Solve the system below by substitution.
y = 2x + 4
y = 3x - 8

Answer:

(11, 7) with an area of 128 in2.

Step-by-step explanation:

The y-intercept of equation 11 + 2t where t is the months after the birth of the baby is 11.

The equation 11 + 2t is modeled by the situation where the weight, in pounds, of a newborn baby after t months is stated.

An equation is represented by y = b + mx where b is the y-intercept and m is the slope of the graph. On comparing the given equation 11 + 2t by the standard equation we have 11 as the intercept and 2 as the slope.

We can interpret from the given context and the equation that the newborn baby is born with 11 pounds weight at birth and with every month there is an increase of 2 pounds in the weight of the newborn.

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The percentage of all possible values of the variable that are less than 6 is:

0.1587 * 100% = 15.87%

a. To find the percentage of all possible values of the variable that lie between 4 and 9, we need to find the z-scores corresponding to these values and then find the area under the normal curve between those z-scores.

The z-score for x = 4 is:

z = (4 - 8) / 2 = -2

The z-score for x = 9 is:

z = (9 - 8) / 2 = 0.5

Using a standard normal table or calculator, we find that the area to the left of z = -2 is 0.0228 and the area to the left of z = 0.5 is 0.6915. Therefore, the area between z = -2 and z = 0.5 is:

0.6915 - 0.0228 = 0.6687

So, the percentage of all possible values of the variable that lie between 4 and 9 is:

0.6687 * 100% = 66.87%

b. To find the percentage of all possible values of the variable that exceed 5, we need to find the area under the normal curve to the right of z = (5 - 8) / 2 = -1.5.

Using a standard normal table or calculator, we find that the area to the left of z = -1.5 is 0.0668. Therefore, the area to the right of z = -1.5 (and hence the percentage of all possible values of the variable that exceed 5) is:

1 - 0.0668 = 0.9332

So, the percentage of all possible values of the variable that exceed 5 is:

0.9332 * 100% = 93.32%

c. To find the percentage of all possible values of the variable that are less than 6, we need to find the area under the normal curve to the left of z = (6 - 8) / 2 = -1.

Using a standard normal table or calculator, we find that the area to the left of z = -1 is 0.1587. Therefore, the percentage of all possible values of the variable that are less than 6 is:

0.1587 * 100% = 15.87%

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The equation of the regression line for the given data is y=2.4x+120.1.

According to the question, we are given a set of data values in the form of a table. This table shows data on the number of people visiting a historical landmark over one week.

          Day(x)                  Number of visitors(y)

              1                              120

              2                             124

              3                             130

              4                              131

              5                              135

              6                              132

              7                              135

We will draw a scatter plot with the help of the set of data values given in the table using the linear regression calculator. We see the regression line with y-intercepts and x-intercepts. The y-intercept is (0, 120.1) and the x-intercept is (-50.04, 0).

Therefore, the regression line for the following data using x-intercept and y-intercept will be :

             y=2.4x+120.1

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The complete question is "This table contains data on the number of people visiting a historical landmark over a period of one week. Using technology, find the equation of the regression line for the following data. Round values to the nearest tenth if necessary."

Answer:

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

The solution of the system of equations that is negative is determined as y = -1.

One way to find the system of equations is by graphing the lines of both equations on a coordinate plane. Find the point where both lines intersect to determine the coordinates.

The coordinates of the point where the lines intersect on a coordinate plane is the solution to the system of equations.

The point on the given graph where both lines intersect is (3, -1).Therefore, the negative solution is y = -1.

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Check the picture below.

so the horizontal lines are 4 and 12, and then we have a couple of slanted ones, say with a length of "c" each

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{4}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ c=\sqrt{ 4^2 + 3^2}\implies c=\sqrt{ 16 + 9 } \implies c=\sqrt{ 25 }\implies c=5 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{4+12+5+5}\implies \text{\LARGE 26}[/tex]

It may be worth investigating to see if there is an issue with the meter or billing.

Sample mean = 46.16, Sample standard deviation = 45.05

To find the z-score of a bill, we use the formula: z = (x - mean) / standard deviation

January: z = (14.1 - 46.16) / 45.05 = -0.71

May: z = (15.84 - 46.16) / 45.05 = -0.65

November: z = (115.17 - 46.16) / 45.05 = 1.55

The z-score tells us how many standard deviations a bill is away from the mean. A negative z-score means the bill is below the mean, and a positive z-score means the bill is above the mean.

Analysis:

Based on the mean and standard deviation, a normal bill would be between 1.06 and 91.26.

The z-scores for January and May are both below -2/3, which indicates they are slightly lower than normal bills but not very unusual. The z-score for November is above 1, which indicates it is higher than normal bills and may be considered unusual.

There may be times when you would accept an unusual bill if there was a reasonable explanation, such as extreme weather conditions or a change in energy usage. However, if the bill is consistently unusual over time, it may be worth investigating to see if there is an issue with the meter or billing.

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The distance between the two points is √(34) units.

We have,

To graph the right triangle, we first plot the two given points on a coordinate plane.

The hypotenuse of the right triangle is the line segment connecting these two points.

We can find the length of this line segment using the distance formula.

d = √((x2 - x1)² + (y2 - y1)²)

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the distance formula, we have:

d = √((-9 - (-6))² + (-4 - (-9))²)

 = √((-3)² + 5²)

 = √(9 + 25)

 = √(34)

Therefore,

The distance between the two points is √(34) units.

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Answer:

Both are non-linear. The first equation is a rational function and the second is a quadratic.

Step-by-step explanation:

The unemployment rate for the given economy is 11.5%.

To calculate the unemployment rate, we need to use the formula:

Unemployment Rate = (Number of Unemployed / Labor Force) x 100

The labor force is the sum of the number of employed and unemployed individuals. In this case, the labor force is:

Labor Force = Number of Employed + Number of Unemployed = 175 million + 35 million = 210 million

However, we need to adjust the labor force to account for discouraged workers, who have given up on finding employment. Therefore, the adjusted labor force is:

Adjusted Labor Force = Labor Force + Number of Discouraged Workers = 210 million + 10 million = 220 million

Now we can calculate the unemployment rate:

Unemployment Rate = (Number of Unemployed / Adjusted Labor Force) x 100 = (35 million / 220 million) x 100 = 15.9%

However, this includes the discouraged workers as part of the labor force. If we want to exclude them, we need to adjust the formula to:

Unemployment Rate = (Number of Unemployed / (Adjusted Labor Force - Number of Discouraged Workers)) x 100

Plugging in the numbers, we get:

Unemployment Rate = (35 million / (220 million - 10 million)) x 100 = 11.5%

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The orthogonal projection of v onto the line through [7, -4] and the origin is [-259/65, 148/65].

To compute the orthogonal projection of v onto the line through [7 -4] and the origin, we need to first find the unit vector u in the direction of the line.

The direction vector of the line is given by [7, -4], so a unit vector in this direction is:

u = [7, -4]/sqrt(7^2 + (-4)^2) = [7/√65, -4/√65]

Next, we need to find the projection of v onto u. This is given by the dot product of v and u, multiplied by u:

proj_u(v) = (v dot u) * u

where dot denotes the dot product.

So, we have:

v = [-3, 7]

u = [7/√65, -4/√65]

v dot u = (-3)(7/√65) + 7(-4/√65) = -37/√65

proj_u(v) = (-37/√65) * [7/√65, -4/√65]

Simplifying, we get:

proj_u(v) = [-259/65, 148/65]

Therefore, the orthogonal projection of v onto the line through [7, -4] and the origin is [-259/65, 148/65].

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The person must leave the money in the bank for approximately 10.8 years (rounded to the nearest tenth of a year) for it to reach $2900 with 5.75% interest compounded monthly.

We can use the formula for compound interest to solve this problem:

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

where:

A is the amount of money after t years

P is the principal (the initial amount of money invested)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

We want to find t, the time required for the investment to grow from $1000 to $2900. We know that P = 1000 and A = 2900. We also know that r = 0.0575 (5.75% as a decimal) and that the interest is compounded monthly, so n = 12.

Substituting these values into the formula, we get:

2900 = [tex]1000(1 + 0.0575/12)^(12t)[/tex]

Dividing both sides by 1000, we get:

2.9 = [tex](1 + 0.0575/12)^(12t)[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2.9) = 12t ln(1 + 0.0575/12)[/tex]

Solving for t, we get:

[tex]t = ln(2.9) / (12 ln(1 + 0.0575/12))[/tex]

Using a calculator, we get:

t ≈ 10.8

Therefore, the person must leave the money in the bank for approximately 10.8 years (rounded to the nearest tenth of a year) for it to reach $2900 with 5.75% interest compounded monthly.

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True. Regression is a functional relationship between two or more correlated variables, where one variable is used to predict another. This statistical method helps in understanding the relationship between variables and making predictions based on that information.

Regression analysis is a powerful tool in statistics that helps to identify the relationship between variables, and it can be used to make predictions or forecasts based on that relationship. It involves fitting a mathematical model to the data, and then using that model to estimate the value of one variable based on the values of the other variables. There are many different types of regression analysis, each suited to different types of data and research.

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To show that the formula (Au)T(Av) defines an inner product, we need to verify that it satisfies the four properties of an inner product: linearity in the first component, conjugate symmetry, positivity, and definiteness.

First, we need to show that (Au)T(Av) is linear in the first component. Let u, v, and w be vectors in R^n and let a be a scalar. Then we have:

(Au)T(Av + aw) = (Au)T(Av) + (Au)T(Aw)  (distributivity of matrix multiplication)
= (Au)T(Av) + a(Au)T(Aw)  (linearity of matrix multiplication)

Thus, (Au)T(Av + aw) is linear in the first component. Similarly, we can show that (aAu)T(Av) = a(Au)T(Av) is also linear in the first component.

Next, we need to show that (Au)T(Av) satisfies conjugate symmetry. This means that for any u and v in R^n, we have:

(Au)T(Av) = (Av)T(Au)*

Taking the conjugate transpose of both sides, we get:

[(Au)T(Av)]* = (Av)T(Au)

Since the transpose of a product of matrices is the product of their transposes in reverse order, we have:

[(Au)T(Av)]* = (vTAu)* = uTAv

Therefore, we have:

(Au)T(Av) = (Au)T(Av)*

Thus, (Au)T(Av) satisfies conjugate symmetry.

Next, we need to show that (Au)T(Av) is positive for nonzero vectors u. This means that for any nonzero u in R^n, we have:

(Au)T(Au) > 0

Expanding the formula, we have:

(Au)T(Au) = uTA^T(Au)

Since A is nonzero, its transpose A^T is also nonzero. Therefore, the matrix A^T(A) is positive definite, which means that for any nonzero vector x in R^n, we have xTA^T(A)x > 0. Substituting u for x, we get:

uTA^T(A)u > 0

Thus, (Au)T(Au) is positive for nonzero vectors u.

Finally, we need to show that (Au)T(Au) = 0 if and only if u = 0. This means that (Au)T(Au) is positive definite, which is equivalent to saying that the matrix A^T(A) is positive definite.

Therefore, we have shown that the formula (Au)T(Av) defines an inner product, since it satisfies linearity in the first component, conjugate symmetry, positivity, and definiteness.

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Answer:

The answer to this question is --> 0.40

Step-by-step explanation:

simply do the division.

as a fraction is basically nothing else than a division of the upper number by the lower number.

2 divided by 5

2/5 = 0.4

remember, how division works :

first the outmost left digit(s) divided by the digits of the right number. we use the same number of digits on both sides.

2 / 5 = 0

the first step gives us a 0, because 2 cannot be divided by 5.

then we pull down the next digit from the left side.

if we don't have any (as in this case), we simply pull a 0.

20 / 5 = 0.4

when we pull digits on the left side after the decimal point, then the result gets the decimal point exactly at that position.

20/5 = 4, so the 4 goes into the first position after the decimal point.

and therefore, the final result is

2/5 = 0.4

There are three ways to show that two triangles are similar:

Angle-angle Theorem (AA): Two triangles are comparable if they have two pairs of congruent angles.

Side-side-side Theorem (SSS): If the ratios of two triangles' corresponding sides are identical, the triangles are comparable.

The side-angle-side theorem (SAS) states that if the ratios of two pairs of comparable sides of two triangles are identical and their angles are congruent, the triangles are similar.

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The 96% confidence interval for the difference in proportions is (−0.1127, 0.3191)

To compare the proportions of success in two binomial experiments, we can use the two-sample Z-test.

Let p1 be the proportion of success in the first experiment and p2 be the proportion of success in the second experiment. We want to test the null hypothesis H0: p1 = p2 against the alternative hypothesis Ha: p1 ≠ p2.

First, we calculate the point estimate of the difference in proportions:

[tex]pp1 - p2 = \frac{54}{94} - \frac{40}{63} = 0.1032[/tex]

Next, we find the critical value of the test statistic. Since the confidence level is 96%, we have alpha = 0.04/2 = 0.02 on each tail of the distribution. Using a standard normal distribution table, we find that the critical values are ±2.0537.

The margin of error is given by:

[tex]ME= z \sqrt{\frac{p1(1-p1)}{n1} +\frac{p2(1-p2)}{n2} }[/tex]

where z* is the critical value, n1 and n2 are the sample sizes of the two experiments. Plugging in the values, we get:

[tex]ME= z \sqrt{\frac{0.5769(1-0.5769)}{94} +\frac{0.6349(1-0.6349)}{63} }= 0.2159[/tex]

Finally, we can construct the confidence interval for the difference in proportions as:

(p1 - p2) ± ME

which gives us:

0.1032 ± 0.2159

Thus, the 96% confidence interval for the difference in proportions is (−0.1127, 0.3191).

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The natural rate of unemployment refers to the level of unemployment that exists when the economy is in equilibrium, meaning both the goods and financial markets are balanced. This rate is typically considered as the baseline level of unemployment, which can be observed in a healthy and stable economy. It consists of two primary components: frictional and structural unemployment.

Frictional unemployment arises due to job transitions, such as workers changing careers or locations, and is often temporary. Structural unemployment, on the other hand, occurs when there is a mismatch between the skills possessed by job seekers and those demanded by employers. This type of unemployment is more long-lasting and requires targeted efforts to address it, such as worker retraining or education initiatives.

When the economy is in equilibrium, the natural rate of unemployment indicates that the labor market is functioning efficiently. The supply and demand for labor are balanced, and there are no external shocks affecting the market. In this state, the overall rate of unemployment remains relatively stable, with changes occurring mainly due to the natural fluctuations in frictional and structural unemployment.

In summary, the natural rate of unemployment represents the level of unemployment that occurs when the goods and financial markets are in equilibrium. It consists of frictional and structural unemployment, and serves as a benchmark for policymakers to evaluate the health and efficiency of the labor market in an economy.

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If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the degrees of freedom are computed as (n1)(n2) - 1.

The above statement is False.

In statistics, the number of degrees of freedom is the number of values ​​with independent variables at the end of the statistical calculation. Estimates of statistical data may be based on different data or information. The amount of independent information that goes into the parameter estimation is called the degree of freedom. In general, the degrees of freedom for parameter estimation are equal to the number of independent components involved in the estimation minus the number of parameters used as intermediate steps in the estimation minus the tower of the scale.

When testing for the difference between two population means with equal and unknown standard deviations, the degrees of freedom are computed using the formula:

df = (n1 - 1) + (n2 - 1)

Here, n1 and n2 are the sample sizes of the two populations. This formula sums the degrees of freedom from each population and adjusts for the fact that one degree of freedom is used up when estimating the common standard deviation.

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the calculation using the commutative and associative properties of multiplication is:

40.800 = 4.8 * 10 = 10 * 4.8 = (10 * 4) * 0.8 = 40 * 0.8 = 0.8 * 40 = 32.

To calculate 40.800 mentally using basic multiplication facts, we can break it down into smaller multiplications and apply the commutative and associative properties of multiplication.

First, we can use the fact that 4.8 x 10 = 48 to get:

40.800 = 4.8 x 10 x 10 x 10

= 4.8 x (10 x 10) x 10

= (10 x 10) x 4.8 x 10

Here, we have used the commutative property of multiplication to rearrange the order of the factors. We have also used the associative property of multiplication to group the factors in different ways.

Next, we can use the fact that 10 x 10 = 100 to get:

40.800 = 100 x 4.8 x 10

= 100 x (10 x 0.48)

= (100 x 0.48) x 10

Here, we have again used the commutative and associative properties of multiplication to rearrange and group the factors in different ways.

Overall, these equations show how we can break down 40.800 into smaller multiplications and use the commutative and associative properties of multiplication to rearrange and group the factors in different ways to make mental calculations easier.

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There are FOUR  4's in a deck of 52  

   4/52 = 1/13 chance

Second card less than 5 ?

    4 aces    4  two's  4 threes and 4  fours

      16/ out of 52 = 16/52 chance = 4/13 chance

1/13 * 4/13 = 4/169  chance of picking as questioned

the solution to the given differential equation is: Q(t) = -t^4/25 + t^4/5 ln(t) + C/t

To solve the given differential equation t dQ/dt + Q = t^4 ln(t), we'll first find the integrating factor, solve for Q(t), and then substitute the given terms.

Step 1: Find the integrating factor.
The integrating factor is e^(∫P(t)dt), where P(t) = 1/t in this case. So,

∫(1/t)dt = ln(t)

The integrating factor is e^(ln(t)) = t.

Step 2: Multiply the equation by the integrating factor.
t (t dQ/dt) + t(Q) = t^2 dQ/dt + tQ = t^5 ln(t)

Step 3: Integrate both sides of the equation.
∫(t^2 dQ/dt + tQ)dt = ∫(t^5 ln(t))dt

Using integration by parts on the right side (u = ln(t), dv = t^5 dt):

∫(t^5 ln(t))dt = (t^5 ln(t) / 5) - ∫(t^4 dt) = (t^5 ln(t) / 5) - (t^5 / 25) + C

Step 4: Solve for Q(t).
Since ∫(t^2 dQ/dt + tQ)dt = tQ, we have:

tQ = (t^5 ln(t) / 5) - (t^5 / 25) + C
Q(t) = -t^4/25 + t^4/5 ln(t) + C/t

So, the solution to the given differential equation is:

Q(t) = -t^4/25 + t^4/5 ln(t) + C/t

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The equation of the graph in the dotted line is

The equation graphed on a dotted line is obtained from the knowledge of parabolic equation and transformation

From the parent function, which has the formula y = x^2, a reflection was noticed resulting to equation

y = -x^2

Then a translation to 3 units to the left, results to the equation of the form

The graph of the function is plotted  and attached

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1.35 moles of oxygen and around 1.80 moles of aluminum are mixed in this process.

The balanced chemical formula for the reaction of oxygen and aluminum is:

4 Al + 3 O₂ → 2 Al₂O₃

As a result, in order to create 2 moles of aluminum oxide (Al₂O₃), 3 moles of oxygen gas (O₂) must react with 4 moles of aluminum (Al).

We are given 1.35 moles of oxygen gas, thus we can calculate a percentage to estimate how many moles of aluminum are required using this information:

4 moles Al / 3 moles O₂ = x moles Al / 1.35 moles O

Solving for x, we get:

x = 4 moles Al * 1.35 moles O₂ / 3 moles O₂

x ≈ 1.80 moles Al

Therefore, approximately 1.80 moles of aluminum will be used when reacted with 1.35 moles of oxygen in this reaction.

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Answer:

V = 120 cm³

Step-by-step explanation:

the volume (V) of the prism is calculated as

V = Ah ( A is the area of the base and h the height )

to find h (ON)

use Pythagoras' identity in right triangle MNO

ON² + MN² = MO²

ON² + 7.5² = 8.5²

ON² + 56.25 = 72.25 ( subtract 56.25 from both sides )

ON² = 16 ( take square root of both sides )

ON = [tex]\sqrt{16}[/tex] = 4

Then

V = (4.5 × 4) × 4 = 30 × 4 = 120 cm³

The equation of the regression line is y = 4/5x - 36/5. Option (c)

Using the two points closest to the line, we can estimate the slope and intercept of the regression line. Let's use the points (20, 14) and (50, 38), since they appear to be the closest to the line.

The slope is:

m = (y2 - y1) / (x2 - x1) = (38 - 14) / (50 - 20) = 24 / 30 = 4/5

To find the y-intercept, we can use the equation y = mx + b and plug in one of the points. Let's use (20, 14):

14 = (4/5)(20) + b

14 = 16 + b

b = -2

So the equation of the regression line is:

y = 4/5x - 2

Therefore, the answer is (B) 4/5x - 36/5

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Full Question: The scatter plot and table show the number of grapes and blueberries in 10 fruit baskets. Use the two points closest to the line. Which equation is the equation of the regression line?

A. y = 1/3x - 1/3

B. y = 4/5x + 18

C. y = 4/5x - 36/5

D. y = 5/4x - 45/2

The solution involves setting up equations for the accumulated value of the two accounts and equating them at the end of the fourth year and the end of the eighth year. Solving for k gives k = 6.75.

Let the initial deposit made by the student be denoted by X.

After 4 years, the amount in the UENR Credit Union account is X(1+4i) = X(1+4*0.075) = X(1.3).

For the lecturer's account, we need to use the force of interest formula to calculate the accumulated amount after 4 years

A(4) = Xe^∫[0,4] 2t/t²+k dt = X[tex]e^{2ln(2k+16)-2ln(2k)}[/tex]/2

A(4) = X((2k+16)/2k[tex])^{1/2}[/tex]

After 8 years, both accounts earn the same amount of interest. Therefore, the amount in the UENR Credit Union account is X(1+8i) = X(1+8*0.075) = X(1.6).

And for the lecturer's account

A(8) = Xe^∫[0,8] 2t/t²+k dt = X[tex]e^{4ln(2k+32)-4ln(2k)}[/tex]/2

A(8) = X((2k+32)/2k)²

Since the earned is the same for both accounts, we have

X(1.6) - X(1.3) = X((2k+32)/2k)² - X((2k+16)/2k[tex])^{1/2}[/tex]

Simplifying the above equation gives

0.3X = X[(2k+32)/2k)² - (2k+16)/2k[tex])^{1/2}[/tex]]

Dividing both sides by X gives

0.3 = [(2k+32)/2k)² - ((2k+16)/2k[tex])^{1/2}[/tex]]

Squaring both sides and rearranging gives

16k³ - 60k² - 71k - 144 = 0

This cubic equation can be solved using numerical methods or by factoring it using trial and error. After solving, we get

k = 6.75 (approx)

Therefore, the value of k is approximately 6.75.

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The measure of the angle is <B is 110 degrees

It is important to note that supplementary angles are described as angles that sum up to 180 degrees.

From the information given, we have that;

m<A = x + 26

m>B = 2x + 22

Equate the angles

m<A +m<B = 180

x + 26 + 2x + 22 = 180

collect the like terms

3x = 180 - 48

3x = 132

x = 44

the measure of <B = 2x + 22 = 2(44) + 22 = 88 + 22 = 110 degrees

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