There is a square with line segments drawn inside it. The line segments are drawn
either from the vertices or the midpoints of other line segments. We colored 1/8 of the
large square. Which one is our coloring?

The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.

Given that

Dimension of matrix  = 7×5

Rank of matrix = 4

The range space of A,

Which is a subspace of R, is known as R(A).

It is made up of all conceivable linear combinations of A's columns.

The dimension of R(A) =  rank of A,

Which is 4 in this case.

The null space of the transpose of A,

Which is also a subspace of R, is designated as N(AT).

All potential answers to the equation ATx = 0,

Where x is a R column vector, are included in it.

N(AT) has a dimension = nullity of A,

which in this case is 3 in this example.

The range space of the transposition of A, is designated as R(AT).

The rows of A are arranged in all conceivable linear configurations.

The rank of A = 4

Thus it equal to dimension of R(AT).

N(A) is the null space of A.

Axe = 0, where x is a column vector in R, are included in it.

The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).

To learn more about matrix visit:

https://brainly.com/question/29132693

#SPJ1

All the statements are true statements for a linear function

The list of options represent the given parameters in this question

Next, we test each of the options and state if they are true or not

So, we have

A. The rate of change is non-zero.

This is true because a linear function that has a zero rate is just a horizontal line

B. The domain is all real numbers.

This is true, otherwise when stated

C. The range is all real numbers.

This is true, otherwise when stated

D. There is one x-intercept.

This is true, because it intersects with the x-axis once

E. There is one y-intercept.

This is true, because it intersects with the y-axis once

Read more about linear functions at

https://brainly.com/question/30318449

#SPJ1

The coordinates of the reflected figures are C'(-2,-4), D'(1,-5), and E'(1, -2)

Given that we have the figure of the vertices CDE

With the coordinates C(-2,4), D (1,5), and E(1, 2)

The transformation is given as

Reflection over the x-axis

The rule of this transformation is

(x, y) = (x, -y)

So, we have

Image = C'(-2,-4), D'(1,-5), and E'(1, -2)

Recall that

the rule of this transformation is (x, y) = (x, -y)

This means that the x-coordinate remains unchanged while the y-coordinate is negated as a result of this reflection.

Read more about transformation at

brainly.com/question/1355808

#SPJ1

The shortest distance between point P and Q is 9.4.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point P (-4,-2)

x₁ = -4

y₁ = -2

Point Q ( 4,3)

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 4 - (-4) )² + ( 3 - (-2) )² )

D = √( ( 4 + 4 )² + ( 3 + 2 )² )

D = √( 8² + 5² )

D = √( 64 + 25 )

D = √89

D = 9.4

Therefore, the distance is 9.4.

Learn more about the distance formula here: brainly.com/question/24509115

#SPJ1

Answer: Felix spent 5 hours doing chores and 3 hours doing homework

Step-by-step explanation:

It says that x represent chores, y represents homework

Answer:

(5, 3)

Step-by-step explanation:

x represents hours of chores y represents hours of homework

a) The exact solution of the exponential equation [tex]8^{1-x}=9[/tex] in terms of logarithms is:  [tex]x=1-(\frac{2}{3}\times \frac{ln(3)}{ln(2)} )[/tex]

b)  An approximation to the solution rounded to six decimal places = 0.056642

Consider the exponential equation [tex]8^{1-x}=9[/tex]

Taking ln (log to the base e) on both the sides of above exponential equation,

ln([tex]8^{1-x}[/tex]) = ln (9)

We solve this equation for x.

We know that the rule of logarithm that [tex]log(a^m)=m\times log(a)[/tex]

Using this rule we get,

(1 - x) ln(8) = ln(3²)                          ............(3² = 9)

(1 - x) × ln(2³) = 2  × ln(3)

(1 - x) × 3 × ln(2) = 2  × ln(3)

1 - x = (2/3) × (ln(3) / ln(2))

x = 1 - [(2/3) (ln(3) / ln(2))]

x = 1 - [(2/3) × 1.584963]

x = 1 - 1.056642

x = 0.056642

This is the required value of x.

Learn more about an equation here:

https://brainly.com/question/28243079

#SPJ1

The required expression that is used to find the number of servings Riley will have is (15/2) ÷ (3/4).

We can find the number of servings Riley will have by dividing the total amount of salsa by the amount in each serving. Since the total amount of salsa is given as 7 1/2 cups or 15/2 cups, we can divide this by 3/4 cups per serving to get:

(15/2) ÷ (3/4) = (15/2) × (4/3) = 30/3 = 10

Thus, the required expression that is used to find the number of servings Riley will have is (15/2) ÷ (3/4).

Learn more about ratios here:

brainly.com/question/13419413

#SPJ1

The answers for the conversion of the given masses in grams and kilograms are:

The conversion factor between kilogram and grams is given below:

The conversion of the given masses is as follows:

19 3/5 kg = 19 × 1000 + 3/5 × 1000

19 3/5 kg = 19,600 g

3.4 kg + 3/10 kg = 3,400 g + 300 g / 10

3.4 kg + 3/10 kg = 3,700 g

8.5 kg - 45 g = 8,500 g - 45 g

8.5 kg - 45 g  = 8,455 g

The mass of the dictionary is 1200 g = 1.2 kg

The difference in mass between the dictionary and the book is 1.2 kg - 0.4 kg = 0.8 kg

difference in mass = 800 g

1/2 kg + 50 g + 3.9 kg = 500 g + 50 g + 3,900 g

1/2 kg + 50 g + 3.9 kg = 4,450 g

3 kg 15 g = 3,015 g

1/4 kg = 250 g

3,015 g - 250 g = 2,765 g

7/10 kg + 7/100 kg = 700 g + 7 g

7/10 kg + 7/100 kg = 707 g

8 kg 8 g + 4 1/2 kg = 8,008 g + 4 × 1000 + 500 g

8 kg 8 g + 4 1/2 kg = 12,508 g

8 kg 8 g + 4 1/2 kg = 12.508 kg

Lisa's mass = 2/5 × 75 kg = 30 kg

Lisa's mass = 30,000 g

Mass of one box = 0.6 kg = 600 g

Mass of 12 boxes = 12 × 600 g

Mass of 12 boxes = 7,200 g

Learn more about kg to grams at: https://brainly.com/question/30391620

#SPJ1

No. It is not possible to directly convert between pounds and inches or inches and cups.

It is not possible to directly convert between pounds and inches or between inches and cups because they are measuring different things.

Pounds are a unit of weight or mass, while inches are a unit of length or distance. Cups are a unit of volume, which is also different from weight or length.

Thus, all other things being equal it is not possible to directly convert between these units.

More on conversion between units can be found here: https://brainly.com/question/5725710

#SPJ1

Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.

Here, we have,

The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.

They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.

The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.

The lake's brilliant blue hue is a result of Tahoe's clean air and water.

There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.

Learn more about lake here-

brainly.com/question/24386402

#SPJ1

complete question:

As you respond to Part A, Part B, and Part C, follow the directions below.

​

​Address all of the instructions in each prompt.

​Use evidence from the information provided and your own knowledge of science to support your responses.

Part A

​

Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.

a) The relative rate of growth of the bacteria population is approximately 6,300%.

b) The initial size of the culture was approximately 2 bacteria.

c) The function that models the number of bacteria is n(t) = [tex]27e^{(0.88t)[/tex]

d) The number of bacteria after 4.5 hours is approximately 3,106.

e) It takes approximately 5.51 hours for the number of bacteria to reach 25,000.

(a) To find the relative rate of growth of the bacteria population, we can use the formula:

Relative rate of growth = (Final count - Initial count) / Initial count x 100%

Using the values given in the problem, we get:

Relative rate of growth = (12,800 - 200) / 200 x 100% ≈ 6,300%

(b) To find the initial size of the culture, we can use the formula:

Final count = Initial count x e^(relative rate of growth x time)

We can rearrange this formula to solve for the initial count:

Initial count = Final count / e^(relative rate of growth x time)

Using the values given in the problem and solving for the initial count, we get:

Initial count = 200 / [tex]e^{(6300\% \times 2)[/tex] ≈ 2

(c) The function that models the number of bacteria n(t) after t hours is:

n(t) = n₀[tex]e^{(rt)[/tex]

To find the values of n₀ and r, we can use the values given in the problem:

n(2) = 200 = n₀[tex]e^{(2r)[/tex]

n(6) = 12,800 = n₀[tex]e^{(6r)[/tex]

Dividing the second equation by the first equation, we get:

[tex]e^{(4r)[/tex] = 64

Taking the natural logarithm of both sides, we get:

4r = ln(64)

r = ln(64) / 4 ≈ 0.88

Substituting this value of r into the first equation and solving for n₀, we get:

200 = n₀[tex]e^{(0.88 \times 2)[/tex]

n₀ ≈ 27

Therefore, the function that models the number of bacteria is:

n(t) = [tex]27e^{(0.88t)[/tex]

(d) To find the number of bacteria after 4.5 hours, we can use the function we found in part (c):

n(4.5) = 27[tex]e^{(0.88 \times 4.5)[/tex] ≈ 3,106

(e) To find the number of hours it takes for the number of bacteria to reach 25,000, we can use the function we found in part (c):

25,000 = 27[tex]e^ {(0.88t)[/tex]

Dividing both sides by 27 and taking the natural logarithm of both sides, we get:

ln(925.93) = 0.88t

t ≈ 5.51

In summary, we used the formula for relative rate of growth to find the rate of growth of the bacteria population, and used this information to find the initial size of the culture using exponential growth functions.

We found the function that models the number of bacteria, and used it to find the number of bacteria after a given time and the time it takes for the number of bacteria to reach a certain value.

To learn more about population click on,

https://brainly.com/question/28905286

#SPJ1

The solutions are S={2,4}

Explanation:

Let's rewrite the equation

|3x−8|−x=0

|3x−8|=3x−8, if 3x−8≥0

and

|3x−8|=−(3x−8)=−3x+8, if 3x−8<0

Let f(x)=|3x−8|−x=0

Let's build a variation table

aaaaxaaaaaaaa−∞aaaaaaaa0aaaaaaaaaa83aaaaaaa+∞

aaaaxaaaaaaaaaaaaa−aaaa#color(white)(aaaaa)+#aaaaaaaa+

aaaa|3x−8|aaaaaa−3x+8a#color(white)(aaa)-3x+8#aaaaa3x−8

aaaaf(x)aaaaaaaaaaax=2a#color(white)(aaaaa)x=2#aaaaaax=4

The solutions are S={2,4}

graph{|3x-8|-x [-7.9, 7.904, -3.95, 3.95]}

At a $170 unit price, the producer's excess is $0.

To calculate the producer's surplus at a unit price of p = 170, we need to find the corresponding quantity supplied.

We can start by setting the supply equation equal to the unit price and solving for q:

p = 150 + 0.01q

170 = 150 + 0.01q

20 = 0.01q

q = 2000

So at a unit price of p = 170, the quantity supplied is q = 2000.

To find the producer's surplus, we need to calculate the cost of producing the 2000th unit, which is the marginal cost at this level of production. We can do this by taking the derivative of the supply equation with respect to q:

C(q) = 150q + 0.005q^2

MC(q) = dC/dq = 150 + 0.01q

At q = 2000, the marginal cost is:

MC(2000) = 150 + 0.01(2000) = 170

So the cost of producing the 2000th unit is $170.

The producer's surplus is the difference between the unit price and the marginal cost at the corresponding level of production:

PS = p - MC(q) = 170 - 170 = $0

Therefore, the producer's surplus at a unit price of $170 is $0.

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

The probability that 2 of the apples have blemishes will be 0.0746.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as,

[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]

The probability is calculated as,

P(X = 2) = ¹⁰C₂ * (0.05)² * (0.95)⁸

P(X = 2) = 0.0746

More about the binomial distribution link is given below.

https://brainly.com/question/14565246

#SPJ1

Coordinates of P = [tex][(3 * xB + xC + 4 * xD) / 8, (3 * yB + yC + 4 * yD) / 8][/tex]

Coordinates of P = [tex][(4 * xC + 2 * xD + 3 * xE) / 9, (4 * yC + 2 * yD + 3 * yE) / 9][/tex]

Leave the directions of point B alone (x1, y1) and the directions of point D be (x2, y2). Then, at that point, the directions of P are:

[tex][(3x1 + x2)/4, (3y1 + y2)/4][/tex]

Let the directions of point A be (x1, y1) and the directions of point E be (x2, y2). Then, at that point, the directions of P are:

[tex][(x1 + 2x2)/3, (y1 + 2y2)/3][/tex]

Leave the directions of point B alone (x1, y1), the directions of point C be (x2, y2), and the directions of point D be (x3, y3). Then, at that point, the directions of P are:

[tex][(3x1 + x2 + 4x3)/8, (3y1 + y2 + 4y3)/8][/tex]

Leave the directions of point C alone (x1, y1), the directions of point D be (x2, y2), and the directions of point E be (x3, y3). Then, at that point, the directions of P are:

[tex][(4x1 + 2x2 + 3x3)/9, (4y1 + 2y2 + 3y3)/9][/tex]

These recipes can be inferred utilizing the weighted typical equation:

[tex][(w1x1 + w2x2 + ... + wnxn)/(w1 + w2 + ... + wn), (w1y1 + w2y2 + ... + wnyn)/(w1 + w2 + ... + wn)][/tex]

where wi is the heaviness of point I and (xi, yi) are the directions of point I. Subbing the given loads and facilitates into the equations for every issue gives the directions of P for each situation.

To learn more about Coordinates, refer:

https://brainly.com/question/30533433

#SPJ1

The complete question is:

Find the coordinates of P that represent the weighted average of each set of points based on the given conditions. 12. Point B weighs three times as much as point D. 13. Point E weighs twice as much as point A. 14. Point B has a weight of 3 , point C has a weight of 1 , and point D has a weight of 4. 15. Point C has a weight of 4 , point D has a weight of 2 , and point E has a weight of 3.

Using the given information, the total distance travelled by the golf ball is 288 m

Now, From the question, we are to calculate the total distance travelled by the golf ball

The distance travelled by the golf ball can be calculated by using the formula,

Distance = Speed × Time

From the given information,

The golf ball rolls at a speed of 8 m/s for 12 seconds

Thus, The distance travelled at this time is

Distance = 8 m/s × 12 s

Distance = 96 m

Also, Mandy hits the golf ball and it rolls for 16 seconds at a speed of 12 m/s

The distance travelled at this time is

Distance = 12 m/s × 16 s

Distance = 192 m

So, The total distance travelled by the golf ball is 96 m + 192 m

= 288 meters

Hence, the total distance travelled by the golf ball is 288 m

Learn more on total distance here:

brainly.com/question/11607177

#SPJ1

The total thickness of a stack that contains 1 dime and 1 penny would be 40 millimeters.

If one should find the combined thickness of a collection containing 1 dime and 1 penny, adding both coins' individual thicknesses together is a suitable solution. According to the listed table, a dime's measure is 1 millimeter, while a penny's is 1 7 / 20 millimeters. Consequently, the complete depth of this selection could be calculated as follows:

= Thickness of dime + thickness of penny

= 1 7 / 20 + 1 1 / 2

= 27 / 20 + 3 / 2

= 27 / 20 + 30 / 20

= 57 / 20

= 2 17 / 20 mm

Find out more on thickness at https://brainly.com/question/4894239

#SPJ1

Answer:

Step-by-step explanation:

Hello! Here is a key for you:

Translation up some amount: y + that amount
Translation down some amount: y - that amount
Translation right some amount: x + that amount
Translation left some amount: x - that amount
Reflection across y-axis: (-x, y)
Reflection across x-axis: (x, -y)

7 - Correct
8 - Correct
9 - Correct
10 - This is correct, but your work is incorrect. The formula for reflection across the y-axis is (-x, y). So, you have to take all the points and make their x-values negative. A is located at (-2, -5). -2 = x, so -(-2) = 2 because negative x negative = positive. A' is located at (2, -5), D' is not. C' = (2, 0) is correct, because C is located at (-2, 0). B' = (3, 0) is correct because B was originally at (-3, 0). D' is located at (-2, -2) because D was originally located at (2, -2). So, all you have to do is swap what you wrote for A and D next to the graph, but the graph is completely correct.
11 - Correct
12 - Your answer for 12 isn't visible. I can see you said that P is located at (3, -2) and that P' is located at (-4, -1) which is correct. This means that (x - 7, y + 1) is the correct rule for this question because 3 - 7 = -4 and -2 + 1 = -1.
13. Your answer for 13 is incorrect. This is a reflection across the x-axis, not a translation. So there should be no adding/subtracting in the rule. The formula for reflection across the x-axis is (x, -y). We can find if this graph is a reflection across the x-axis by seeing if each of the prime versions of the original coordinates are a negative y version of the original coordinates.

U is located at (-4, 4), V is located at (-2, 4), and T is located at (-5, 2).

U' is located at (-4, -4), V is located at (-2, -4), and T is located at (-5, -2).

Since U' is located at (-4, -4) and U is located at (-4, 4), the y value turned negative, meaning that U' was a reflection across the x-axis because of (x, -y). Since V' and T' have negative y values of their corresponding original coordinates, Triangle U'V'T' is a reflection over the x-axis.

So, the correct rule you should put for question 13 is (x, -y).

14 - Correct

15 - Incorrect. All y-values turned negative, meaning this is another case of reflection over the x-axis. The correct rule is (x, -y).

16 - Correct

17 - Correct

18 - Correct

19 - Correct

20 - Incorrect. This was a translation over the x-axis, because all y-values turned negative. The correct rule is (x, -y).

For example, J is located at (-1, -1). J' is located at (-1, 1). The y-value turned negative because -(-1) = 1.


--Suggestion: Keep the formulas for the reflection across the x-axis and y-axis by you while doing homework like this.

Reflection across the x-axis formula: (x, -y).
Reflection across the y-axis formula (-x, y).
Translation up/down: (x, y +/- __)
Translation right/left: (x +/-, y)

Apply these formulas to each coordinate, not just one, to see if they all match up.

Good luck! I hope you understand this now.

The value of the variable x is 1/4

It is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, factors and coefficients.

Algebraic expressions are also described as expressions that are composed of mathematical or arithmetic operations.

These operations are listed thus;

We have that;

12= 3/x

cross multiply the values

12x = 3

Make 'x' subject

x = 1/4

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

One of the potential rational roots of 5x³-7x+11 is ±1, ±11, ±1/5, ±11/5. The correct answer is (B).

Rational Root Theorem states that if a polynomial has integer coefficients, then any rational root of the polynomial must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

For the given polynomial:

f(x) = 5x³-7x+11

constant term is 11

leading coefficient is 5.

Therefore, any potential rational roots of f(x) must have the form:

p/q

where p is a factor of 11 and q is a factor of 5.

The factors of 11 are ±1 and ±11, and the factors of 5 are ±1 and ±5. Therefore, the potential rational roots of f(x) are:

±1/1, ±11/1, ±1/5, ±11/5

which simplify to:

±1, ±11, ±1/5, ±11/5

Learn more about rational root theorem here:

https://brainly.com/question/30098119

#SPJ1

Answer:

o determine whether there is a significant difference in weight loss between two levels of exercise program, regardless of gender, we would need to conduct a statistical hypothesis test. We would use a two-sample t-test to compare the mean weight loss between the two levels of exercise program.

The null hypothesis would be that there is no significant difference in weight loss between the two levels of exercise program, while the alternative hypothesis would be that there is a significant difference in weight loss between the two levels of exercise program.

We would then calculate the p-value, which represents the probability of observing a test statistic as extreme as the one calculated from the sample data, assuming the null hypothesis is true. If the p-value is less than the significance level (usually set at 0.05), we would reject the null hypothesis and conclude that there is a significant difference in weight loss between the two levels of exercise program.

Without knowing the data, it is not possible to determine the appropriate p-value or make a decision about the significance of the difference in weight loss between the two levels of exercise program.

The volume of the solid as shown in the diagram is 756 ft³.

Volume is the space occupied by a solid.

To caculate the volume of the solid, we use the formula below

Note: The solid is made up of a prism and a pyramid.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Learn more about volume here: https://brainly.com/question/1972490

#SPJ1

Answer:

Third Angle Projection method

Step-by-step explanation:

The Third Angle projection method is preferred in the United States. In this type of projection, the object lies below the horizontal plane and behind the vertical plane

Answer: The mixed numbers in ascending order are:

2 5/9 , 3 2/9 , 3 3/9 , 3 4/9 , 4 1/9

Step-by-step explanation:

To put these mixed numbers into ascending order, we need to convert all of them to improper fractions and then compare them.

3 4/9 = 31/9

4 1/9 = 37/9

3 3/9 = 30/9

3 2/9 = 29/9

2 5/9 = 23/9

so  in ascending order (from smallest to largest)

2 5/9 , 3 2/9 , 3 3/9 , 3 4/9 , 4 1/9

The equation of the line in slope-intercept form is y = -2x - 3.

In this case, we know that the line passes through the point (-6,9) and has a slope of -2. Therefore, we can use the point-slope form of the equation to find the equation in slope-intercept form.

Point-slope form:

y - y₁ = m(x - x₁)

Substituting the values we know, we get:

y - 9 = -2(x - (-6))

y = -2x - 3

Therefore, the equation of the line in slope-intercept form is y = -2x - 3.

Learn more about the equation of line here:

https://brainly.com/question/9682526

#SPJ1

A transversal t intersects two parallel lines a and b, forming two groups of angles.

On top line a, starting from the top left, clockwise, angles are 1, 2, 3, and 4. On the below line b, starting from the top left, clockwise, angles are 5, 6, 7, and 8.

In the figure, angles 1 and 5 are corresponding angles, and both lines are intersected by transversal t. Complete the statements to prove that m∠1 = m∠5.

(given) m∠1 + m∠3 = 180° (Linear Pair Theorem)

m∠5 + m∠6 = 180° (Linear Pair Theorem)

m∠1 + m∠3 = m∠5 + m∠6 (Vertical Angles Theorem)

m∠3 = m∠6 (Subtraction Property of Equality)

m∠1 = m∠5 (Subtraction Property of Equality)

Thus, this can be concluded regarding the given scenario.

For more details regarding transversal, visit:

https://brainly.com/question/17987539

#SPJ1

Answer:

Mackenzie would need to invest approximately $91,670, to the nearest ten dollars, for the value of the account to reach $194,000 in 11 years.

Step-by-step explanation:

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

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

where:

A = the amount of money in the account after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

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

t = the number of years

In this case, we want to find the principal amount P, given that A = $194,000, r = 6.5% = 0.065, n = 12 (compounded monthly), and t = 11 years. Plugging in these values, we get:

194000 = P(1 + 0.065/12)^(12*11)

Simplifying the right side, we get:

194000 = P(1.00541666667)^132

Dividing both sides by (1.00541666667)^132, we get:

P = 194000 / (1.00541666667)^132

P ≈ $91,670.

Therefore, Mackenzie would need to invest approximately $91,670, to the nearest ten dollars, for the value of the account to reach $194,000 in 11 years.

By definitions of supplementary angles and by algebra properties, the value of the angle is equal to 118°.

In this problem we get a geometric system formed by a line cutting two parallel lines, from which we find two angles that are supplementary, that is, two angles whose sum equals 180°. Thus, the expression is described below:

(3 · n - 47) + (n + 7) = 180°

Now we proceed to determine to clear variable n by algebra properties:

4 · n - 40 = 180

4 · n = 220

n = 55

And the value of angle ABC is equal to:

m ∠ ABC = 3 · n - 47

m ∠ ABC = 3 · 55 - 47

m ∠ ABC = 118°

To learn more on supplementary angles: https://brainly.com/question/18362240

#SPJ1

Answer:

False

Step-by-step explanation:

This is because runner 1's median line falls on 5.6-5.7s while runner 2's falls on 6.4s

(Hopes this helps :) )

The solution is,  the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water is

y-29 = -7/2 (x-6).

Here, we have,

The given data is

time (h):    2   4   6   8

gallons:  43 36 29 22

A graph of the data shows a linear relationship.

Therefore in slope-intercept form, let

(y - 29)/(x - 6) = m

where m = the slope of the straight line.

Calculate the slope.

m = (43 - 22)/(2 - 8) = -7/2

Answer:  y-29 = -7/2 (x-6)

Hence, The solution is,  the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water is

y-29 = -7/2 (x-6).

To learn more on equation click:

brainly.com/question/24169758

#SPJ1