The equation
Ax+By=−18
A
x
+
B
y
=
−
18
goes through the coordinates (-3, 10) and (6, -2).

Answer:

a) velocity

b) displacement

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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Pygmy rabbit is 22.61-10 meters longer than the wasp.

Given:

A wasp is 1.39-10 meters long.

A pygmy rabbit is 24-10¹ meters long.

Pygmy rabbit longer than the wasp = size of pygmy rabbit - size of wasp.

= (24 - 1.39)-10meters

= 22.61-10 meters.

Therefore pygmy rabbit is 22.61-10 meters longer than the wasp.

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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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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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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

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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Answer:

m=3.7

Step-by-step explanation:

m²=14

m=√14

m=3.7416573868

m=3.7(2 d.p)

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: candidate 2 has 90 votes

Step-by-step explanation:

165-75=90

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

Answer:

Never

Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45

Answer:

Step-by-step explanation:

never

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

side length: 15

perimeter: 368

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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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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Answer:

D? I'm not sure tho so don't be mad if it's wrong

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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Answer:

a = 7

Step-by-step explanation:

Substitute x for 2 and f(x) for 14

14 = -2(2³) + a(2²) + 2

14 = -16 + 4a + 2

14 = -14 + 4a

14 + 14 = 4a

28 = 4a

4a = 28

Divide both sides by 4

4a/4 = 28/4

a = 7

Alternative:

Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.

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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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.

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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Answer:

5x=325+160

Step-by-step explanation:

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

By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let Warren has drawn 5x pictures of animals and 2x pictures of people

Warren has drawn 18 more pictures of animals than people in his notepad

By the problem,

5x - 2x = 18

3x = 18

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

x = 6

Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]

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The rate of change for cost is =  $2 per hour .

In the question ,

it is given that

the fixed rent for the bicycle is =$20

per hour charge of the bicycle is = $2

let the number of hours we rent a bicycle is = x

and let the total cost for renting the bicycle is = y

So , the equation to represent the cost becomes

y = 20 + 2x

to find the rate of change we differentiate the equation with respect to x .

we get

dy/dx = 2

Therefore , The rate of change is $2 per hour .

The given question is incomplete , the complete question is

You rent a bicycle for $20 plus $2 per hour. What is the rate of change of Cost ?

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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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The 160 feet range and 70 feet height of the path of Gunter Money which can be described with a quadratic equation, gives;

(a) The path is; y = -1.09375×10²·x² + 1.75·x

(b) The vertex form of the equation is; y = -1.09375·(x - 80)² + 70

(c) The angle at the start is approximately 60.3°

A quadratic equation is a single variable polynomial equation of the second degree.

The points in the path which is a path of a projectile and has a shape of a parabola are;

(0, 0), (80, 70), and (160, 0)

The equations are;

y₁ = a·x₁² + b·x₁ + c

y₂ = a·x₂² + b·x₂ + c

y₃ = a·x₃² + b·x₃ + c

Plugging in the coordinates of the three points in the path gives;

The matrix becomes;

[tex]A = \begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}[/tex]

[tex]X = \begin{bmatrix}a \\b \\c\end{bmatrix}[/tex]

[tex]Y = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

We have;

A·X = Y, which gives;

[tex]\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}\cdot \begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

[tex]X = \dfrac{Y}{A} = A^{-1}\cdot Y[/tex]

Where;

A⁻¹ = The inverse of the matrix A

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \frac{ \begin{bmatrix}0 \\70 \\0\end{bmatrix}}{\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}} = \begin{bmatrix}\dfrac{1}{12800} & -\dfrac{1}{6400} & \dfrac{1}{12800} \\\\-\dfrac{3}{160} &\dfrac{1}{40} & -\dfrac{1}{160} \\\\1 &0 &0 \\\end{bmatrix}\bullet \begin{bmatrix}0\\ \\70\\ \\0\end{bmatrix}=\begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]a = -\dfrac{7}{640}[/tex]

[tex]b = \dfrac{7}{4}[/tex]

c = 0

The equation for Gunter Money's path is therefore;

[tex]y = -\dfrac{7}{640} \cdot x^2 + 1\dfrac{3}{4} \cdot x + 0 = -1.09375\times 10^2 \cdot x^2 + 1.75\cdot x[/tex]

(b) The vertex of the path is (h, k) = (80, 70)

The vertex form of a quadratic equation is; y = a·(x - h)² + k

The equation of Gunter Money's path in vertex form is therefore;

[tex]y = -\dfrac{7}{640} \cdot \left(x - 80)^2 + 70 = -1.09375\times 10^2\cdot (x - 80)^2+70[/tex]

(c) The angle of the parabolic path of Gunter Money's motion at a point is given by the value of the arctangent of the differentiation of the function for the motion at the point as follows;

[tex]y' = -\dfrac{7\times 2}{640} \cdot x + 1\dfrac{3}{4}[/tex]

At the point Gunter Money takes off,  (0, 0), we have;

[tex]tan(\theta) = y' = -\dfrac{7\times 2}{640} \times 0 + 1\dfrac{3}{4} = 1\dfrac{3}{4} = 1.75[/tex]

[tex]\theta = arctan(1.75) \approx 60.3^{\circ}[/tex]

The angle is approximately 60.3°

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Answer:

Tuition and Fees = $5,992.93

Room = $5,115.92

Board = $4,044.01

Computer Costs = $1,088.15

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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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