two stores sell identical sandwich rolls in different size packages, store A sells a six pack for $5.28 store B sells a four pack for $3.40, which store offers the better per-roll price

The answer to each part is -

        y = mx + c    

        where -

        [m] : slope of line
        [c] : y - intercept                    

Given is the graph of a straight line as shown.

[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -

(0, 4) and (4, 1)

Let the line be -

y = mx + c

m = (1 - 4)/(4 - 0) = -3/4

m = -3/4

So, the equation will be -

y = (-3/4)x + 4

[B] -

For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.

Therefore, the answer to each part is -

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1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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Answer:

1 -  $15

2-  $30

3 - $45

4 - $60

Step-by-step explanation:

$15/hour

1 -  $15 =1*15

2-  $30 =2*15

3 - $45 =3*15

4 - $60=4*15

Answer:

i think that answer is correct

Step-by-step explanation:

Answer:

New price = 0.06 x Original price

New price $1,968

Using the given data, the number of suspects is; 7

The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.

However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Now, we are told that;

Total number of people in the office = 30 people

Number of people wearing a white button down shirts = 22

Number of people wearing black pants = 16

Number of people wearing a multicolored tie = 7

Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;

The number of suspects =  A ∩ B ∩ C = 7 people

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The number of petals that the flower should have is of:

8 petals.

A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.

In this problem, we want the flower to have a rotation symmetry of 45 degrees.

The total angle measure of the flower is given as follows:

360º.

Then the number of petals needed for the flower to have a rotational symmetry of 45º is calculated as follows:

360/n = 45.

Applying cross multiplication, we have that:

45n = 360

n = 360/45

n = 8 petals.

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The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;

Tickets sold by Madelyn is; y = 22 + 30·x

Tickets sold by Kaia is; y = 53 + 20·x

A system of equation obtained from the details in the question can be presented as follows

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.

The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.

An equation consists of two expressions that are joined by the 'equals to' (=) sign.

The number of tickets for the Winter Dance Madelyn sold = 22

Number of tickets per day Madelyn sold after that = 30 per day

Number of tickets Kaia sold on Monday = 53

Number of tickets per day Kaia sold after that = 20 per day

Let x represent the number of days since Monday, and let y represent the number of tickets sold

Therefore;

The number of tickets Madelyn sold, y = 22 + 30·x

The number of tickets Kaia sold, y = 53 + 20·x

The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x

30·x - 20·x = 53 - 22 = 31

10·x = 31

x = 31 ÷ 10 = 3.1

The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days

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The number of adult tickets  which were sold that day as calculated from the given data  is 29.

First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.

To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.

This is represented by the following equation,

$8.90A + $5.30C = $928

Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:

3 * C = A

Now we can answer our first problem by substituting 3 * C for A.

8.9 (3C) + 5.3C = 928

26.7C + 5.3C = 928

32C = 928

C = 29

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Answer:

144cm²

Step-by-step explanation:

If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.

48/4 = 12cm

Then, to find the area, you need to multiply 12 by 12.

12 cm x 12 cm = 144cm²

Hope this helps :)

Answer:

Step-by-step explanation:

11.1

The approximate value of y - x is 17.2°.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given a right triangle LMN.

Using the tangent function,

tan (y) = 19.1 / 14.1

          = 1.3546

y = tan⁻¹ (1.3546) = 53.56°

We know that,

x + y = 90°, since the other angle is 90°.

x = 90 - 53.56° = 36.44°

y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°

Hence the value of y - x is 17.2°.

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Answer:12

Step-by-step explanation:

270/3=90, this is the amount it costs for 1 person to go

1080/90=12

12 people can go for $1080

Answer:

Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.

Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:

x &= 3y - 4

2x - 2y &= 8

Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

Answer:

D

Step-by-step explanation:

(7+-6)/2

(7-6)/2

1/2

(-6+(-8)/2

(-6-8)/2

-14/2

-7

(.5,-7)

It will take 38 weeks a student to save enough money for the ticket.

Mathematical operations come in several types, with division being one. The phrases or numbers are divided into the same number of components during this operation.

Given,

a student must save at least $675 plus 3% tax to buy a round-trip ticket to London.

3% of 675

= 3 x 675 / 100

= 20.25

The student has $98 saved already.

Now student needs ($675 - $98) + 20.25 = $577 + 20.25

= $597.25

If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost.

That means, $32 / 2 = $16 per week.

To find the amount of enough money:

Divide $597.25 by $16.

597.25 /16

= 37.328125

≈ 38 weeks

Therefore, student will save for 38 weeks.

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Parent function is represented by the graph is

B. The quadratic parent function

What is Parent function?

A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.

A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

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Step-by-step explanation:

it is the process of changing rows to columb

The null and different hypotheses for hypothesis test are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

Null hypotheses

Given that:

sample size (η)= 196

sample proposition (p^) = 114/196

Let p denote the population proportion of people who use a loyalty card.

The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]

Hence, the null and alternative hypothesis are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

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Answer:

a. [tex]\frac{x+2}{x+6}[/tex]

Step-by-step explanation:

[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]

a. Harold's monthly payment is given as follows: $164.13.

b. The total amount paid is given as follows: $9,847.8.

c. The finance charge is of: $847.8.

The monthly payment formula is defined as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The values of these parameters for this problem are given as follows:

P = 9000, r = 0.036, n = 5 \times 12 = 60.

Then:

r/12 = 0.036/12 = 0.003.

Then the monthly payment is calculated as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]

A = $164.13.

Then the total amount paid is of:

Total = 60 x 164.13 = $9,847.8.

Meaning that the finance charge is given as follows:

9847.8 - 9000 = $847.8.

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The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.

2. The insurance company then computes the interquartile range of the prices for each practice.

3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

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Answer:

Step-by-step explanation:

The rocket's height after 3 seconds is 6.3 sec.

The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.

A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.

To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:

h = -5*t2 + 30*t + 10

h = -5(2)2 + 30(2) + 10

h = -5(4) + 30(2) + 10

h = -20 + 60 +10

h = 50 m

The height of the rocket 2 seconds after launching it is 50 meters.

To find the x-coordinate of the vertex of a parabola, we use the formula:

[tex]xvertex = -b / 2a[/tex]

t - 3 = ± √(11)

t = 3 ± √(11)

t = 3 ± 3.3

Solving for t, we get two solutions:

t = 3 - 3.3

t = -0.3 sec

and

t = 3 + 3.3

t = 6.3 sec

Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.

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Answer:

All Real Numbers

Step-by-step explanation:

I assume you are solving for x.
The Interval Notation would be: (-∞,∞)

Answer: 59

Step-by-step explanation:

The number of quizzes still need to be graded is 17quizzes.

There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.

For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.

Algebraic equations in mathematics frequently have one or more variables.

It is given that,

grades of the teacher out of 48 quizzes before school = 16

grades of the teacher of the remaining quizzes after school = 15

Let us assume 'X' as the number of quizzes still need to be graded.

then X= 48-16+15

          =48-31

          =17

Hence, The number of quizzes still need to be graded is 17quizzes.

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The number of quizzes still need to be graded is 17 quizzes.

   then X= 48-=48-31

    =17

Hence, The number of quizzes still need to be graded is 17 quizzes.

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Yes , the triangles ΔSTU and ΔSRQ are similar triangles

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔSTU

Let the second triangle be ΔSRQ

Now , for the triangles to be similar , the corresponding sides of the triangles should be in the ratio

So , on simplifying , we get

The measure of side ST = 21

The measure of side SU = 35

The measure of side SQ = 6

The measure of side SR = 10

Now , for similar triangles ,

ST / SQ = SU / SR

Substituting the values in the equation , we get

21 / 6 = 35 / 10

3.5 = 3.5

Therefore , the corresponding sides of the triangles are equal

Hence , the pair of triangles are similar triangles

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