13. Sofia's car can travel 228 miles on 6 gallons of gas.
a. Write an equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.

The output value of f( 38 ) in the function f( x ) = x/2 is 19.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To determine the output value of f( 38 ), replace all the occurrence of x with 38 in the function and simplify.

f( x ) = x/2

f( 38 ) = 38/2

Divide 38 by 2

f( 38 ) = 38/2

f( 38 ) = 19

Therefore, the output value is 19, this forms an ordered pair of ( 38,19 ).

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It is to be noted that Saturn is 1.29 *x 10⁹ km further from the sun than Venus.

Recall that we are given:
approximate distance from the sun for a few different planets.  

Hence, to detect how much farther (in km) from the sun Saturn is than Venus we initiate a series of subtractions.

Recall that
Planet             approximate distance from the sun ( km)

Mercury          5.8 x 10⁷

Venus             1.1 x 10⁸

Earth               1.5 x 10⁸

Saturn             1.4 x 10⁹

The distance of Saturn form the sun and Venus is given as

= Distance of Saturn from Sun - Distance of Venus from Sun

= 1.4 x 10⁹  - 1.1 * 10⁸  [Multiply 1.4 x 10 and we've got]

= 14 x 10⁸  - 1.1 * 10⁸  

= (14 - 1.1) * 10⁸ [ Collect like terms and consolidate]

= 12.9  x 10⁸  [Revert back to the power of 9 and we have]

=  1.29 x 10⁹ km

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Full Question:

The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus?  Express your answer in scientific notation.

Planet                                  Approximate distance from the Sun (in km)

Mercury                                        5.8 x 10⁷

Venus                                           1.1 x 10⁸

Earth                                             1.5 x 10⁸

Saturn                                           1.4 x 10⁹

It is found that Saturn is 1.29 x 10⁹ km further from the sun than Venus.

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq a < 10[/tex]

We have been given that the approximate distance from the sun for a few different planets.  

Hence, to determine the farthest distance (in km) from the sun Saturn is than Venus, we get;

Planet             the approximate distance from the sun ( km)

Mercury          5.8 x 10⁷

Venus             1.1 x 10⁸

Earth               1.5 x 10⁸

Saturn             1.4 x 10⁹

The distance between Saturn from the sun and Venus can be calculated as;

= Distance of Saturn from Sun - Distance of Venus from Sun

= 1.4 x 10⁹  - 1.1 x 10⁸

= 14 x 10⁸  - 1.1 x 10⁸  

= (14 - 1.1) x 10⁸

= 12.9  x 10⁸

=  1.29 x 10⁹ km

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Answer: y = 4x-1

Step-by-step explanation:

1) Choose two points for the later equation.

For this example, I will use (-1,-5) and (2,7)

2) Place it in a rise/run equation. (y/x)

[tex]\frac{y2-y1}{x2-x1} \\\\\frac{7-(-5)}{2-(-1)} \\\\\frac{12}{3} \\\\4[/tex]

The Slope is 4.

3) Find the y-intercept

So, we can place a given point and slope into a y=mx+b function.

[tex]y=4x+b[/tex]

Next, we can substitute the point and slope.

[tex]7 = 4(2)+b\\7=8+b\\-1=b[/tex]

4) Finally, place it all in slope intercept form

y = 4x-1

Answer:

$2.39, hope this helps,

Step-by-step explanation:

1.50+0.89=2.39

Answer: $2.39

Step-by-step explanation: 0.89 + 1.50

0.8 + 1.5 = 2.3

89 + 50 = 139

2.39

ok

MPG = 66.8

The values of the following functions are:-

f(-4) = 20

f(2) = -1

f(6) = 11

f(0) = -5

Given that ,

          -3x + 8, -6 ≤ x ≤ -3

f(x) =   [tex]x^2-5[/tex],  -2 ≤ x ≤ 3

          (1/2)x + 8 , 5  ≤ x  ≤10

We have to find the values of f(-4) , f(2),  f(6) and, f(0).

As, -6 < 4 < -3

So, we will write,

f(-4) = -3(-4) + 8 = 12 + 8= 20

As, -2 < 2 < 3

So, we will write,

f(2) = [tex](2)^2-5[/tex] = 4 - 5 = -1

As, 5 < 6 < 10

So, we will write,

f(6) = (1/2)(6) + 8 = 3 + 8 = 11

As, -2 < 0 < 3

So, we will write,

f(0) = [tex](0)^2-5[/tex] = 0 - 5 = -5

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Simplified expression for [tex] \frac{1}{( {5n⁴})^{- 3} } [/tex] is 1/125n¹².

As per the rule of exponents, the powers will be multiplied. Representing the mentioned rule in the form of example -

[tex]( {{a}^{m} })^{n} = {{a}^{m} }^{ \times n} [/tex]

Another rule of exponent to be used in the question is : [tex] {a}^{ - x} = \frac{1}{ {a}^{x} } [/tex]

Now, simplifying the expression mentioned in question as per the above written rule.

Rewriting the equation according to second rule.

Value = [tex] \frac{1}{( {5n⁴})^{ 3} } [/tex]

Now, solving the equation by taking cube according to first rule

Value = 1/125n¹²

Thus, the simplified expression is 1/125n¹².

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Answer: your answer in in the screenshot

Step-by-step explanation:

Answer:

Your missing number is -87.5.

Step-by-step explanation:

You want to follow reverse order of operations to isolate your variable x

First, you plug in y= 700 to get::

700 = (24x)/7 +1000

Then subtract 1000 from both sides to get:

-300 = (24x)/7

Then multiply both sides by 7 to get:

-2100 = 24x

Then, divide by 24 to get:

-87.5 = x

Thus, your answer x= -87.5

Answer:

-21/2

Step-by-step explanation:

-5-2= - 7

7-4=3(+, - = -)

-7×3/2= - 21/2

Answer:

f(x) = 0

px^2 + qx - 4p = 0

abc-Formula: x = (-b ± √(b^2 - 4·a·c))/(2·a)

x = (-q ± √(q^2 - 4·p·(-4p)))/(2·p)

x = (-q ± √(q^2 + 4^2·p^2))/(2·p)

Because q^2 + 4^2·p^2 > 0 there are two roots.

Recall that the ratio 9:8 can be written as follows:

therefore, when 64 is increased in the ratio 9:8 we get:

Answer: 72.

Answer:

72

Step-by-step explanation:

Since X : 64 = 9 : 8

Then we know X/64 = 9/8

Multiplying both sides by 64 cancels on the left64 × (X/64) = (9/8) × 64

X = (9/8) × 64Then solving for X X = 64 × (9/8)X = 72

Therefore 72 : 64 = 9 : 8

The approximate value of the expression given will be equal to -6.3.

An approximation may be defined bringing the value of a certain entity which is almost similar, but not exactly equal to the correct value. The expression can be written as −12 + √32. The value of √32 can be written as 5.656. Since, after decimal 6 to the right of 5 is greater than 5 so to the nearest tenth, we can write as 5.66. Therefore, √32 = 5.66

For the required value of the expression we can write,

−12 + √32

Putting the value of √32 = 5.66 in the expression we get

-12 + √32 = -12 + 5.66

After solving we get

⇒ -12 + √32 = -6.34

To the nearest tenth it will be -6.3.

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Answer:

672 sq km

Step-by-step explanation:

Area of a regular polygon
[tex]A = \dfrac{P}{2} \times a[/tex]

P = perimeter of the polygon

a = apotherm which is defined as
The distance from the center of a regular polygon to the midpoint of a side.

The given polygon has 8 sides and each side is 12 km
So the perimeter P = 12 x 8 = 96 km

The apotherm is given as 14 km

So area
[tex]A = \dfrac{96}{2} \times 14 = 672 \text { sq km}[/tex]

Seven people sharing the rent would make the cost $120 per person.

When two quantities are inversely proportional, that is, when an increase in one causes a decrease in the other and vice versa, they are said to be inversely proportional.

The general equation for inverse variation is y = k/x, where k is the proportionality constant and x and y are two variables.

Given:

The price paid by Four friends on a ski trip to share the rent of a cabin = $210

The cost per person varies inversely with the number of persons.

Let the cost be C and the number of persons be n,

C ∝ 1/n

So, the equation becomes, k = Cn.

Putting the values in the equation we obtain the value of k,

k = 210×4 = 840

We have to find the number of people sharing the rent that would make the cost $120 per person.

Using the equation,

k = Cn

840 = 120 × n

n = 840/120 = 7

Therefore, seven people sharing the rent would make the cost $120 per person.

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Given expression:

[tex]7p+\frac{q}{3}[/tex]  , given that p = 6 and q = 12.

Here, we need to substitute the values of p and q in the given expression to  obtain the value of the expression.

On substitution, the expression becomes,

[tex]7X6+\frac{12}{3}[/tex]  ,

Here we use BODMAS rule ( Brackets, Orders, Division, Multiplication, Addition, Subtraction) , hence initially we do the division operation, then the multiplication operation and at last the addition operation,

= 7x6 + 4 =  42 + 4 = 46.

Hence, option D) 46 is the correct option.

These type of expressions can be solved by simply substituting the given values of the variables such as p, q and so on.

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Answer:

Step-by-step explanation:

13

The determined value of the number of nickels and the number of dimes that Grayson has is

This is further explained below.

Generally, The following phrase represents Jayden's complete financial worth:

Nickels are worth $0.05 each.

The dime value is equal to $0.10

The total value is equal to the sum of the values of the nickels and dimes.

where;

[tex]1.20= (0.05*2 x) +(0.1*x)[/tex]

0.1 x+0.1 x=1.2

0.2 x=1.2

[tex]x=\frac{1.2}{0.2}[/tex]

x=6

y=2

In conclusion, the Total number of dimes=6

Total number of nickels=12

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1 2/3 divided by 4/5

= 5/3 ÷ 4/5

make common denominators:

[tex]\frac{25}{15} /\frac{12}{15}[/tex]

invert one and multiply across:

[tex]\frac{25}{15} * \frac{15}{12}[/tex]

= 375/180

reduce:

25/12 or 2 1/12

Answer:

A = (1, 1)

B = (3, 2)

C = (2, 4)

Step-by-step explanation:

Vertices of the triangle:

Mapping rule for a 90° clockwise rotation about the origin:

(x, y) → (y, -x)

Therefore:

Mapping rule for a reflection in the x-axis:

(x, y) → (x, -y)

Therefore:

Therefore, the coordinates of the new triangle are:

Based on the price of the cell phone in November and December, the price of the cell phone in March was $39

To find the price of the cell phone in March, you need to first find the price of the cell phone in November.

The price of the cell phone in November was $25 more than the price in December:

= 25 + 53

= $78

The price in November was double the price in March so the price in March was:

= 78 / 2

= $39

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The number 27 is a natural number, whole number, rational, real and an integer .

The number 27

And this number is a natural number and thus it is a natural number and a rational number too.

This is also an integer .

Reason: Natural number : A natural number is one that naturally and frequently appears. It is a whole, non-negative number as a result. N, the collection of natural numbers, can be defined in one of two ways: N = {0, 1, 2, 3, ...}

whole number: the sum of all natural numbers plus zero. neither a decimal nor a fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. 0, the negative, or a counting number.

Rational number: A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.

Real number: Rational, irrational, entire, and natural numbers are all examples of real numbers. Negative, positive, and zero numbers are all examples of integers.

Integer : An integer, pronounced is a whole number that can be positive, negative, or zero and is not a fraction.

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Answer:

A goes to K. C goes to M. B goes to L.

Step-by-step explanation:

:)

The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

expand the bracket

Volume, v = 4/ 3 (392.5)

Volume, v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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The Supplement postulate can be used to prove that the angles ∠CAB and ∠CAD are supplementary.

According to the Supplement Postulate, two angles are supplementary if they create a linear pair.

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By the analysis of the graph, the constant of proportionality is 2.

By analyzing the graph given we can infer that  If five rooms are reserved, he must provide ten towels.

So x is the number booked and y is the number of towels, Then

x is directly proportional to y,

The given graph is linear in nature, as we increase x, there will be a significant increase increase in y, The constant of proportionality(k) tells us how much y will change when x changes.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

Now, 10= k *5

        [tex]k =\frac{10}{5} \\k =2[/tex]

Hence, the constant of proportionality k is 2.

and the equation of the given graph is y = 2x

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