A line passes through the points (1,1/2) and (3,2) which is the equation of the line

Answer:

The least number of pizza make deal 1 better than deal 2 is 4

The cost of deal 1 is $53.99 and the cost of deal 2 is $60

The cost per pizza of deal 1 is $5.399

The better deal is deal 1

Step-by-step explanation:

* Deal 1 becomes better if it costs less than deal 2

- Assume that the number of pizza are n

* Deal 1:

∵ The cost of one large pizza = $8.99 for first 1 and = $5 for each

   additional one

∵ They ordered n large pizza

∴ The cost = 8.99 + 5(n - 1)

- Multiply the bracket by 5

∴ The cost = 8.99 + 5n - 5

- Add like terms

∴ The cost = 3.99 + 5n

∴ The cost of deal 1 = 3.99 + 5n

* Deal 2:

∵ The cost of any large pizza is $6

∵ They ordered n large pizza

∴ The cost = 6 × n = 6n

∴ The cost of deal 2 = 6n

- We need Deal 1 better than deal 2

- Then, put the cost of deal 1 < the cost of deal 2

∵ 3.99 + 5n < 6n

- Subtract 5n from both sides

∴ 3.99 < n

∴ n > 3.99

∴ n = 4

* The least number of pizza make deal 1 better than deal 2 is 4

∵ n = 10

∴ The cost of deal 1 = 3.99 + 5(10) = 53.99

∴ The cost of deal 2 = 6(10) = 60

* The cost of deal 1 is $53.99 and the cost of deal 2 is $60

∵ The cost per one pizza = total cost ÷ the number of pizza

∴ The cost per pizza of deal 1 = 53.99 ÷ 10 = 5.399

* The cost per pizza of deal 1 is $5.399

∵ The unit price of deal 1 is $5.399

∵ The unit price of deal 2 is $6

∵ $5.399 < $6

∴ The unit rate of deal 1 is less than the unit price of deal 2

* The better deal is deal 1

Deal #1 becomes a better deal at 4 pizzas. The cost of 10 pizzas for Deal #1 is $43.99, and for Deal #2 is $60.00. The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. Deal #1 is the better deal when ordering 4 or more pizzas because the cost per pizza decreases as more pizzas are added to the order.

To determine at what number of pizzas Deal #1 becomes a better deal than Deal #2, we need to compare the total cost of pizzas under each deal.

For Deal #1, the cost structure is as follows:

The first pizza costs $8.99.

Each additional large pizza on the same order costs $5.

For Deal #2, the cost is a flat rate of $6.00 per large pizza.

Let's first find out at what point the total cost of pizzas under Deal #1 equals the total cost under Deal #2. We'll denote the number of additional pizzas (after the first one) as 'n'.

The total cost for Deal #1 can be expressed as:

[tex]\[ C_1 = 8.99 + 5n \][/tex]

The total cost for Deal #2 is:

[tex]\[ C_2 = 6(n + 1) \][/tex]

We set [tex]\( C_1 \) equal to \( C_2 \)[/tex]  to find the break-even point:

[tex]\[ 8.99 + 5n = 6(n + 1) \][/tex]

[tex]\[ 8.99 + 5n = 6n + 6 \][/tex]

[tex]\[ 8.99 - 6 = 6n - 5n \][/tex]

[tex]\[ 2.99 = n \][/tex]

Now let's calculate the cost of 10 pizzas for each deal:

For Deal #1:

[tex]\[ C_{10} = 8.99 + 5(10 - 1) \][/tex]

[tex]\[ C_{10} = 8.99 + 5 \times 9 \][/tex]

[tex]\[ C_{10} = 8.99 + 45 \][/tex]

[tex]\[ C_{10} = \$43.99 \][/tex]

For Deal #2:

[tex]\[ C_{20} = 6 \times 10 \][/tex]

[tex]\[ C_{20} = \$60.00 \][/tex]

The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. As the number of pizzas increases, the average cost per pizza decreases.

Answer:

10. 5556 discs per month

11. 3.33 hours; 0.196%

Step-by-step explanation:

I find "appropriate technology" for questions like these to be a graphing calculator.

10. Put the given function definitions into the formula for profit and look for the peak of the profit curve. It is found at x ≈ 5556.

___

11. The peak of the graph is found at t=3.333. The value of A(t) there is about 0.1962.

_____

If these are part of a calculus course, you can find the maximum values by differentiating the P(x) or A(t) functions and setting the derivative to zero. You get a linear equation in each case, so finding the independent variable value is not difficult:

10. 5 -.0009x = 0

11. (.16 -.048t)e^(-.3t) = 0

Answer:

Option B)

Step-by-step explanation:

The intersection of two sets M and N consists of all the elements that are in both M and N.

So if M = {5, 10, 15, 20, 25} and N ={10, 20, 30, 40, 50}, then M ∩ N = {10, 20}

Then, the union of two sets L and C is to add to L all the elements that are in C

Where: C = M ∩ N

So, if  L = {0, 20, 40, 80, 100} and  M ∩ N = {10, 20}, then:

L ∪ (M ∩ N) =  {0, 10, 20, 40, 80, 100}

Finally the correct option is B) {0, 10, 20, 40, 80, 100}

Answer:

B) {0, 10, 20, 40, 80, 100}

Step-by-step explanation:

The INTERSECTION of two sets is the set of elements which are in both sets.

The UNION of two sets is the set of elements which are in either set.

Answer:

a) ±5

b) ±9

Step-by-step explanation:

In each case, the expression on the left is the square of the expression you're asked to find the value of. Then the value of your expression is the square root of the constant on the right. That square root can be either positive or negative.

___

a) a^2 +2ab +b^2 = (a +b)^2 = 25

(a +b) = ±√25 = ±5

___

b) a^2 -8ab +16b^2 = (a -4b)^2 = 81

(a -4b) = ±√81 = ±9

Answer:

50%

Step-by-step explanation:

you need to figure out what percent ok AK is BG

so we know that AK is 20 units long 10-(-10)=20

and BG is 10 units long 8-(-2)=10

so then you can solve with a proportion

10/20 = x/100

cross multiply that out

20x=1000

divide by 20

x= 50

50%

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

3(m + -2) + -5 = 8 + -2(m + -4)

Reorder the terms:

3(-2 + m) + -5 = 8 + -2(m + -4)

(-2 * 3 + m * 3) + -5 = 8 + -2(m + -4)

(-6 + 3m) + -5 = 8 + -2(m + -4)

Reorder the terms:

-6 + -5 + 3m = 8 + -2(m + -4)

Combine like terms: -6 + -5 = -11

-11 + 3m = 8 + -2(m + -4)

Reorder the terms:

-11 + 3m = 8 + -2(-4 + m)

-11 + 3m = 8 + (-4 * -2 + m * -2)

-11 + 3m = 8 + (8 + -2m)

Combine like terms: 8 + 8 = 16

-11 + 3m = 16 + -2m

Solving

-11 + 3m = 16 + -2m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '2m' to each side of the equation.

-11 + 3m + 2m = 16 + -2m + 2m

Combine like terms: 3m + 2m = 5m

-11 + 5m = 16 + -2m + 2m

Combine like terms: -2m + 2m = 0

-11 + 5m = 16 + 0

-11 + 5m = 16

Add '11' to each side of the equation.

-11 + 11 + 5m = 16 + 11

Combine like terms: -11 + 11 = 0

0 + 5m = 16 + 11

5m = 16 + 11

Combine like terms: 16 + 11 = 27

5m = 27

Divide each side by '5'.

m = 5.4

Simplifying

m = 5.4

Equation:

Variable:

Answer:

Step-by-step explanation:

Answer:

Message instructor about this question

Step-by-step explanation:

The question does not provide the appropriate information for a suitable answer. The equation tells you height above sea level, but the question asks when the height above ground level will be zero. No information is given as to where ground level is in relation to sea level.

The best choice is "Message instructor about this question." Ask the instructor where ground level is in relation to sea level.

___

In any event, the equation can be made somewhat simpler by factoring -16 ouf of it. Then you get ...

h(t) = -16(t^2 -7t -18) = -16(t -9)(t +2)

For h(t) = 0, solutions are ...

0 = -16(t -9)(t +2)

A product will be zero only when at least one of the factors is zero.

t = 9 or -2 . . . . . values that make the factors zero

The rocket comes back to sea level 9 seconds after launch.

___

If the rocket is launched from ground level (288 ft), then we want to find t when ...

h(t) = 288 = -16t^2 +112t +288

Subtracting 288 and factoring out -16, we get ...

0 = -16(t^2 -7t) = -16t(t -7)

Solutions are ...

t = 0 or t = 7

It is no surprise that the rocket is at ground level at t=0, since we have assumed that is where it is launched from. The other solution, t=7, tells us the rocket returns to gruond level 7 seconds after launch.

_____

Possible solutions are ...

9 seconds if "ground level" means "sea level."

7 seconds if "ground level" means "launch height."

... something else if "ground level" is not one of these

  D. hypotenuse/opposite

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

You know that

  csc = 1/sin

so

  csc = 1/(opposite/hypotenuse) = hypotenuse/opposite . . . . matches D

The correct answer to the definition of the cosecant function in a right triangle is D. hypotenuse/opposite, which is the length of the hypotenuse divided by the length of the opposite side.

The right triangle definition of the cosecant function is the length of the hypotenuse divided by the length of the side opposite the angle in question. According to this definition, the correct answer to the student's question is D. hypotenuse/opposite.

In a right triangle, suppose we have an angle 0 (theta), which is not the 90-degree angle. The side opposite this angle is called the 'opposite side', and the side that is not the hypotenuse or the opposite side is called the 'adjacent side'. The hypotenuse is the longest side, opposite the right angle, denoted by c in the Pythagorean theorem, a2 + b2 = c2. Therefore, the cosecant of angle 0 is given by c / opposite side, where c is the hypotenuse.

Answer:

15 rentals

Step-by-step explanation:

You can (and may be expected to) set up an equation that equates the total cost at one store to the total cost at the other store. When you work through the solution of this equation, you find that the "break even" number of rentals is the ratio of the difference in fixed cost (setup fee) to the difference in per-use cost (rental charge).

Here, that ratio is ...

(15.00 -7.50)/(2.25 -1.75) = 7.50/0.50 = 15

15 rentals will make the total costs the same.

so after 15 movie sales they will be equal

A car's speed is a measure of velocity. One method for finding (final) velocity is using the formula v = u + at where u is initial velocity, a is acceleration, and t is time.

Answer:

81/π square cm

Step-by-step explanation:

Area can be expressed in terms of circumference by ...

A = C²/(4π)

Filling in the given dimension, you have ...

A = (18 cm)²/(4π) = 81/π cm²

Answer:

81/π

Step-by-step explanation:

If r is the radius of the circle, then the circumference is 2πr. Setting 2π r equal to 18 cm, we find r=9/π cm. The area of the circle is πr^2= π (9/π)^2 = 81/π square centimeters.

A)

recall that there are 180° in π radians.

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=10\\ r=5 \end{cases}\implies 10=5\theta \implies \cfrac{10}{5}=\theta \implies \stackrel{\textit{radians}}{2=\theta } \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ x&2 \end{array}\implies \cfrac{180}{x}=\cfrac{\pi }{2}\implies 360=x\pi \\\\\\ \cfrac{360}{\pi }=x\implies 114.59\approx x[/tex]

B)

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=5\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(5)^2}{2}\implies A=25[/tex]

Answer:

  60 miles per hour

Step-by-step explanation:

Let s represent the speed in miles per hour during the first part of the trip. Then s-10 will be the speed during the last part of the trip.

For speed/time/distance problems, the appropriate relation is the one that is posted on every speed limit sign:

  speed = miles/hour = distance/time

Rearranging this relation gives you the expression for time:

  time = distance / speed

You are given time and distance and you need to find speed. The time you're given is the total for the two parts of the trip, so ...

  4 = 84/s + 130/(s-10) . . . . . . total time = time1 + time2

Multiplying by the product of the denominators, this becomes ...

  4s(s-10) = 84(s-10) +130s

  4s^2 -254s +840 = 0 . . . . . . subtract the right side to put in standard form

This can be solved using any of several methods for solving quadratic equations. Solutions are ...

  s = 60, s = 3.5 . . . . . only the first solution makes any sense in the problem

The speed during the first part of the trip is 60 miles per hour.

Answer:

Step-by-step explanation:

a) Apparently, you're to put the given values into a table. The first 5 entries of the table below are the given values. The next few are the result of using the recursive formula. (The formula bar shows the formula that is in the selected cell.)

__

b) The first differences of the terms of this sequence are ...

These are not constant, so the sequence is not arithmetic. The ratios of terms are not constant (2/-1 ≠ 10/2), so the sequence is not geometric.

The second differences are ...

These are constant, which tells us the sequence is a polynomial sequence of 2nd degree (since 2nd differences are constant).

In terms of the differences and second differences we can write the expression for the n-th term

  first difference with term before: a[n] -a[n-1]

  first difference between previous two terms: a[n-1] -a[n-2]

The difference between these two differences is 5, so we can write ...

  (a[n] -a[n-1]) -(a[n-1] -a[n-2]) = 5

Solving for a[n], we get ...

  a[n] = 5 + 2·a[n-1] -a[n-2] . . . . . the desired recursive relation

__

c) As indicated in part (b), this sequence is quadratic. As "proof", we offer that the sequence can be described by an explicit quadratic formula that can be derived from the first sequence term (d0) and the first and second differences (d1 and d2):

  f(n) = d0 + (n-1)(d1 +(n-2)/2·d2) = -1 +(n-1)(3 +(n-2)/2·5)

  f(n) = 5/2n² -9/2n +1

Answer:

[tex](-3, \frac{9}{5})[/tex]

Step-by-step explanation:

We have the equation [tex]2x + 5y-3 = 0[/tex].

The ordered pairs of this equation have the form [tex](x_0, y_0)[/tex]

Where x is the independent variable and y is the dependent variabe.

That is, the points belonging to the line [tex]2x + 5y-3 = 0[/tex] have the form [tex](x_0, f (x_0))[/tex]

For [tex]y = f(x)[/tex].

So, we need to find [tex]f(x_0)[/tex] for x_0 = -3.

Then we substitute x = -3 into the equation and clear the value of y.

[tex]2(-3) + 5y -3 = 0[/tex]

[tex]-6 + 5y = 3\\\\5y = 9\\\\y = \frac{9}{5}[/tex].

Then the ordered pair is:

[tex](-3, \frac{9}{5})[/tex]

Trigonometry

[tex]Sine\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite} \\S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]

Depending on which angle you use, decides which formula you use.

We'll use the top right angle.

9 is the adjacent.

x is the opposite.

So you need to use

[tex]Tan\frac{Adjacent}{Opposite} \\Tan45\frac{9}{x} \\x = \frac{9}{Tan45} \\x = 9[/tex]

If you solve y, you can check this is correct by doing pythagoras' theorem.

[tex]Cos\frac{Adjacent}{Hypotenuse} \\Cos45\frac{9}{y} \\y = \frac{9}{cos45} \\y = 9\sqrt{2}[/tex]

[tex]\sqrt{9^{2}+9^{2} } = 9\sqrt{2}[/tex]

16 ounces = 1 pound, 8 ounces is half of 16, so 8 ounces = 1/2 pound.

1 pound of salmon cost 17.98.

Divide the cost for one pound in half:

8 ounces cost: 17.98 / 2 = $8.99

Answer:

AC

Step-by-step explanation:

A chord is a line segment connecting two points on a circle.

Basically, it means that a chord is a line that has both endpoints on the edge of the circle.

the general term for the sequence m, -m, m, -m, . . . is

The correct option is (A).

The given sequence is: m, -m, m, -m, ...

Let's analyze the pattern:

1. For n = 1, the term is m.

2. For n = 2, the term is -m.

3. For n = 3, the term is m.

4. For n = 4, the term is -m.

5. And so on...

From the pattern, we can see that the sign alternates between positive and negative, and the term alternates between m and -m. This suggests that we can use [tex](-1)^(n-1)[/tex] to control the sign alternation and m to control the alternation between m and -m.

Now, let's check the options one by one:

A. [tex]m(-1)^(n-1)[/tex]

  Substituting n = 1, we get[tex]m * (-1)^(1-1) = m * (-1)^0 = m * 1 = m[/tex]

  Substituting n = 2, we get [tex]m * (-1)^(2-1) = m * (-1)^1 = m * -1 = -m[/tex]

  This matches our sequence. So, Option A seems correct.

B.[tex](-m)^n[/tex]

  This doesn't match our sequence because it would give us [tex](-m)^1 = -m,[/tex][tex](-m)^2 = m^2, (-m)^3 = -m^3[/tex], and so on, which doesn't alternate between m and -m.

C.[tex](-1)m^(n + 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 + 1) = (-1)m^2 = -m^2[/tex]

  Substituting n = 2, we get [tex](-1)m^(2 + 1) = (-1)m^3 = -m^3[/tex]

  This doesn't match our sequence because it doesn't alternate between m and -m.

D.[tex](-1)m^(n - 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 - 1) = (-1)m^0 = -1[/tex]

  Substituting n = 2, we get[tex](-1)m^(2 - 1) = (-1)m^1 = -m[/tex]

  This also doesn't match our sequence because it doesn't alternate between m and -m.

So, the correct answer is Option A:[tex]m(-1)^(n-1).[/tex]

Answer:

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr^2

where the radius (r) is half the diameter. For a circle with a diameter of 20 units, the radius is 10 units and the circle area is ...

  A = π·(10 units)^2 = 100π units^2 ≈ 314.16 square units

__

When there are 20 congruent sectors, each sector has an area of 1/20 of the circle area, so

  sector area = (1/20)·100π unit^2 = 5π units^2 ≈ 15.7 square units

Answer:

1/6

Step-by-step explanation:

Number of orange crayons = 2

Total number of crayons = 2 + 4 + 1 + 2 + 3 = 12

Probability is calculated as:

[tex]\frac{\text{Number of Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Here the favorable or desired outcome is picking up an orange crayon. So number of favorable outcomes will be 2 as 2 orange crayons are available.

Total number of outcomes is 12 which is the sum of all the crayons available.

So, the probability the crayon she pulls out will be orange = [tex]\frac{2}{12}=\frac{1}{6}[/tex]

The probability of Jill drawing an orange crayon from her bag is 1/6. This is calculated by dividing the number of desired outcomes (orange crayons) by the total number of outcomes (total crayons).

To solve this problem, we have to calculate the probability of picking an orange crayon from the bag. First, we calculate the total number of crayons Jill has in the bag. So Jill has 2 black, 4 blue, 1 yellow, 2 orange, and 3 purple crayons, which add up to a total of 12 crayons.

Probability is calculated by dividing the number of desired outcomes (in this case, drawing an orange crayon) by the total number of outcomes (the total number of crayons). Jill has 2 orange crayons, so the total number of desired outcomes is 2. As calculated earlier, the total number of outcomes is 12 crayons. So the probability of Jill drawing an orange crayon from her bag is 2 (orange crayons) divided by 12 (total crayons), or 1/6.

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The absolute value |2x+7| simplifies differently depending on values of x. If x > -7/2, |2x+7|=2x+7. If x=-7/2, |2x+7|=0. If x<-7/2, |2x+7|= -(2x+7).

The absolute value |2x + 7| measures the distance of the value 2x + 7 from zero on the number line. To simplify the equation and determine for what values of x the absolute value results are positive, negative or zero, we must consider the following conditions:

In the first case, the inside of the absolute value is positive and thus its value is itself. In the second case, the inside of the absolute value equals to zero and the absolute value of zero is zero. In the third case, the inside of the absolute value is negative and thus its absolute value is the negation of it.

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Answer:

False. He is not correct.

Step-by-step explanation:

To find the percent increase subtract  the old time from the new time then divide that number by the old time. 25-20=5. 5/20=.25. There was a 25% increase in time worked. Evan worked 125% of the original time but only worked 25% more time.

y^2-14y+49

(y-7)(y-7)

Answer:

y^2-14y+49 I hope i can help you out

A solid has 6 faces

Answer:

z = 0.33

Step-by-step explanation:

Mean = u = 500

Standard Deviation = s = 60

Scores of Jake = x = 520

Step 1: Finding the z score

In order to find the percentage who scored below Jake first we have to convert the scores of Jake to z scores. The formula to find z value is:

[tex]z=\frac{x-u}{s}[/tex]

Using the given values in this formula, we get the z scores:

[tex]z=\frac{520-500}{60}=0.33[/tex]

Thus, rounded of to two decimal places, the z-value for Jake's score is 0.33

Step 2: Find probability from the z-table

In the given table, from first column we will find the value 0.3. In the row across 0.3 we will find the value directly below 0.03 as 0.3 + 0.03 = 0.33

This value comes out to be 0.6293

The image attached below shows this process of finding the probability.

Step 3: Converting the probability to percentage

In order to convert this probability to percentage simply multiply it be 100.

So, 0.6293 = 62.93 %

62.93% rounded to nearest whole number will be 63%

This tells us that approximately 63% students scored below Jake i.e. below 520.

Answer: 18 gallons.

Step-by-step explanation:

Let's call the total gallons that the container can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{4}{9}x+4=\frac{2}{3}x[/tex]

Now, you must solve for x, as you can see below. Therefore, you obtain the following result:

[tex]\frac{4}{9}x+4=\frac{2}{3}x\\\\4=\frac{2}{3}x-\frac{4}{9}x\\\\4=\frac{2}{9}x\\\\4*9=2x\\\\36=2x\\\\x=18\ gallons[/tex]

To solve the container problem, we set up a proportion based on the given fill levels and found that the total capacity of the container is 18 gallons.

To solve how many gallons the container can hold, we need to set up a proportion based on the information given. The container was initially 4/9 full, and after adding 4 gallons of water, it became 2/3 full. We can use this ratio to find the total capacity of the container.

Therefore, the container's total capacity is 18 gallons.

Answer:

{1;-2}

Step-by-step explanation:

[tex]...=\left \{ {{x=2y+5} \atop {7x-3y=13}} \right. =\left \{ {{x=2y+5} \atop {14y+35-3y=13}} \right.=\left \{ {{x=2y+5} \atop {y=-2}} \right.=\left \{ {{x=1} \atop {y=-2}} \right.[/tex]

Answer:

  756 m²

Step-by-step explanation:

The ratio of areas is the square of the ratio of linear dimensions. Hence the area of the red solid is ...

  (6/4)²×336 m² = 756 m²

Answer:

Correct Answer 7/10

Step-by-step explanation: