Two parallel lines are cut by a traversal. If the measure of 4 is 110°, what is the measure of 5?

Part(1)

The measure of the angle will be 45°.

Part(2),

The formula for the shadow is,

6² + x² = 16²

A basic mathematical theorem relating to the lengths of a right-angled triangle's sides is known as the Pythagorean theorem. According to this rule, the square of the length of the hypotenuse (the side that faces the right angle) in any right-angled triangle equals the sum of the squares of the lengths of the other two sides.

Part(1),

To find the angle x, we can use the inverse tangent function. Let's call the length of Joel's shadow "s". Then we have:

tan(x) = opposite/adjacent = 16/s

Taking the inverse tangent of both sides, we get:

x = tan⁻¹(16/s)

We know that Joel's height is 6 ft, so the hypotenuse of the right triangle formed by Joel and his shadow is:

= √(6² + s²)

Now we can use the Pythagorean Theorem to solve for s. Rearranging the formula for h, we have:

s = √(h² - 6²)

Substituting the value of h with the expression above, we get:

s = √((√(6² + s²))² - 6²)

Simplifying this expression, we get a quadratic equation in terms of s:

s² - 256 = 0

Solving for s, we get:

s = ±16

Since s represents the length of the shadow, it must be positive. Therefore, s = 16 ft.

Substituting s into the equation for x, we get:

x = tan⁻¹(16/16) = tan⁻¹(1) = 45°

So the measure of the angle x is 45 degrees.

Part(2),

The formula for a shadow can be written as,

6² + x² = 16²

To know more about the Pythagorean theorem follow

https://brainly.com/question/21332040

#SPJ1

All the work is correct since the volume of the cube is 132.651 cubic inches as it is given.

From the given figure we can see that,

Length of the base (L) = 5.1 inches.

Width of the base (W) = 5.1 inches.

The Area of the Base of the Cube = (B) = L*W = 5.1*5.1 = 26.01 square inches.

The height of the cube (h) = 5.1 inches.

The Volume of the Cube is given by,

V = B*h

V = 26.01(5.1)

V = 132.651 cubic inches.

Hence the work is correct, the volume of the cube is 132.651 cubic inches.

To know more about Volume here

https://brainly.com/question/27710307

#SPJ1

The question is incomplete. The complete question will be -

"determine if the work is correct or incorrect:

"

Answer:

it is 5.4 kilometers from White Beach across the lake to the Lodge.

Step-by-step explanation:

Based on the information provided, we can calculate the distance from White Beach across the lake to the lodge by adding the distances from Canoeville to White Beach and from Canoeville to the lodge.

Distance from Canoeville to White Beach: 2.4 km

Distance from Canoeville to the Lodge: 3.0 km

Total distance from White Beach across the lake to the Lodge:

2.4 km + 3.0 km = 5.4 km

So, it is 5.4 kilometers from White Beach across the lake to the Lodge.

The appropriate test to use for examining the correlation between age in years and score on a driving test (0-100) is the Pearson correlation coefficient test, assuming the data meets the assumptions of normality and linearity.

Based on the information provided, the appropriate test to use would be the Pearson correlation coefficient test, which is used to measure the strength and direction of the linear relationship between two continuous variables.

However, before conducting the Pearson correlation test, it is important to ensure that the data meets the assumptions of normality and linearity. The Shapiro-Wilk test you ran assesses normality, but you need to also check for linearity.

If the data meets the assumptions of normality and linearity, you can then use the Pearson correlation test to determine the strength and direction of the relationship between age and driving test score.

Learn more about Pearson correlation test here

brainly.com/question/30101950

#SPJ4

(50/100)×60= 30

(5/100)× 60= 3

(1/100)×60= 0.6

Two gallons, or eight quarts, of green paint were purchased by Blanca. She still has 2 and 1/2 quarts of paint after using 5 and a half quarts.

The 2 gallons of green paint that Blanca bought can be divided into 8 quarts.

She applied 5 and 1/2 liters of paint to her front patch and swing.

We can deduct the amount utilized from the initial amount to get the amount of paint she still has.

8 quarts minus 5 and a half quarts equals 2 and a half quarts.

It's crucial to remember that having extra paint on hand for touch-ups or unforeseen scenarios is always a smart idea when working with paint.

Blanca may want to consider purchasing an additional quart of paint to ensure she has enough for her project.

Hence,  Blanca still has 2 and 1/2 quarts of paint after using 5 and a half quarts.

Learn more about paint:

https://brainly.com/question/15008921

#SPJ4

Answer:

x = (3 ± sqrt(-47)) / 2.

Step-by-step explanation:

If x - 6 is a factor of f(x), then we know that (x - 6) must divide evenly into f(x), which means that there is another factor of f(x) that we can find by polynomial long division or synthetic division.

Using synthetic division:

We start by writing the coefficients of f(x) in order:

1 3 -22 24

We then write the factor (x - 6) to the left of the coefficients, and draw a line:

6 | 1 3 -22 24

We bring down the first coefficient: 1

1 3 -22 24

1

We multiply 6 by the first coefficient and write the result under the second coefficient: 1

6 | 1 3 -22 24

-6

-3

If x - 6 is a factor of f(x), then we know that (x - 6) must divide evenly into f(x), which means that there is another factor of f(x) that we can find by polynomial long division or synthetic division.

Using synthetic division:

We start by writing the coefficients of f(x) in order:

1 3 -22 24

We then write the factor (x - 6) to the left of the coefficients, and draw a line:

6 | 1 3 -22 24

We bring down the first coefficient:

Copy code

1

6 | 1 3 -22 24

1

We multiply 6 by the first coefficient and write the result under the second coefficient:

Copy code

1

6 | 1 3 -22 24

-6

Copy code

 -3

We add the second and third coefficients to get -19, then multiply by 6 and write the result under the third coefficient:

1

6 | 1 3 -22 24

-6

-3

42

66

We add the last two numbers to get 90. This means that we can write f(x) as:

f(x) = (x - 6)(x² - 3x + 14)

To find the zeros of f(x), we need to solve the equation (x - 6)(x² - 3x + 14) = 0.

The first factor gives us x = 6.

To solve the quadratic factor, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -3, and c = 14. Substituting these values into the formula, we get:

x = (3 ± sqrt(3² - 4(1)(14))) / 2(1)

x = (3 ± sqrt(-47)) / 2

Since the square root of a negative number is not a real number, the quadratic factor does not have any real zeros.

Therefore, the zeros of f(x) are x = 6, and the complex numbers x = (3 ± sqrt(-47)) / 2.

The figure have area of the hexagon equal to 432 cm², area of the circle equal to 254.6 cm², and the area of the shaded region equal to 177.4 cm² to the nearest tenth.

Area of the hexagon = 1/2 × 6 × 16cm × 9cm

Area of the hexagon = 432 cm²

Area of the circle = 22/7 × 9cm × 9cm

Area of the circle = 254.6 cm²

Area of the shaded region = 432 cm² - 254.6 cm²

Area of the shaded region = 177.4 cm²

Therefore, the figure have area of the hexagon equal to 432 cm², area of the circle equal to 254.6 cm², and the area of the shaded region equal to 177.4 cm² to the nearest tenth.

Read more about area here:https://brainly.com/question/15424654

#SPJ1

Answer:

Since complete angle B (<DBA) is = <DBC + <CBA

<DBA = 20° + 30°

<DBA = 50°

Hence complete angle B is 50°

Answer:

[tex]|x-8|=6[/tex]

Step-by-step explanation:

Let's begin by finding the midpoint of 2 and 14. To do this, we'll add the numbers and then divide by 2.

2+14=16

16/2=8

The number that is the same distance between 2 and 14 is 8.

Now, let's find how far away each number is from 8.

8-2=6

14-8=6

2 and 14 are 6 away from 8.

Let's set up the absolute value equation using these two values.

Since 8 is the midpoint, this will be what the absolute value expression is equal to.

Since each number is 6 away from 8, this is the number (6) we will be taking away from 2 and 14.

Remember that absolute value is just distance.

In other words, 2 is 6 away from 8, and 14 is also 6 away from 8.

Or, the distance between a number x and 8 is 6.

Using this knowledge, we have:

[tex]|x-8|=6[/tex]

Answer:

|x-8|=6

Step-by-step explanation:

i checked rsm its correct :3

Note that the TOTAL amount deducted from Hope's latest paycheck is $315.21

If you examine the paycheck it clearly states under current deductions, that 315.21 was deducted form hopes paycheck.

A paycheck is a written document (a cheque) provided by an employer to pay an employee for services done. It is sometimes spelled paycheque, pay check, or pay cheque.

Employers withhold (or deduct) a portion of their employees' wages to meet payroll and income taxes. A portion of a paycheck may also be removed or withdrawn to pay for retirement or health benefits.

Learn more about paycheck at:

https://brainly.com/question/3117139

#SPJ4

Full Question:

Although part of your question is missing, you might be referring to this full question:

What was the TOTAL amount deducted from Hope's latest paycheck?

answer choices

$90.00

$284.79

$315.21

$600.00

The ratio of the area of triangle XBY to the area of triangle ABC is 9/25. The height of XBY with respect to BY is 24/7, and the height of ABC with respect to BC is 40/7.

To find the ratio of the area of triangle XBY to the area of triangle ABC, we need to first find the heights of both triangles with respect to base BC.

Let's use the formula for the area of a triangle

Area = 1/2 * base * height

For triangle ABC, the base is BC, which has length 5, and let h₁ be the height of triangle ABC with respect to BC.

Area of ABC = 1/2 * 5 * h₁

For triangle XBY, the base is BY, which has length 3, and let h₂ be the height of triangle XBY with respect to BY.

Area of XBY = 1/2 * 3 * h₂

Since the triangles share the same base, we can use the following proportion to find the ratio of their heights

h₁/h₂ = BC/BY

h₁/h₂ = 5/3

We can solve for h₂

h₂ = (3/5)h1

Now, we need to find h1. We can use the fact that the area of triangle ABC is equal to the sum of the areas of triangles ABY and BCY.

Area of ABC = Area of ABY + Area of BCY

1/2 * 5 * h₁ = 1/2 * 3 * (3+h2) + 1/2 * 2 3/2 * (2 3/2 - h₂)

Simplifying the above equation and substituting h₂ = (3/5)h1, we get

5h₁ = 3(3 + 8/5 h₁) + 3h₁/5

Solving for h1, we get

h₁ = 40/7

Substituting h₁ = 40/7 and h₂ = (3/5)h₁ = 24/7 into the formulas for the areas of the triangles, we get

Area of ABC = 1/2 * 5 * 40/7 = 100/7

Area of XBY = 1/2 * 3 * 24/7 = 36/7

Therefore, the ratio of the area of triangle XBY to the area of triangle ABC is

Area of XBY / Area of ABC = (36/7) / (100/7) = 9/25

Hence, the required ratio is 9/25.

To know more about area of triangle:

https://brainly.com/question/19305981

#SPJ4

The x-coordinate of the point of intersection of the two lines is 2.

To get the x-coordinate of the spot where the two lines intersect:

1. We can solve the system of equations given by the two lines simultaneously, which means we need to eliminate one of the variables (x or y) to obtain an equation in one variable that we can solve.

2. One way to eliminate a variable is to add or subtract the two equations in a way that cancels out one of the variables. In this scenario, we can combine the two equations:

(7x + 4y) + (9x - 4y) = 18 + 14

16x = 32

Dividing both sides by 16, we get:

x = 2

So the x-coordinate of the point of intersection of the two lines is 2.

Learn more about coordinates here

https://brainly.com/question/15806120

#SPJ1

Yes (-3,-2) is true.

No (1,6) is false

No (0,4)  is false

To determine if an ordered pair is a point of intersection between the line and the parabola, we need to check if the coordinates satisfy both equations.

(-3, -2)

y = 2x + 4 => -2

= 2(-3) + 4 => -2 = -2 (True)

y = x² + 4x + 1 => -2

= (-3)² + 4(-3) + 1 => -2 = -2 (True)

Answer: Yes

(1, 6)

y = 2x + 4 => 6

= 2(1) + 4 => 6 = 6 (True)

y = x² + 4x + 1 => 6

= (1)² + 4(1) + 1 => 6 ≠ 6 (False)

Answer: No

(0, 4)

y = 2x + 4 => 4

= 2(0) + 4 => 4 = 4 (True)

y = x² + 4x + 1 => 4

= (0)² + 4(0) + 1 => 4 ≠ 1 (False)

Answer: No

Read more on ordered pairs here:https://brainly.com/question/1528681

#SPJ1

The mean is 89, the median is 89, the mode is 89, and the range is 22.

The mean is 72.6, the median is 76, there is no mode, and the range is 25.

The mean is 60.5, the median is 57.5, there is no mode, and the range is 55.

The mean, median, mode, and range of the given data are calculated as follows:

Mean = sum of values/ number of values

The median is the middle score when the scores are arranged in order from lowest to highest

Mode is the number that occurs most

The range is the difference between the largest and smallest values

1. Mean = (98 + 89 + 76 + 93 + 89) / 5

Mean = 89

76, 89, 89, 93, 98

The median is 89.

The mode is also 89.

Range = 98 - 76

Range = 22

2. Mean = (59 + 63 + 84 + 76 + 81) / 5

Mean = 72.6

Median: 59, 63, 76, 81, 84

The median is 76.

There is no mode for this set of score

Range = 84 - 59

Range = 25

3. Mean = (36 + 48 + 67 + 91) / 4

Mean = 60.5

Median: 36, 48, 67, 91

Median = (48 + 67) / 2

Median = 57.5

The data has no mode

Range = 91 - 36

Range = 55

Learn more about mean and median at: https://brainly.com/question/14532771

#SPJ1

Answer:Without additional information about the circle C or the position of point C, it is not possible to determine the radius of the circle.

Step-by-step explanation:

Without a visual of the tree diagram mentioned in the problem, it is difficult to provide an exact answer. However, we can use the fundamental counting principle to determine the number of possible combinations.

If there are, for example, 4 colors of balloons and 5 types of toys, then the number of different combinations a child may receive would be:

4 (number of colors) x 5 (number of types of toys) = 20

Therefore, the child may receive 20 different combinations of one color of balloon and one type of toy. However, this number may vary depending on the actual number of colors and types of toys available.

Answer: 40% drive and 60% take the bus.

Step-by-step explanation:

    We will divide the number of students who drive to school by the total number of students, and then multiply by 100 to turn it into a percentage.

         [tex]\displaystyle \frac{250}{250+375} *100= 40\%[/tex]

    Next, we will divide the number of students who ride the bus to school by the number of students who ride the bus, and then multiply by 100 to turn it into a percentage.

         [tex]\displaystyle \frac{375}{250+375} *100= 60\%[/tex]

The volume of the silo is 3612.56 cubic feet, under the condition that sphere in the top of the silo is a hemisphere with a radius of 12 feet.

Here, we have to implement the formula for deriving the volume of hemisphere,
The volume of a hemisphere with radius 12 feet can be calculated using the formula for the volume of a hemisphere which is (2/3)πr³
here r = radius of the hemisphere.

Staging r=12 feet in the formula
(2/3)π(12 feet)³
= (2/3)π(1728 cubic feet)
= 1152π cubic feet
≈ 3612.56 cubic feet

Then, the volume of the silo is approximately 3612.56 cubic feet.

To learn more about volume,
https://brainly.com/question/30395212
#SPJ4

$259,587 of Cheyenne's household belongings would be covered.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The amount of personal property coverage provided by the insurance is 80% of the insured value of the home:

Personal property coverage = 0.8 x insured value of home

Personal property coverage = 0.8 x $324,484

Personal property coverage = $259,587.20

Therefore, $259,587 of Cheyenne's household belongings would be covered.

Learn more about percentagess, by the following link.

https://brainly.com/question/24304697

#SPJ4

The number of elements in power set A where A = { x: x² + 3 < 2, x ∈R }  is equal to  n[P(A)] = 1.

The set A represented as ,

A = { x: x² + 3 < 2, x ∈R }

First, we need to determine the set of values that satisfy the inequality

x² + 3 < 2.

Subtracting 3 from both sides of the inequality gives us,

⇒ x² < -1

However, this inequality has no real solutions, since the square of any real number is always non-negative.

This implies,

The set A is empty,  A = {}.

The power set of the empty set contains only the empty set itself,

so P(A) = {{}}.

This implies, the number of elements in P(A) denoted as n[P(A)] is 1.

Therefore, the number of elements in power set A is equal to  n[P(A)] = 1.

Learn more about set here

brainly.com/question/28492445

#SPJ1

Answer:

Step-by-step explanation:

To find the solution for p(x) = m(x), we need to set the two expressions equal to each other and solve for x:

2ln(x) - 1 = ln(x+6)

First, we can simplify the left side by using the logarithmic identity that states ln(a^b) = b ln(a):

ln(x^2) - 1 = ln(x+6)

Next, we can eliminate the natural logarithm by exponentiating both sides with the base e:

e^[ln(x^2) - 1] = e^[ln(x+6)]

e^[ln(x^2)] * e^[-1] = x + 6

x^2 * 1/e = x + 6

Multiplying both sides by e gives:

x^2 = e(x + 6)

Expanding the right side gives:

x^2 = ex + 6e

Rearranging gives:

x^2 - ex - 6e = 0

This is a quadratic equation in x. We can solve for x using the quadratic formula:

x = [e ± sqrt(e^2 + 4*6e)]/2

Simplifying gives:

x = [e ± sqrt(e^2 + 24e)]/2

Therefore, the solution for p(x) = m(x) is x = [e ± sqrt(e^2 + 24e)]/2.

Answer:

x ≈ 3.40295

Step-by-step explanation:

We want to find the value(s) of x that satisfy the equation p(x) = m(x), where p(x) = 2ln(x) - 1 and m(x) = ln(x + 6).

So, we have:

2ln(x) - 1 = ln(x + 6)

First, let's simplify the equation by using the properties of logarithms:

ln(x^2) - ln(e) = ln(x + 6)

ln(x^2/e) = ln(x + 6)

Now we can eliminate the natural logarithm by taking the exponential of both sides:

x^2/e = x + 6

x^2 - ex - 6e = 0

We can solve this quadratic equation using the quadratic formula:

x = [-(-e) ± sqrt((-e)^2 - 4(1)(-6e))] / (2(1))

Simplifying:

x = [e ± sqrt(e^2 + 24e)] / 2

Therefore, the solutions for p(x) = m(x) are:

x = [e + sqrt(e^2 + 24e)] / 2  or  x = [e - sqrt(e^2 + 24e)] / 2

Note that since the argument of the natural logarithm must be positive, we must discard the negative solution, which is not valid. So the only solution is:

x = [e + sqrt(e^2 + 24e)] / 2

We can approximate this value using a calculator or computer software. For example, if we use e = 2.71828, we get:

x ≈ 3.40295

Therefore, the solution for p(x) = m(x) is x ≈ 3.40295.

55% percentage of matches has sparx FC won.

We have,

Number of games won = 11

Drawed games= 3

Lost games= 6

So, the percentage of won

= 11 / 20 x 100

= 11 x 5

= 55%

Thus, 55% of games won.

Learn more about percentage here:

https://brainly.com/question/29306119

#SPJ1

Answer: 63 minutes

Step-by-step explanation:

Use proportions:

8/84 = 6/x

Cross multiply to get:

8x = 504

Simplify by dividing by 8 on both sides.

x = 63.

The correct answer is b. On average, LinkedIn users would send between 5.48 and 8.72 total messages per year with the new algorithm.

The 95% confidence interval provided by Yue Bing suggests that the true difference in the average number of messages sent per year between the two groups of users (those using the new algorithm and those using the old algorithm) is likely to be between 5.48 and 8.72. This means that we can be 95% confident that the true difference in the average number of messages sent per year falls within this range. It does not necessarily mean that all LinkedIn users will send more or fewer messages with the new algorithm, but rather that the average number of messages sent by users using the new algorithm is likely to be within this range.
Your answer: d. On average, all LinkedIn users would send more messages with the new algorithm than with the old algorithm.

Explanation: Yue Bing computed a 95% confidence interval for the difference between the two parameters, which is (5.48, 8.72) messages per year. Since the entire interval is positive, this indicates that the new recommendation algorithm likely leads to an increase in the average number of messages sent by LinkedIn users compared to the old algorithm.

Learn more about confidence interval at: brainly.com/question/24131141

#SPJ11

log 72 to the base 2n is equal to log 18 to the base n if n is equal to [tex]2^{1/10}[/tex].

We can use the change-of-base formula to convert both logarithms to a common base, such as base 10:

log 72 / log 2n = log 18 / log n

We can simplify log 72 as follows:

[tex]log 72 = log (2^3 * 3^2) = 3 log 2 + 2 log 3[/tex]

Similarly, we can simplify log 18 as:

[tex]log 18 = log (2 * 3^2) = log 2 + 2 log 3[/tex]

Substituting these expressions into the original equation, we get:

(3 log 2 + 2 log 3) / log 2n = (log 2 + 2 log 3) / log n

Multiplying both sides by log n * log 2n, we get:

(3 log 2 + 2 log 3) log n = (log 2 + 2 log 3) log 2n

Expanding the logarithms using the power rule, we get:

[tex]3 log (n^3) + 2 log (n^2) = log (2n) + 2 log (n^3)[/tex]

Simplifying and rearranging terms, we get:

[tex]3 log (n^3) - 2 log (n^3) = log (2n) - 2 log (n^2)[/tex]

[tex]log (n^9) = log (2n / n^2)[/tex]

[tex]log (n^9) = log (2/n)[/tex]

Taking the exponential of both sides, we get:

[tex]n^9 = 2/n[/tex]

Multiplying both sides by n, we get:

n^10 = 2

Taking the 10th root of both sides, we get:

[tex]n = 2^{1/10}[/tex]

Therefore, log 72 to the base 2n is equal to log 18 to the base n if n is equal to [tex]2^{1/10}[/tex]

know more about logarithm visit:

https://brainly.com/question/30085872

#SPJ1

Answer:

I believe it is D. A line passes through the point (0, 0) and continues through the point (12, 3).

Step-by-step explanation:

Please give brainliest thx

The unit for force is the Newton (N). The equation for gravitational force is given by Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

where: F is the gravitational force (in Newtons, N) G is the gravitational constant (approximately 6.674 × 10^-11 N·m²/kg²) m1 and m2 are the masses of the two objects (in kilograms, kg) r is the distance between the centers of the masses (in meters, m)

Gravitational force decreases as you move away from Earth because the force is inversely proportional to the square of the distance (r^2) between the objects. If the radius between the centers (r) were to be cut in half, the gravitational force would increase by a factor of 4, since the force is inversely proportional to the square of the distance.

So if r becomes (1/2)r, the force would be inversely proportional to (1/4)r^2, leading to a 4 times increase in force.

Learn more about Gravitational force,

https://brainly.com/question/27943482

#SPJ11

Answer: 10    C

Step-by-step explanation:

Variability is the range of numbers.

here it goes from 2-12

so

12-2=10

The closure property for subtraction holds for integers, but not necessarily for whole numbers.

Closure property is an important concept in mathematics. It refers to the property of a set of numbers to produce a result within the same set when a mathematical operation is performed on any two numbers in that set.

Whole numbers are a subset of integers and include only non-negative numbers, whereas integers include both positive and negative numbers along with zero.

When we subtract two whole numbers, the result may not always be a whole number. For instance, if we subtract 3 from 2, the result is -1, which is not a whole number. This is why Karim concluded that whole numbers are not closed under subtraction.

On the other hand, when we subtract two integers, the result will always be an integer. For example, if we subtract 3 from 2, the result is -1, which is an integer. This is why Ali concluded that integers are closed under subtraction.

To know more about integer here

https://brainly.com/question/15276410

#SPJ4