A truck driver is driving from Nome, Alaska, to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.

Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (2 points)

Part B: Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points)

Part C: In January 1989, the temperature in Nome, Alaska, dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not? (4 points)

Answer: 5 small bags and 3 large bags

Step-by-step explanation:  5+5+5+5+5=25    7+7+7=21    21+25=46

Answer:

[tex]y<5[/tex]

Step-by-step explanation:

[tex]3y-4<11 \\ \\ 3y<15 \\ \\ y<5[/tex]

The cost of admission to the library for each student will be $0.3125. And the admission cost of the zoo will be $156.

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

Mrs. Hudson's class of 18 understudies is going to the zoo. Every understudy will pay for confirmation and purchase lunch. Mr. Weaver's class of 24 understudies is going to the library. Every understudy will pay for affirmation and pay for transport passage.

Let 'x' be the cost of admission to the library for each student. Then the equation is given as,

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

Simplify the equation, then we have

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

$7.50 + $148.5 + $103.5 = 24x + $252

$259.5 - $252 = 24x

x = $0.3125

And the admission cost of the zoo will be given as,

⇒ $7.50 + $8.25 × 18

⇒ $156

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The coordinates of T' after the transformations are given as follows:

A. T'(8,8).

The coordinates of T are given as follows:

T(5,2).

Meaning that:

Then the translation is given as follows:

(x, y) → (x – 1, y + 2).

Meaning that the translated coordinates are of:

T'(5 - 1, 2 + 2) = T'(4, 4).

(as one was subtracted from the x-coordinate and 2 was added to the y-coordinate).

Then the dilation by a scale factor of 2 means that each of the coordinates is multiplied by two, hence:

T'(8,8).

Meaning that option A gives the correct coordinates of the image of the vertex T of the quadrilateral.

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Answer:

8,10

Step-by-step explanation:

i took the test

Answer:

y = 6x

Step-by-step explanation:

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\frac{24-6}{4-1}[/tex]

[tex]\frac{18}{3}[/tex]

m = 6

y = mx + b

y = 6x + b

6 = 6(1) + b

6 = 6

b = 0

Answer:

[tex]\frac{-r}{2} +12\\[/tex]

Step-by-step explanation:

Combine multiplied terms into a single fraction, find the common denominator, then combine fractions with the common denominator.

Answer:

The school ordered more than enough concrete to completely fill in the court, so the number of bags of concrete ordered, represented by x, must be greater than the number of cubic yards of concrete needed to fill the court. This can be represented by the inequality x > 60 cubic yards / 0.5 cubic yards/bag. Solving for x, we get x > 60 * 2 = 120. Therefore, the inequality that describes the problem is x > 120.

Answer:

x= 3.5 and x= -3.5

Step-by-step explanation:

4x^2 -49=0

x^2=49/4

x= 3.5 and -3.5

The measure of x is 22.5 and the angle ADE is 67.5 degrees

The complete question is added at the end of this solution as an attachment

From the question, we have the following angle measures that can be used in our computation:

Angle A = x

Angle B = 3x

The sum of angles in a triangle is 180

So, we have

x + 3x + 90 = 180

Evaluate the like terms

4x = 90

Divide by 4

x = 22.5

From the attached figure, we have

Angle ADE = Angle B

So, we have

Angle ADE = 3x

This gives

Angle ADE = 3 x 22.5

Evaluate

Angle ADE = 67.5

Hence. the angle is 67.5 degrees

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Answer:

2-23x

Step-by-step explanation:

Answer:

The profit or loss on selling a fixed asset will be

Step-by-step explanation:

We know that,

Depreciation = Original value - Scrap value / Estimated life of an asset

-> 100,000 - 0/ 5

= Rs 20,000 for every year

for 3 years,

Depreciation= 3 * 20,000 = Rs 60,000

The value of the asset after 3 years of depreciation = 100,000- 60,000

=Rs 40,000 ---(1)

If it is sold for Rs 45,000 ---(2)

Profit = (2) - (1)

= 45,000-40000

= Rs 5,000

The function's standard form equation is equivalent to

y=(1/2)x²+(-7x)+24.

A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.

The standard form of a quadratic equation in mathematics is represented by;

ax² + bx + c = 0

y=ax² + bx + c

The information in the table above would then be used to create a set of equations:

The points are (4, 4), (6, 0), (8, 0), (10, 4)

4=a(4)²+b(4)+c

16a+4b+c=4 ------(1)

0=a(6)²+b(6)+c

36a+64b+c=0  ------(2)

0=a(8)²+b(8)+c

64a+8b+c=0  -------(3)

By solving 2 and 3 equations, we get

Eq2-Eq3,

We get b= -14a

By substituting b value in eq2 we get,

36a+6b+c=0

36a+6(-14a)+c=0

35a-84a+c=0

c=48a

By substituting a, b values in eq1 we get,

16a+4(-14a)+48a=4

16a-56a+48a=4

-40a+48a=4

8a=4

a=1/2

Then, b=-14a

b= -7

c=48a

c=24

Now, by substituting these a, b, c values in,

y=ax² + bx + c

y=(1/2)x²+(-7x)+24

By  checking the above equation is correct or not,

We consider the fourth value x=10

When x=10,

y=(100/2)-70+24

y=50-70+24

y=4

From the given table if x=10 then y=4,

So it satisfies with the equation we get.

Therefore, the function's standard form equation is equivalent to

y=(1/2)x²+(-7x)+24.

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The combined mass of the Earth and Moon is 6.07342 × 10^24.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

Mass of Earth = 6 × 10^24

Mass of Moon = 7.342 × 10^22

The combined mass of the Earth and Moon will be:

= (6 × 10^24) + (7.342 × 10^22)

= 6.07342 × 10^24

The mass is 6.07342 × 10^24.

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The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

What is distance?

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.

The formula for measuring distance between two lines, the total length of all a polygon's sides, the perimeter of a polygon on a coordinate plane, the area of a polygon, and many other things are all found in analytical geometry. For instance, we can use the distance formula to find the lengths of a triangle's sides and decide if it is scalene, isosceles, or equilateral.

It is given that, a taxi charges a flat rate of $1.75 plus an additional fee of $0.75 per mile.

We have to find the maximum distance it could travel at most with $10

Let the maximum distance be x miles.

Thus, the fare would be

$(1.75 + 0.75x) = 10

⇒ 0.75x = 8.25

⇒ x = 8.25/0.75

⇒ x = 11

The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

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We move all the characters to the left:

We add all the numbers and all the variables.

We add all the numbers and all the variables.

Multiply

We add all the numbers and all the variables.

We move all terms containing x to the left side, all other terms to the right side

Answer:

x = 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

no

Answer: y= mb + xe

Step-by-step explanation:

Answer: first, second, and third images.

Step-by-step explanation:

to determine if something is a function, the domain must not have more than one answer in the range. My class calls it the y axis test, if you were to graph it, you cannot draw a line straight down that will go through two points. it's easy to understand with images like these, because all you need to know is that arrows cannot go from one number on the left to multiple on the right. Vice versa is a function, because it passes the y axis test.

The paintings' width-to-length ratios are different because the ratio 3 to 2 is not equal to 9 to 6. The correct option is B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The width-to-length ratios of the paintings differ because 3 to 2 is not equal to 9 to 6.

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Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of 24 points and made 2 more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made, x, and the number of three point shots made, y.

x = the number of two point shots made

y = the number of three point shots made

Each two point shot scores 2 points, so x two point shots would score 2x points. Each three point shot scores 3 points, so y three point shots would score 3y points.

Therefore, the total number of points scored 2x + 3y equals 24 :
2x+3y=24

Since Landon made 2 more two point shots than three point shots, if we add 2 to the number of three point shots made, we will get the number of two point shots made, meaning x equals y + 2.

                                                                                    x = y + 2

Write System of Equations:

​2x + 3y = 24

         x = y + 2

Solve for y in each equation:

The midsegment has length 25 then the value of x exists 14.

The length of the midsegment is half that of the base, according to the theorem.

A segment that joins the midpoints of two triangle's sides is referred to as a midsegment. According to the midsegment theorem, the third side of a triangle is parallel to the middle two sides of the triangle, and the midsegment is half its length.

Find the midpoints of two of any triangle's sides. A section joins these midpoints. This section will then be half the length of the third side and parallel to it.

The midsegment has length 25.

The base has length x.

x/2 = 25

simplifying the above equation, we get

x = 12.5

Therefore, the value of x exists 12.5.

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x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

(7x - 3)/9 more than or equal to 8 - 2x

(7x-3)/9 ≥ 8-2x

7x-3 ≥ 9(8-2x)

7x-3 ≥ 72-18x

Add 18x on both sides

7x+18x-3 ≥ 72

25x-3 ≥ 72

Add 3 on both sides

25x ≥ 75

Divide both sides by 25

x ≥ 3

Hence, x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.

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Answer:

$3.25

Step-by-step explanation:

This is division

29.25 divided by 9

9 goes into 29.25 3 times

29.25-27=2.25

2.25 is 1/4 of 9

2.25*4=9 because 2*4=8 and .25*4=1 so 8+1=9

So the answer is 3 1/4 or $3.25

Answer:

Step-by-step explanation:

Here we have:

90% confidence level:

α=1-0.90=0.10

[tex]Z_{crit}=z_{\alpha /2}=z_{0.10/2}=1.645[/tex]

Hence the required Z value at 90% confidence level is 1.645

Answer:

3.24

Step-by-step explanation:

The Hundredth is the second decimal place

Since 6 is greater than 5, round up

Answer:

------------------------

Let the missing side be x.

Use Pythagorean to find its value:

The value of the equation A + ( 9 + 8 ) = ( 15 x 9 ) + ( 15 x 8 ) is 238

where A = 238

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as = P

Now , the value of P is given by

Let the unknown variable in the equation be A

A + ( 9 + 8 ) = ( 15 x 9 ) + ( 15 x 8 )

On simplifying the equation , we get

The value of A + 17 = 135 + 120

On adding the values in the equation , we get

The value of A + 17 = 255

On subtracting 17 on both sides of the equation , we get

The value of A = 238

Therefore , the value of A is 238

Hence , The value of the equation A + ( 9 + 8 ) = ( 15 x 9 ) + ( 15 x 8 ) is 238

where A = 238

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If the two bikes are racing a distance of 100 feet, the bike that will win the race is: D. Bike 1 will win because the slope of the line for Bike 1 is 3/2, which is greater than the slope of the line for Bike 2.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would calculate the slope of the line representing the distance covered by each of the bikes based on the data points on their graph.

For Bike 1, the slope is given by;

Slope, m = (6 - 3)/(4 - 2)

Slope, m = 3/2

Slope, m = 1.5.

For Bike 2, the slope is given by;

Slope, m = (10 - 5)/(8 - 4)

Slope, m = 5/4

Slope, m = 1.25.

Therefore, the slope of Bike 1 is greater than the slope of Bike 2.

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Answer:

Step-by-step explanation:

            400                            ÷                                           80

Number of cookies        Divde by         Number of peanut butter cookies

= 5 Total cups

The difference between 96 and 72 by 12 can be expressed as

(96 - 72) / 12 and 24 / 12.

We have to find the difference between  between 96 and 72 by 12.

The difference between 96 and 72 can be expressed as,

96 -72

= 24

Next we have to divide the answer that is 24 by 12.

It becomes,

24/12

= 2

As a result, the required expressions for the following calculation is:

(96 - 72) / 12 and 24 / 12.

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The equivalent equation for the given equation m = ca is a = m/c. The equivalent equation has no effect on the original equation's actual function.

An equivalent equation is one that yields the same solution as the original equation.

The equivalent equation is obtained by removing a variable from the given equation. There will be the same number of equivalent equations as there are variables in an equation.

Given that,

m = ca

Here m, c, and a are the three variables in the given equation.

We can write the equation into two more forms as follows:

W.r.t variable 'c',

m = ca

Dividing both sides by 'a'

⇒ ca/a = m/a

c = m/a

W.r.t variable 'a',

m = ca

Dividing both sides by 'c'

⇒ ca/c = m/c

a = m/c

The missing image is attached with the answer.

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