The relationship between the number of $4 lunches you buy with a $105 school lunch card and the money remaining on the card

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

A symbol (typically a letter) used in algebra to represent an unknowable numerical value in an equation. X and Y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are examples of frequently used variables (arc length).

The price to produce x yearbooks will be 15x.

Additionally, software has a fixed cost of $800.

So the total price would be:

y = 800 + 15x

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Step-by-step explanation:

l = number of Levi's cards

j = number of James' cards

l = 4j

l + j = 600

whey we use the first identify in the equation we get

4j + j = 600

5j = 600

j = 120

l = 4j = 4×120 = 480

Levi has 480 cards, James has 120 cards.

The equations for the coordinates of the endpoint F should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.

In this problem we know the coordinates of the endpoint E and the midpoint M of the line segment EF and we need to derive expressions of the coordinates of the endpoint F by the midpoint formula:

M(x, y) = 0.5 · E(x, y) + 0.5 · F(x, y)

2 · M(x, y) = E(x, y) + F(x, y)

F(x, y) = 2 · M(x, y) - E(x, y)

If we know that M(x, y) = (35, - 3) and E(x, y) = (15, 26), then the coordinates of the endpoint F are:

F(x, y) = 2 · (35, - 3) - (15, 26)

F(x, y) = (70, - 6) + (- 15, - 26)

F(x, y) = (55, - 32)

The equations should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.

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The endpoint F's coordinates should be given by the formula

x = 2×35 - 15 and y = 2×(- 3) - 26.

In order to solve this problem, we need to derive expressions for the coordinates of the endpoint F using the midpoint formula.

We know the coordinates of the endpoint E and the midpoint M of the line segment EF.

M(x, y) = 0.5×E(x, y) + 0.5×F(x, y).

2×M(x, y) = E(x, y) + F(x, y).

F(x, y) = 2×M(x, y) - E(x, y).

Given that M(x, y) = (35, -3) and E(x, y) = (15, 26), the endpoint F's coordinates are,

F(x, y) = 2×(35, - 3) - (15, 26).

F(x, y) = (70, - 6) + (- 15, - 26).

F(x, y) = (55, - 32).

The equations should be x = 2×35 - 15 and y = 2×(- 3) - 26.

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Answer:

7.08661

Step-by-step explanation:

Answer: Choice D

Step-by-step explanation

First, subtract Ax from both sides:

Ax - Ax + By = C - Ax

By = C - Ax

Now, divide B from both sides:

[tex]\frac{By}{B}[/tex] = [tex]\frac{C - Ax}{B}[/tex]

y = [tex]\frac{C - Ax}{B}[/tex]

Finally, to get an equivalent answer for an answer choice, divide each term by B on the right side of the equation:

y = [tex]\frac{C}{B}[/tex] - [tex]\frac{Ax}{B}[/tex]

     or

y = -[tex]\frac{Ax}{B}[/tex] + [tex]\frac{C}{B}[/tex]

     or

y = [tex]\frac{-Ax}{B}[/tex] + [tex]\frac{C}{B}[/tex]

This answer is the same as answer choice D, and so D is the correct answer.

Answer: D.

Step-by-step explanation:

[tex]Ax+By=C\\Ax+By-Ax=C-Ax\\By=C-Ax\\[/tex]

Divide both parts of the equation by B:

[tex]\displaystyle\\y=\frac{C-Ax}{B} \\\\y=\frac{C}{B}-\frac{Ax}{B} } \\\\y=-\frac{Ax}{B} +\frac{C}{B}[/tex]

Answer:

11/8 or 1.375

Step-by-step explanation:

2 3/4 => 11/4

1/2 x 11/4 = 11/8

Answer:0.4

Step-by-step explanation:

just do y2-y1 over x2-x1 which gives 5/14

and convert that to a decimal which is .3571 and round it to get .4

The value of the variable k in the equation given as 2k + 6k = h is k = h/8

From the question, the equation is given as

2k + 6k = h

Evaluate the like terms

i.e. We add 2k and 6k together.

This gives 8k

So, we have the following equation

8k = h

Divide both sides of the equation by 87

So, we have the following equation

8k/8 = h/8

Evaluate the quotient in the equation

k = h/8

The equation cannot be further simplified

Hence, the solution for k is k = h/8

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Answer:

Sarah earned $10 per hour for babysitting

Step-by-step explanation:

The solution for x of the given equation ax + b = 0 is x = -b/a.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

As per the given equation,

ax + b = 0

Add -b both side

ax + b - b = 0 - b

ax = -b

Divide by both side

ax/a = -b/a

x = -b/a

Hence "The solution for x of the given equation ax + b = 0 is x = -b/a".

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Answer:

343.75

Step-by-step explanation:

dividing the number of miles by the number days to get fewest equal number miles per each day

y=x+23 is the linear equation that gives the rule for the given table .

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

The following is how the linear equation can be expressed in a slope-intercept form:

y = mx + b

where

slope = m

y-intercept = b

Using the table we get two points:

(1,24) and (2,25)

slope= y2-y1/x2-x1

= 25-24/2-1

=1

Now we have to calculate B using the point (1,24) and putting values in equation y=mx+b

24=1+b

b=23

So the equation is :

y=x+23

Therefore the linear equation for the given set of data table is  y=x+23.

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Some of the terms of an equation that has missing terms will be eliminated.

100 is the missing term that transforms (x² - 20) into a perfect square.

What is a  perfect square?

A perfect square is a number that can be written as the product of an integer multiplied by itself or as the integer's second exponent. For instance, the number 25, which is the product of the integer 5 multiplied by itself, is a perfect square because 5 x 5 = 25.

The missing term will be calculated in the next step.

Use k to represent the x-coefficient.

We thus have:

k = -20

Divide both sides by 2

k/2 = - 10

squaring both the sides,

(k/2)² = (- 10)²

=> (k/2)² = 100

This means that the term that is lacking is 100.

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Question:

What is the missing constant term in the perfect square that starts with x^2 -20x?

Given:

Taking the first equation:

Taking the second equation:

If 4m=5n,

If 4m=-5n,

Range of n in terms of p:

The skid distance value that will be used when calculating the skid speed formula is 58.5 ft.

What is average of values and how is it defined?
The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. As a result, the following is the mathematic average formula:
Average = Sum of values/Set of values = (x₁ + x₂ + ... + xₙ)/n

Given, the first skid distance calculated, in feet = x₁ = 55
The second skid distance calculated, in feet = x₂ = 55
The third skid distance calculated, in feet = x₃ = 62
The fourth skid distance calculated, in feet = x₄ = 62
Therefore using the formula for average mentioned in the literature at n=4, we have,
Average skid distance = (55 + 55 + 62 + 62)/4 = 234/4 = 58.5 ft.
Thus, the skid distance value that will be used when calculating the skid speed formula is 58.5 ft.

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Required:

We need to fill the given diagram with suitable words.

Explanation:

Consider the first line.

There is a choice of fish-bottled water is coming from fish and bottled water.

Consider the second like there is Chicken-bottled water and we have bottled water.

There must be chicken under food.

There are only three types of drink that are Bottled water, Soft drink, and juice.

In drinks for fish, there are already two drinks Bottled water and juice so the remaining is Soft drinks.

Chicken and juice give a choice of Chicken-Juice.

Vegetable and Juice give a choice of Vegetable- Juice.

Two lines are perpendicular when their slopes are opposite.

You have the equation;

You can identify the slope as the number next to the x (y=mx+b, m is the slope)

the slope in the given equation is 1/2

The slope of the perpendicular line will be the opposite

The compound interest comes into the picture when interest adds on the principal amount. The total value of $4080 after 4 years with a rate of interest of 5.7% is $4124.83.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount but after 1 year it will convert into $550.

As per the given,

Principle amount P = $4080

Rate of interest r = 5.7% = 0.057

Time period t = 4 years.

The formula for total value is given as,

V = P[tex]e^{rt}[/tex]

V = 4080[tex]e^{(0.057\times4)}[/tex]

V = $5124.83

Hence "The compound interest comes into the picture when interest adds on the principal amount. The total value of $4080 after 4 years with a rate of interest of 5.7% is $4124.83".

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The given question is incomplete complete question follows;

The quadratic function has an equation of f(x) = -2x² - 4x - 3

From the question, the ordered pairs are given as

(−1,−1), (2,−19), and (3,−33).

A quadratic function is represented as

f(x) = ax²+ bx + c

Using the point (-1, -1), we have

a(-1)²+ b(-1) + c = -1

So, we have

a - b + c = -1

Using the point (2, -19), we have

a(2)²+ b(2) + c = -19

So, we have

4a + 2b + c = -19

Using the point (3, -33), we have

a(3)²+ b(3) + c = -33

So, we have

9a + 3b + c = -33

So, we have

a - b + c = -1

4a + 2b + c = -19

9a + 3b + c = -33

Using a graphing tool, we have

a = -2, b = -4 and c = -3

Substitute a = -2, b = -4 and c = -3 in f(x) = ax²+ bx + c

So, we have

f(x) = -2x² - 4x - 3

Hence, the equation is f(x) = -2x² - 4x - 3

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Answer: n + 3

Step-by-step explanation:

Solution

n+3

Evaluate

(n 2 +n−6)

(n−2)

​Remove the parentheses

n−2n 2 +n−6

​Factor the expression

n−2

(n+3)(n−2)

Answer: 14a + 1

Step-by-step explanation:

( 7a x 3 - 2a - 2 ) + ( -5a + 3 )

( 21a - 2a - 2 ) + ( -5a + 3 )

21a - 2a - 2 - 5a + 3

14a + 1

Answer:

Step-by-step explanation:

n-2=10n+42

add 2 to both sides

n-2+2=10n+42+2

simplify

n=10n+44

subtract 10n from both sides

n-10n=10n+44-10-n

simplify

-9n=44

divide both sides by -9

-9n/-9=44/-9

n=-44/4

Answer: -85403

Step-by-step explanation:

Gagu will be paid £1248 per month after the increase.

Given,

The amount Gagu is paid = £1200 per month

The increase he is going to get = 4%

We have to find the amount Gagu gets after the increase:

First we have to find the increment amount:

That is,

4% of 1200

= 1200 × (4/100)

= 12 × 4

= 48

Here,

£48 is the increment amount Gagu will get.

Now we can calculate the monthly amount gagu will be paid after the increase.

That is,

1200 + 48 = 1248.

Therefore,

Gagu will be paid £1248 per month after the increase.

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Answer:

A) 1060 (corrected to the nearest 10) B) 1700

Step-by-step explanation:

A) the answer is 1058 which taken to the nearest 10 is 1060

B) the answer is 1700 which does not need to be corrected

The statements about Alina's and Cesar’s estimates should be completed as follows:

Percentage error is also referred to as percent error and it can be defined as a measure of the extent to which an experimental numerical value differs from the actual (theoretical) numerical value.

Mathematically, percentage error can be calculated by using this expression;

[tex]Percent\; error = \frac{Actual\;value - Experimental\;value}{Experimental\;value} \times 100[/tex]

For the Alina's result, we have:

Difference = Actual mileage - Estimated mileage

Difference = 50 miles - 45 miles

Difference = 5 miles.

Next, we would determine Alina's percentage error as follows:

Percentage error = 5/50 × 100

Percentage error = 500/50

Percentage error = 10%.

For the Cesar's result, we have:

Difference = Actual mileage - Estimated mileage

Difference = 200 miles - 190 miles

Difference = 10 miles.

Next, we would determine Cesar's percentage error as follows:

Percentage error = 10/200 × 100

Percentage error = 1000/200

Percentage error = 5%.

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Complete Question:

Alina and Cesar estimated the number of miles they drove during a trip. Alina estimated the number of miles they drove in the morning. Cesar estimated the number of miles they drove in the afternoon. Use the drop-down menus to complete the statements about Alina's and Cesar’s estimates.

Alina's Estimate Actual Mileage

45 miles                 50 miles

Cesar's Estimate Actual Mileage

190 miles                200 miles

Alina is ___ miles off the actual mileage of 50 miles. That is a percent error of %.

Cesar is ___ miles off the actual mileage of 200 miles. That is a percent error of %.

Because Alina's mileage is _____ than Cesar's mileage, each mile of error results in a ____ percent error.

The interpretations are

The slope

From the question, the slope is given as

Slope = 2 1/4

From the question, we have

y = Amount of money

x =Number of hot dogs

This means that the amount of money per 1 hot dog is $ 2 1/4

The y​-intercept

From the question, the y​-intercept is given as

y​-intercept = 10

From the question, we have

y = Amount of money

x =Number of hot dogs

This means that the initial amount of money is $10

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Answer:

(10, 1) is a solution to this equation.

Answer: your answer will be (10, 1)

Step-by-step explanation:

i just watch a mathematics video

Given the equation of a line as shown below :

To determine the slope and the y - intercept of the line, compare the equation with straight line equation

After comparing the equation of a line

Therefore slope = -3 and y - intercept = -2