Linear Functions: Model from Two Points-Quiz - Level H
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»Nevaeh uses a gift card to buy a cup of coffee every morning. The table shows the amount of
money remaining on the card, y, as a function of the number of cups of coffee she buys, c.
The rate of change is -3 since each cup of coffee costs $3.

Answer:

Step-by-step explanation:

it is a

The equivalent cost will be $5.4 per gallon.

The equivalent is the expression that is in different forms but is equal to the same value. Conversion means to convert the same thing into different units.

In September 2016, the cost of gasoline in Berlin was around 1.25 euros per liter.

We know that 1 U.S. dollar = 0.876 euros and 1 gallon = 3.785 liters.

The equivalent cost would be dollars per gallon will be

⇒ 1.25 euros per liter

⇒ 1.25 x [(1/0.876) / (1/3.785)] dollars per gallon

⇒ 1.25 x 1.1415 / 0.2642

⇒ $5.4 per gallon

The equivalent cost will be $5.4 per gallon.

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The number of kilometers that is equivalent to 8,000 meters is 8 kilometers

From the question, we are to determine how Amy can determine how many kilometers are equivalent to 8,000 meters

Let the value be x kilometers

From the given information, we have that

The table showed that 2 kilometers are equivalent to 2,000 meters

If 2 kilometers are equivalent to 2,000 meters

Then,

x kilometers will be equal to 8,000 meters

x = (2×8000)/2000

x = 16000/2000

x = 8 km

Hence, the number of kilometers that are equivalent to 8,000 meters is 8 kilometers

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Answer: Part A = y=−7.5x+15

Part B = 5 mi/hr

Step-by-step explanation:

Answer: 4366

Step-by-step explanation:

Sophie earns a weekly retainer $355 , a commission of 10% sales then the Sophie total earning each week = 39.44$

Sophie earns a weekly retainer = $355

Commission = 10% sales

That means 10%x sales

Let us assume,

Sophie total earning for a week if she made the following sales = x

We can write,

Sophie earns a weekly retainer $355 + commission of 10% sales

x = $355 +10% x

10%  means,   10/100 = 0.1x

Then,

x =  $355 + 0.1x

We can calculate the product,

x - 0.1x = 35.5$

x(1-0.1) = 35.5$

We can subtract the values,

0.9x = 35.5$

x = 35.5$/0.9

x = 39.44$

The value of x from the equation is 39.44$

Therefore,

Sophie earns a weekly retainer $355 , a commission of 10% sales then the Sophie total earning each week = 39.44$.

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Answer: 132.3

Step-by-step explanation:

-

Split it into different magnitudes.

-

Answer:

2 batches:1/4 which is 25 min. so 1 batch would be half of that. So just divide 25 by 2, which would get you 12.5 12 minutes, and 30 seconds. Hope this helped~ is 1/2 because for 2 is 1/4 and for the half of 1/4 is 1/2 and if u add 1/2 and 1/2 it equals 1/4 so the answer is 1/2 Incorrect.

Step-by-step explanation:

you couldn't do this on ur own?

Answer:

length= 10 width=5

Step-by-step explanation:

Answer:

It think it is 35

Step-by-step explanation:

So Jon's rates were approximately 69.55 mph on his way to his parents' house and 48.55 mph on his way back home.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, as well as functions such as sine, cosine, and logarithms. Equations can be solved to find the value of the unknown variable that makes the equation true. Solving an equation often involves performing operations on both sides of the equation to isolate the variable. Equations are used in many fields of mathematics and science to model real-world phenomena and to make predictions or solve problems.

Here,

Let's call Jon's speed on his way to his parents' house "x" (in mph). Then his speed on his way back home would be "x-21" (since it was 21 mph slower).

We know that the total distance he traveled was 396 miles, and that he spent a total of 11 hours driving. Using the formula:

distance = rate × time

we can set up two equations based on this information:

396 = x × t1 (for the trip to his parents' house)

396 = (x-21) × t2 (for the trip back home)

We also know that the total driving time was 11 hours, so we have:

t1 + t2 = 11

Now we can solve this system of equations to find the values of x and t1 (and then t2).

From the first equation, we have:

t1 = 396 / x

From the second equation, we have:

t2 = 396 / (x-21)

Substituting these expressions for t1 and t2 into the third equation, we get:

396/x + 396/(x-21) = 11

Multiplying both sides by x(x-21), we get:

396(x-21) + 396x = 11x(x-21)

Expanding and simplifying, we get:

792x - 8316 = 11x^2 - 231x

Putting this in standard form, we get:

11x^2 - 1023x + 8316 = 0

We can solve this quadratic equation using the quadratic formula:

x = [1023 ± sqrt(1023^2 - 4×11×8316)] / (2×11)

x ≈ 69.55 or x ≈ 60.09

Since x is Jon's speed on his way to his parents' house, we can discard the negative solution and conclude that Jon's speed on his way to his parents' house was about 69.55 mph. His speed on his way back home would then be:

x - 21 ≈ 48.55 mph

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Answer:

6

Step-by-step explanation:

you add all of the numbers, take the sum and divide between however many numbers are present.

Ira took hours to reach the same distance as Ravi at the rate of 64miles per hour.

The ratio of two related quantities expressed in several units is known as a rate.

Speed is a rate defined as the amount of distance covered in a given amount of time.

The rate or speed is calculated by the formula:

Distance travelled = speed × time

Lets us solve the following question using the above formula.

The rate of Ravi is 73 mph.

In 15 hours Ravi travels= 15×73=1095 miles.

Now Ira also travels the same distance as Ravi.

So Ira Travels 1095 miles.

Given the rate of Ira=64 mph

Time taken by Ira to cover the distance= Distance ÷ speed(rate)

Hence time taken=1095÷64=17.109375 hours

Therefore the time taken by Ira to cover the same distance as Ravi is approximately 17.11 hours.

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21. Point A is (1,5) and represents that the dog walker made $5 for one dog walked.

22. Point B is (5,25) and represents that after walking 5 dogs the dog walker made $25.

23. The dependant is the amount earned(y) and the independent is the number of dogs walked (x).

The value of a and b are a = 3 and b = 4√3 which are real numbers.

According to the question the solution that we have been given is:

                            z = 3 + √-48

the general form of the solution given in the question is

                             x = a + bi        (1)

 where , i is known as the iota whose value is equal to √-1

Now to find the value of a and b we will expand the equation given above

                             z = 3 + √-48

                             z = 3 + √(-1)(48)

                             z = 3 + (√-1)(√48)

                             z = 3 + √48 i

                             z = 3 + 4√3 i       (2)

Which is equal to the general equation. Now comparing equation (1) and (2) we get

            a = 3 and b = 4√3

Hence the value are :  a = 3 and b = 4√3.

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Answer:

Step-by-step explanation:

91 - 42 = 49 (amount of regular sodas sold)

Answer: 49:42

Finding the number of problems per week,

So, she solves 25 problems per week.

If we let the number of weeks be x,

[tex]25x \geq 827 \\ \\ x \geq 827/25 \\ \\ \therefore \lceil x \rceil=\boxed{34}[/tex]

The current age of the older brother is 16 years while that of the girl is 13 years.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the girl age, y the younger brother age and z the older brother age. Hence:

x = y + 5  

y = x - 5    (1)

Also:

z = x + 3   (2)

In two years time:

(y + 2)(z + 2) = 12(x + 2)

(x - 5 + 2)(x + 3 + 2) = 12(x + 2)

(x - 3)(x + 5) = 12(x + 2)

x² + 2x - 15 = 12x + 24

x² - 10x - 39 = 0

x = -3 and x = 13

Age must be positive, hence x = 13

z = x + 3 = 13 + 3 = 16 years

The current age of the older brother is 16 years while that of the girl is 13 years.

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Answer:

6

Step-by-step explanation:

We have y ∝ x which is another way of saying y varies directly with x

We can rewrite the direct proportion relation y ∝ x as y = k.x where k is a constant - the constant of proportionality

So y = kx or x = y/k

using y and x values know, we can solve for k and then solve for any x given y

We have

y = 37.4 =  k (17)

Therefore k = (37.4/17) = 2.2

To find x given y = 13.2, use the second equation
x = y/k = 13.2 / 2.2 =  6

Answer:

$ 1665 for 53 people to attend

Step-by-step explanation:

75 + 30(53) = 1665  for 53 people in attendance

Answer:

$1,665

Step-by-step explanation:

Side note: The question is quite unclear. In my opinion, the correct question should be - The cost of a school banquet is $75 + 30n, where n is the number of people attending. What is the cost for 53 people?

We know that the value of "n" is the number of people attending at the school banquet. Therefore, if we want to determine the cost of 53 people, we must substitute n = 53.

⇒ $75 + $30n

⇒ $75 + $30(53)                                                     [Substituting n = 53]

⇒ $75 + $1590                                                                [Simplifying]

⇒ $1665                                                                         [Simplifying]

Therefore, the total cost of 53 people attending the school banquet is $1665.

The pizza heats up an average of 7.50 degrees per minute.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

The table shown

Time (minutes)        Temperature (degrees Celsius)

4                                          25

6                                          40

8                                          55

Since the pizza was heated at a constant rate, we can model the experiment as a line, where the slope represents how fast the pizza was heated

Slope

m   =  (y2 - y1)/(x2 - x1)

Let

(x1,y1) = (6, 40)

(x2,y2) = (8, 55)

m = (55 - 40) / ( 8 - 6 )

m = 7.5 degrees per minute.

The pizza heats up an average of 7.50 degrees per minute

Therefore, pizza heats up an average of 7.50 degrees per minute.

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The cardinality of set {red, yellow}∪{blue} is 3.

The cardinality of set {∅, {{1}}} is 2.

The cardinality of set {5, 1}∪{1, 2, 5} is 3.

Cardinality is the quantity of elements in a particular mathematical set.

The number of cardinal (fundamental) members of a set is referred to as cardinality. A non-negative integer can have a limited or infinite degree of cardinality.

from the question three sets are given

1. {red, yellow}∪{blue}

2. {∅, {{1}}}

3. {5, 1}∪{1, 2, 5}

1. we know that

When A and B are two sets that are not connected, n(A U B) = n(A) + n (B) = 2 + 1.

so there are 3 elements.

so the cardinality of set {red, yellow}∪{blue} is 3.

2. {∅} is a set with a single element. That component is a set in and of itself, means there are two elements.

so, the cardinality of set {∅, {{1}}} is 2.

3. {5, 1}∪{1, 2, 5}

When A and B are two sets that are not connected, n(A U B) = n(A) + n (B).

Here 5 and 1 is common in both so that there are 3 elements.

so, the cardinality of set {5, 1}∪{1, 2, 5} is 3.

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Answer:

The distance between the two numbers, -2.2 and 8.4 on a number line is:10.6 units.Distance of two numbers on a number line can be calculated by finding the absolute value of the their difference.Thus:if a and b are two numbers on a number line, their distance would be:|a - b| Given two numbers on a number line are:-2.28.4Distance between them = |-2.2 - 8.4| = 10.6 unitsTherefore, the distance between the two numbers, -2.2 and 8.4 on a number line is: 10.6 units.

Step-by-step explanation:

The following equation represents the elevation change c after s seconds:

                      c = -2.5s

Given,

A mountain climber is moving 2.5 feet per second down a cliff.

Writing an equation to represent the change in elevation after s seconds is necessary.

How do we symbolize ascent and descent?

Elevation denotes upward movement, thus we interpret it as a positive distance

Descent implies a downward motion, thus we interpret it as a negative distance.

Find the rate at which the climber descents.

2.5 ft = 1 second

Find the equation that, in seconds, reflects the descents c.

We have got

2.5 ft = 1 second

So,

s x 2.5 ft = s x 1 seconds

2.5 s ft = s seconds

That means,

We will have a 2.5s distance descending in s seconds.

This can be expressed as an equation:

c = change in elevation

c = - 2.5s

Thus the equation modeling the change in elevation c after s seconds is,

                      c = -2.5s.

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Answer:

p = 6x

Step-by-step explanation:

Perimeter is the distance around a figure.

p = 2x + 1/2x +1/2x + 2x + x  if we combine all of the x's we get

p = 6x

Answer:

From top to bottom

radical

rational

exponential  

polynomial  

Step-by-step explanation:

It would have been nice if the graph was clearer so I could see x, y values but here goes

From top to bottom

radical :  appears to be a cube root function, [tex]a$\sqrt[3]{x}$ + b[/tex]

rational : of the form [tex]a\dfrac{1}{x} + b[/tex]. Appears to be a function of the reciprocal of x so rational

exponential  of the form [tex]a^x + b[/tex]

polynomial  of the form [tex]ax^2 + bx + c[/tex]

Part (a)

[tex]\overline{x}=\frac{\sum x}{n} \\ \\ \boxed{\sum x=n\overline{x}}[/tex]

Part (b)

[tex]\sum x^2-2\overline{x}(n\overline{x})+n\overline{x}^2 \\ \\ =\sum x^2 -2n\overline{x}^2+n\overline{x}^2 \\ \\ =\boxed{\sum x^2-n\overline{x}^2}[/tex]