Please help me with this Problem!

The first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

Given is an arithmetic sequence, [tex]a_{k+1} = a_k-20[/tex] and [tex]a_1 = 300[/tex],

we need to find the first five terms,

a₂ = a₁-20

a₂ = 300-20

a₂ = 280

a₃ = a₂-20

a₃ = 260

a₄ = a₃ - 20

a₄ = 240

a₅ = a₄ - 20

a₅ = 220

aₙ = aₙ₊₁ - 20

d = 20

Hence, the first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20

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The another example that supports Hilary's conjecture are, 26² - 21²

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

Given that,

Hilary was examining the differences between perfect squares of numbers separated by 5.
The differences always have the digit 5 in the ones place.

Another example that supports Hilary's conjecture is:

= 26² - 21²

= 676 - 441

= 235

As we can see, the difference between the perfect squares of 26 and 21 is 235,

which ends in the digit 5 in the ones place, confirming Hilary's conjecture that the differences between perfect squares of numbers separated by 5 always have the digit 5 in the ones place.

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Answer:

0.262

Step-by-step explanation:

1 - 0.738 = 0.262

0, 738 + 0.262 = 1

We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is  [tex]\mathrm{\dfrac{1}{m^4}}[/tex] .

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In language, a phrase by itself may contain an action, but it does not constitute a complete sentence.

The following are some examples of expressions and word phrases that they relate to:

Expression: 3 + 7

Given

⇒ [tex]\mathrm{(m)^6^{(-2/3)}}[/tex]

⇒ [tex]\mathrm{(m)^{(-12/3)}}[/tex]

⇒ [tex]\mathrm{(m)^{(-4)}}[/tex]

⇒ [tex]\mathrm{\dfrac{1}{m^4}}[/tex]

We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is  [tex]\mathrm{\dfrac{1}{m^4}}[/tex]

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(a) Conversion of 15 minutes and r minutes into hours, 0.25 hours & r/60 hours.

(b) An equation in terms of t and solution of it,  S = 0.04r miles and  r = 10

(c) Alex's average speed for the whole journey is, 3.33 mph

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

(a) 15 minutes is equal to 0.25 hours (15/60) and r minutes is equal to r/60 hours.

(b) Let's use the formula:

distance = speed x time for both jogging and walking.

Distance traveled while jogging = 4 mph x 0.25 hours

                                                     = 1 mile

Distance traveled while walking = 2.4 mph x (r/60) hours

                                                     = 0.04r miles

Total distance traveled = 1 mile + 0.04r miles

                                      = 1.4 miles

Solving for r, we get:

0.04r = 0.4

r = 10

So, Alex walked for 10 minutes.

(c) Total time taken = 15 minutes + 10 minutes

                                = 25 minutes

                                = 0.42 hours

Total distance traveled = 1.4 miles

Average speed = Total distance / Total time

                          = 1.4 miles / 0.42 hours

                          = 3.33 mph (rounded to two decimal places).

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56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

What is Total price?

In order to calculate the total price of something is by using this formula. Purchase Price = Cost Price + Margin.

To find out how much gas will be needed to make 27 brackets, we need to multiply the amount of gas required for making one bracket by the number of brackets to be made.

So, the total amount of gas needed to make 27 brackets would be:

2.1 cu ft * 27 = 56.7 cu ft

Therefore, 56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

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Answer:46

Step-by-step explanation:

180=104+30+x

134+x=180

x=46

The length and width of the rectangular wall of a barn given the area is 22 feet and 5 feet respectively.

Area of the rectangular wall of a barn = 110 square feet

Width of the barn = w

Length of the barn= 2w + 12

Area of a rectangle = length × width

110 = (2w + 12) × w

110 = 2w² + 12w

equate to 0

2w² + 12w - 110 = 0

w² + 6w - 55 = 0

using factorization method of solving quadratic equation

w² + 11w - 5w - 55 = 0

w(w + 11) - 5(w + 11) = 0

(w - 5) (w + 11) = 0

w = 5 or w = -11

The width of the rectangular barn cannot be negative

Therefore,

Width of the barn = w

= 5 feet

Length of the barn= 2w + 12

= 2(5) + 12

= 10 + 12

= 22 feet

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Answer:

2

:

5STEP

2

:

Trying to factor as a Difference of Squares:

2.1 Factoring: 5-3x2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

2

:

5 - 3x2 = 0

STEP

3

:

Solving a Single Variable Equation:

3.1 Solve : -3x2+5 = 0

Subtract 5 from both sides of the equation :

-3x2 = -5

Multiply both sides of the equation by (-1) : 3x2 = 5

Divide both sides of the equation by 3:

x2 = 5/3 = 1.667

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 5/3

The equation has two real solutions

These solutions are x = ±√ 1.667 = ± 1.29099

Two solutions were found :

x = ±√ 1.667 = ± 1.29099

The fraction of Mrs. Stanford's class that came late and brought notes that day was 1 / 4

To find the fraction of Mrs. Stanford's class that came late and brought notes that day, the relevant formula would be:

= Fraction of students who came late x Fraction of late students who brought notes

Fraction of students who came late = 3 / 4

Fraction of students who were late and brought notes = 1 / 3

The fraction of total students who were late and brought notes were ;

= 3 / 4 x 1 / 3

= 3 / 12

= 1 / 4

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The missing side length from the given figure is 6 ft.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

Missing side = x

Now,

The expression we can make from the figure.

= 16 - 10

= 6 ft

Thus,

The missing side length is 6 ft.

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radius = 9 cm

height = 26,5 cm

as we know that

volume of cylinder = πr^2h

= 3,14x9x9x2x26,5

= 13.480 cm cubic

The proofing will be illustrated thus:

1.  Seg. AC bisects ∠BAD                                 1.  Given

2.  (m=measure) m∠BAC=∠CAD                      2.  Definition of angle bisector

   Therefore, m∠BAC≅∠CAD.

3.  AC=AC                                                      3.  reflexive property

4.  ∠ABC =∠ADC                                            4.  Given

5.  Triangle ABC≅Triangle ADC                        5.  Angle-Angle-Side (AAS postulate).

6.  Therefore, BC=DC                                     6. CPCTC

It should be noted that AAS stands for Angle-Angle-Side. In this case, ehen two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Corresponding parts of congruent triangles are congruent.

Here, the two pairs of angles correspond, but there is a shared side that is not between the angles.

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Given: AC bisects \angle BAD

Given: AC bisects \angle BAD

\angle ABC=\angle ADC

Write a two-column proof to prove= BC=DC

The equation of the polynomial is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following readings:

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 3)(x + 2)(x - 1)(x - 3)^2

The y-intercept is 2

So, we have

a * (0 + 3)(0 + 2)(0 - 1)(0 - 3)^2 = 2

This gives

a = -1/27

Hence, the expression is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

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Answer:

The [tex]66[/tex]th term is [tex]363[/tex].

Step-by-step explanation:

To find the [tex]n[/tex]th term, the formula is [tex]7n - 99[/tex]. Since we want to find the [tex]66[/tex]th term, we can plug [tex]n[/tex] for [tex]66[/tex]. So our expression is now [tex]7 \cdot 66 - 99 =[/tex] [tex]66[/tex]th term. Solving this we have

[tex]462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\[/tex]. Therefore, the [tex]66[/tex]th term is [tex]\boxed{363}[/tex].

Answer:

a₆₆ = 363

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then

a₆₆ = - 92 + (65 × 7)

      = - 92 + 455

     = 363

The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Domain: The domain of the function is the set of all real numbers greater than -8, since the argument of the logarithm, x + 8, must be positive.

Range: The range of the function is all real numbers.

Asymptotes: The function does not have any vertical asymptotes.

Transformation: The function is a reflection of the standard logarithmic function over the x-axis, with a vertical scaling factor of -2. This means that the function will start from the origin and increase without bound.

Behavior near x = -8: As x approaches -8 from the right, the value of the function approaches negative infinity. As x approaches -8 from the left, the value of the function approaches positive infinity.

The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.

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Answer:

Step-by-step explanation:

To calculate 8% of 350, we can first calculate 1% of 350 and then multiply it by 8.

1% of 350 is equal to 0.01 times 350 which can be calculated as:

0.01 * 350 = 3.5

Since 1% of 350 is equal to 3.5, 8% of 350 can be calculated as follows:

8 * 3.5 = 28

So, 8% of 350 is equal to 28.

Opposite sides JK and ML are equal and parallel (with slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ are equal and parallel (with slopes of 7/3 or 7). /3) We can conclude that JKLM is a parallelogram. 

To determine if JKLM is a parallelogram, we need to check if its opposite sides are parallel and equal in length.

First, we can find the lengths of the sides using the distance formula:

JK = [tex]\sqrt{(1 - (-4))^2 + (3 - 2)^2} = \sqrt{25} = 5[/tex]

KL = [tex]\sqrt{(-4 - (-1))^2 + (2 - (-5))^2} = \sqrt{58}[/tex]

LM = [tex]\sqrt{(-1 - 4)^2 + (-5 - (-4))^2} = \sqrt{26}[/tex]

MJ = [tex]\sqrt{(4 - 1)^2 + (-4 - 3)^2} = \sqrt{50}[/tex]

Next, we can find the slopes of the sides using the slope formula:

Slope of JK = (2 - 3)/(-4 - 1) = -1/5

Slope of KL = (-5 - 2)/(-1 - (-4)) = 7/3

Slope of LM = (-4 - (-5))/(4 - (-1)) = 1/5

Slope of MJ = (3 - (-4))/(1 - 4) = 7/3

Since opposite sides, JK and ML have the same length and are parallel (they have slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ have the same length and are parallel (they have slopes of 7/3 and 7/3, respectively), we can conclude that JKLM is a parallelogram.

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f is increasing on (-infty, -4) and (2,infty) since that's where you'd be walking uphill.

f is never decreasing.

f is constant on (-4,2), since that's where it's completely flat.

Let's assume the width of the rectangular pool is w. According to the problem, the length of the pool is 12 feet shorter than the width, so the length can be represented as w - 12.

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. We know that the area of the pool is 640 square feet, so we can set up the equation:

A = L x W

640 = (w - 12) x w

Simplifying the equation:

640 = [tex]w^{2}[/tex] - 12w

[tex]w^{2}[/tex] - 12w - 640 = 0

We can solve for w by using the quadratic formula:

w = [-(-12) ± [tex]\sqrt{-12}^{2}[/tex]- 4(1)(-640))] / (2 x 1)

w = [12 ± [tex]\sqrt{(12^{2}+2560)[/tex]] / 2

w = [12 ± [tex]\sqrt{2596}[/tex]] / 2

w = [12 ± 51] / 2

We can ignore the negative solution, so:

w = (12 + 51) / 2

w = 31.5

Therefore, the width of the pool is 31.5 feet. We can use this value to find the length:

L = w - 12

L = 31.5 - 12

L = 19.5

Therefore, the length of the pool is 19.5 feet.

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Answer:

2250ml

Step-by-step explanation:

The concentrate-to-water ratio is 2:9. This means 2ml of concentrate requires 9ml of water. We have 500ml of concentrate, which is 250 times more than 2ml, so to find the amount of water, we also multiply 9ml by 250:

2ml concentrate : 9ml water

(Multiply both sides by 250)

500ml concentrate : 2250ml water

The solution of the inequality is -4≤x<7. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -12≤2x-4<10.

Here, -12≤2x-4

Add 4 on both the sides of an inequality, we get

-8≤2x

Divide 2 on both the sides of an inequality, we get

-4≤x

Now, 2x-4<10

Add 4 on both the sides of an inequality, we get

2x<14

Divide 2 on both the sides of an inequality, we get

x<7

So, the solution of the inequality is -4≤x<7

Therefore, option D is the correct answer.

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According to the information, it can be inferred that the option that the quote explains is: The outcome... is situational irony because the opposite of what was expected is what happening.

To identify the correct option that explains the quote we must read the text carefully and the options. Once we have read and understood this information, we can infer which option explains the quote.

In accordance with the above, option A would be the one that explains the quote because options B and C by discarding are fragments of the quote. So these fragments could not explain the same quote that is being used in the text. On the contrary, the paragraph of option A does explain the situation clearly.

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Answer:

The solution is 13

Step-by-step explanation:

x+8/3 = 7

x+8 = 7×3

x+8 = 21

x = 21-8

x = 13

Answer:

yes

Step-by-step explanation:

2*(4+7) = ( 2 * 4 ) + ( 2 * 7 )

To fill a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden, you will need 79.33 cubic yards.

The volume is the product of the multiplication of the thickness, length, and width.

The thickness of the topsoil = 6 inches

12 Inches = 1 Feet

6 inches = 0.5 Feet (6/12)

The length of the garden = 28 feet

The width of the garden = 17 feet

The thickness of the soil = 0.5 feet

Volume of the topsoil = 28 x 17 x 0.5

= 238 ft³

3 Feet to 1 Yard

238 ft³ = 238/3 yards

= 79.33 cubic yards

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The required proof has been below that ΔJKL ≅ ΔLMN due to the SAS postulate.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The triangles are given in the question, as shown.

As per the given figure, we have

JK = LM

∠LJK ≅ ∠NLM (same side inner angles)

Since L is the midpoint of JN. (Definition of midpoint)

Then JL ≅ LN

Now, for triangles ΔJKL and ΔLMN

JK ≅ LM (sides)

∠LJK ≅ ∠NLM (angle)

JL ≅ LN (sides)

By SAS postulate, ΔJKL ≅ ΔLMN.

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Answer:8

Step-by-step explanation:

Because Angle GJH is 90 degrees, Angle HJZ is also 90 degrees. (Because all right angles are 90 degrees)

Now, find Angle WJZ

90 - 18 = 72 degrees

By the Vertical Angles Theorem, Angle GJL is congruent to Angle ZJW

Now solve for x

72 = 9x

x = 8