A linear function includes the points (2, 3) and (6, 8). What is the rate of change of the linear function?
Write the answer as an improper fraction (fraction greater than one) in lowest terms.

Answer:

x = − 3 y + 7

Step-by-step explanation:

Reorder  7  and  − 3

The expression for the area of a rectangle is \(2x^3-7x^2+6x-2\).

It is given in the question that the length of the rectangle is \(2x^2-3x+1\) and width is (x - 2).

We have to find a expression for the area of a rectangle.

We know that,

Area of a rectangle = l * b

Where,

l represents the length of the rectangle

b represents the breadth of the rectangle

Hence, using the data given in the question, we can write,

Area of a rectangle = \((2x^2-3x+1)*(x-2)\)

Area of a rectangle = \((2x^3)+(-4x^2)+(-3x^2)+(6x)+(-2)\)

Area of a rectangle = \(2x^3-7x^2+6x-2\)

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The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

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Answer:

factorise form of

x²+2x = x(x+2)

The matrix representation of the transformation L is:

L =

[ 1 2

-2 1 ]

The matrix representation of a linear transformation is found by evaluating the transformation on each element of a basis for the domain and then writing the resulting vectors as a column vector. In this case, the domain is the set of all 2x2 matrices and the basis is the set of matrices [1 0; 0 1], [0 1; 1 0], and [1 1; 1 1]. The transformation L can be evaluated on these matrices as follows:

L[1 0; 0 1] = [1 2; -2 1]

L[0 1; 1 0] = [-2 1; 1 2]

L[1 1; 1 1] = [3 3; 3 3]

Writing these vectors as a column vector gives us the matrix representation of L:

L =

[ 1 2

-2 1 ]

This matrix can be used to find the image of any 2x2 matrix under the transformation L.

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The overflow rate of the tank is 0.0006 m³/m².s and the detention time is 5333.33 seconds or 1.48 hours or 1 hour 29 minutes and 17.99 seconds.

The given primary settling tank receives an average flow rate of 0.540 m³/s, has a tank surface area of 900 m² and depth of 3.2 m.

We can compute the overflow rate and detention time using the formulas as follows;

Overflow rate formula:

Overflow rate = Flow rate / Surface area

Overflow rate = 0.540 / 900Overflow rate = 0.0006 m³/m².s

Detention time formula:

Detention time = Volume of tank / Flow rate

Volume of tank = Surface area × Depth

Volume of tank = 900 × 3.2Volume of tank = 2880 m³

Detention time = 2880 / 0.540

Detention time = 5333.33 seconds or 1.48 hours or 1 hour 29 minutes and 17.99 seconds.

Therefore, the overflow rate of the tank is 0.0006 m³/m².s and the detention time is 5333.33 seconds or 1.48 hours or 1 hour 29 minutes and 17.99 seconds.

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The length of hypotenuse is 4.5 meters.

The length of hypotenuse can be calculated using Pythagoras theorem. Writing the Pythagoras theorem below -

Hypotenuse² = Base² + Perpendicular²

The given other two sides will be base and perpendicular. So, keeping the values in mentioned equation of Pythagoras theorem to find the value of Hypotenuse.

Hypotenuse² = 2² + 4²

Taking square of the numbers to find the value of Hypotenuse

Hypotenuse² = 4 + 16

Performing addition to find the value of Hypotenuse

Hypotenuse² = 20

Hypotenuse = \(\sqrt{20}\)

Taking square root to find the value of Hypotenuse

Hypotenuse = 4.5 meters

Hence,  the length in meters of a right triangle's hypotenuse is 4.5 meters

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The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].

Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.

Let A is a 3 x 5 matrix and B is a 5 x 7 matrix

We know that matrix multiplication of A and B is possible if

Number of columns of A = Number of rows of B

Since in the given problem

Number of columns of A = Number of rows of B = 5

So the product is possible

Now the product AB is a matrix of order 3 × 7

Now the order of the product AB is 3 × 7

If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.

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Answer:

it is $142

Step-by-step explanation:

Answer:

142

Step-by-step explanation:

To take a fraction off of a price, simply divide:

568

568/4=142$

To fact check this, we can times this by four to see that it equals the original price:

142x4=568$

The domain of the function will be the value x≥-5 and the range is y ≥ -5.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

Given function is f(x)=1/2(x+3)²-5. The domain of the function will be all the real numbers and the range will be,

Range = 1/2(x+3)²-5

Range = 1/2(-5 + 3)² - 5

Range = 1/2(-2)² - 5

Range = -3

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Answer:

D.8

Step-by-step explanation:

A cube's volume is basically the side length multiplied by itself 3 times, so if it was increased by a factor of 2, it would mean 2x2x2 which equals 8.

Answer:

11:

since diagonal are equal of rectangle

QS=RT

4x+6=6x-4

6+4=6x-4x

2x=10

x=10/2

x=5

now

diagonal :4x+6=4*5+6=26

12.

again

QS=RT

9x+12=11x-10

12+10=11x-9x

2x=22

x=11

now

diagonal=9*11+12=99+12=111

The alternative hypothesis(h1) says that the treatment causes a change in the scores.

What is a hypothesis test?

In statistics, hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The data type used and the study's purpose will determine the methodology the analyst uses.

Using sample data, hypothesis testing determines whether a claim is plausible. These data could originate from a broader population or a process that creates data.

Hence, the alternative hypothesis(h1) says that the treatment causes a change in the scores

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The variable expense ratio is calculated by dividing variable expenses by a certain value. This ratio is used to assess the proportion of variable expenses in relation to the value being measured.

The variable expense ratio is a financial metric that helps analyze the relationship between variable expenses and a specific measure or base. Variable expenses are costs that change in direct proportion to changes in the level of activity or production. To calculate the variable expense ratio, we divide the total variable expenses by the chosen base or measure. The base or measure used in the denominator of the ratio depends on the context and the specific analysis being conducted. It could be units produced, sales revenue, labor hours, or any other relevant factor that varies with the level of activity. By dividing the variable expenses by the chosen base, we obtain the variable expense ratio, which represents the proportion of variable expenses relative to the chosen measure. The variable expense ratio is often used in cost analysis and budgeting to understand the impact of changes in the level of activity on variable expenses. It helps businesses assess the cost structure and make informed decisions regarding pricing, production levels, and resource allocation.

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Answer:

y + y+ y is 3y

Step-by-step explanation:

Step-by-step explanation:

3(7 + x) = 3×7 + 3x = 21 + 3x

remember, when you multiply two expressions, you need to multiply every term of the first expression with every term of the second expression, and then add all partial results (by considering the individual signs, of course).

Answer:

5.4

Step-by-step explanation:

Sum = 11.9

One decimal = 6/5

x = 11.9 - 6.5

  = 5.4

Therefore x is 5.4 :)

Answer:

To solve this problem, we can use the following equation:

T = 2π√(r/g)

where T is the period (time for one complete revolution), r is the length of the rope, and g is the acceleration due to gravity.

First, we need to find the length of the rope. We can use trigonometry to do this:

sin(12°) = r/1.55m

r = 1.55m * sin(12°) = 0.319m

Next, we need to find g. We can use the value of 9.81 m/s^2 for the acceleration due to gravity.

Now we can plug in our values and solve for T:

T = 2π√(0.319m/9.81 m/s^2)

T ≈ 0.807 s

Therefore, the period of the tetherball's motion is approximately 0.807 seconds.

Answer:

  see below

Step-by-step explanation:

If your equations are the ones shown in the second attachment, then their solution is the one shown in the first attachment.

_____

Apparently, your "interactive graph" needs two points to draw a line through. For these equations, the x- and y-intercepts are found easily enough.

  -3x +3y = 9

To find the x-intercept, set y=0 and divide by the coefficient of x: 9/-3 = -3

To find the y-intercept, set x=0 and divide by the coefficient of y: 9/3 = 3.

  2x -7y = -14

Same procedure: x-intercept = -14/2 = -7; y-intercept = -14/-7 = 2.

All of these intercepts are shown in the third attachment. Using them, you can use your tool to plot the lines and estimate their point of intersection.

1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

1 + 2 = 3

As we know, from the definition:

Arithmetic can be defined as, an operation in which we do the addition of numbers, subtraction, multiplication, and division.

For the addition of two numbers:

The two numbers are 1 and 2:

Draw a vertical line 1:  |

Draw two vertical lines 2:  | |

Count the lines:  | | | = 3

Thus, 1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

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Answer:

Below

Step-by-step explanation:

Domain is the 'x' values a function can have   for this one  {1,3,4,5}

Range is the 'y' values a function has   {6,8,10}

The average value of f(x) is "b" for both intervals [-1, 1] and [-k, k].

Given that f(x) = mx + b.

To find the average value of f(x) over the interval [-1, 1] and [-k, k].

The average value of f(x) over an interval [a, b] is given by the formula; \(\[\frac{1}{b-a} \int\limits_{a}^{b} f(x) dx\]\)

a) Over the interval [-1, 1]

Average value of f(x) over the interval [-1, 1] is given by, \(\[\frac{1}{2} \int\limits_{-1}^{1} f(x) dx\]Substitute f(x) = mx + b.\[\frac{1}{2} \int\limits_{-1}^{1} mx + b \, dx\]Applying the integral property, \[\frac{1}{2} \left [ \frac{m}{2}x^{2}+ bx \right ]_{-1}^{1}\]\[\frac{1}{2} \left [ \left ( \frac{m}{2}(1)^{2}+ b(1) \right ) - \left ( \frac{m}{2}(-1)^{2}+ b(-1) \right ) \right ]\]\[\frac{1}{2} \left [ \left ( \frac{m}{2} + b \right ) - \left ( \frac{m}{2} - b \right ) \right ]\]\[\frac{1}{2} \left [ 2b \right ]\]\[= b\]\)

Therefore, the average value of f(x) over the interval [-1, 1] is b.

b) Over the interval [-k, k] Average value of f(x) over the interval [-k, k] is given by,\(\[\frac{1}{2k} \int\limits_{-k}^{k} f(x) dx\]Substitute f(x) = mx + b.\[\frac{1}{2k} \int\limits_{-k}^{k} mx + b \, dx\]\)

Applying the integral property,\(\[\frac{1}{2k} \left [ \frac{m}{2}x^{2}+ bx \right ]_{-k}^{k}\]\[\frac{1}{2k} \left [ \left ( \frac{m}{2}(k)^{2}+ b(k) \right ) - \left ( \frac{m}{2}(-k)^{2}+ b(-k) \right ) \right ]\]\[\frac{1}{2k} \left [ \left ( \frac{mk^{2}}{2}+ bk \right ) - \left ( \frac{mk^{2}}{2} - bk \right ) \right ]\]\[\frac{1}{2k} \left [ 2bk \right ]\]\[= b\]\)

Therefore, the average value of f(x) over the interval [-k, k] is b.

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The roots of the equation will be imaginary. Then the number of real solutions will be zero.

The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as

D = b² - 4ac

The type of roots will be given below.

The equation is given below.

x² + 4x + 5 = 0

The discriminant of the given equation will be

D = 4² - 4 x 1 x 5

D = 16 - 20

D = - 4

D < 0

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

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Answer:

3x+14

Step-by-step explanation:

2(3x+4) -3(x-2)

6x+8 -3(x-2)

6x+8 -3(x-2)

6x+8 -3x+6

6x+8-3x+6

6x+ 14 -3x

6x +14 -3x

3x +14

Answer:

40

Step-by-step explanation:

Let's call blueberries, raspberries, grapes and cherries b, r, g, and c respectively. We can write:

b + r + g + c = 280 (1)

r = 2b (2)

g = 3c (3)

c = 4r (4)

We can plug (2) into (1) to get b + 2b + g + c = 280. Then, we can re-write (4) into r = c / 4 and plug that into (2) which gets us c / 4 = 2b, and when we re-write that we get c = 8b (5). Let's plug that into (1) to get b + 2b + g + 8b = 280. Next, we'll re-write (3) to get g / 3 = c, and we can plug that into (5) to get g / 3 = 8b so then g = 24b and plug that into (1) to get b + 2b + 24b + 8b = 280 → 35b = 280 → b = 8. We can plug this into (5) to get c = 8 * 5 = 40. Hope this helps!

Answer:

Step-by-step explanation:

if the middle point of the circle is the letter O

2a.

if the middle point is the letter O

answer: LOM is a central angle

central angle means it comes from the center and each part of it is a radius

central angle is the same degree as the degrees of its arc

so it would also be 84 degrees

2b.

answer: points LM make a minor arc because its less than 180

2c

answer: points LKN make a semi circle

2d

answer: LKNM is a major arc because its more than 180

2e

LKM = 360 - 84 = 276

answer: 276

2f

84*2=168 -> 360-168 = 192 -> 192 divided by 2 is 96

answer: LK is 96

2g

answer: MN is 96

2h

NK is like LM so its 84

answer: 84

2i

LKN is 84+ 96 = 180

answer: 180

2j

360-96 = 264

answer: 264

The probability that a person selected at random to have the test until (s)he passes the test is, 0.03125

Given, a test occurred 5 times in a class.

we have to find that how many times a person selected at random to have the test until (s)he passes it.

the probability of getting pass in the exam be, 1/2

and similarly the probability of getting fail in the exam also be, 1/2

so, the probability that a person selected at random to have the test until (s)he passes the test is,

(1/2)^5

= 1/32

= 0.03125

Hence, the probability that a person selected at random to have the test until (s)he passes the test is, 0.03125

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The rocket is at its highest point 3.5 seconds after launch.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

To determine the time when the rocket is at its highest point, we need to find the value of t when h is a maximum. To do this, we can take the derivative of h with respect to t, and set it equal to 0.

h = -16t²+112t

∂h/∂t = -32t + 112 = 0

Solving for t we get,

t = 112/32 = 7/2 = 3.5 seconds

Thus, the rocket is at its most elevated point 3.5 seconds after launch.

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Answer:

1.7

Step-by-step explanation:

Answer:

P=1.7

Step-by-step explanation:

Subtract 0.6 on both sides to get p alone. Therefore 2.3-0.6=1.7.