Use the graph to write a linear function that relates y to x.

The speed of the tennis ball is 6.2 metres per seconds.

Speed is measured as the ratio of distance to the time in which the distance was covered.

Therefore, speed can be represented mathematically as follows;

speed = distance / time

Hence, the table tennis travels 12.4 metres south in 2 seconds.

The speed of the tennis can be computed as follows:

distance = 12. 4 metres

time = 2 seconds

Therefore,

speed = 12.4 / 2

speed = 6.2 meters per seconds.

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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.

Given that,

Katie and her best friend Liam play tennis every Saturday morning.

When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.

The speed of the tennis can be found by using formula

speed=distance/time

distance = 12. 4 metres

time = 2 seconds

Now speed=12.4/2

speed=6.2

Hence speed of the tennis ball is 6.2m/s

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If  a triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. No it is not a right triangle.

We would be making use of converse of Pythagoras' theorem to determine whether the triangle is a right triangle.

In a situation were we have a right triangle the square on longest side will be the same with the sum of square of other sides

Longest side

45²  =  2025

Other side

30 ² + 35 ²

900 + 1,225

= 2125

Hence,

2025 ≠ 2125

Based on the above it is  not a right triangle because the longest side did not equate the other side.

Therefore it is not a right triangle.

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As 2125 ≠ 2025 therefore it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.

This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers.

∴ 30² + 35² = 45².

900 + 1225 = 2025.

2125 ≠ 2025.

It is not a right-angle triangle because it didn't satisfy the property of Pythagoras's theorem.

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The value of x will be 8.

And, Graph of the line y = -x + 2 is shown in figure.

What is Equation of line?

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The condition is;

The line containing the points (4, -2) and (x,-6) is perpendicular to the line containing the points (-2, -9) and (3,-4).

Since, Multiplication of Slopes of perpendicular lines are -1.

That is;

m₁ m₂ = -1

Where, m₁ is slope of first perpendicular line and m₂ is slope of second perpendicular line.

Now, Find the slopes of lines as;

m₁ = (-6 - (-2)) / (x - 4)

m₁ = - 6 + 2 / x - 4

m₁ = - 4 / (x - 4)

And, Slope of second line,

m₂ = (-4 - (-9)) / (3 - (-2))

m₂ = (-4 + 9) / (3 + 2)

m₂ = 5 / 5

m₂ = 1

Hence,

m₁ m₂ = -1

Substitute all the values, we get;

- 4 / (x - 4) × 1 = -1

4 = x - 4

x = 4 + 4

x = 8

Thus, The points on the line is (4 , -2) and (8 , -6).

So, Slope (m₁) = (- 6 - (-2)) / (8 - 4)

                     = (-6 + 2) / 4

                     = - 4 / 4

                     = -1

Thus, The equation of line passing through the points (4 , -2) and

(8 , -6) with slope -1 is;

y - (-2) = - 1 (x - 4)

y + 2 = -x + 4

y = - x + 4 - 2

y = - x + 2

Therefore,

The value of x will be 8.

And, Graph of the line y = -x + 2 is shown in figure.

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Jack paid $ 2.10 more than last week for tinned tomatoes.

The answer is in dollars.

Given that:-

Price of small tomato tins = 50 cents

Price of pasta packet = $ 2

Price of large tomato tins = 2*50 cents =  $ 1

Total price of 6 large tins and a pasta packet = $ 7.50

Price of 4 small tins of tomatoes this week = $ 1.60

Price paid by Jack last week for 18 large tins and 3 pasta packets = 7.50*3 = $ 22.50

Price of 18 large tins = 22.50 - 2*3 = 22.50 - 6 = $ 16.50

As 18 large tins equals 36 small tins, we can write,

Price Jack would have paid this week = 36*1.60/4 = $ 14.40

The amount Jack paid more for tinned tomatoes = 16.50 - 14.40 = $ 2.10

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The question asks us to solve the following system of equations by elimination:

Solution

Answer

The solution to the system of equation is:

x = -8

y = 9

a. np = 8.91 and nq = 18.09 where n = 27 and p = 0.33

b. np = 3.75 and nq = 21.25 where n = 25 and p = 0.15

c. np = 9.68 and nq = 34.32 where n = 44 and p = .22

a. Given n =  27

          p = 0.33

np = 27 x 0.33

     = 8.91

nq = 27 x (1 - 0.33)

    = 18.09

For the approximation of binomial distribution, the sample size must be greater than 10 for both the products np and n(1-p) to approximate the binomial distribution by a normal distribution.

Since here np < 10 approximation is not applicable.

μp = np = 27 x 0.33  

             = 8.91

σp = √npq = √(27)x (.33) x (1 - 0.33)

              = 2.443

b.  n = 25 and p = 0.15

   np = 25 x 0.15

         = 3.75

   nq = 25 x (1 - 0.15)

    = 21.25

Approximation is not possible because np < 10.

c. n = 44 and p = .22

   np = 44 x 0.22

         = 9.68

   nq = 44 x (1 - 0.22)

    = 34.32

Since here np< 10 approximation is not possible.

μp = np = 44 x 0.22  

             = 9.68

σp =√npq = √(44)x (.22) x (1 - 0.22)

              = 2.747

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The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).

We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.

To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.

Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.

Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.

Hence, the correct answer would be option (A).

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Answer:

36

Step-by-step explanation:

Unit price: 9 / 5 = 1.8

20 box price: 1.8 * 20 = 36

shooting percentage: 0.425 (decimal)

To express in percentage:

0.425 x 100 = 42.5%

(3) He made 42.5% of the baskets he attempted.

And also

17/40 = 0.425

(4) He made 17 out of every 40 baskets he attempted

The value of x + y in the system of equations is  0.82125.

Given system of equations:-

8x + 9y = 4.92  ...(1)

9x + 14y = 6.93 ...(2)

We have to find the value of x + y in the system of equations.

Multiplying (1) by 9 and (2) by 8, we get,

72x + 81y = 44.28  ...(3)

72x + 112y = 55.44 ...(4)

(4) - (3), we get,

0x + 31y = 11.16

31y = 11.16

y = 11.16/31

y = 0.36

Putting the value of y in (1), we get

8x + 9*(0.36) = 6.93

8x + 3.24 = 6.93

8x = 6.93 - 3.24

8x = 3.69

x = 0.46125

Hence,

x + y = 0.46125 + 0.36 = 0.82125

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[tex]2x = 76[/tex]

Due to alternate angles

[tex] \frac{2x}{2} = \frac{76}{2} \\ x = 38[/tex]

40°+(y-8)°+76°=180°(sum of angles in a triangle)

[tex]40 + y - 8 + 76 = 180 \\ y + 108 = 180 \\ y = 180 - 108 \\ y = 72[/tex]

ATTACHED IS THE SOLUTION.

Answer:

x = 38 ; y = 72

Step-by-step explanation:

180 = 76 + 40 + (y - 8)

180 = 108 + y

72 = y

The triangle has parallel lines, so the uppermost right angle is also 90 degrees.

90 - 76 = 14

180 = 90 + 14 + 2x

180 = 104 + 2x

76 = 2x

38 = x

Given

x - y + (- z) where x and z are positive real numbers and y is a negative real number.

Find

i) What are the directions of motion for this calculation ?

ii) Is the final answer positive , negative , or undetermined ?

Explanation

i) as we have given

x - y + (- z)

x - y - z

(x - y) - z

right -left - left

ii) for this we take examples

let x = 2 , y = -1 and z = 2

2- (- 1) + (- 2) = 1 , positive

now

let x = 2 , y = -1 and z = 5

2 - (- 1) + (- 5) = 3 - 5 = -2 , negative

so , it is both negative or positive

hence it is undetermined

Final Answer

Hence , the correct option is

i) Right, left , left

ii) Undetermined

Consider the following problem.

A student library has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student academic meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.

The conditions of this problem give rise to the following system of equations

Multiplying the second equation by 1/2 and the third equation by 12, we get:

Now, multiply the first equation by -2 and add it to the second equation. In this way we obtain:

Multiply the first equation by -6 and add it to the last equation. In this way we obtain:

Finally, the process is completed by adding the second multiplied by 3 to the third equation.

then, if we perform back substitution we get the desired solutions:

and

We can conclude that the correct answer is:

Problem:

A student cafeteria has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.

System of equations:

Solution for this system of equations:

The area of the figure given below is 56.6 units² .

In the question ,

a figure is given

where there is one rectangle and two semicircles .

the length of the rectangle is given as 11 units

and the breadth of the rectangle is = 4 units

we know that the area of the rectangle is = length × breadth

on substituting the values ,

we get

area = 11 × 4

area = 44 units²

the radius of the semicircle = 2 units

the are of the semi circle = (1/2)*π*r²

since there are two semicircle , the area of the two semi circle will be

= 2 * (1/2)πr²

= π*r²

On substituting , the value of radius = 2 ,

we get the area is = 3.14*(2)² = 12.56       using π = 3.14

so the area of the complex figure is = 44 + 12.56 = 56.56

≈ 56.6

Therefore , The area of the figure given below is 56.6 units²  .

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Write the inequality for the statement and solve for v

It means that v is less than or equal to -4. The solution set for this inequality is:

Answer:  400 gradians

Reason:

100 gradians = 90 degrees

4*100 gradians = 4*90 degrees

400 gradians = 360 degrees

Type 1 error is the error occurs when a test indicates a significate  difference between two or more populations.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes. The significance level you select (alpha or ) determines the likelihood that you will make this mistake.

Data cleansing—also known as data cleaning, data scrubbing, or data rectification—is the process of correcting inaccurate, insufficient, duplicate, or other wrong data in a data set. It entails locating data mistakes and then correcting them by modifying, updating, or eliminating data.

Using independent samples from two independent groups, the two-sample (independent groups) t-test is used to assess whether the unknown means of two populations are different from one another.  

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Order of the operations: parentheses, exponentials, division and multiplication, addition and subtraction.

1. Solve operations in parentheses:

2. Solve exponentials:

3. Solve division:

4. Solve multiplication:

5. Solve subtraction:

Answer: Answer is 20( please make me brainliest i just did this all in my head)

Step-by-step explanation: soo (14-2) =12  12divided by 3=4 so (2*3)= 6 so 4x6=24 24-2*2 =20 (2*2)=4 so 24-4=20 well this is confusing but i tried my best so hope my answer wasn't toooo confusing lol :)

Answer:

D. 1.75

Step-by-step explanation:

Absolute value cannot be negative, so that gets rid of A & B. The point is at -1.75 so it has to be D.

Answer:

[tex]\frac{109}{20}[/tex]

Step-by-step explanation:

.45 mean [tex]\frac{45}{100}[/tex] so  5.45 means 5 [tex]\frac{45}{100}[/tex]  = [tex]\frac{9}{20}[/tex]  If I divide the top and bottom of [tex]\frac{45}{100}[/tex] by 9

5 [tex]\frac{9}{20}[/tex] is a mixed number.  I can make this an improper fraction by changing 5 to 1+1+1+1+1  Another name for 1 is any number over itself as a fraction.

I am going to write 1 as [tex]\frac{20}{20}[/tex]

5 can be written

[tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] = [tex]\frac{100}{20}[/tex]

5 [tex]\frac{9}{20}[/tex]  Can be written

[tex]\frac{100}{20}[/tex] + [tex]\frac{9}{20}[/tex] = [tex]\frac{109}{20}[/tex]

Answer:

(109/20) Is the answer.

Answer:

2

Step-by-step explanation:

512÷2=256

256÷2=128

128÷2=64

64÷2=32

32÷2=16

16÷2=8

8÷2=4

4÷2=2

2÷2=1

=(2^2)+(2^2)+(2^2)+(2^2)+2

When 2 is multiplied it will make it a perfect square.

512×2=1024

√1024

=32

Answer:

y=2x+6

y=2x+6

Explanation:

Given the equation:

The equation written as a system of equations is:

Opening the bracket in the first equation gives:

For the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).

As given in the question,

Given points :

B (-1, -10)

Reflected over the line y = x

Reflected represents the transformation which shows the movement of original points to the new location. There are different types of transformation such as reflection, rotation, dilation , and translation.

Reflection represents the flipping of the points over the line y =x.

B(x, y) and B'(y, x).

For the given points B (x, y) = (-1,-10) is reflected over the line y =x , the coordinates of B'(y, x) = ( -10 , -1).

Therefore, for the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).

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Answer: Plugging in -1 for n.

Step-by-step explanation:

Equation:

(n+1) / n

Given the equation above what can we plug in for n to make the equation less than or equal to 1?

(-1 + 1) / -1 = 0/-1 = 0

Inputting negative one will cause the statement to be false.

Answer:

11n

Step-by-step explanation:

We need to identify the true statement for every polynomial P with degree n.

The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial

has degree 3, since the highest power of x has exponent 3.

Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.

About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.

As an example, for P(x) = x²+4, we have:

The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.

Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.

Therefore, (c) is True.

We can see that (d) is False from the following example:

the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.

Answer:

c) The graph of P has at most n-1 turning points

The values of the vectors obtained from the vector diagram are;

[tex]\overrightarrow{AB} = - a + b[/tex]

[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]

[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

K = 2.5

A vector can be expressed as a line segment that has a direction.

The given parameters are;

The straight lines are; OAN, OMB, APB, and MPN

AN = 3•OA

The midpoint of OB = M

The vectors

[tex] \overrightarrow{OA} = a[/tex]

[tex] \overrightarrow{OB} = b[/tex]

[tex]\overrightarrow{AP} = K \cdot \overrightarrow{AB} [/tex]

From the question diagram, we have;

[tex]\overrightarrow{AB} = - a + b[/tex]

[tex]\overrightarrow{AP} = K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]

[tex]\overrightarrow{AN} [/tex] = 2•a

[tex]\overrightarrow{NP} = \overrightarrow{AP} - \overrightarrow{AN} [/tex]

[tex]\overrightarrow{NP} = -2\cdot a + K \cdot ( - a + b)[/tex]

[tex] \overrightarrow{MB} = 0.5 \cdot b[/tex]

[tex]\overrightarrow{PB} = -a + b - K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MP} =0.5 \cdot b - -a + b - K \cdot ( - a + b) = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

Given that we can write;

[tex]x \cdot \overrightarrow{NP} = \overrightarrow{NM}[/tex]

x × (-2•a + k•(-a + b)) = -3•a + 0.5•b

-2•x•a - k•x•a + x•k•b = -3•a + 0.5•b

Which gives;

-2•x - k•x = -3...(1), and x•k = 0.5...(2)

From (2), x = 0.5÷k

From (1), -2×(0.5÷k) - k×(0.5÷k) = 3

-k - 0.5 = -3

-k = -3 + 0.5 = -2.5

k = 2.5

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The method used to prove the specified geometric relationship between the angles and sides of the triangles are as follows:

24. ΔDAE ≅ ΔBAC by SAS postulate, therefore

25. ΔACD ≅ ΔBCD by ASA postulate

26 ΔACD ≅ ΔBCD               LH postulate.

The congruency postulates include, SSS, Side-Side-Side, AAS, Angle-Angle Side, SAS, Side-Angle-Side, HL, Hypotenuse Leg.

24. The two column proofs are presented as follows;

Statements            Reasons

1. [tex]\overline{CD}[/tex] bisects [tex]\overline{BE}[/tex] 1. Given

2. [tex]\overline{BA}[/tex] = [tex]\overline{AE}[/tex]             2. Definition of bisected line

3. . [tex]\overline{BA}[/tex] ≅ [tex]\overline{AE}[/tex]           3.. Definition of congruency

4. [tex]\overline{CA}[/tex] = [tex]\overline{AD}[/tex]             4. Definition of bisection of line [tex]\overline{CD}[/tex]

5. [tex]\overline{CA}[/tex] ≅ [tex]\overline{AD}[/tex]            5. The definition of congruency

6. ∠DAE ≅ ∠BAC   6. Vertical angles theorem

7. ΔDAE ≅ ΔBAC    7. SAS congruency postulate

8. ∠B ≅ ∠E              8. CPCTC

The acronym, CPCTC represents Corresponding Parts of Congruent Triangles are Congruent

25. Statement                 Reasons

1. [tex]\overline{CD}[/tex] ⊥ [tex]\overline{AB}[/tex]                     1. Given

2. [tex]\overline{CD}[/tex] bisects ∠ACB     2. Given

3. ∠3 = ∠4 = 90°            3. Definition of bisected lines

4. ∠1 ≅ ∠2                      4. Definition of bisected angle ∡ACB

5. ΔACD ≅ ΔBCD          5. ASA congruency postulate

6. ∡A ≅ ∡B                     6. CPCTC

26. Statement                                        Reason

1. m∠1 = m∠2 = 90°                                1. Given

2. ΔACD and ΔBCD are right triangles 2. Definition

3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]                                             3. Given

4.  [tex]\overline{CD}[/tex] ≅  [tex]\overline{CD}[/tex]                                          4. Reflexive property

5. ΔACD ≅ ΔBCD                                   5. LH Congruency postulate

6 ∡A ≅ ∡B                                               6. CPCTC

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Answer: [tex]m=\frac{y2-y1}{x2-x1}[/tex]

Step-by-step explanation:

Choose two points and insert them for x and y.

(3,0) and (0,-4) will work

If you need extra help ask me, I'd be glad to help but i encourage you to try to solve it yourself

The time taken to completely fill the pool is 5/4 hour

From the question, the given parameters are:

Time =3/4 hour

Size of the pool = 3/5

The time to fill the pool is then calculated as

Time = Given time/Proportion of the pool

Substitute the known values in the above equation

So, we have the following equation

Time = 3/4 hour ÷ 3/5

Express the quotient as product

So, we have the following equation

Time = 3/4 hour x 5/3

Evaluate the products

Time = 5/4 hour

Hence, the time taken is 5/4 hour

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