can anyone please help with this! it’s so confusing! 100 points to whoever can help me with all of them! and please show how u did it not just answers!! tysm

The description of the motion of the ant which is a geometric series is as follows;

a) After covering 63/32 meters, the ant will have made 6 turns

b) The distance the ant will eventually travel is 2 meters

Geometric series is an infinite sum of terms in which the ratio between consecutive terms is a constant.

The distances traveled by the ant is a geometric progression of the form;

The sum of the distance is given by the sum of the geometric progression as follow;

[tex]S_n = \dfrac{a\cdot \left(1 - r^n \right)}{(1 - r)}[/tex]

Where;

aₙ = The distance traveled in the nth turn

Sₙ = The sum of the distances

a = The first term = 1 meter

r = The value of the common ratio = 0.5 meter ÷ 1 meter = 0.5

a) The number of turns the ant will have made after covering a distance of 63/32 meters is therefore;

[tex]S_n =\dfrac{63}{32} = \dfrac{1\times \left(1 - 0.5^n \right)}{(1 - 0.5)}[/tex]

31.5 = 32 × (1 - 0.5ⁿ)

32 × 0.5ⁿ = 32 - 31.5 = 0.5

0.5ⁿ = 0.5 ÷ 32

n = ln(0.5 ÷ 32) ÷ ln(0.5) = 6

b) The distance the ant travels eventually is given by the formula for the sum to infinity of a geometric progression as follows;

[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]

Which gives;

[tex]S_{\infty} = \dfrac{1}{1-0.5} = 2[/tex]

The distance the ant eventually travels is 2 meters

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Answer:

$22,000 at 5%, $10,000 at 11%

Step-by-step explanation:

Let x be the amount invested at 5%.

[tex].05x = .11(32000 - x)[/tex]

[tex].05x = 3520 - .11x[/tex]

[tex].16x = 3520[/tex]

[tex]x = 22000[/tex]

$22,000 at 5%, $10,000 at 11%

Answer:

-6a -13b - 12c + 4

Step-by-step explanation:

-12a + -5b - 12c + 6a - 8b - (-4)

-12a + -5b - 12c + 6a - 8b + 4   [a "- -" = +]

(-12a + 6a) -(5b -8b) - 12c + 4    [Group like terms.]

-6a -13b - 12c + 4

The top of the 20-foot ladder used for painting will be  19 feet up from the base of the house

information given in the question

Brian borrowed a 20-foot extension ladder: hypotenuse = 20-foot ladder

he sets the base of the ladder six feet from the house

adjacent = 6 feet from the house

opposite =  how far up will the top of the ladder reach = ?

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = adjacent² + opposite²

substituting the values into the equation

let x be thow far up will the top of the ladder reach

20² = 6² + x²

400 = 36 + x²

400 - 36 = x²

x² = 364

x = √364

x = 19.08

The ladder Brain borrowed will go 19 feet high

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complete question

Brian borrowed a 20-foot extension ladder to use to paint his house. If he sets the base of the ladder six feet from the house how far up will the top of the ladder reach?

Answer:

0.302

Step-by-step explanation:

Answer: 0.302

Step-by-step explanation:

The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .

The equation that would model the cost of the van rental is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.

The general form of linear equations is: y = a + bx

Where:

a = intercept

b = slope

The form of the equation that models the cost is:

Total cost = cost of renting the van + [cost per mile x (m - 120 miles)

$598.74 = $183 + [$0.39 x (m - 120)

$598.74 = $183 + $0.39m - 46.80

$598.74 = 136.20 + $0.39m

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Answer:

44.24

Step-by-step explanation:

The 2 in the thousandths place is lower than 5 therefore it does not round the 4 to a 5

Answer:

44.24

Step-by-step explanation:

hopes this helps please mark brainliest

Answer:

the other 2 sides equal 70.5 ...but I am not for sure because you did not give me enough information (like a picture)

Answer:

Step-by-step explanation:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

The six frequent factors between 72 and 90 are 1, 2, 3, 6, 9, and 18.

Consequently, 18 is the number that links 72 and 90 most frequently.

Answer:

2.5√2 units

Step-by-step explanation:

The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.

~~~~~~~~~~~~~~~~~~~~~    

y = - x + 5 , slope m = - 1

Slope of perpendicular line is opposite reciprocal. In our case is 1 .

G ( 6 , 4 )

y - 4 = 1 × ( x - 6 )

y = x - 2

x - 2 = - x + 5 , x = 3.5

y = 1.5  

Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )

OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units

The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]

Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

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Answer:

Domain: {2, 3, 4, 5} Range: {12, 13, 14}

Step-by-step explanation:

The relationship is a function even though two different inputs have the same output.

Answer:

vyfyxfrr6c*"8&"; hxh6 byhd,tf7zg5gzyfe55eE4E45w522

Step-by-step explanation:

6dyxg9yyfz6t bztrfr 4.Sabina the tortoise is an 56,123 way of Policy for recharge of the angles and tricks of Policy in order for me and I have a wonderful experience and a

Answer:

Step-by-step explanation:

Yes, of course!

A parabola's direction is based on whether its "a" value is positive or negative and whether it is opening vertically or horizontally (y= or x =)!

The angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.

What is trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry". Therefore, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.

Given, the length of the ramp = h = 17 feet
Height at which ramp is placed on truck = p = 4 feet
Let the angle that the ramp makes with the ground = ∅
Taking the length and height of ramp as basis, on assuming a right triangle with the length as hypotenuse and the height as perpendicular, we have:
sin ∅ = Perpendicular/Hypotenuse = h / p = 17/4 = 4.25
⇒ ∅ = sin⁻¹ (4.25) ⇒ ∅ = 10.48°
Thus, the angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.

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Answer:

Step-by-step explanation:

Re-order terms so constants are on the left

Then divide both sides by the same factor its -2

then Simplify answer is 1

Answer:

9x + 16

Step-by-step explanation:

Let's simplify step-by-step.

5(x+2)−3(x−2)+7x

Distribute:

=(5)(x)+(5)(2)+(−3)(x)+(−3)(−2)+7x

=5x+10+−3x+6+7x

Combine Like Terms:

=5x+10+−3x+6+7x

=(5x+−3x+7x)+(10+6)

=9x+16

Please give me brainiest!

The solutions to the given simultaneous equations as required in the task content are; (1.4, 9.2) and (-0.9, 2.3).

It follows from the task content that the solution to the simultaneous equations as given in the task content is to be determined.

Given: y = 3x + 5 and y = 4x² + x.

Therefore, since y = y; it follows that the equation which holds true is;

3x + 5 = 4x² + x

4x² - 2x - 5 = 0.

Therefore, the quadratic equation above can be solved for the values of x so that by approximation, we have;

x = 1.4 OR x = -0.9.

Therefore, the corresponding values of y are;

y = 3(1.4) + 5 = 9.2

OR

y = 3(-0.9) + 5 = 2.3

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Answer: 0.86 pounds of fruit

Step-by-step explanation:

8.3-7.44=0.86

Answer:

Olumide will practice 40 minutes of playing the piano

Step-by-step explanation:

Olumide practices piano and guitar in the ratio of 5:8

64 minutes of guitar playing means that Olumide has had 8 individual practicing sessions of guitar (64 / 8 = 8), so he has also had 8 practicing sessions of piano.

5 x 8 = 40 minutes of piano practice

a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

Given that,

In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.

We have to find

a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.

b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.

We solve

a) We just multiply

8×11=88

b) 12×7=84

Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

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An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

Given that;

The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,

Let 'T' be the number of times the price is decreased.

So, price;

     p = 38 – 5x

     x = (38 - p) / 5

And as per the given condition attendance;

a = 1000 + 50x

So, the Revenue is;

To develop an equation for revenue (r) as a function of p, the price of tickets;

R = p * a

R= p * (1000 + 50x)

But,  x = (38 - p) / 5

Then,

R = P * (1000 + 50(38 - p)/5)

  = p * (1000 + 380 - 10p)

  = p * (1380 – 10p)

  = 1380p - 10p²  → (I)

To get R(25) from (I);

R(25) = 1380(25) - 10(25)²

         = 34500 - 6250

         = 28250

Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

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The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A burger consistently cost $6.00 each extra fixing cost $0.59.

Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,

c = 0.59t + 6

On Monday the expense of the burger just is half off. Then the equation is given as,

c = 0.50(0.59t + 6)

c = 0.295t + 3

The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.

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Answer:

We may use the logarithm formula,

N = ln(EV/SV) ÷ ln(1+r), where (1+ r) is the value of 1 plus interest for 1 year.

EV is end value, SV is start value.

EV is 20000, SV is 12000, interest is 5.6% semi annual

(1+r) is obtained as,

Step-by-step explanation:

3409.1 In exponential form is 3.4091 * 10^3

Writing a number in exponential form is a way of writing numbers using base and exponents

Scientific notations is among the ways numbers appears in exponential forms

using scientific notation we have

= 3409.1

converting to fractions

= 34091 / 10

applying the scientific notation

= 3.4091 / 10 * 10000

eliminating the fraction by dividing by 10

= 3.4091 * 1000

applying exponential notation

= 3.4091 * 10^3

rewriting gives

= 3.4091 E+3

In scientific notation 10^3 is E+3 and it is called kilo and can be represented as k

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The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)

Given equation y = 3x + a / 2x - 5

= y(2x - 5) = 3x + a

= 2xy - 5y = 3x + a

= 2xy - 3x = a - 5y

= x(2y-3) = a - 5y

Hence, x = (a - 5y) / (2y - 3)

First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).

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The given two equations are Perpendicular to each other .

What is intersection of lines ?

 It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.

Here the equation of line is y=mx+b .

Where m = slope . then,

=> y = x-7 where here slope m1= 1 and

=> y = -x+3 where here slope m2 = -1 .

Here the m1= -m2

Hence the given two equations are Perpendicular to each other .

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The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5  .

In the question ,

it is given that

the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .

the slope is = (5 -(-2))/(-8 -6)

= 7/(-14)

= -1/2

so , the slope of the required line is = 2 .

The equation of the line passing through the point (3,1) with slope 2 is

(y - 1) = 2*(x-3)

y -1 = 2x - 6

y = 2x - 6 + 1

y = 2x - 5

the equation of line is y [tex]=[/tex] 2x - 5

the perpendicular slope is = 2

the y intercept is -5 .

Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5)  is y = 2x - 5 .

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