The temperature at 1 am was 40 degrees. The temperature dropped steadily for the next 6 hours to reach the daytime low of 20 degrees. Create an equation for the relationship between temperature and the time.

Answers

Answer 1

The equation relating temperature and time is given by 3y = -10x + 130

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the temperature be represented as y

Let the time be represented as x

Now , let the first point be P = P ( 1 , 40 )

Let the second point be represented as Q = Q ( 7 , 20 )

The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 40 - 20 ) / ( 1 - 7 )

On simplifying the equation , we get

Slope m = -20/6

Slope m = -10/3

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 40 = ( -10/3 ) ( x - 1 )

On simplifying the equation , we get

y - 40 = ( -10/3 )x + 10/3

Adding 40 on both sides of the equation , we get

y = ( -10/3 )x + 130/3

Multiply by 3 on both sides of the equation , we get

3y = -10x + 130

when x = 1 am

3y = -10 + 130

3y = 120

y = 40 degrees

when x = 7am

3y = -70 + 130

3y = 60

y = 20 degrees

Hence , equation representing temperature and time is 3y = -10x + 130

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Related Questions

Tracy, a political campaign organizer, realizes that the number of hours needed to get out a mailing for her candidate is inversely proportional to the number of campaign workers she has. If she uses the information in the accompanying graph, how many hours would it take to do the mailing if 125 workers are used?

Answers

Answer: It is impossible for me to answer this question as I do not have access to the accompanying graph that Tracy is using. The graph would be needed to determine the relationship between the number of hours needed to get out a mailing and the number of campaign workers used. Without this information, it is not possible to determine how many hours it would take to do the mailing if 125 workers are used.

Step-by-step explanation:

Simplify this fraction 12/16 to lowest terms and find an equivalent fraction that has a denominator of 32.
A. 3/4, 12/32
B. 2/6, 24/32
C. 3/4, 24/32
D. 6/8, 28/32

Show your work on how you got your answer

Answers

Answer: C

Step-by-step explanation:

12/4=3

16/4=4

3*8=24

4*8=32

To simplify 12/16 to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 4:

12/16 = 3/4

Now we need to find an equivalent fraction with a denominator of 32. To do this, we can multiply both the numerator and denominator of 3/4 by 8:

3/4 = (38)/(48) = 24/32

So the answer is C. 3/4, 24/32.

i need help with #5 pleaseee

Answers

Answer:

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: g(x)=√x

Horizontal Shift: None

Vertical Shift: Up 3 Units

Reflection about the x-axis: Reflected

Vertical Stretch: Stretched

Jamal sliced an orange into four equal pieces he ate one slice what fraction of the orange did Jamal eat?

Answers

it would be 3/4 with is three over four

Jamal ate 1/4 of the orange, and there is 3/4 left.

Find the growth/decay rate given the exponential function.
g(x) = 6(.83)

Answers

Answer:

Decay Rate = 17 percent

Step-by-step explanation:

1.00 - 0.83 = 0.17

WILL GIVE BRANIST
What is the shape of the front of the Mexican tote bag? Use the drop-down menus to describe the shape. ➡ Click the arrows to choose an answer from each menu. The shape of the front of the tote bag is a trapezoid of sides that are perpendicular two pairs because it has

Answers

The shape of the front of the Mexican tote bag can be described as a trapezoid. A trapezoid is a quadrilateral with one pair of parallel sides and the other pair of non-parallel sides.

In this case, the sides of the trapezoid are perpendicular two pairs, meaning that one pair of non-parallel sides is perpendicular to the other pair of non-parallel sides.

The front of the Mexican tote bag typically has a wider top and a narrower bottom, which creates the parallel sides of the trapezoid. The wider top provides a larger opening for easy access to the contents of the bag, while the narrower bottom helps maintain the bag's shape and stability.

This trapezoidal shape is commonly seen in tote bags as it offers practicality and functionality. The wider top allows for convenient storage and retrieval of items, while the narrower bottom helps distribute the weight evenly and prevents the bag from sagging.

The trapezoidal shape of the front of the Mexican tote bag combines both style and functionality. It not only provides an aesthetically pleasing design but also offers practicality in terms of storage capacity and easy access to the bag's contents.

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Please help me with this math question! Thank you!

Answers

The expression that illustrate the diagram below is f(x) = 47-2x

What are linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

In the diagram, the total no of box is 45 and 2 boxes are missing on the second box. Therefore the constant in the the expression is 45+2 = 47. Let x be the variable.

Therefore f(x) = 47-2x

when it is pattern 1

x= 1

f(1) = 47-2 = 45

when it's pattern 2

f(x) = 47-2×2 = 43

when it's pattern 3

f(x) = 47- 2×3 = 41

therefore the expression that can illustrate the diagrams is f(x) = 47-2x

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Find the 2 two-digit numbers that divide 179 with a remainder of 4.

Answers

The two digit number that will make a remainder of 4 when it divides 179 is 35

How to find the two digit number

The number 179 is a prime number hence it's only factors are 1 and 179.

For the number to have a remainder of 4, it means that subtraction 4 from 179 will give a number that will divide it without remainder

The subtracted 4 will serve as the remainder

179 - 4 = 175

factors of 175: 1, 5, 7, 25, 35 and 175.

175 / 35 = 5

because of this we can say that (175 + 4) / 35 will give a remainder of 4.

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Write 94/4 as a percent.

(Round to 3 decimal places if necessary.)

Answers

Answer:

2350%

Step-by-step explanation:

In percentage:

94/4 x 100% = 2350%

(Converting from fraction to percentage, simply multiply the fraction by 100)

There is no need to round off the answer to 3 decimal places as the answer is already a pure whole number with no decimal places.

Question 4
Solve by Completing the Square: x² + 12x + 21 = 0
O {-12 ± √15}
O {-6± √15}
O {6 ± √15}
O {-6 ± √57}

Answers

answers to the equation as the Completing the Square: x = 6 ± √15 ≈ {2.13, 9.87} as  x² + 12x + 21 = 0 .

what is square ?

According to Euclidean geometry, a square has four equal sides and four equal angles, making it an equilateral quadrilateral. Another name for it is a rectangle with two adjacent sides that are the same length. An equilateral quadrilateral is one that has four equal sides and four equal angles, like a square. Angles that are 90 degrees or straight are square angles. The square's diagonals are also split at a 90-degree angle and are evenly spaced. a rectangle with two equal sides that is adjacent. a quadrilateral with four equal sides and straight angles on all four sides. a parallelogram with two adjacent sides that are equal and create a right angle. rhombus with straight sides.

given

the square can be completed by adding the square of half the x-coefficient: (-12/2)² = (-6)² = 36.

x² -12x +36 = -21 +36

(x -6)² = 15 . . . . . . . . the form you want for your answer template

Taking the square root gives ...

 x -6 = ±√15

answers to the equation as the Completing the Square: x = 6 ± √15 ≈ {2.13, 9.87} as  x² + 12x + 21 = 0 .

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The pentagons and are similar.
Find the length of .
B
E
A
4
2
4
3
5
C
K
N
J
4.8
x
4.8
3.6
6
L

Answers

The value of x that is the measure of LM is 2.8 units.

What is similar polygons?

Two polygons with the same shape but different sizes are said to be similar polygons. Comparable polygons have corresponding sides that are proportional and corresponding angles that are congruent.

If the corresponding sides have a constant ratio and the corresponding angles are congruent, two polygons are said to be similar.

Let the pentagons ABCDE and JKLMN are similar.

Means their shape is same but differ in size.

Each side of pentagon JKLMN is 0.8 units greater than the pentagon ABCDE.

The measure of CD is 2 units.

⇒ The measure of LM = 2 + 0.8 = 2.8

Hence, the value of x that is the measure of LM is 2.8 units.

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The number 1500 can be said correctly as "one-thousand five hundred" or as "fifteen hundred."
Write out at least four different ways to say 743.

Answers

The four words are Seven hundred forty-three, Seven-four-three, Seven four three, Seven hundred and forty-three.

What is number?

Number is a mathematical object used to count, label, and measure. It is a fundamental concept in mathematics and is used in many different ways. Numbers can be used to represent anything from quantities of objects to ideas and concepts. Additionally, numbers are used to describe relationships between different objects or concepts. Numbers are also used to represent positions in space, as well as represent data in a graph or table.

1. Seven hundred and forty-three
2. Seven four three
3. Seven fourty-three
4. Seven hundred forty-three.

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What is the perimeter of this figure?

Answers

There are 2 semi circles.

One that is on left side ( say S1)and the other one at the bottom(say S2) of the figure. Both these semi circles have diameter 30.

perimeter of S1 = (2*pi*15)/2

perimeter of S2 = (2*pi*15)/2

There is another figure which is of a semicricle(say S3). The radius is 30.

Perimeter of S3 = (2*pi*30)/4

Required perimeter

= S2+ S3-S1

= [(15*pi)/2] + [(15*pi)]- [(15*pi)/2]

= (15*pi)

= (15*3.14)

= 47.1

the value of which of these expressions is closest to e?

Answers

The value of e is closest to the (1+1/22)^22 .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents.

Given, expressions

the expression whose value is closest to e

we know that , the Value of e is 2.718

[tex](1+1/19)^{19}[/tex] = [tex]( 19+1/ 19 )^{19}[/tex] = (20/19 )^19 = 2.65

(1+1/22)^22 = (22+1/22)^19 = (23/22)^19 = 2.659

(1+1/20)^22 = (20+1/20)^22 = (21/20)^22 = 2.653

(1+1/21)^21 = (21+1/21)^21 = (22/21)^21 = 2.656

Therefore, The value 2.659 is the closest to the value of e.

So, option B. is correct.

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which expression is equal to 1/64?

Answers

Answer:  There are many but these are some of them

2/128

4/256

6/384

8/512

Step-by-step explanation:

The population of River City in the year 2000 was 400. Assume the
population increase at a rate of 6.75% per year. What's the populati
2020?

Answers

The population of the  River City expanded by 10% between 2000 and 2010, and it is anticipated to grow by 8% between 2010 and 2020.

what is percentage ?

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.

given

population increase at a rate of 6.75% per year

then divide that number by the initial population and multiply by 100.

The population of the  River City expanded by 10% between 2000 and 2010, and it is anticipated to grow by 8% between 2010 and 2020.

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DUE SOON! PLEASE HELP!

Answers

Answer:

C

Step-by-step explanation:

You have to work the math

Answer:

B

Step-by-step explanation:

900mm is the current size of the pawn

The original size was 30mm which means we divide 900mm by 30mm

So,

900 ÷ 30 = 30

Which means b is the answer

C can't be the answer because if the original size of the pawn was 30mm and you say it was enlarged by 450mm, it means the current size will have to be 30 × 450 = 13500mm, and this is not the case

Explain how solve 4^x + 3 = 7 using the change of base formula . Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answers

By algebra properties and base change formula, the value of x of the exponential function 4ˣ ⁺ ³ = 7 is equal to 1 / ㏒₇ 4 - 3

How to solve an exponential function by means of change base formula

In this question we find an exponential function that must be solved, this can be done by combining algebra properties and base change formula. Change base formula is a property that changes the base of a logarithm into another, defined below:

㏒ₐ x = ㏒ₙ x / ㏒ₙ a

Where:

n - Original basea - Resulting base

First, write the entire expression:

4ˣ ⁺ ³ = 7

Second, use logarithm operators on both sides:

㏒₄ 4ˣ⁺³ = ㏒₄ 7

Third, use logarithm properties to simplify the expression:

(x + 3) · ㏒₄ 4 = ㏒₇ 7 / ㏒₇ 4

x + 3 = 1 / ㏒₇ 4

Fourth, clear x within the expression by algebra properties:

x = 1 / ㏒₇ 4 - 3

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For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1

Answers

The equations for which "8" is a solution are as follows:

x + 2 = 10 x minus 4 = 4 3 x = 24

Step-by-step solution:

x + 6 = 2

⇒x=2-6

⇒x= -4

x + 2 = 10

⇒x=10-2

⇒x= 8

x minus 4 = 4

⇒x-4=4

⇒x=4+4

⇒x=8

x minus 2 = 10

x-2=10

x= 10+2

⇒x= 12

2 x = 4

⇒2*x=4

⇒x=4/2

⇒x=2

3 x = 24

⇒3*x=24

⇒x=24/3

⇒x=8

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If AB = 25 what is AC?

Answers

Answer:In the first paragraph, we establish that AC has to equal 50 since B is the midpoint and AB = 25. That means segment BC is also equal to 25. Thus AB + BC = 50. Since x is 6, (8x + 2) (the formula for the line AC) is 50, as expecte

Step-by-step explanation:

WILL GIVE BRAINLIEST

In kite WXYZ, m

Answer Here

Answers

Answer:

What atre u asking me to solve?

Step-by-step explanation:

2. Triangle XYZ is rotated 90° clockwise about the origin to form triangle
XYZ.
Y
N
у
6
L
3
N
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
N
12
3 4 5
X
67
X

Which state ment is true

Answers

Answer:

21 because 21x2 is 21 rrrr

Write and expression using only positive exponents for the width w of the rectangle
Area= 72 X^7Y^2 and L= 24 X^2Y^3

Answers

Answer:

[tex]\boxed{W = \dfrac{3X^5}{Y}}[/tex]

Step-by-step explanation:

Area A = [tex]72 X^7Y^2[/tex]

Length L = [tex]24 X^2Y^3[/tex]

A = L x W where W = width

W = A/L

[tex]\dfrac{72 X^7Y^2}{24 X^2Y^3}\\\\\\= 3X^{(7-2)}Y^{(2-3)}\\\\= 3 X^5Y^{-1}\\\\\\[/tex]

[tex]\textrm{Using the identity }x^{-1} = \dfrac{1}{x}\\\\[/tex]

we get

[tex]W = \dfrac{3X^5}{Y}[/tex]

Solve the inequality
Show clear algebraic working.

m² + 3> 21
—————
4

Answers

Therefore , the solution of the given problem of inequality comes out to be m > 4.24.

What is inequality, exactly?

In mathematics, an inequality is a relationship of linear solution or integers without the equal sign. Inequity inevitably leads to imbalance. When two numbers are not equal, there is an inequality between them. Between equality and inequality, there are differences. In instances when the variables aren't similar or equal, I've used the most common symbol (). There are many inequalities that may be utilised to compare values regardless of how small or huge they are.

Here,
Given :

=> m² + 3> 21

=>  m² > 21-3

=>  m² >  18

=> m > √18

=> m > 4.24

Therefore , the solution of the given problem of inequality comes out to be m > 4.24.

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When do we flip the Inequality Signs?
Show All Steps​

Answers

Explanation: Inequalities can be solved just like equations can, with one important caveat if you multiply or divide by a negative number, you have to flip the direction of the inequality sign.

Definitions if don't know what some words mean :D

Inequalities- different in size

caveat- A warning

Example

I hope this helps

A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 10,000
3%
10,001 - 50,000
5%
50,001 - 100,000
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter

Answers

To calculate the state income tax owed on a $50,000 per year salary, we need to apply the progressive tax rate based on the income range.

What does money interest mean?

You pay interest on any loans or borrowings of money. the portion of the loan's value that lenders use to calculate interest. Consumers can earn interest by lending money (via a bond or certificate of deposit, for example), or by putting money into an interest-bearing bank account.

The first $10,000 of the salary will be taxed at 3%, the next $40,000 (from $10,001 to $50,000) will be taxed at 5%, and the remaining $0 will be taxed at 5.5%

Tax on first $10,000 = $10,000 x 3% = $300

Tax on next $40,000 = $40,000 x 5% = $2,000

Tax on remaining $0 = $0 x 5.5% = $0

Total tax owed = $300 + $2,000 + $0 = $2,300

Therefore, the state income tax owed on a $50,000 per year salary is $2,300.

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Martin has 6,150 in doctor bills for the year his deductible is 500. His policy pays 80% once he has met his deductible for the year how much in all did Martin pay including his deductible

Answers

Answer:

  1630

Step-by-step explanation:

You want to know what Martin paid to cover 1650 in doctor bills when his insurance pays 80% after a deductible of 500 has been met.

Copayment

When insurance pays 80% of the amount over 500, Martin pays the other 20%. Martin's share of the bill is ...

  500 + 0.20(6150 -500)

  = 500 +0.20(6150) -0.20(500) = 400 +0.20(6150)

  = 400 +1230 = 1630

Martin paid 1630 in all, including the deductible.

Evaluate the expression for w=2 and x=2 2w+12 ÷(2x)

Answers

Answer: The expression is (22) +12/(22) = 4 + 12/4 = 4 + 3 = 7.

Step-by-step explanation:

To evaluate the expression 2w+12 ÷ (2x) for w=2 and x=2, we need to substitute the given values into the expression and simplify.

First, we substitute the value of w=2 into the expression, giving us 2(2)+12 ÷ (2x).

Next, we simplify the expression by multiplying 2 and 2, getting 4+12 ÷ (2x).

Then we add 4 and 12, getting 16 ÷ (2x).

Finally, we substitute the value of x=2 into the expression, giving us 16 ÷ (2(2)) = 16 ÷ 4 = 4.

So the final value of the expression 2w+12 ÷ (2x) for w=2 and x=2 is 4.

the sum of 5 consecutive numbers is 100 what is the 1st number

Answers

Answer:

18

Step-by-step explanation:

What is the k value to this problem

Answers

The k value of the given problem is 8. The solution is obtained using the concept of algebra.

What is algebra?

A branch of mathematics known as algebra deals with symbols and the fine operations performed on them. Variables are the name given to these symbols because they warrant set values.

Algebra aids in the result of fine problems and enables the derivate of unknown figures, similar as interest rates, rates, and probabilities. In order to remake the equations, we can express the associated unknown amounts using variables from algebra.

We are given equation: y=8x.

General form of an equation is y=kx where k is the constant of variation.

Also, y varies directly with both i.e. k and x.

So, from the above explanation, we find that k=8.

Hence, the k value of the given problem is 8.

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