Cross braces help keep the deck posts straight. Find the measure of each angle.

The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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The conjugate base of the weak acid hc2h3o2 (acetic acid) can be determined by removing a proton (H+) from the acid molecule. The formula for the conjugate base is C2H3O2- (acetate ion).

The formula for acetic acid (hc2h3o2) suggests that it consists of the elements hydrogen (H), carbon (C), and oxygen (O). To determine the formula of its conjugate base, we remove a proton (H+) from the acid molecule. Removing a proton results in the formation of an anion, which has a negative charge to maintain overall charge neutrality.

The removal of a proton from hc2h3o2 leads to the formation of the acetate ion, which has a formula of C2H3O2-. The C2H3O2- ion is referred to as the conjugate base of acetic acid.

In summary, the formula for the conjugate base of the weak acid hc2h3o2 (acetic acid) is C2H3O2- (acetate ion).

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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The number of siblings is 41.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

we have given,

The graph represents the number of siblings each student in a class.

the graph which represents the frequency of the number of students on the y-axis and the number of siblings on the x-axis.

Number of siblings = (0 * 6) + (1 * 7) + (2 * 4) + (3 * 2) + (4 * 5)

= 41

Hence, the number of siblings is 41.

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Answer:

$18

Step-by-step explanation:

1 pound of raisins = $2

1 pound of almonds = $5

Let the number of raisins be represented by a

Let the number of almonds be represented by b

We are told in the question that:

Six pounds of a trail mix contains 2 more pounds of raisins than almonds.

a + b = 6 pounds

Hence, Almonds = 2 pounds

Raisins = 4 pounds

The cost of the 6 pounds of trail mix

= 4 × $2 + 2 × $5

=$8 + $10

= $18

Answer:

the answer is 27

Step-by-step explanation:

for the show your work all you have to do is write 3x3x3=27

Answer:

==========================

Simplify in steps below:

Answer:

√(-180) = 6i√(5)

Step-by-step explanation:

Given problem,

→ √(-180)

Let's simplify the problem,

→ √(-180)

→ √(-1) × √(180)

→ i√(180)

→ i√(36) × √(5)

→ i × 6 × √(5)

→ 6i√(5)

Hence, the answer is 6i√(5).

(a) To find g(-x), we substitute -x into the function g(x) = 3x + 8:

g(-x) = 3(-x) + 8

= -3x + 8

(b) To find -g(x), we multiply g(x) by -1:

-g(x) = -1 x (3x + 8)

= -3x - 8

(c) To find g(x + 2), we substitute x + 2 into the function g(x) = 3x + 8:

g(x + 2) = 3(x + 2) + 8

= 3x + 6 + 8

= 3x + 14

So, the simplified expressions are:

(a) g(-x) = -3x + 8

(b) -g(x) = -3x - 8

(c) g(x + 2) = 3x + 14

In summary, to find g(-x), we simply negate the x coefficient while keeping the constant term. To find -g(x), we multiply the entire function by -1. To find g(x + 2), we substitute x + 2 into the function and simplify the expression.

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Answer:

30 months total

Step-by-step explanation:

15+5=20

600÷20=30

The dot plot represents the number of pets owned by the students. The options provided will be explained in the following paragraph.

A dot plot is a simple graphical representation of data that uses dots to represent individual values. Each dot corresponds to a student's response indicating the number of pets they own. The dot plot for the given data would look as follows:

0: XXX

1: XXXX

2: XXX

4: XX

8: X

In this dot plot, each "X" represents one student's response. The numbers on the left side of the plot represent the number of pets, and the dots are placed above the corresponding number. The dot plot clearly shows the distribution of pet ownership among the students.

Now, let's examine the answer choices to find the one that matches the dot plot we drew. Since the dot plot shows the frequencies of different responses, we need to look for an answer choice that represents the same frequencies.

Among the answer choices, the option that matches the dot plot is: "2 students own 4 pets, and 4 students own 1 pet." This option correctly reflects the data presented in the dot plot, where we can see 2 dots above the number 4 and 4 dots above the number 1, indicating the corresponding frequencies.

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we have

15!12!(4−1)!

15!12!(3!)=3,758,268,687,305,932,800,000

therefore

the answer is

The evaluated quantities are:

a) −17 mod 2 = -1

b) 144 mod 7 = 4

c) −101 mod 13 = -10

d) 199 mod 19 = 9

To evaluate the given quantities, we will calculate the remainder when the given numbers are divided by the divisor.

a) −17 mod 2:

To find −17 mod 2, we divide −17 by 2 and calculate the remainder:

−17 ÷ 2 = -8 remainder -1

Therefore, −17 mod 2 is -1.

b) 144 mod 7:

To find 144 mod 7, we divide 144 by 7 and calculate the remainder:

144 ÷ 7 = 20 remainder 4

Therefore, 144 mod 7 is 4.

c) −101 mod 13:

To find −101 mod 13, we divide −101 by 13 and calculate the remainder:

−101 ÷ 13 = -7 remainder -10

Therefore, −101 mod 13 is -10.

d) 199 mod 19:

To find 199 mod 19, we divide 199 by 19 and calculate the remainder:

199 ÷ 19 = 10 remainder 9

Therefore, 199 mod 19 is 9.

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The scale factor is 1/2.

What is a scale factor?

When both the original dimensions and the new dimensions are known, the scale factor may be determined. The following is a basic formula to determine a figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.

Here, we have

Given: ΔDEF is a dilation image of ΔABC.

Let

z is the scale factor

z = DE/AB

We have

DE = 4units

AB = 8units

z = 4/8

z = 1/2

Hence, the scale factor is 1/2.

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you should mix 4.5 quarts of 100% juice and 1.5 quarts of 20% juice. a=4.5, b= 1.5

The US liquid quart is equivalent to two liquid pints, or one-fourth US gallon (57.75 cubic inches, or 946.35 cubic centimetres), and the US dry quart is equivalent to two dry pints, or 1/32 bushels (67.2 cubic inches, or 1,101.22 cubic cm). 32 ounces, 2 pints, 4 cups, and 14 gallon are all equivalent to one US liquid quart. When converting any dry component, keep in mind that a dry quart is equivalent to 4.6546 cups. A quarter gallon is equal to one quart in English (symbol: qt). The liquid and dry quarts of the US customary system and the imperial quart of the British imperial system are the three types of quarts now in use. They all generally measure one litre.

Let you should mix a quarts of 100% juice and b quarts of 20% juice.

\(a+b=6\)

100%a+20%b=6*8%

By solving the system of equation.

a=4.5

b= 1.5

So you should mix 4.5 quarts of 100% juice and 1.5 quarts of 20%.

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A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.

Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.

People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".

A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.

Therefore, the correct option for this question is C.

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So the two possible values are 2.5 + (3√7/2)i and 2.5 - (3√7/2)i.

To simplify the expression (20 ± i√1008)/8, we can start by simplifying the square root of 1008.

√1008 can be simplified as follows:

√1008 = √(16 × 63)

= √16 × √63

= 4√63

Now we can substitute this value back into the expression:

(20 ± i√1008)/8 = (20 ± i(4√63))/8

Next, we can simplify the expression by dividing both the numerator and the denominator by 4:

(20 ± i(4√63))/8 = 20/8 ± i(4√63)/8

Simplifying further:

20/8 = 2.5

(4√63)/8 = √63/2

= (√9 × √7)/2

= 3√7/2

The simplified expression is:

(20 ± i√1008)/8 = 2.5 ± (3√7/2)i

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Answer:

x=50°

Step-by-step explanation:

Since a right triangle equals a total area of 180°
you have 40° given and since it is a right triangle you also have 90° given so all we have to do is add 40° + 90° = 130° subtract 130° - 180° which would give you 50°

Answer:

x= 50 °

Step-by-step explanation:

all angles of a triangles is equal to 180

x= 180° - (90° +40°)

x= 180° - 130°

x= 50°

Company Z provides electricity to 19 houses in this neighborhood. To find the number of houses in the neighborhood that Company Z provides electricity to, we need to subtract the number of houses that Company X and Company Y provide electricity to from the total number of houses.

Number of houses provided electricity by Company X = \frac{1}{8} x 40 = 5

Number of houses provided electricity by Company Y = \frac{2}{5} x 40 = 16

Total number of houses provided electricity by Company X and Company Y = 5 + 16 = 21

Therefore, the number of houses that Company Z provides electricity to = Total number of houses - Number of houses provided electricity by Company X and Company Y

= 40 - 21 = 19

So, Company Z provides electricity to 19 houses in this neighborhood.

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The total cost for a waiting line does NOT specifically depend on d. the cost of a lost customer.

The cost of a waiting line system is typically determined by the cost of waiting and the cost of providing service. The cost of waiting can include factors such as the value of customers' time and the negative impact of waiting on customer satisfaction. The cost of service can include factors such as employee wages and overhead costs. The number of units in the system can also have an impact on the total cost, as higher demand may require more resources and lead to longer wait times. However, the cost of a lost customer is not typically considered a direct cost of the waiting line system, as it is not directly related to the operation of the system itself but rather to the potential impact on business revenue and customer loyalty.

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The monthly payment amount is $217.42 and the finance charge is $413.02.

The payment amount and finance charge can be found by using the formula below

Payment amount formula: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

Finance charge formula: Finance charge = Total payment - Loan amount

Where P = Loan amount

R = Interest rate per period

N = Number of periods

Given that a loan is made for $4800 with an APR of 12% and payments made monthly for 24 months

Therefore,P = $4800R = 12% / 12 = 1% per month

N = 24

Using the Payment amount formula above: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

PMT = ($4800 x 0.01 x (1 + 0.01)^24) / ((1 + 0.01)^24 - 1)

PMT = $217.42

Hence, the monthly payment amount is $217.42 (rounded to two decimal places).

Using the finance charge formula above: Finance charge = Total payment - Loan amount

Total payment = Payment amount x Number of periods

Total payment = $217.42 x 24 = $5213.02

Finance charge = $5213.02 - $4800

Finance charge = $413.02

Hence, the finance charge is $413.02 (rounded to two decimal places).

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Given z²+1/z² =14

using above equation,

z²+1/z² = 14

add 2 on both side,

z² + 1/z² + 2 = 14 + 2

the LHS is whole square of z + 1/z

so we can write it

(z + 1/z)² = 16z + 1/z = 4

Now we know,

(a + b)³ = a³ + b³ + 3ab(a+b)

here, a = z and b = 1/z,

substituting a and b in equation we will get,

(z + 1/z)³ = z³ + 1/z³ + 3z/z( z+ 1/z)

4³ = z³ + 1/z³ + 3×4

z³+ 1/z³ = 64-12

z³ + 1/z³ = 52

Answer:

52.

Step-by-step explanation:

Using the identity a^3 + b^3 = (a + b)(a^2 - ab + b^3):

z^3 + 1/z^3 = (z + 1/z)(z^2 - z *1/z + 1/z^2)

= (z + 1/z) (z^2 - 1 + 1/z^2)

= (z + 1/z) (14 - 1 )

= 13(z + 1/z).

Now using the identity a^2 + b^2 = (a + b)^2 - 2ab:

z^2 + 1/z^2 = ( z + 1/z)^2 - 2(z * 1/z)  = 14 So:

( z + 1/z)^2 - 2 = 14

( z + 1/z)^2 = 16

Taking z + 1/z = 4 we therefore have:

z^3 + 1/z^3 =  13 * 4 = 52.

Answer: The LCD is x(x-3)(x+1) the answer is c

Step-by-step explanation:

Answer:

Step-by-step explanation:

two angles are adjacent if they have a common side and a common vertex.

basically two angles that share a line

Verticcal angles are angles that are opposite of each other. like in ur example of the triangle for question 3,

angle 3 and 4 are vertical angles

Answer:Using the triangle inequality, we can conclude that the distance between towns B and C must be less than 121 km (the sum of the distances between towns A and B, and between towns A and C).

To find the exact length of the road connecting towns B and C, let's use the Pythagorean theorem.

Let x be the length of the road connecting towns B and C. Then we have:

x^2 = 61^2 + 60^2

x^2 = 3721 + 3600

x^2 = 7321

x ≈ 85.6 km

Therefore, the length of the road connecting town B and C is approximately 85.6 km.

Step-by-step explanation:

Samuel needs to score at least 96 on his next exam to achieve an average of 85.

Given that Samuel scored a 72, 92 and 80 on his first three exams,

We need to find his minimum score in the next exam so that he can have an average of 85 overall.

To find the minimum score Samuel needs to get on his next exam to achieve an average of 85, we can use the formula for the average:

Average = (Sum of scores) / (Number of scores)

Since we have the average and three exam scores, we can solve for the fourth score (let's call it "x"):

85 = (72 + 92 + 80 + x) / 4

To find "x," first, let's simplify the equation:

85 × 4 = 72 + 92 + 80 + x

340 = 244 + x

Now, isolate "x" on one side:

x = 340 - 244

x = 96

So, Samuel needs to score at least 96.

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Shortest distance between start and end point is 55.9 miles

According to given statement,

Terry had to travel south 50 miles and then west 25 miles.

We are taking X as a start point and Z is end point.

In triangle XYZ, we are taking angle Y to be of 90 degrees, which qualifies the Triangle XYZ to qualify Pythagorean theorem [The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right angle triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.]

XY = 50 miles

YZ= 25 miles

XZ^2 = XY^2 + YZ ^2

XZ^2 = (50) ^2 + (25) ^2 = 3125

XZ = 55.9

Shortest distance between start and end point is 55.9 miles

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Answer:

36 / 21 = h / 168 so h = 168 (12 / 7)

Step-by-step explanation:

i dont know how to explain it

Answer:

Total Area = 532 m²

Step-by-step explanation:

Triangle = ½bh.

Rectangle = lw.

Total Area = sum of individual areas =

(8 m × 16 m) / 2 + (16 m × 18 m) / 2

+ (18 m × 18 m) =

(64 m²) + (144 m²) + (324 m²) =

532 m²