Drag each expression to the correct location on the table.
Match each expression to its simplified form.

The average rate of change of the resistance of the thermistor for each degree change in the temperature, when the temperatures changes from 0 °C and 2 °C is A. 4 ohms/°C

The average is calculated by adding the values in the dataset then dividing the result by the count of the numbers or values in the set. The average is also known as the arithmetic mean.

The function for finding the resistance of the thermistor is; R(t) = t³ + 5

The unit of the R = Ohms

The unit of t = Degrees Celsius, °C

The resistance of the thermistor when the temperature is t = 0 °C is found as follows;

R(0) = 0³ + 5 = 5

Therefore;

When the temperature is 0 °C the resistance of the thermistor is 5 Ohms

When the temperature is t = 2 °C, we have;

R(2) = 2³ + 5 = 13

The resistance of the thermistor at t = 2 °C is 13 Ohms

The average rate of change of a function, f(x), is found using the formula;

[tex]A(x) = \dfrac{f(x_2) - f(x_1) }{x_2-x_1}[/tex]

The average rate of change of the resistance per degree change in the temperature, between the temperature interval of 0 °C and 2 °C is therefore;

[tex]A(x) = \dfrac{R(2) - R(0)}{2 - 0}[/tex]

Which gives;

[tex]A(t) = \dfrac{13 -5}{2 - 0}= 4[/tex]

The average rate of change of the resistance of the thermistor between the temperatures of t = 0 °C and t = 2 °C is 4 Ohms/°C

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Simplification of the given expression 2cd³ (c - d +5) is given by

2c²d³ − 2cd⁴ + 10cd³.

As given in the question,

Given expression is equal to :

2cd³ (c - d +5)

Law of exponents for multiplication is given by:

mᵃ × mᵇ  =mᵃ⁺ᵇ

Simplification of the given expression by open the parenthesis we have,

= 2cd³ × c - 2cd³ × d + 2cd³ × 5

Apply law of exponents for multiplication we get,

= 2c¹⁺¹d³ -2cd³⁺¹ + (2×5)cd³

= 2c²d³ -2cd⁴ + 10cd³

Therefore, simplification of the given expression 2cd³ (c - d +5) is given by 2c²d³ − 2cd⁴ + 10cd³.

The complete question is:

Simplify : 2cd³ (c - d +5)

a. 2cd³− 2c²d⁴ + 10c²d³

b. 2c²d³ − 2cd⁴ + 10cd³

c. 2cd³ − 2cd³ + 10cd³

d.  2c²d³− 2c²d⁴ + 10cd²

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Tiffany needs to pay $8,084.44 in total.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.

Given:

P= 8000

R= 7%= 0.07

Time= 8 years.

Now, Amount = P[tex](1 + r/n)^{nt[/tex]

Amount = 8000 [tex](1 + 0.07/15)^{12 . 15[/tex]

Amount = 8000 x (1 + 5.8333333333333E-5)

amount = $8,084.44

Hence, Tiffany needs to pay $8,084.44 in total

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Step-by-step explanation:

Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?​

Looking at your chart:

cost/length in inches

6/100 = $0.06 per inch

8.1/135 = $0.06 per inch

9.6/160 = $0.06 per inch

10.8/180 = $0.06 per inch

So the rate stays at a constant rate of $0.06 per inch.

Andy needs 24 feet or 288 inches at a constant rate of $0.06 per inch.

= 288 * $0.06  

= $17.28

________________________________

Emily needs 15 yards or 540 inches at a constant rate of $0.06 per inch.

= 540 * $0.06  

= $32.40

Answer:

Tuition and Fees = $5,992.93

Room = $5,115.92

Board = $4,044.01

Computer Costs = $1,088.15

Answer:

Your question is missing some parts

and the degree seems off is it 90⁰

Answer:

x=19/24

Step-by-step explanation:

3/8=15/5x-2

3/8= 3x -2 |*8

3=24x-16

24x=19

x=19/24

Perimeter meaning: the continuous line forming the boundary of a closed geometric figure.

side length: 15

perimeter: 368

The linear regression equation from the given scatter plot is:

y = -1.62x + 215.64.

Using this function, the estimate of his weight 15 weeks into the diet is:

191.34 pounds.

The linear regression equation is obtained inserting the points of the scatter plot of the situation into a linear regression calculator.

From the given scatter plot, the points are given as follows:

(0,216), (1,214), (2,213), (3,210), (4,210), (5,207), (6,206), (7,202), (8,203), (9,202), (10,200)

Inserting these points into a calculator, the line of best fit is given as follows:

y = -1.62x + 215.64.

The estimate weight at the 15th week of the diet is the numeric value of the function when x = 15, that is, the lone instance of x in the function is replaced by 15, as follows:

y = -1.62(15) + 215.64 = 191.34 pounds.

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Answer:

220.

Step-by-step explanation:

If you plug in 4 for L and 6 for W, you are left with 25(4) + 20(6), which is equivalent to 100+120 = $220

Answer:

220

Step-by-step explanation:

Answer:

a) velocity

b) displacement

Answer:

4(m+10)

Step-by-step explanation:

sum is adding

Hopes this helps please mark brainliest

Answer:

m=3.7

Step-by-step explanation:

m²=14

m=√14

m=3.7416573868

m=3.7(2 d.p)

The length of the second rectangle is 8 in

Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where

So, making Wsubject of the formula, we have

W = A/L

Since

Substituting these into the equation, we have

W = A/L

W = 48 in²/6 in

W = 8 in

Now, since the  second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where

So, making L subject of the formula, we have

L = A/W

Since

Substituting these into the equation, we have

L = A/W

L = 64 in²/8 in

L = 8 in

So, the length of the second rectangle is 8 in

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A value for x is therefore represented by the first number in an ordered pair, and a value for y is represented by the second.The x- and y-coordinates are the names given to these values.

The Method of Elimination

To ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable number in step one.

Step 2: Reverse the first equation and subtract the second one.

Step 3: Find y using this new equation.

Step 4: Change Equation 1 or Equation 2 above to y = 2 and then solve for x.

multiply the equation y = x - 6 by -6.

You will then get the equation: 6y = -6x + 36

The two equations will be:

6y = -6x + 36

y = 6x - 19

And you can see that if you add them, you will be able to eliminate x. answer is -6.

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If  a vegetarian dish will be first. The number of different ways that are there to place the dishes on the table is 576.

There are 4 vegetarian dishes = P4 = 4!

There are 4 meat dishes =P4 =4!

Now let find the number of different  ways

Number of different  ways = 4! × 4!

Number of different  ways = 24 × 24

Number of different  ways = 576 different ways

Therefore the number of different ways  is 576.

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If the plumber charges a customer $45 , then the visit was 0.5 hours long .

In the question ,

it is given that

the fixed charge to visit a client's home is = $35

additional per hour charge of plumber is = $20 .

let the time taken by plumber in the customer house be "x" .

So , according to the question

the equation for total charge is

total charge = 35 + 20x

given the customer paid $45 ,

So , 45 = 35 + 20x

20x = 45 - 35

20x = 10

x = 10/20 = 0.5

Therefore , If the plumber charges a customer $45 , then the visit was 0.5 hours long .

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Using the circle graph, the costs to attend the public university are as follows:

A circle graph, or a pie chart, is used to visualize information and data.

Therefore, the circle graph is shows the percentage cost for tuition/fees, room, board, and computer costs.

The cost to attend a public university in a recent year is $16,241.

Using the pie chart, let's find the cost of the various fees.

Therefore,

cost of tuition and fees = 36.9% of 16,241

cost of tuition and fees = 36.9 / 100 × 16241

cost of tuition and fees = 599292.9 / 100

Therefore,

cost of tuition and fees = $ 5992.929

cost of room = 31.5% × 16241

cost of room = 31.5 / 100 × 16241

cost of room = $5115.915

Hence,

cost of board = 24.9% of 16241

cost of board = 24.9 / 100 × 16241

cost of board = $ 4044.009

Hence,

computer cost = 6.7% of 16241

computer cost = 6.7 / 100 × 16241

computer cost =  $1088.147

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Answer:

[tex]y= \frac 12 x -3\\y=0.5x -3[/tex]

Depending if you can imput fractions, or decimal numbers.

Step-by-step explanation:

The slope can easily calculated as [tex]m=\frac{\Delta y}{\Delta x} = \frac {0-(-3)}{6-0} = \frac 36 = \frac12[/tex]

The y intercept can be easily read from the graph as and is -3

Using elimination method in the equation 2x+y=7 and 2x*3y=3, x is 3 and y is 1.

Two equations are given solving it by using rule of elimination,

2x+y=7....(1) and 2x*3y=3. (2)

Multiply equation (1) by three to get 6x+3y=21. (3)

Add equations (2) and (3) together to get

8x=24

x=24/8

x= 3

Replace this number in equation (1):

2(3)+y=7

6+y=7

y=7-6

y= 1

Consequently, the answer is x=3,y=1.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

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The values that match the various trigonometric identity are;

1) sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀ = 1

2) cos 13 cos 47 + sin 13 sin 47 = 0.5

3) sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π = 0

Trigonometric identities are defined as the equations that involves the trigonometric functions that are true for every value of the variables involved.

1) We know that the trigonometric identity sin(A + B) is expressed as;

sin(A + B) = sinAcosB + cosAsinB

We are given;

sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀

Applying the trigonometric identity above, gives us;

sin(²/₅π + π/₁₀)

= sin(5π/10)

= sin(π/2)

= 1

2) We know that the trigonometric identity sin(A + B) is expressed as;

cos(A + B) = cosAcosB − sinAsinB.

We are given;

cos 13 cos 47 + sin 13 sin 47

Applying the trigonometric identity above, gives us;

cos(13 + 47)

= cos 60

= 0.5

3) We know that the trigonometric identity sin(A + B) is expressed as;

sin(A + B) = sinAcosB + cosAsinB

We are given;

sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π

Applying the trigonometric identity above, gives us;

sin(²/₅π + ⁸/₅π)

= sin(¹⁰/₅π)

= sin(2π)

= 0

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Answer:

5x=325+160

Step-by-step explanation:

this was very easy but i guess with so many words it could confuse people

The dimension of the rectangular room in the actual building are 55 feet by 30 feet.

Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.

A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building.

The dimensions of this rectangular room in the actual building can be found as follows:

let's find the length of the actual room

1 inches = 10 feet

3 inches  = ?

cross multiply

length = 30 ft

Let's find the width of the room

1 inches = 10 feet

5.5 inches  = ?

cross multiply

width = 55 ft

Therefore, the width and length of the room are 55 feet and 30 ft respectively.

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Let the number be n.

Then the expression is:

Answer:

Step-by-step explanation:

Forming the expression,

→ 4x + x

Let's solve the expression,

→ 4x + x

→ 5x

Hence, the answer is 5x.

Answer:

the slope is 1.75

Step-by-step explanation:

Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight.  For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb

Answer:

Joseph's present age=3 yrs

David's present age=9 yrs

Step-by-step explanation:

Let Joseph's present age be x.

David's present age=3x

__________________

Ater 3 yrs,

Joseph's age=x+3

David's age=2(x+3)

Also, we can add 3 to David's present age to get age After 3 yrs. So, David's age after 3 yrs would also be 3x+3.

Now, balance them.

3x+3=2(x+3)

3x+3=2x+6

x=3

D"s prsent age=9

J's present age=3

The given system of linear equations has no solution. By solving the equations using substitution method we get (11, 0) where no solution exists.

How many solutions can a system of linear equation can have?

A system of linear equations is usually a set of two linear equations with two variables.

The solution to a system of linear equations is the point at which the lines representing the linear equations intersect.

With linear systems of equations, there are three possible outcomes in terms of number of solutions:

How to identify the number of solutions?

Rewrite both equations in slope-intercept form, y = mx + b.

Compare the slopes of the lines, m, and their y-intercepts, b, to determine the number of solutions.

According to the given question:

Given system of linear equation are: y = -x + 11 and -4x -4y = 44

Rewriting the equations in slope-intercept form

        Simplifying further by dividing the equation with -4 on both side

        y = x - 11 ------ 2)

Clearly, both the equation have different m-values.

Hence the system of equation have one solution.

Now solving by substitution method

Substituting 2) in 1)

x - 11 = -x + 11 (since y = x -11 from 2))

2x = 22

∴ x = 11

Now substituting x = 11 in equation 2) to get the value of y

y = 11 - 11

∴ y = 0

So, the system of equation has no solution at (11, 0).

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Answer:

x = 15

Step-by-step explanation:

since the sides are bisected, the inner line is parallel to the largest side.

8x+9 + 5x-24 = 180

The amount of Tritium that bottle contains now will be 439,421.

Consider the function:

y = a (1 - r)ˣ

Where x is the number of times this decay occurs, a = initial amount, and r = fraction by which this decay occurs.

Tritium is a radioactive isotope of hydrogen that rots by around 5% each year. An enormous container of water that contained 856,000 tritium iotas stayed undisturbed for a very long time.

Then the amount of Tritium that bottle contains now will be given as,

y = 856,000 (1 - 0.05)¹³

Simplify the equation, then we have

y = 856,000 (1 - 0.05)¹³

y = 856,000 (0.95)¹³

y = 856,000 (0.51334)

y = 439,421

The amount of Tritium that bottle contains now will be 439,421.

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