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Fuel Usage.

The slope can be used to represent the average rate of change, or how much one quantity changes, on average, relative to the change in another quantity. An example of a slope that changes in real-life involves units of measure such as beats per minute or kilowatts per hour.



Over a 45-day period, the amount of propane in a tank that stores propane for heating a home decrease from 500 gallons to 344 gallons.











1. Use a graph or the slope formula to show the average rate of change in the amount of propane used over the 45-day period.



2. Show all work.



3. Explain what your solution represents in the context of the situation.

Answer:

[tex]13\frac{1}{8}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(-5 \frac{5}{8}\right) \cdot \left(-2 \frac{1}{3} \right)[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator, adding it to the numerator of the fraction, and placing this as the numerator:

[tex]\implies -\dfrac{5 \cdot 8+5}{8} \cdot -\dfrac{2 \cdot 3+1}{3}[/tex]

[tex]\implies -\dfrac{40+5}{8} \cdot -\dfrac{6+1}{3}[/tex]

[tex]\implies -\dfrac{45}{8} \cdot -\dfrac{7}{3}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c}{b \cdot d}:[/tex]

[tex]\implies \dfrac{-45 \cdot -7}{8 \cdot 3}[/tex]

[tex]\implies \dfrac{315}{24}[/tex]

Convert the improper fraction into a mixed number:

[tex]\implies 315 \div 24 = 13\: \text{r}\:3[/tex]

[tex]\implies 13\frac{3}{24}[/tex]

[tex]\implies 13\frac{1}{8}[/tex]

Answer:

Product = 13 1/8

Step-by-step explanation:

The equation is,

→ (-5 5/8) × (-2 1/3)

Now the product of equation will be,

→ (-5 5/8) × (-2 1/3)

→ (-45/8) × (-7/3)

→ (-15 × -7)/8

→ 105/8

→ 13 1/8 {mixed fraction}

Therefore, the product is 13 1/8.

Answer: 20

Step-by-step explanation:

By solving a system of equations, we can see that each geranium costs 3 dollars.

First, let's define the two variables:

x = price of one rose bush.

y = price of one geranium

Now, with the information on the problem we can write two equations, thus, we will have a system of equations:

$122 = 14*x + 8*y

$120 = 12*x + 12*y

We want to solve that system, if we isolate x on the first equation we will get:

x = ($122 - 8y)/14

Now we can replace this on the other equation:

$120 = 12*($122 - 8y)/14 + 12*y

Now we can solve this for y.

14*$120 = 12*($122 - 8y) + 12*14*y

$1,680 = $1,464 + 72y

($1,680 - $1,464 )/72 = y = $3

Each geranium costs 3 dollars.

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Answer: 209 square inches, 182 cubic inches

Step-by-step explanation:

The lateral surface area is the sum of the areas each of the four faces.

The area of one face is [tex](1/2)(11)(9.5)[/tex]. Multiplying this by 4, we get 209 square inches.

To find the volume, we use the formula [tex]V=\frac{1}{3}Bh[/tex]. This gives us that the volume is [tex](1/3)[(1/2)(11)(11)](9)[/tex], or about 182 cubic inches.

From the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

As given,

Given numbers:

A. −√5 :It is an irrational number.

Therefore belongs to real numbers.

B. -1/2 :In p/q form .

It is a rational and real number.

C. -50,000,000

It is a negative integer and real number.

D. -1.5 =-15 /10

          =3/2

It is a rational and real number.

Therefore, from the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

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Answer:

192 [in²]

Step-by-step explanation:

Area=(4*4)*2+(4*10)*4=192.

a The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.

b The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.

Given data

a, b, c, and x be real numbers.

|ax| + b = c

The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.

|ax + b| = c

Here the modulus sign covers both ax and b hence the absolute values  of ax + b is considered.

|ax| + b ≤ c

The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.

|ax + b| ≥  c

Here the modulus sign covers both ax and b hence the absolute values  of ax + b is considered.

Note that absolute values do not consider the signs

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Answer:

  (b)  √(4x+2)√(25x-4)

Step-by-step explanation:

Given two functions f(x) = √(4x+2) and g(x) = √(25x-4), you want the function fg.

The product fg is a bit of shorthand notation:

  [tex]fg = fg(x) = f(x)\cdot g(x)[/tex]

Substituting the given function definitions, we have ...

  [tex]f(x)\cdot g(x) = \sqrt{4x+2}\cdot\sqrt{25x-4}[/tex]

The product of the radicals could be combined into one radical, but that has not been done in your answer choices. This means ...

  [tex]\boxed{fg=(\sqrt{4x+2})(\sqrt{25x-4})}[/tex]

Answer:

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

The actual width of Tyrone's patio using the scale drawing is 16 feet's

The scale from the backyard to the drawing is 2 ft to 1 inches.

The width of the patio on the drawing is 8 inches.

Therefore, the width of the Tyrone's actual patio is as follows;

Hence,

1 inches = 2 feet's

8 inches = ?

cross multiply

actual length of Tyrone's patio = 8 × 2

actual length of Tyrone's patio = 16 feet's

Therefore, using the scale drawing, the actual length of Tyrone's patio is 16 feet's.

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Answer:

the answer is the 3rd to the 4th power and

The end behavior of the polynomial y=-4x+8x-21'+3 is y = -4x^3.

Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).

Thus, in the degree of the polynomial is 3 as the highest power in its terms is 3.

(power and exponent are same thing)

We are given that;

The functions (a) 1=3x-2x+12

(b) 1-10-8.x2

(c) y=6r-4r+x-120

(d) y=-3x+2x-4x+7

(e) y=5x+2x2

(f) y=-4x+8x-21'+3

Now,

To find the power function that best represents the end behavior of a polynomial, we need to look at the leading term (the term with the highest degree) of the polynomial.

(a) The leading term of this polynomial is 3x. So the power function that best represents its end behavior is y = 3x.

(b) The leading term of this polynomial is -8x^2. So the power function that best represents its end behavior is y = -8x^2.

(c) The leading term of this polynomial is 6r. So the power function that best represents its end behavior is y = 6r.

(d) The leading term of this polynomial is -3x^3. So the power function that best represents its end behavior is y = -3x^3.

(e) The leading term of this polynomial is 2x^2. So the power function that best represents its end behavior is y = 2x^2.

(f) The leading term of this polynomial is -4x^3. So the power function that best represents its end behavior is y = -4x^3.

Therefore, by polynomials the answer will be y = -4x^3.

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The expressions can be simplified as follows-

1. (9 − 3) 2− (5 • 4)0 = 12

2. (2 + 3)5 ÷ (5 × 2)2 = 5/4

3. 4 × 2 ÷ (6 − 2)4 = 1/2

4. [(1 + 7) 2] 2• (12 2 )0 = 0

Let us look at each expression one by one-

1. (9 − 3) 2− (5 • 4)0

Zero multiplied by any number is 0 itself. Thus, the expression becomes-

= (9 - 3) 2

= 6 × 2

= 12

2. (2 + 3)5 ÷ (5 × 2)2

According to the rules of BODMAS, we first solve the brackets-

(5)5 ÷ (10)2

= 25 ÷ 20

= 25/20

= 5/4

3. 4 × 2 ÷ (6 − 2)4

= 4 × 2 ÷ (4)4

= 8 ÷ (4)4

= 8/16

= 1/2

4. [(1 + 7) 2] 2• (12 2 )0

= [(8)2]2• 0

= 0

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Answer:

4×9=36

1-3=-2

36÷2=18

Step-by-step explanation:

4×+1,9×-1.

4×9=36

1-3=-2

The expected foot length of an adult male who is 1.8 m tall is 30.8 cm.

Based on the information given, Jerry surveyed adult males to study the relationship between their high and the length of their footwear both are measured in centimeters and he found the equation y equals 75 + 3.4 x.

This will be illustrated as:

y = 75 + 3.4x..

y = 1.8m = 180

Therefore, y = 75 + 3.4x.

180= 75 + 3.4x

180 = 75 + 3.4x

Collect like terms

3.4x = 180 - 75

3.4x = 105.

Divide

x = 105 / 3.4

x = 30.8 cm

Therefore, the expected foot length of an adult male who is 1.8 m tall is 30.8 cm.

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Answer: ABD=67 degrees

CBD=67 degrees

ABC=134 degrees

Step-by-step explanation:

ABC=ABD+CBD

25x+34=ABD+11x+23

14x+34=ABD+23

ABD=14x+11

ABD=CBD ==> Bisected angles are equal to each other since angle ABC is divided into two equal angles when bisected.

14x+11=11x+23

3x+11=23

3x=12

x=4

ABD=14x+11

ABD=14(4)+11

ABD=56+11

ABD=67 degrees

CBD=11x+23

CBD=11(4)+23

CBD=44+23

CBD=67 degrees

ABC=25x+34

ABC=25(4)+34

ABC=100+34

ABC=134 degrees

Answer:

∠ ABD = 67° , ∠ CBD = 67° , ∠ ABC = 134°

Step-by-step explanation:

since BD bisects ∠ ABC , then

∠ ABD = ∠ CBD = 11x + 23

∠ ABC = ∠ ABD + ∠ CBD ( substitute values )

25x + 34 = 11x + 23 + 11x + 23

25x + 34 = 22x + 46 ( subtract 22x from both sides )

3x + 34 = 46 ( subtract 34 from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Then

∠ ABD = 11x + 23 = 11(4) + 23 = 44 + 23 = 67°

∠ CBD = ∠ ABD = 67°

∠ ABC = 25x + 34 = 25(4) + 34 = 100 + 34 = 134°

Answer:

Aisha is ten years old and Mpho is seven

The age of Aisha is 10 years old and the age of Mpho is 7 years old.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Aisha is three years older than Mpho. Together their ages add up to 17 years.

Let x be the age of Aisha and y be the age of Mpho. Then the equations are given as,

x = y + 3               ...1

x + y = 17             ...2

From equations 1 and 2, then we have

y + 3 + y = 17

2y = 14

y = 7

Then the value of 'x' is given as,

x = 7 + 3

x = 10

The age of Aisha is 10 years old and the age of Mpho is 7 years old.

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Answer:

3796 length of the box

Step-by-step explanation:4,238-26×17=3,796

The real court is 9 by 18 meters in length and width.

The length of something is its width or size measured across its entire surface. Or, to put it another way, it is the larger of a geometric shape's higher two or three dimensions.

This statement implies that the court's original dimensions have been reduced by 22.5 for every 1 centimeter in the size of the current drawing, which is 40 cm by 80 cm. To get the original dimension, we will multiply the required dimension by each 22.5 cm as shown. Original length for a 40-cm length = 40 * 22.5 originally 900 cm long 100 cm equals one meter in metres. Multiply 900cm by x to get 9m: 100x = 900*1x = 900/100x Therefore, 900cm = 9m For the 80-cm width: Original width is equal to 80 * 22.5, or 1800 cm. 100 cm equals one meter in metres. multiplying 1800cm by x yields 100x, 1800*1, 1800/100x, and 18m. So 1800cm = 9m. As a result, the real court is 9 meters long and 18 meters wide.

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By using the method of division,  circle=20 , triangle= 35.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given that,

The circles are 3

Which have the total of 60.

So, the total value divided by total number of circles.

60/3= 20

20 is the value of each circle.

The triangles are 2 including one circle

Which have the total of 90

90 - 20(circle)= 70

So, the total value divided by total number of triangles.

70/2= 35.

35 is the value of each triangle.

Therefore, circle=20 , triangle= 35

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The two expressions to represent the perimeter of this rectangle include the following:

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Substituting the given variables into the given expression, we have;

P = 2(2x + 6 + x)    ......expression 1.

For the second expression, we have:

P = 2(2x + 6 + x)

P = 2(3x + 6)        ......expression 2.

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Complete Question:

The length of a rectangle is 2x+6 and the width is x. Write two expressions to represent the perimeter.

Answer:

Step-by-step explanation:

Answer:

19 in and 35 in

Step-by-step explanation:

Let the width be w and the length be 2w-3. Then,

[tex]2(w+2w-3)=108 \\ \\ 3w-3=54 \\ \\ 3w=57 \\ \\ w=19 \\ \\ \implies 2w-3=35[/tex]

There were 61 youth tickets sold and 34 general admission tickets in linear equation .

What in mathematics is a linear equation?

GA= GENERAL ADMISSION =$10

Y= YOUTH =$8

GA+Y= 95

GA=95-Y

10GA+8Y=828

10(95-Y)+8Y=828

950-10Y+8Y=828

-2Y= 122 MULTIPLY BY (-1)

2Y= 122

Y= 61

GA= 34

There were 61 youth tickets sold and 34 general admission tickets.

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The set of points on this graph is a relation but not a function

We know that every function can be a relation but every relation cannot be a function.

A relation means the connection between the input and the output.

A function means that for every input there should only be one output.

Here, we have the data as:

(2,5), (1,2), (3,4), (3, 1), (6,5) and  (5,3)

We can say that it is a relation as for every input, there is an output.

But, it is not a function.

This is because the input 3 has 2 outputs as 1 and 4 which is not possible in a function.

Therefore, the set of points on this graph is a relation but not a function.

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Answer:

Step-by-step explanation:

ln(xy²/z)

Answer:

no

Step-by-step explanation:

it is divisble by 1, 2, 4, 8, 89, 178, 356, 712