Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 2,5,9,14,. . . . .

The total amount subtracted from her account after 6 months of having the membership is −6|20| = −$120. option C

Given:

Cost of membership

Cost per month for a car wash membership = $20

Number of months = 6 months

Total amount subtracted from her account = Number of months × Cost per month for a car wash membership

= 6 (-20)

= -120

Therefore, the total amount subtracted from her account after 4 months of having the membership is −6|20| = −$120.

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Answer:

a) [tex]\sqrt{3}[/tex]

b) 2

Step-by-step explanation:

a) tan 30 = opposite side / adjacent side 1/[tex]\sqrt{3}[/tex] so AC is [tex]\sqrt{3}[/tex]

b)3

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]1^{2}[/tex] +[tex]\sqrt{3} ^{2}[/tex] = [tex]c^{2}[/tex]

1 + 3 = [tex]c^{2}[/tex]

4 = [tex]c^{2}[/tex]

[tex]\sqrt{4}[/tex] =[tex]\sqrt{c^{2} }[/tex]

2 = c

The length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The right-angled triangle ABC has an angle BAC of 30º.

The length of BC  be one unit

We have to find the length of AC

tan (30)= opposite side/ adjacent side

1/√3 = opposite side/ adjacent side

The adjacent side is √3  which is length of AC

Now let us find the length of AB by using pythagoras theorem

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

AB² = AC² + BC²

AB²=√3² + 1²

AB²= 4

AB = 2 units

Hence, the length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem

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Answer:

Slope of a perpendicular line:
[tex]\boldsymbol{\dfrac{1}{9}}[/tex]

Slope of a parallel line:
[tex]\boldsymbol{-9}[/tex]

Step-by-step explanation:

A line perpendicular to a line y = mx + b will have its slope as[tex]-\dfrac{1}{m}[/tex]
Here slope of given line = -9
[tex]\displaystyle \mathrm {reciprocal\; of\;} -9 = -\dfrac{1}{9}[/tex]

[tex]\mathrm {negative\; of \;reciprocal\;}= -\left(-\dfrac{1}{9}\right) = \dfrac{1}{9}\\[/tex]

parallel lines have the same slope so a parallel line will have slope = -9

The value of the other angles

∠1 = 180 - 82°

∠2 = ∠1 = 98°

∠3 = ∠ = 98°

∠4 = ∠5 = 82°

According to the given data,

m∠5=82° given

∠5 = ∠7 = ∠4 = ∠8 = ∠6 = ∠12

∠1 = ∠10 = ∠2 = ∠11 = ∠3 = ∠ 12 = 180° - ∠5

we get, measures of other angles

∠1 = 180 - 82°

∠2 = ∠1 = 98°

∠3 = ∠ = 98 °

∠4 = ∠5 = 82°

A transversal is a line that intersects two coplanar lines at two different points. In the figure,

line t is a transversal. The table summarizes the names of angle pairs formed by a transversal.

Corresponding angles lie on the same side of the transversal and on the same

sides of the intersected lines. ∠1 and ∠5

Same-side interior angles lie on the same side of the transversal and between

the intersected lines. ∠3 and ∠6

Alternate interior angles are nonadjacent angles that lie on opposite sides of

the transversal between the intersected lines. ∠3 and ∠5

Alternate exterior angles lie on opposite sides of the transversal and outside

the intersected lines. ∠1 and ∠7

Same-Side Interior Angles Postulate

If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure.

Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure.

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The latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks and He must arrive at his friend’s house by 7:00 p.m.

The time it takes Lyle to drive to his friend's house is given by t = d/v where

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, we have that

Substituting the values of the variables into t, we have

t = d/v

= 720 km/80 km/h

= 9 h

So, it takes Lyle 9 hours to drive.

Now, since Lyle takes an hour for Lunch and two 15 minutes breakes, this extra time is t' = 1 h + 2 × 15 min

= 1 h + 30 min

= 1 h + 30 min/60 min × 1h

= 1 h + 0.5 h

= 1.5 h

So, the total time Lyle takes to reach his friend's house is T = t + t'

= 9 h + 1.5 h

= 10.5 h

Since Lyle must reach his friend's place no later than 7:00 pm, 10.5 hrs from 7:00 pm is 8:30 am.

So, Lyle must leave no later than 8:30 a.m

So, the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

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The street can be represented in slope intercept form as follows:

y = x + 4

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Parallel lines have the same slope.

The street goes by the name y = x + 17.

The slope of the street is 1.

Therefore, the street parallel to that one should have the same slope.

The street can be represented in slope intercept form is as follows:

y = x + 4

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The equation of the parabola in vertex form is

P is -[tex]\frac{1}{2}[/tex]

(0,-[tex]\frac{1}{2}[/tex])

y=[tex]\frac{-1}{2}[/tex][tex]x^{2}[/tex] -[tex]\frac{1}{2}[/tex]

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a variety of seemingly unrelated mathematical descriptions, all of which may be shown to define the same curves.

One definition of a parabola includes a line and some extent  (the focus) (the directrix). The directrix isn't the main focus. The locus of points therein plane that is equally spaced apart from the directrix and the focus is known as the parabola. A right circular conical surface and a plane parallel to a different plane that is tangential to the conical surface intersect to form a parabola, which is additionally known as a conic section.

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The quadratic equation of the form ax² + bx + c = 0.

The value of x = 4 and x = -3

No solution

No real-valued solution

The quadratic equation of the form

ax² + bx + c = 0.

The form is called the standard form of the quadratic equation.

Let the given equation be x² = x + 12

By using quadratic equation, ax² + bx + c = 0

ax² + bx + 12 = 0

x² = x + 12

⇒ x² - x - 12 = 0

Let the quadratic equation be

[tex]$x=\frac{\left(-b\right)\pm \sqrt{\left(b)^2-4\cdot \:a\cdot \left(c)}}{2\cdot \:a}[/tex]

a = 1, b = -1 and c = -12

Substitute the values in the above equation, we get

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-12\right)}}{2\cdot \:1}[/tex]

simplifying the above equation, we get

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \:7}{2\cdot \:1}[/tex] and

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a++ \:7}{2\cdot \:1}[/tex]

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a+- \:7}{2\cdot \:1}[/tex]

x = 4 and x = -3

Therefore, the value of x = 4 and x = -3

No solution

No real-valued solution

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Answer:

f^-1 (x)= -6x+24

Step-by-step explanation:

the inverse function would be negative six (x) plus 24

Answer:

Step-by-step explanation:

History(H),Economics(E),Literature(L)

1a).To find History(H) only is

H only =H-HE-HL+HEL

H only =60-30-16+10=24

b).E only=50-30-22+10=8

c). L only=48-22-16+10=20

2).no of candidates who sat for the exam is 24+8+20=52

Answer:

Step-by-step explanation:

F = 9/5 C + 32 is the correct formula.

9/5 C = F - 32

C = 5/9(F - 32)

So, 68 degrees Fahrenheit

= 5/9(68 - 32)

= 5/9 * 36

= 20 degrees C.

Using the digits 1 to 9 at most one time each to make the largest quotient is 98 ÷ 12 .

According to the question we have to use digits 1 to 9 at most one time each to make the largest quotient.

Now we know that the number that is being divided is known as the dividend and the number by which we divide is known as the divisor.

Now dividend should be greater than the divisor.

So tot make the largest quotient the dividend and the divisor will be

98 and 12 respectively.

That is,     98 ÷ 12 = 8.2 which is the largest quotient.

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After solving the equation, the value of y = x/4 for the equation 12 y=3 x.

⇒ 12 y=3 x

⇒ y = 3x/12

⇒ y = x/4

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).

Difference of two squares is a particular case of a second order polynomial whose form is the following:

a² - b² = (a + b) · (a - b)

Now we proceed to demostrate the equivalence between the two expressions:

a² - b² → (a + b) · (a - b)

a² - b²                             Given

(a² - b²) + 0                     Modulative property

(a² - b²) + a · b - a · b      Existence of additive inverse

(a² + a · b) + (- b² - a · b) Associative property

a · (a + b) - b · (a + b)      Definition of power / Distributive property / (- a) · b = - a · b

(a + b) · (a - b)                 Commutative and distributive property /  

(a + b) · (a - b) → a² - b²

(a + b) · (a - b)                 Given

(a + b) · a + (a + b) · (- b) Distributive property

a² + a · b - a · b - b²        Distributive property / (- a) · b = - a · b / Definition of power

(a² - b²) + (a · b - a · b)    Associative property

a² - b²                             Existence of the additive inverse / Modulative property / Result

Hence, the difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).

The statement is incomplete. The complete form is: What is a difference of two squares?

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Refer to the graph below for the graphical representation of the given equation y = 49x.

Graph:

Refer to the graph given below for the equation y=49x.

Therefore, the graph of the given equation y=49x is shown below.

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  The value of the geometric mean of the numbers 36 and 24 is.

Gm ( 36, 24) = 12√6

     The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (36, 24) = √ab = √36×24

Gm (36, 24) = √864

Gm (36, 24) = √6×144

Gm ( 36, 24) = 12√6

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Equation of line B is y=7/2x

A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

Straight line formulas= y=mx+ c

                                                  = y-y1=m(x-x1)

              slope, m= (y1-y2)/(x1-x2)

given that, B passes through P and parallel to A

so one of the points on the line  is P(2,7)

and one more point is O(0,0) if we extend line B parallelly to A

So we can conclude that B passes through O and P

we know equation of straight line is y-y1=m(x-x1)

on solving we get equation of line B is, y=7/2x

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Answer:

Line B's equation is y=7/2x.

Step-by-step explanation:

An object in geometry known as a line is simply one that extends on all sides and has zero width. Simply put, a straight line is a line devoid of curves. A straight line is one that does not curve and extends to infinity on both sides.

Straight line formulas= y=mx+ c

                                                 = y-y1=m(x-x1)

             slope, m= (y1-y2)/(x1-x2)

given that, B passes through P and parallel to A

so one of the points on the line  is P(2,7)

Moreover, if we stretch line B parallel to A, the final position is O(0,0).

Therefore, we can say that B goes through O and P.

Y-y1=m is the straight line's known equation (x-x1)

After solving, we obtain the equation y=7/2x for line B.

Answer:

1. 68.1

2. 61.983

Step-by-step explanation:

nearest tenth is one digit after the decimal. nearest thousandth is three digits after the decimal. since 4 is less than 5, the 1 remains the same. in the second problem, the fourth digit is 6 which is greater than 5 so you change the 2 to a 3.

Answer:

AC is the longest side

Step-by-step explanation:

• the longest side is side opposite largest angle in the triangle

• the shortest side is opposite the smallest angle in the triangle

the largest angle is ∠ B = 68°

the longest side is then AC

The sequence 23,27,31,35,39, . . . . is arithmetic and the tenth term is: 59

We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".

To solve this exercise we are going to apply the formula of the arithmetic sequence:

Where:

Information about the problem:

Calculating the "d" term, we have:

d = aₙ₊₁ - aₙ

d = 27 - 23

d = 4

Calculating the tenth term, we get:

aₙ= a + (n-1) * d

a₁₀= 23 + (10-1) * 4

a₁₀= 23 + (9) * 4

a₁₀= 23 + 36

a₁₀= 59

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

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Answer:

Step-by-step explanation:

given: 5^3/5^7

= 1/5^(7-3)

= 1/5^4

= 1/625

final answer: 1/625

Answer:

[tex]5^{-4}[/tex]

Step-by-step explanation:

using the rules of exponents

• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]\frac{5^{3} }{5^{7} }[/tex]

= [tex]5^{(3-7)}[/tex]

= [tex]5^{-4}[/tex]

= [tex]\frac{1}{5^{4} }[/tex] ← if required with a positive exponent

Answer:

No, Dell does not have enough soil to fill the planter.

Step-by-step explanation:

 x = -2 is  input value produces the same output value for the two functions .

What are the function's input values?

The domain of the function is the collection of input values. The range of the function is the collection of output values.

What input and output functions are used?

The fundamental functions for input and output are getchar, putchar, puts, scanf, and printf. To transfer single characters, utilize the first two functions, getchar and putchar.

Which four sorts of functions are there?

Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

The input  value which produces the same input .

value for two function is  x = -2

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the correct option is D, the inverse relation is only a function if it passes the vertical line test.

A relation maps elements from one set (called the domain) into elements of another set (called the range).

A relation is a function only if each element in the domain is mapped into only one element of the range. So, there is something called the vertical line test.

It says that if at any part of the graph of the relation you can draw a vertical line that intercepts the graph of the relation more than once, then it is not a function. Passing the vertical line test means that no vertical line intercepts the graph more than once.

Then the correct option is D, the inverse relation is only a function if it passes the vertical line test.

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Answer:

[tex] \sf{49}[/tex]

Step-by-step explanation:

Given that,

m => 4

p => 7

Let us solve the given expression by using the given values.

[tex] \sf \: {p}^{2} m \div 4 \: \: \: \: \: \\ \sf{(7)}^{2} \times 4 \div 4 \\ \sf 49 \times 4 \div 4 \\ \sf196 \div 4 \: \: \: \: \: \: \\ \sf49 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

The given geometric sequence, with first term = 4 and ratio = 0.1, has the formula for its nth term: a(n) = 4 . 0.1ⁿ⁻¹. The first five terms are: 4, 0.4, 0.04, 0.004, 0.0004

The formula of the nth term of a geometric sequence is:

a(n) = a₁ . r^(n-1)

with a₁ is the first term and r is the ratio. In a geometric sequence, the ratio is constant and equal to a(n)/a(n-1).

In the given problem,  a₁ =4, r=0.1, therefore:

a(n) = a₁ . r^(n-1)

a(n) = 4 . 0.1ⁿ⁻¹

To find the first five terms, replace n with 1, 2, 3, 4, and 5.

a₁ = 4

a(2) = 4 . 0.1²⁻¹

       = 4 . 0.1¹ = 0.4

a(3) = 4 . 0.1³⁻¹

       = 4 . 0.1² = 0.04

a(4) = 4 . 0.1⁴⁻¹

       = 4 . 0.1³ = 0.004

a(5) = 4 . 0.1⁵⁻¹

       = 4 . 0.1⁴ = 0.0004

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