A line includes the points (1, 10) and (0, 8). What is its equation in slope-intercept form?

Answer:

0.302

Step-by-step explanation:

Answer: 0.302

Step-by-step explanation:

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 given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval  (4, −∞).

What is an increasing and decreasing functions?

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We have,

[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]

[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 4, 4i, −4i, 10, 8

∴ f′(x) = 0  

   x = 4,

Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)

In interval (−∞, 4),  f′(x) < 0

Hence, the given function (f) is strictly decreasing in interval (−∞, 4)

​

In interval (4, −∞),  f′(x) > 0

Hence, the given function (f) is strictly increasing in interval  (4, −∞)

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​

As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.

Here,

Calculate the length of sides by distance formula.

RS=√(y2-y1)²+(x2-x1)²

=√(2-4)²+(-2-2)²

=√4+8

=√(12

=2√3 units

ST=√(y2-y1)²+(x2-x1)²

=√(0-2)²+(-1-(-2))²

=√(4+1)

=√5 units

TU=√(y2-y1)²+(x2-x1)²

=√(2-0)²+(3-(-1))²

=√(4+8)

=√12

=2√3 units

UR=√(y2-y1)²+(x2-x1)²

=√(4-2)²+(3-2)²

=√(4+1)

=√5 units

RT=√(y2-y1)²+(x2-x1)²

=√(0-4)²+(-1-2)²

=√(16+9)

=√25

=5 units

US=√(y2-y1)²+(x2-x1)²

=√(2-2)²+(-2-3)²

=√(0+25)

=√25

=5 units

Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.

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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:

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 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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The identification of the missing angles and their congruency names are;

a. ∠4 and ∠7 = Consecutive interior

b. ∠2 and ∠11 = alternate exterior angles

c. ∠12 and ∠16 = corresponding angles

d. ∠8 and ∠13 = alternate interior angles

e. ∠11 and ∠15 = corresponding angles

f. ∠7 and∠10 = none

g. ∠1 and ∠14 = alternate exterior angles

h. ∠12 and ∠15 = Consecutive interior

i. ∠6 and ∠7 = none

j. ∠1 and ∠3 = corresponding angles

k. ∠12 and ∠16 = corresponding angles

l. ∠6 and ∠15 = alternate exterior angles

m. ∠5 and ∠10 = alternate interior angles

n. ∠8 and ∠14 = corresponding angles

Corresponding angles are defined as the angles which are formed in corresponding corners with the transversal in a case where two parallel lines are intersected by any other line.

Alternate interior angles are defined as the angles formed when a transversal intersects two coplanar lines.

Alternate exterior angles are defined as the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.

Therefore, the angles given can be classified similarly using the image as:

a. <4 and <7 are Consecutive interior angles

b. <2 and <11 are alternate exterior angles

c. <12 and <16 are corresponding angles

d. <8 and <13 are alternate interior angles

e. <11 and <15 are corresponding angles

f. <7 and <10 are none

g. <1 and <14 are alternate exterior angles

h. <12 and <15 are Consecutive interior

i. < 6 and <7 are none

j. <1 and <3 are corresponding angles

k. <12 and <16 are corresponding angles

l. <6 and <15 are alternate exterior angles

m. <5 and <10 are alternate interior angles

n. <8 and <14 are corresponding angles

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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:

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

The value of 9 and a half will be 9 1/2.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Here, we want to find the value of 9 and half. This will be:

= 9 + 1/2

= 9 1/2

The value is 9 1/2.

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Answer:

a)A=4B

b)A=20

c)B=9

If it is directly proportional it means that A=kB.

you can substitute the numbers to find k.

12=k3

k=4

so the formula is A=kB.

For part b and c it is just substitution

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

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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 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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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:

$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:

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.

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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I eat pizza or drink bottled water, for example, is a symbolic representation of the following statement.

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Considering the expression in this problem, it is found that:

a) The part of the expression that gives the amount of taxes that has to be paid is: 0.096(14f).

b) The expression would be of: C(f) = 15f + 0.096(15f).

The expression for the total cost in this problem is presented as follows:

C(f) = 14f + 0.096(14f).

The meaning of each term is given as follows:

If the cost per square foot was of $15 instead of $14, the complete expression would be as follows:

C(f) = 15f + 0.096(15f).

That is, the two instances of 14 in the equation were replaced by 15.

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Answer:

Option A

Step-by-step explanation:

→ Multiply both sides by 2

2s = a + b + c

→ Minus b and c from both sides

2s - b - c = a

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

The total number of points scored by the other 7 team members in Euclid high school's last basketball game is 11.

For the given question.

Let 't' be the total points scored.

Alexa = 1/4 t.

Brittany = 2/7 t

Chelsea = 15

Let 'x' be the points scored by remaining 7 team.

Thus, the two variable equation becomes.

1/4 t +  2/7 t + 15 + x = t   .....eq 1

Where, x ≤ 14 ( for 7 terams)

Simplifying eq 1.

15 + x = 13/ 28 t

28x + 28 = 13 t

Now, t must be divisible by 28.

Let t = 28 u, u ≥ 0 and divisible by 28.

Thus,

x + 15 = 13u.

Then, u = 2( t = 56) has been the only candidates for which x = 11.

Thus, the total number of points scored by the other 7 team members is 11.

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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:

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:

Given the graph, the vertex does not exist and the transformations from are

The graph represents the given parameter

In the above graph, we can see that the graph is a cubic function

By definition, cubic functions do not have vertex. This is because they have no minimum or maximum

So, we can conclude that the graph has no vertex

In (a), we have

We can see that the graph is a cubic function

This function is represented as

y = ∛x

In this graph, we can see that the graph is 4 units to the left

i.e. y = ∛(x - 4)

And 2 units below the origin

i.e. y = ∛(x - 4) + 2

So, the transformation is (b) and (c)

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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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