3 Dylan needs to buy new contact lenses. His ophthalmologist sells 8-lens boxes in
packs of 2 for $52 and 10-lens boxes in packs of 4 for $120. Which option is the
better deal?

The graph of the system of linear inequalities 2x + y < 1 and y ≥ 12x + 2 is attached.

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Inequalities is used for the non equal comparison of numbers and variables.

The graph of 2x + y < 1 and y ≥ 12x + 2 is attached.

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On solving the provided question we can say that - the coordinates from the graphs will be P' = (0.0); Q' = (1,0); R' = (1,1); S' = (0,1)

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is r

A fixed point serves as the dilation's center.

Dk is used to represent dilation, where k is the scale factor.

Dk (x, y) = for a dilation centered on the origin (kx, ky)

Let's assume that you have a PQRS rectangle where

P = (0,0)

Q = (4,0)

R = (4,4)

S = (0,4)

You must multiply each coordinate by 1/4 to achieve the dilation of this PQRS to P'Q'R'S' with a scale factor of 1.

P' = (0.0)

Q' = (1,0)

R' = (1,1)

S' = (0,1)

You may plot both of these rectangles to see that they are the same size and are centered on the origin, but they have different shapes.

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The height of the building can be  649.44 ft

What is angle of elevation ?

angle of elevation states that the angle which is formed between line of sight and horizontal line.

Given,  the base of the triangle is 1.75 mile. The angle opposite of the tall side, x, is 4 degrees.

height of the building is an unknown variable (x) .

tan(angle) = opposite length /adjacent length.

Opposite length is x, adjacent length is 1.75 mile, angle is 4 degrees.

tan(4º) = x / 1.75

rearrange for x

x = 1.75*tan(4º) = ~1.75*0.0699  miles.

x = ~0.123

Now to get feet, just multiply by 5,280 ft in one mile

Height of the building is 0.123 miles * 5280 ft/mile = 649.44 ft

Hence , The height of the building can be  649.44 ft .

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We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -

[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]

Given is the inequality -

3 (m + n)! ≥ m! + n!

We have -

3 (m + n)!

3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}

3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)

3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)

Now, for (m! + n!) --

(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

It can be seen that -

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥

m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

Hence, it can be seen that -

3 (m + n)! ≥ m! + n!

Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.

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Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

given

Rewrite the above expression as:

[tex]2ab\sqrt[3]{3*4^{3} *ab^{2} } - 5\sqrt[3]{3*3^{3} * a^{4}b^{5} }[/tex]

Evaluate the cube roots

[tex]2ab {4\sqrt[3]{3ab^{2} } } - 5 {3ab\sqrt[3]{3ab^{2} }[/tex]

Evaluate the differences

-7ab(2√3ab²)

Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

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Answer:

x = 15

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 9² + 12² = 81 + 144 = 225 ( take square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

Answer:

x = 15

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into Pythagoras Theorem and solve for x:

[tex]\implies 9^2+12^2=x^2[/tex]

[tex]\implies 81+144=x^2[/tex]

[tex]\implies 225=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{225}[/tex]

[tex]\implies x=15[/tex]

To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.

Attached photo shows the steps to the solution :P

Answer:

b = -8

Step-by-step explanation:

To determine the value of b, we can use the factoring method. We can factor the expression

(5b + 16)(b + 32) as (b + 8)(5b + 16).

Setting each factor to 0, we get b + 8 = 0 and 5b + 16 = 0.

Solving for b in the first equation, we get b = -8.

Substituting this value into the second equation, we get 5(-8) + 16 = 0, which simplifies to -40 + 16 = 0.

This equation is true only when the value of b is -8. Therefore, the value of b is -8.

On solving the provided question, we can say that - here in the slope intercept [tex]2y / 2 = -4x /2 + 24 / 2 = > y = -2x + 12\\[/tex]

The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.

y = mx + c

m = slope, c = y-intercept

[tex]4x + 2y = 24\\2y = -4x + 24\\2y / 2 = -4x /2 + 24 / 2\\y = -2x + 12\\[/tex]

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A) The linear equation is:

y = (3/4)*x + 3

B) The sets with only positive elements are:

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here, we do know that the y-intercept of the linear equation is (0, 3), then we know that b = 3.

Then the line is something like:

y = a*x + 3

We also know that the line passes through (-4, 0), then we can replace these values in the equation above to get:

0 = a*-4 + 3

4a = 3

a = 3/4

Then the linear equation is:

y = (3/4)*x + 3

The sets where all the numbers are positive are:

{x| x ∈ N}

Where N is the set of the natural numbers, these are all the integers equal to or larger than 1, so all are positives.

{y| 0 < y < 1}

There we can see that y must be larger than zero, so all the elements are positive.

{y| 3 ≤ y ≤22}

Here the elements are between 3 and 22, so all of these are positve.

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The length of segment AB is given as follows:

AB = 20 units.

Similar triangles are triangles that share these two features given as follows:

The similar triangles for this problem are given as follows:

ABD and CDE.

Hence the proportional relationship that can be established between the side lengths is given as follows:

AB/DE = BC/CD = AC/CE.

The side lengths are given as follows:

CD = 3, CE = 5, DE = 4, DB = 18.

As CD = 3 and DB = 18, using the segment addition postulate, we have that:

BC = BD - CB

BC = 18 - 3

BC = 15 units.

Hence the length AB is obtained as follows:

AB/4 = 15/3

AB/4 = 5

Applying cross multiplication, we have that:

AB = 4 x 5

AB = 20 units.

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Answer:

if it’s asking for a numerical answer it would be 1.67

(Rounded to the nearest two)

Step-by-step explanation:

please help!!! HURRY!!

System of equations y = 5x + 11 and y = 5x has no solution,  y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.

Two or more expressions with an Equal sign is called as Equation.

The given system of equations are

a. y = 5x + 11 and y = 5x

Substitute the y value in first equation

5x=5x+11

So the system of equations y = 5x + 11 and y = 5x has no solution.

b. y = 6x + 3 and y = 3x

Substitute the y value in first equation

3x=6x+3

-3x=3

x=-1

y=-3

The system of equations has one solution

c. x + 4y = 8 and y = -1/4x + 2

x+4(-1/4x + 2)=8

x-x+2=8

The  system of equations has one solution has no solution

Hence, system of equations y = 5x + 11 and y = 5x has no solution,  y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.

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The solution to the equation is

x = b/a ± √(b^2/a^2) / a.

Generally, To solve the equation using the completing the square method, we first move all the terms to one side of the equation by subtracting abx and 2b² from both sides, giving us:

a²x² = abx + 2b²

Which is

a²x² - abx - 2b² = 0

Next, we need to add and subtract a term so that the left side of the equation can be written as a perfect square.

We need to find the square of half of the coefficient of the x term, which is -ab/2a.

So we add and subtract (ab/2a)^2 = (b^2/a^2) on the left side of the equation:

a²x² - abx - 2b² + (b²/a²) - (b²/a²) = 0

This gives us the left side of the equation as

(ax - b/a)² = b²/a².

We can then take the square root of both sides:

ax - b/a = ±√(b²/a²)

Finally, we can add b/a to both sides to get the solution:

x = b/a ± √(b²/a²) / a

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Answer: A y-intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.

Slope - A number that describes both direction and steepness of the line.

Step-by-step explanation: If a line intersects the y-axis at point 5 then its y-intercept will be c= 5. As we denote y-intercept with c.

The slope is denoted by m.

Answer: y^2+8x+12

Step-by-step explanation:

Answer:£21.00

Step-by-step explanation:

One pizza: (£35/5) =£7

Three pizza's: (£7x3)=£21

Therefore , the solution of the given problem of expression comes out to be probably 4 slices.

In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.

Here,

you figure if a toaster takes about 1-2 minutes to toast a piece of bread  and a toaster usually can fit 2 slices at a time i would say 4.

Preheat oven broil to high. Move oven rack to highest position.

Place sliced bread on an ungreased baking sheet. 4 slices of bread.

Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...

Top with butter, jam, or any other favorite topping!

The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).

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The wrist circumference in relation to height tells us how big our body frames are.

The wrist circumference in relation to height tells us how big our body frames are. A man who is above 5' 5" tall and with a wrist measurement of 6" would be considered to have tiny bones.

The following chart can be used to establish whether a person has tiny, medium, or large bones by measuring their wrist with a measuring tape and comparing the results.

Women:

under 5'2" in height"

Medium wrist size is between5.5" and5.75" Small wrist size is less than5.5" "

Large is defined as a wrist size of 5.75 or greater."

between 5'2" and 5'5" tall

smaller than 6 inches around the wrist"

Bracelet size 6 is medium "Medium = wrist size between 6.25" and 6.5" Large

Over 5' 5" in height"

Small wrists measure less than 6.25", Medium wrists measure 6.25" to 6.5," and Large wrists measure over 6.5."

Example :

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

x² + 7x + 12 = 4x + 14

x² + 3x - 2 = 0

(x + 3 / 2 )² = 17 / 4.

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Answer:

pro tip: crop your screen before you post it....

I think it's B

I did this 2 years ago in middle school

The domain of the given graph is (-∞ < x < ∞)

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

Given is a graph,

For f(x) = x, there is no restriction on x

Both the domain and range are the set of all real numbers.

Hence, The domain will be (-∞ < x < ∞)

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The transformation of f (x) exists g (x) = f (x) - 4.

A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

A function that has a positive constant increased to a variable exponent, other than 1, is referred to as an exponential function. By solving at a certain input value, a function is assessed. When the beginning value and growth rate are known, an exponential model can be discovered.

We observed that:

f (0) = 2

For the function g (x) we have:

g (0) = -2

Therefore,

g (x) = f (x) - 4

Looking for intersection with axis and we have:

g (0) = f (0) - 4

g (0) = 2 - 4

g (0) = -2 (correct demonstration)

The transformation of f (x) is: A. g (x) = f (x) - 4

Therefore, the correct answer is option A. g (x) = f (x) - 4.

The complete question is;

Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.

Which of the rules given below shows the transformation of f?

A. g(x) = f(x) - 4

B. g(x) = f(x - 4)

C. g(x) = f(x) + 4

D. g(x) = f(x + 4)

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Pacquiao will have enough money (a future value of up to P7,000) to buy the gift if he deposits his money (P6,000) in an account paying 8 percent compounded semi-annually.

The future value is the compounded present value at an interest rate.

The future value can be determined using an online finance calculator, FV table, or FV formula.

N (# of periods) = 4 (2 years x 2)

I/Y (Interest per year) = 8%

PV (Present Value) = P6,000

PMT (Periodic Payment) = P0

Results:

Future Value (FV) = P7,019.15

Total Interest = P1,019.15

Thus, in 2 years' time, Pacquiao will have P7,019 enough to buy his mom a new bicycle.

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Answer:

The question is not detailed enough

Answer:

In step 2, Nathan did not simplify 5x - 3x correctly.

Step-by-step explanation:

In step 2, Nathan was one number off the correct simplification.

The number of expected times to pick a card without strips is 130.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The percentage of stripes from the 120 times.

= 42/120 x 100

= 35%

Now,

Based on this experiment,

The number of strip cards out of 200 times.

= 35% of 200

= 35/100 x 200

= 35 x 2

= 70

The number of times to pick a card without strips.

= 200 - 70

= 130

Thus,

The expected number of times to pick a card without stripes is 130.

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The complete question is given below.

According to the given cosecant function the value of csc 0 is equal to 6/5.

The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.

It is given that:

[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]

According to trigonometric identity,

[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]

Therefore the value of csc 0 is equal to 6/5.

Complete question;

Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]

find csc 0.

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Answer: 10:30 am

Step-by-step explanation: If you need to seat a passenger every 30 seconds, (half of a minute, which is 60 seconds), for every minute, 2 passengers will be seated. So, if you seat 2 passengers for a min each until you have seated 110 people, you will have taken up 55 minutes in total. (110 divided by 2 passengers a min). And finally, 55 minutes past 9:35 am would be 10:30 am. Hope this helps!

The value of u is given by the equation u = 37°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the sum of total internal angles of a triangle be = 180°

Now , the triangle be ΔABC

The measure of ∠A = u + 4°

The measure of ∠B = u

The measure of ∠C = ( 180° - ( u + 41° ) ) ( angles on a straight line = 180° )

From the triangle theorem ,

u + 4° + u + ( 180° - ( u + 41° ) ) = 180°   be equation (1)

On simplifying the equation , we get

2u + 184° - u - 41° = 180°

u + 143° = 180°

Subtracting 143° on both sides of the equation , we get

u = 37°

Therefore , the value of u is 37°

Hence , the value of u in the triangle is 37°

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Answer:

  363 = 11223₄

Step-by-step explanation:

You want 363 written in base 4.

We can convert to base 4 by looking at the remainders from repeated division by 4:

  363 ÷ 4 = 90 r 3

  90 ÷ 4 = 22 r 2

  22 ÷ 4 = 5 r 2

  5 ÷ 4 = 1 r 1

  1 ÷ 4 = 0 r 1

Writing the remainders in reverse order gives the base-4 number:

  363 = 11223₄