Find the 9th term of the arithmetic sequence − 5 � + 1 −5x+1, − 8 � + 5 −8x+5, − 11 � + 9 , . . . −11x+9,...

The value of the variable x in first figure will be 15.

The value of the variable x in second figure will be 20.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

There are two figure is shown in figure.

Now,

In first figure;

The sum of all the interior angle in a triangle is 180°.

So, We can formulate;

⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°

Solve for x as;

⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°

⇒ 6x - 10 + 2x + 20 + 3x + 5 = 180°

⇒ 11x + 15 = 180

⇒ 11x = 180 - 15

⇒ 11x = 165

⇒ x = 15

Thus, The value of the variable x in first figure will be 15.

For second figure;

We can formulate by the corresponding angle of the parallel lines as;

⇒ x + 50 = 70

⇒ x = 70 - 50

⇒ x = 20

Thus, The value of the variable x in second figure will be 20.

Therefore,

The value of the variable x in first figure will be 15.

The value of the variable x in second figure will be 20.

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The area of the rectangular garden is (56 + 7/20) ft^2

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case, we have:

Length = (5 + 3/4)ft

Width = (9 + 4/5)ft

Taking the product we get:

A = (5 + 3/4)ft*(9 + 4/5)ft = 45ft^2 + 4ft^2 + 27/4ft^2 + 12/20 ft^2

                                        = 49ft^2 + 147/20 ft^2

                                        = 49ft^2 + 7ft^2 + 7/20ft^2

                                         = (56 + 7/20) ft^2

The area of the garden is (56 + 7/20) ft^2

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The relationship between two equal amounts is described by the characteristics of equality

The relationship between two equal amounts is described by the characteristics of equality. To maintain balance, each mathematical operation that is done to one side of an equation must also be applied to the opposing side.

a = 2b, then a-c = 2b - c

This is Subtraction Property of Equality

According to the Subtraction Property of Equality, if two equal things have an equal value subtracted from them or deleted, the outcome is a new equal quantity. When two equivalent sides of a mathematical statement are separated by an equal sign, an equation is being expressed. The subtraction property has the expression if a = b, then a - c = b - c.

X = X

This represents the Reflexive Property

In algebra, a number is always equal to itself according to the reflexive property of equality.

3(p-7) = 3p - 21

This represent distributive property.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

-7k = -42 then k= 6

This is Division Property of Equality

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

m + n = 15 and n = 2, then m + 2 = 15

This represent Substitution Property

x/4 = -5 then x = -20

This is Multiplication Property of Equality

w² = 2x and 2x = y, then w² = y

This is Transitive Property

c-9 = -1, then c = 8

This is Addition Property of Equality

n = -3, then -3 = n

This is Symmetric Property

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Answer: question#7 is 7/12

question#8 is 1  3/8

question#5 is 1/2

question#6 is 12

question#9 is 1  1/6

question#10 is 31/40

question#11 is 3/4

Step-by-step explanation: give brainliest

Question #5: Option A, \(\frac{1}{2}\)

Question #6: Option A, 12

Question #7: Option A, \(\frac{7}{12}\)

Question #8: Option D, \(1\frac{3}{8}\)

Question #9: Option D, \(1\frac{1}{6}\)

Question #10: \(\frac{31}{40}\)

Question #11: \(\frac{3}{4}\)

Pls mark brainliest

Your answer will be D 13

Answer:

90

Step-by-step explanation:

Angles 2 and 3 are complementary; this means that they sum 90 degrees. You know that they are complementary because the 2 non-right angles in a right triangle always sum to 90. This makes sense because all triangles equal 180 and one of the angles is 90 degrees; therefore, the others must equal 90. In this case, angles 1 is 90 degrees because it forms a linear pair with a 90-degree angle.

a)Total material to be excavated: 1,613 cubic yards

b) Number of days to complete the work: 11 days

c) Number of weeks to complete the work: 2 weeks

d) Labor and material cost: $17,600

e) Rate per cubic yard of material removed: $260

a) The volume of the lake:

Area of the lake = 1 acre

Average depth of the lake = 5 feet

Convert the area to square feet: 1 acre = 43,560 square feet

Volume of the lake = Area × Depth = 43,560 cubic feet

Convert the volume to cubic yards: 43,560 / 27 = 1,613 cubic yards

b) The number of days to complete the work:

The contractor can remove 150 cubic yards of material in 1 shift.

Divide the total volume of the lake by the amount removed in a shift: 1,613 / 150 = 10.75 ≈ 11 days

c) The number of weeks to complete the work:

The contractor removes 100 cubic yards of material per day for 2 days of the week.

The contractor removes 150 cubic yards of material per day for the remaining 5 days of the week.

Calculate the total amount of material removed in a week:

(100 × 2) + (150 × 5) = 950 cubic yards

Divide the total volume of the lake by the amount removed in a week:

1,613 / 950 = 1.7 ≈ 2 weeks (rounded to whole number)

d) The labor and material cost:

The cost of the operator and helper per hour is $200.

Calculate the total production:

Amount produced on Mondays and Fridays

=100 cubic yards per day × 2 days = 200 cubic yards

Amount produced on the remaining 5 days

= 150 cubic yards per day × 5 days = 750 cubic yards

Total production in the first week

= 200 + 750 = 950 cubic yards

The total hours worked in the first week:

Hours worked on Mondays and Fridays

= 2 days × 8 hours/day = 16 hours

Hours worked on the remaining 5 days

= 5 days × 8 hours/day = 40 hours

Total hours worked in the first week

= 16 + 40 = 56 hours

The labor and material cost in the first week:

Labor and material cost per hour = $200

Total labor and material cost in the first week

= 56 hours × $200/hour = $11,200

The amount produced in the second week and total hours worked:

Amount produced in the second week = Total volume - Amount produced in the first week

= 1,613 - 950 = 663 cubic yards

Total hours worked in the second week

= 3 days × 8 hours/day + 2 days × 8 hours/day = 32 hours

The labor and material cost in the second week:

Labor and material cost in the second week = Total hours worked in the second week × $200/hour

= 32 hours × $200/hour = $6,400

Total labor and material cost = Labor and material cost in the first week + Labor and material cost in the second week = $11,200 + $6,400 = $17,600

e) The rate per cubic yard of material removed:

A 30% markup is required.

Calculate the markup amount: 30% × $200 = $60

Calculate the rate per cubic yard: $200 + $60 = $260 per cubic yard

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The equation of line is y = -5/7 x -4/7.

we have the points (9,−7) and ( − 5 , 3 ).

So, slope of line

= (3 + 7)/ (-5 -9)

= 10 / (-14)

= -5/7

and, the equation of line is

y + 7 = -5/7 (x - 9)

y+ 7 = -5/7 x + 45/7

y = -5/7 x + 45/7 - 7

y = -5/7 x -4/7

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In this experimental design, the y variable is the testosterone levels.

A variable is defined as any symbol or letter that is used to express an unknown quantity. There are two types of variables: the dependent variable (y variable) and the independent variable ( x variable).

An independent variable (x variable) is the variable which causes the change in another variable.

A dependent variable (y variable) is the result or effect of that change in the dependent variable.

If we are interested in what happens to testosterone levels as the men age in adult men ages 18 years and older, then the x variable is the age and the y variable is the testosterone levels.

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If derivative of \(f(x)=ln(x+4+e^{(-3x)})\), then f '(0) = -2/5.

What is derivative?

In calculus, the derivative of a function is a measure of how the function changes as its input changes. More specifically, the derivative of a function at a certain point is the instantaneous rate of change of the function at that point.

To find f'(0), we first need to find the derivative of f(x) with respect to x. Using the chain rule, we get:

\(f'(x) = 1 / (x+4+e^{(-3x)}) * (1 - 3e^{(-3x)})\)

Now we can find f'(0) by substituting the value x=0:

\(f'(0) = 1 / (0+4+e^{(-3(0))}) * (1 - 3e^{(-3(0))})\)

f'(0) = 1 / (4+1) * (1 - 3)

f'(0) = -2/5

Therefore, f'(0) = -2/5.

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Answer:

2/5

Step-by-step explanation:

Answer:

\(A=28.1\ cm^2\)

Step-by-step explanation:

The area of a circular sector with a central angle θ and radius r is given by:

\(\displaystyle A=\frac{1}{2}r^2 \theta\)

Note: The angle must be in radians.

We need to find both the radius and the angle in radians.

Diameter = 9.6 cm

Radius r=Diameter/2=4.8 cm

Angle in radians= Angle in degrees*π / 180

θ = 140*π / 180 = 2.4435 rad

Now we calculate the area:

\(\displaystyle A=\frac{1}{2}(4.8)^2 2.4435\)

\(\boxed{A=28.1\ cm^2}\)

The domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0. a) The domain of the vector function r(t) = [ln(6t), -t + 16, 1/(10t)] can be determined by considering the individual components.

The natural logarithm, ln(6t), is defined only for positive values of 6t, so we need 6t > 0. This implies that t > 0.

The second component, -t + 16, is defined for all real values of t.

The third component, 1/(10t), is defined as long as 10t ≠ 0, which means t ≠ 0.

Putting these conditions together, we find that the domain of r(t) is t > 0.

b) The vector function r(t) = [t - 9, sin(6t), t^2] does not have any explicit restrictions on its domain.

The first component, t - 9, is defined for all real values of t.

The second component, sin(6t), is also defined for all real values of t.

The third component, t^2, is defined for all real values of t.

Therefore, the domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0.

b) The domain of r(t) = [t - 9, sin(6t), t^2] is (-INF, INF).

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The domains of the vector functions r(t) are respectively: for the first one t > 0, for the second one t >= 9 and for the third one it is a union of intervals, t < -6 U t > 6.

The domain of a vector function r(t) is defined as the set of all t-values for which the function is defined.

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Answer:

6 is in the tens place

Step-by-step explanation:

5 is is the hundreds place. 6 is in the tens place and 8 is in the ones place.

\(*GraceRosalia*\\*IAmAnExpertICanHelpYou*\\PleaseMarkBrainliestThankYou\)

Answer: This is what I got??  It doesn't feel right.

X = -5.7

Step-by-step explanation:

Let B = 12/C

Solve the other two equations for A.

Then set both equations, solved for A, equal to each other.

Substitute 12/C for B.

Cross Multiply.

Answer:

See below

Step-by-step explanation:

Step 1: Take the reciprocal of the divisor

Step 2: Multiply the fractions instead

Step 3: Evaluate

Example:

\(\frac{1}{2}\div\frac{2}{3}\)

\(\frac{1}{2}*\frac{3}{2}\)

\(\frac{3}{4}\)

Answer:

Step-by-step explanation:

1) reciprocal: reverse the numerator and denominator of the second fraction.

2) multiply the numerators.

3) multiply the denominators.

4) simplify the resulting fraction if needed.

The original temperature of the hydrogen gas was approximately 90°C.

To find the original temperature of the hydrogen, we can use the ideal gas law equation, which states that the product of pressure (P), volume (V), and temperature (T) is proportional to the number of moles (n) and the gas constant (R). Mathematically, it can be represented as PV = nRT.

In this scenario, the pressure and volume of the hydrogen remain constant, and we need to find the original temperature (T1). We can set up the following equation:

(P1)(V1) / T1 = (P2)(V2) / T2

Where:

P1 and P2 are the initial and final pressures, respectively.

V1 and V2 are the initial and final volumes, respectively.

T2 is the final temperature (140 degrees Celsius).

V2 is the final volume (90.0 L).

Rearranging the equation to solve for T1, we get:

T1 = (P1)(V1)(T2) / (P2)(V2)

Plugging in the given values:

T1 = (P1)(V1)(T2) / (P2)(V2)

T1 = (1 atm)(58.0 L)(140°C) / (1 atm)(90.0 L)

T1 ≈ 90.44°C

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Answer:

b>1

Step-by-step explanation:

\(3(3b-4)> 8b-11\\9b-12> 8b-11\\9b-8b> -11+12\\b> -11+12\\b>1\)

Therefore, this dataset is an essential tool for medical students who want to make informed decisions about their future careers.

Answer: The MedGPA dataset in the Stat2Data package in R comprises 55 applicants' details who have applied for medical schools from a liberal arts college in the Midwest. The dataset consists of eleven variables, including the number of medical schools they applied to. This dataset provides comprehensive information that can be used to analyze and understand the various factors affecting students' application to medical school. The analysis of this dataset can help students make informed decisions about their future educational goals and career paths.

The Apps variable in the MedGPA dataset shows the number of medical schools each applicant has applied to. This variable can help analyze the factors affecting the number of medical schools applied to by different applicants. Other variables in the dataset, such as MCAT, GPA, and Sex, can be used to analyze the relationship between these factors and the number of medical schools applied to by the applicants. The analysis of this relationship can provide insights into the factors that influence students' decisions to apply to medical school and can be used to develop strategies to encourage more students to apply to medical school.

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Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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The remote interior angles of angle BCD is determined as angle CAB and angle CBA.

Remote interior angles are those that don't share a vertex or corner of a triangle with the exterior angle.

The remote interior angles are the angles that are separated by other angles within a given a triangle.

From the diagram of the triangle, the remote interior angles of angle BCD are determined as follows;

Thus, the remote interior angles of angle BCD is determined as angle CAB and angle CBA.

So the correct answer based on the remote interior angles are;

∠ CAB, and

∠ CBA

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The equation first, third, fifth and seventh are equivalent to the fifth, second, fourth and eighth equation.

Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.

Equivalent expression can be found out by simplifying the given equation.

First equation given as,

\(\left(-14+\dfrac{3}{2}b\right)-\left(1+\dfrac{8}{2}b\right)\)

Simplify it further,

\(\left(-14+\dfrac{3}{2}b\right)-\left(1+\dfrac{8}{2}b\right)\\-14+\dfrac{3}{2}b-(1+4b)\\-14+\dfrac{3}{2}b-1-4b\\-15-\dfrac{5}{2}b\)

Third equation in the problem given as,

\(\left(5+2b\right)+\left(2b+\dfrac{3}{2}\right)\\5+2b+2b+\dfrac{3}{2}\\4b+\dfrac{13}{2}\)

Simplify it further,

\(\left(-14+\dfrac{3}{2}b\right)-\left(1+\dfrac{8}{2}b\right)\\-14+\dfrac{3}{2}b-(1+4b)\\-14+\dfrac{3}{2}b-1-4b\\-15-\dfrac{5}{2}b\)

Similarly, the fifth and seventh equation are simplified and equivalent to the fourth and eight respectively.

Thus, the equation first, third, fifth and seventh are equivalent to the fifth, second, fourth and eighth equation.

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Answer:

Step-by-step explanation:

x ÷ 48 = 4

Multiplying both sides by 48 we get:

x ÷ 48 x 48 = 4 x 48

x =  192

20=5x-13+6x

We move all terms to the left:

20-(5x-13+6x)=0

We add all the numbers together, and all the variables

-(11x-13)+20=0

We get rid of parentheses

-11x+13+20=0

We add all the numbers together, and all the variables

-11x+33=0

We move all terms containing x to the left, all other terms to the right

-11x=-33

x=-33/-11

x= 3

Answer:

3

Step-by-step explanation:

First, write the equation.

20=5x-13+6x  Combine like terms on the right side.

20=11x-13       Add 13 on both sides.

+13     +13

33=11x             Divide both sides by 11.

/11  /11

3=x

Hope this helps!! Have a wonderful day :3

To determine the dimensions of the flyer that will result in the maximum printed area, we can use the concept of optimization.

Let's assume the width of the flyer is x inches and the height of the flyer is y inches. We are given that the top and bottom margins are 1 inch each, and the side margins are 1/2 inch each.

The printable area of the flyer is given by the product of the width and height minus the margins. So, the area is given by:

A = (x - 2 * (1/2)) * (y - 2 * 1)

A = (x - 1) * (y - 2)

We are also given that the area of the flyer should be 32 in². So, we can write the equation:

(x - 1) * (y - 2) = 32

Now, we need to maximize the area A, which means we need to maximize the expression (x - 1) * (y - 2).

To find the maximum, we can take the partial derivatives of A with respect to x and y and set them equal to zero:

∂A/∂x = y - 2 = 0

∂A/∂y = x - 1 = 0

Solving these equations, we find x = 1 and y = 2.

Therefore, the dimensions of the flyer that will result in the maximum printed area are x = 1 inch (width) and y = 2 inches (height).

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Answer:

d≈8cm

Step-by-step explanation:

Answer:

8cm

Step-by-step explanation:

Ap3x

A possible confounding variable that that would help explain the relationship between hair length and height of college age students is their gender.

Confounding variable is an extraneous variable that is related to both the dependent and independent variable, and it affects the result of the study. Therefore, it causes the effect of the independent variable on the dependent variable to be distorted. A possible confounding variable that would help explain the relationship between hair length and height of college age students is their gender. If the study didn't control for gender, then it would be difficult to determine if the relationship between hair length and height of college age students was a direct relationship or if it was due to the confounding variable (gender).For example, if the study found that female college age students tend to have shorter hair and are shorter than male college age students. Therefore, this would make the relationship between hair length and height spurious. Hence, a possible confounding variable that would help explain the relationship between hair length and height of college age students is their gender.

A possible confounding variable that would help explain the relationship between hair length and height of college age students is their gender. The gender of college age students could play a role in determining their height and hair length. If the study didn't control for gender, then it would be difficult to determine if the relationship between hair length and height of college age students was a direct relationship or if it was due to the confounding variable (gender). For example, if the study found that female college age students tend to have shorter hair and are shorter than male college age students. Therefore, this would make the relationship between hair length and height spurious. This means that the relationship between the two variables was not a direct one, but was rather due to the confounding variable (gender). Therefore, in order to determine if there is a direct relationship between hair length and height of college age students, the study needs to control for gender.

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Answer:

4

Step-by-step explanation:

6n - n = 5n

13 + 7 = 20

5n = 20

20/5 = 4

n = 4

Answer:

n = 4

Step-by-step explanation:

To solve this, we first have to get the n's on one side:

\(6n - 7 = n + 13\)

↓ add 7 to both sides

\(6n = n + 20\)

↓ subtract n from both sides

\(5n = 20\)

Then, we can divide by 5 on both sides to solve for n.

\(n = 4\)