of A is 585 units²

Hence , the area of the hexagon is A = 585 units²

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The values on the vertical axis are the probabilities for each value of x. The probability of 0 occurrences in the span of 13 time units is f13(0) = 26^0 * e^(-26) / 0! = e^(-26) ≈ 0.0000000000000000000000000003.

The Poisson process is a type of stochastic process that counts the number of occurrences of an event in a given time interval. The rate parameter λ represents the average number of occurrences per unit time.

i. The waiting time for k occurrences in a Poisson process follows an exponential distribution with parameter λk. The probability distributions for X1, X2, X3, and X5 are given by:

X1 ∼ Exp(λ) = Exp(2)

X2 ∼ Exp(λ*2) = Exp(4)

X3 ∼ Exp(λ*3) = Exp(6)

X5 ∼ Exp(λ*5) = Exp(10)

The expected waiting time E[Xk] is given by 1/λk, and the standard deviation σXk is also given by 1/λk. Therefore, we have:

E[X1] = 1/λ = 1/2

E[X2] = 1/(λ*2) = 1/4

E[X3] = 1/(λ*3) = 1/6

E[X5] = 1/(λ*5) = 1/10

σX1 = 1/λ = 1/2

σX2 = 1/(λ*2) = 1/4

σX3 = 1/(λ*3) = 1/6

σX5 = 1/(λ*5) = 1/10

The probability distributions for the interval 0 ≤ x ≤ 7 are shown below:

ii. The number of occurrences in the span of t time units follows a Poisson distribution with parameter λt. The probability distributions ft(x) for t = 13, t = 12, and t = 1.2 are given by:

ft(x) = (λt)^x * e^(-λt) / x!

f13(x) = (2*13)^x * e^(-2*13) / x! = 26^x * e^(-26) / x!

f12(x) = (2*12)^x * e^(-2*12) / x! = 24^x * e^(-24) / x!

f1.2(x) = (2*1.2)^x * e^(-2*1.2) / x! = 2.4^x * e^(-2.4) / x!

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In response to the aforementioned query, we may say that The right equation response is b. 25 virtual currency units (sufficient for Bloxburg purchase).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

You presently have 22 units of virtual currency, and John takes 21, according to the facts provided. You now only have 1 unit of virtual currency.

Consequently, to acquire Blox , you would require an additional 24 units of virtual currency.

The right response is b. 25 virtual currency units (sufficient for Bloxburg purchase).

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The difference between the two groups is likely due to chance and the two groups likely have the same mean.

To conduct the appropriate test of significance for a research situation, you must first identify whether you need to use a one-tailed or two-tailed test. A one-tailed test is used when you are looking to see if the mean of one group is greater or less than the mean of another group. A two-tailed test is used when you are testing the null hypothesis that the two groups have the same mean.

Once you have identified the type of test, you must determine if it is a one or two sample test. A one sample test is used when you are comparing the mean of one group to a known population mean, whereas a two sample test is used when you are comparing the means of two separate groups.

Next, you must select the appropriate alpha level. Alpha levels are a measure of the significance of the test and refer to the probability of rejecting the null hypothesis when it is actually true. Generally, an alpha level of 0.05 is used in research settings.

Once you have selected the appropriate test and alpha level, you can make a decision about the test significance. This is done by comparing the calculated test statistic to the critical value in the test statistic table. If the calculated test statistic is larger than the critical value, the test is statistically significant and the null hypothesis can be rejected. If the calculated test statistic is smaller than the critical value, the test is not statistically significant and the null hypothesis cannot be rejected.

Finally, you must interpret the results of the test. If the test is statistically significant, it means that the difference between the groups is not likely due to chance, and therefore the two groups are likely to have different means. If the test is not statistically significant, it means that the difference between the two groups is likely due to chance and the two groups likely have the same mean.

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To simplify the expression (8d^((3)/(2))*7h^((5)/(6)))(7h^((3)/(2))*8d^((5)/(6))), we need to use the distributive property and the laws of exponents.

First, we can distribute the 8d^((3)/(2)) and 7h^((5)/(6)) to the 7h^((3)/(2)) and 8d^((5)/(6)):
= (8d^((3)/(2))*7h^((3)/(2)))*(7h^((5)/(6))*8d^((5)/(6)))
Next, we can use the laws of exponents to simplify the expressions with the same base:
= (8^2*d^((3)/(2)+(5)/(6))*7^2*h^((5)/(6)+(3)/(2)))
= (64*d^((11)/(6))*49*h^((9)/(6)))
Finally, we can simplify the exponents and multiply the constants:
= (3136*d^((11)/(6))*h^((3)/(2)))

Therefore, the simplified expression is 3136*d^((11)/(6))*h^((3)/(2)).

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The volume of the cone is approximately 94.25π cubic cm.

To find the volume of a cone, we use the formula V = 1/3πr²h, where V is the volume, r is the radius of the base, and h is the height or depth of the cone. In this case, we know that the depth of the cone is 14 cm and the base radius is 9/2 cm.

First, we need to calculate the radius of the base in terms of cm, since the formula requires it. We are given that the base radius is 9/2 cm, so we can substitute this value for r:

r = 9/2 cm

Next, we need to calculate the volume of the cone using the formula. We know that the depth of the cone is 14 cm, so we can substitute this value for h:

V = 1/3πr²h

V = 1/3π(9/2)²(14)

V = 1/3π(81/4)(14)

V = 1/3π(1134/4)

V = 1/3π(283.5)

V = 94.25π

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A. Amplitude: 4,  Asymptotes: None,  Complete Period:  [tex]\(\frac{2\pi}{5}\)[/tex],  Period: [tex]\(2\pi/5\)[/tex],  Phase Shift:  [tex]\(\frac{\pi}{5}\)[/tex].
B. Amplitude: 1, Asymptotes:  [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex], Complete Period:  [tex]\frac{2\pi}{3}\)[/tex],     Period:  [tex]\(2\pi/3\)[/tex],  Phase Shift: [tex]\(\frac{\pi}{6}\)[/tex].

To find the amplitude, asymptotes, complete period, period, and phase shift for each of the given trigonometric functions, we need to use the standard form of the trigonometric functions:[tex]\[f(x)=A\sin(Bx+C)+D\][/tex] and [tex]\[g(x)=A\sec(Bx+C)+D\][/tex]

For function f(x), we have:
A = 4, B = 5, C = -π, and D = 0

The amplitude is |A| = |4| = 4

The period is  [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{5}\)[/tex]

The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi}{5}[/tex] = [tex]\frac{\pi}{5}\)[/tex]

There are no asymptotes for the sine function.

For function g(x), we have:
A = -1, B = 3, C = -π/2, and D = 0

The amplitude is |A| = |-1| = 1

The period is [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{3}\)[/tex]

The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi/2}{3}[/tex] = [tex]\frac{\pi}{6}\)[/tex]

The asymptotes occur when the cosine function is equal to zero, so the asymptotes are at  [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex] , where n is an integer.

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Answer:

The volume of a sphere with a diameter of 8.6 m = 333.0 m^3

Step-by-step explanation:

The solution of the function f(h.g)(x) will be 6x³ -3x² + 5. The correct option is C.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The given functions are,

h(x) = 3x +5

g(x) = 2x³ - x ²

The value of the function f(h.g)(x) will be calculated as,

f(h.g)(x) = 3 ( 2x³ - x² ) + 5

f(h.g)(x) = 6x³ - 3x² + 5

Therefore, the solution of the function f(h.g)(x) will be 6x³ -3x² + 5. The correct option is C.

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To factor the trinomial 2x²+7x-4, you could rewrite it as 2x²+8x-2x-4, and then factor by grouping. The factor pairs of ac are (x+4), (2x-1).

To factor the trinomial 2x²+7x-4 by grouping, we need to find a factor pair of ac that sums to b. In this case, ac = (2)(-4) = -8 and b = 7.

The factor pair of -8 that sums to 7 is 8 and -1. Therefore, we can rewrite the trinomial as follows:

2x²+7x-4 = 2x²+8x-x-4

Next, we can group the first two terms and the last two terms:

(2x²+8x)+(-x-4)

Now, we can factor out the greatest common factor from each group:

2x(x+4)-1(x+4)

Finally, we can factor out the common factor of (x+4):

(x+4)(2x-1)

Therefore, the factored form of the trinomial 2x²+7x-4 is (x+4)(2x-1).

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The percentage of white tiles used out of 25 tiles in Ally's laundry room floor is 32%.

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

From the figure,

We can see that the total number of tiles used for flooring= 16

Out of this, 8 tiles used are white tiles.

Now it is said that the total number of white tiles is 25.

We are asked to find what percentage of 25 tiles are used on the laundry room floor.

We will use a fraction to describe the proportion of white tiles in the box to those used for the floor and then multiply it by 100 to find the percentage.

Percentage = ( white tiles used / Total number of white tiles ) * 100

            = 8/25 * 100 = 32%

Therefore the percentage of white tiles used out of 25 tiles in Ally's laundry room floor is 32%.

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Answer: Your welcome!

Step-by-step explanation:

This linear model tells us that, on average, for every additional square foot of area in a home, the selling price increases by 122.2 dollars. Therefore, this model suggests that the larger the area of a home, the higher the selling price of the home will be.

Answer:

Step-by-step explanation:

The missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.

To find the missing lengths of ΔABC, we can use the properties of a 45-45-90 triangle. A 45-45-90 triangle is a special type of right triangle in which the two legs are congruent and the angles are 45°, 45°, and 90°. The ratio of the sides in a 45-45-90 triangle is 1:1:√2, where the hypotenuse is √2 times the length of each leg.

Since we are given that BC = 6 and ∠A and ∠B are both 45°, we can conclude that ΔABC is a 45-45-90 triangle. Therefore, the lengths of AC and AB are both equal to the length of BC, which is 6.

AC = 6
AB = 6

To find the lengths in simplest radical form, we can multiply the lengths of AC and AB by √2/√2 to get:

AC = 6 * √2/√2 = 6√2/2 = 3√2
AB = 6 * √2/√2 = 6√2/2 = 3√2

To find the approximations correct to two decimal places, we can use a calculator to find the decimal values of 3√2:

AC ≈ 3 * 1.41 = 4.23
AB ≈ 3 * 1.41 = 4.23

Therefore, the missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.

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