in the eight-term sequence $a$, $b$, $c$, $d$, $e$, $f$, $g$, $h$, the value of $c$ is 5 and the sum of any three consecutive terms is 30. what is $a h$?

So, Part A:

By employing the sines law,

So,

Now, Part B:

Area of the mainsail:

Therefore, the answers to both parts are:

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The complete question is given below:

A sailmaker is designing a mainsail for a newly constructed sailboat. The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 50° angle at the head with the leach.

Part A: Determine the length of the leach.

Part B: Find the area of the mainsail.

PLS HELP :) 50 POINTS!!!

An equation to show the relationship between the cost, c, and the gallons of gasoline, g is; c = 4g

The general form of a linear equation in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are told that the cost of 5 gallons of gasoline is $20. Thus, the cost of one gallon of gasoline = 20/5 = $4 per gallons

Therefore if he cost is c, and the gallons of gasoline is denoted by g, then the formula to find the cost with these letters is;

c = 4g

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Raheem's monthly payment given that he paid no additional fees is $78.75

Monthly payment refers to the amount of money paid by a person every month over a period of time.

Amount remaining after down payment = Total cost of HDTV - Down payment

= $880.00 - $250.00

= $630.00

Amount to pay each month = Amount remaining after down payment / Number of months to make equal payment

= $630.00 / 8

= $78.75

In conclusion, the amount Raheem will pay monthly for a period of 8 months if he paid no additional fees is $78.75

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Answer:

yes

Step-by-step explanation:

√225 + √196

15 + 14

29

29 can be written as 29/1 thus 29 is a rational number

Heidi is able to walk 10/3 miles in 1 hour (60 min).

It is a method for determining the value of a single unit by subtracting the value of multiple units and subtracting the value of multiple units from of the value of a single unit.

Now, for the given question;

It takes Heidi 12 minutes to walk 2/3 miles.

Applying the unitary method.

Then, for in 1 minutes Heidi will walk = 2/(3×12).

For walking in 1 hour or 60 min =  (2×60)/(3×12).

Further simplifying;

In 1 hour = 10/3 miles.

Therefore, Heidi would be be able to walk 10/3 miles in 1 hour.

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Answer:

x= -6

Step-by-step explanation:

[tex]x-3(\frac{2}{3}x+3)=3(\frac{-3}{2}+1)-\frac{3}{2}\\\\x-2x-9=\frac{-9}{2}+3-\frac{3}{2}\\\\clear fraction\\\\2x-4x-18=-9+6-3\\\\-2x-18=-6\\\\-2x=12\\\\x=-6[/tex]

The different answer is 4 and the same answer is 10.

The new length of the string that Ed have now is  16.25 feet.

Fraction is some part of a total quantity.

Ed has a kite and a string of length[tex]7\frac{3}{4}[/tex] feet which is = [tex]\frac{31}{4}[/tex] feet.

He wants to extend the sting length so he added another 8.5 feet which is

= [tex]\frac{17}{2}[/tex] feet.

∴ The total length of the string will become

(31/4) + (17/2) feet.

= (31 + 34)/4 feet.

= 65/4 feet.

= 16.25 feet.

So, after he extended his string it has a length of 16.25 feet.

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Answer:

To find the new length of the string, we need to add the length of the new piece of string to the existing length.

The current string length is 7 and 3/4 feet. This can be written as a mixed number, 7 + 3/4 = 7 3/4.

The new piece of string measures 8.5 feet.

To add these two lengths, we can convert the mixed number to an improper fraction and then add the fractions together.

7 3/4 can be converted to an improper fraction as (7 * 4 + 3) / 4 = 31/4.

Now we can add the fractions:

31/4 + 8.5 = (31/4) + (8.5 * 4/4) = 31/4 + 34/4 = 65/4

To simplify the fraction, we can divide the numerator (65) by the denominator (4) to get the whole number part and the remainder.

65 ÷ 4 = 16 remainder 1

So the new length of the string is 16 1/4 feet.

Therefore, the new length of the string is 16 and 1/4 feet.

Step-by-step explanation:

By rationalization and algebra properties, the irrational expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is equivalent to the integer 1.

In this question we find a composite irrational expression formed by a irrational fraction being subtracted by other two irrational fraction. Eliminating the irrational denominators by transforming it into rational numbers is an important step for this question, this can be done by means of rationalization, along with algebra properties.

The complete procedure of this exercise is shown below:

7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)

[7√3 · (√10 - √3)] / [(√10 + √3) · (√10 - √3)] - [2√5 · (√6 - √5)] / [(√6 + √5) · (√6 - √5)] - [3√2 · (√15 - 3√2)] / [(√15 + 3√2) · (√15 - 3√2)]

(7√30 - 21) / 7 - (2√30 - 10) - (3√30 - 18) / (- 3)

(7√30 - 21) / 7 + (10 - 2√30) + (3√30 - 18) / 3

(7√30 - 21 + 70 - 14√30) / 7 + (3√30 - 18) / 3

(49 - 7√30) / 7 + (3√30 - 18) / 3

(147 - 21√30 + 21√30 - 126) / 21

21 / 21

1

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The length of each side of the given tilted square is √41 units.

The formula to find the area of a square is;

Area = x²

Where x is the side length of the square.

Thus;

x = √41

Now, since all sides of a square are always equal, we can easily say that the length of each side of the given tilted square is √41 units.

Thus, our conclusion is that the length of each side of the given tilted square is √41 units.

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Answer:

The answer to your first question would be B. The answer to the second is C.

Step-by-step explanation:

Hope it helps! =D

45,000 square feet  is the largest area that can be enclosed.

What is rectangle?

The largest area will always be a square.

600/4=150 feet on each side but one side is not needed

put this 150 feet not needed with the opposite 150 feet to get 300 feet

you have a rectangle 150 by 300 by 150 by the river

         = 150 * 300 =  45,000 square feet

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The complete question is -

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and the width of the plot that will maximize the area. What is the largest area that can be enclosed?

Answer:

70% i think

Step-by-step explanation:

The solution to the system of equation is -7/2 and 1

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.

Given the quadratic equation below;

(2x-1)(x+3)=4

Expand

2x^2+6x-x-3 = 4

2x^2+5x-3-4=0

2x^2+5x-7=0

2x^2-2x+7x-7=0

2x(x-1)+7(x-1) = 0

2x+7 = 0 and x - 1 = 0

x = -7/2 and x = 1

Hence the solution to the system of equation is -7/2 and 1

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Answer: 4/25

Step-by-step explanation:

[tex](\frac{2}{5}) ^2=\frac{2}{5}\times\frac{2}{5}=\large\boxed{\frac{4}{25} }[/tex]

The constant percent rate of change is of 4%

Using compound interest, it is found that the constant percent rate of change is of 4%.

The formula for an amount of money invested into compound interest is given by:

[tex]A(t) = A(0)(1+r)^{t}[/tex]

In which:

A(t) is the amount after t years.

A(0) is the initial amount.

r is the constant percent rate of change.

t is the time.

The function is:

[tex]g(x)=300(1.04)^{x}[/tex]

Thus, for the constant percent rate of change:

1+r = 1.04;

r = 0.04;

0.04 × 100% = 4%

The constant percent rate of change is of 4%.

An annual percentage rate is expressed as an hobby charge. It calculates what percentage of the major you will pay every year by using taking things inclusive of month-to-month bills under consideration. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.

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Answer:

(C)  [300, ∞)

Step-by-step explanation:

Got it right on my quiz.

Answer:

A) 5n − 11

B) 11 − (n + 5)

C) 11 − 5n

D) 5(n − 11)

Your Welcome ;)

The required verbal algebraic expressions are given as ,
(a)  5x - 11    (b) (x + 5) - 11

(c)  5x - 11     (d) (x - 11)×5

The algebraic expression consists of constants and variables. eg x, y, z etc.

Here,
Let the number x,

a. The product of five and a number, decreased by eleven

⇒ 5x - 11

b. The sum of a number and five less than eleven

⇒ (x + 5) - 11

c. Five times a number fewer than eleven

⇒5x - 11

d. The quantity of a number minus eleven, multiplied by five

⇒(x - 11)×5

Thus, the required expression is shown above

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24 seconds faster time of your personal best after 200 yards.

What in mathematics is a linear equation?

Suppose the number of laps = m

According to the question, each lap of 25 yards is covered 3 seconds faster than the previous one, so the series become

x , x-3 , x-6 , x-9, ............................

25 * m = 200

m = 200/25

m = 8

As m is the number of laps, and each lap is 3 second faster.

So 8 laps will be 8*3 = 24 seconds faster.

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Answer:

this doesn't make sense cuz 15 have red 21 have black and that's 36 kids but the title says there is 21 kids in all ?

Step-by-step explanation:

The equation of the parabola that models the situation is given by:

(x - 1)² = -16(y - 5).

The equation of a quadratic function, of vertex (h,k), is given by:

(x - h)² = 4p(y - k).

The focus is located at point (h, k + p).

For this problem, to find the values of the parameters h and k, we have that:

Hence:

h = 1, k = 5.

And:

(x - 1)² = 4p(y - 5).

For the focus, and subsequently to find parameter p, we have that:

Hence:

k + p = 1.

5 + p = 1

p = -4.

Then the equation of the parabola that models this situation is given by:

(x - 1)² = 4p(y - 5).

(x - 1)² = 4(-4)(y - 5).

(x - 1)² = -16(y - 5).

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The additional information required to prove the SSS Triangle Congruence Postulate is UT = T F

The congruence postulate is given as:

SSS Triangle Congruence Postulate

The above means that the three sides of the triangles are congruent.

From the figure, the following side lengths are said to be congruent

UV and FV

TV and TV

For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent

This is represented as:

UT = T F

Hence, the additional information required to prove the SSS Triangle Congruence Postulate is UT = T F

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The value of the expressions will be:

1. -13.

2. 4

3. -9

4. 27

5. 0

It should be noted that this is an expression. In this case:

minus × minus = plus

plus × minus = minus

1. (-15) - (-2)

= -15 + 2

= -13

2. (-3( - (-7)

= -3 + 7

= 4

3. 4 - 13

= -9

4. 5 - (-22)

= 5 + 22

= 27

5. (-15) - (-15)

= -15 + 15.

= 0

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Value of a and b that completes the mapping diagram will be a=0 and b=1

• Mapping diagram simply means a function that has a special type of relation where the elements of the domain are paired with that of the range.

• Mapping diagram consists of two parallel columns, the first column depicts the domain of the function whereas the second column depicts the range.

• Lines are drawn from first column to second column i.e. from domain to range, to represent the relation between 2 elements.

• Mapping is quite similar to making a flowchart, showing input and output values.

• Point to be noted that every mapping is a relation but every relation is not a mapping.

Value of a and b that completes the mapping diagram will be a=0 and b=1

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Answer: A = 0, and B = 1.

Step-by-step explanation: I put 0, and 1, and it was the perfect answer.

Answer:

[tex]\frac{31}{33}[/tex]

Step-by-step explanation:

You need a common denominator to add.  The smallest number that is divisible by both 11 and 3 is 33.  Rewrite both fractions with a denominator of 33

[tex]\frac{3}{11}[/tex] x [tex]\frac{3}{3}[/tex]         [tex]\frac{3}{3}[/tex] is just another name for 1.  We are making an equivalent fraction.  Multiple 3 x3 for the top and 11 x 3 for the bottom to get:

[tex]\frac{9}{33}[/tex]

Do the same for [tex]\frac{2}{3}[/tex]

[tex]\frac{2}{3}[/tex] x [tex]\frac{11}{11}[/tex]       [tex]\frac{11}{11}[/tex] is just another name for 1.  We are making an equivalent fraction.  Multiple 2 x 11 for the top and 3 x 11 for the bottom to get:

[tex]\frac{22}{33}[/tex]

Now add these two fractions together:

[tex]\frac{9}{33}[/tex] + [tex]\frac{22}{33}[/tex] = [tex]\frac{31}{33}[/tex]

Answer:

Step-by-step explanation:

74 caps

Answer:

The answer is 47.5 because in my math exam i got 47.5 in 50

The possibility that experimental results are due to chance, or some factor other than the experimental variable, is measured by the Probability Value.

Probability value, also called P-value, is defined as:

Under the premise that the null hypothesis is true, the p-value is the likelihood that test findings will be at least as extreme as the result actually observed.

Now,

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