How many cherries tomatoes does he need?

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

10. 1110/3537 + 795/3537 = 1905/3537 or 635/1179

11. 2427/3537 + 2742/3537 = 5169/3537 or 1723/1179

12. 1110/3537 + 795/3537 = 1905/3537 or 635/1179

13. No. These events may be inclusive since there are males that are nursing majors and vice versa.

Answer:

x = -2

Step-by-step explanation:

The line x = - 5 means it is a straight vertical line that has no slope. This means that the slope is undefined.

Now, for this line to be parallel to the line passing through point P(−2, 6), it means the line will be a vertical line too with the equation of form (x = a).

Thus, the equation of the line is x = -2

The equation of the line is given by:

\(x = -2\)

The equation of a line has the following format:

\(y = mx + b\)

In which:

Line x = -5 is a horizontal line, thus, it's slope is undefined.

A line parallel will also be horizontal, with undefined slope.

It passes through point P(-2,6), thus, the equation of the line is:

\(x = -2\)

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The equation of the line passing through the two points (4,2) and (-3,1) is 7y-x-10=0

Equation of a line is an algebraic form of showing the set of points, which together forms a line in a coordinate system.

Given the line passes through the points (4,2) and (-3,1)

Here, x1=4, y1=2, x2=-3, y2=1

So, the slope of the line (m)= \(\frac{y2-y1}{x2-x1}\\\)=\(\frac{1-2}{-3-4}\\\)=\(\frac{1}{7}\)

Now we know, the equation of the line is given as,

y-y1=m(x-x1)

Putting the value of y1 and x1 in the equation we get,

y-2=\(\frac{1}{7}\)(x-4)

7y-14=x-4

7y-x-10=0

Hence the equation of the line that passes through the two points (4,2) and (-3,1) is 7y-x-10=0.

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Answer:

4 cm is the best answer for this one

Answer:

x=31°

Step-by-step explanation:

95°+54°+x=180°{sum of angle of triangle}

149+x=180°

x=180-149

x=31°

hope it helps.

Hello!

area

= 2*25 + (20 - 2)*(25-8)

= 50cm² + 306cm²

= 356cm²

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

54

Step-by-step explanation:

20% of 15 is 3 so Quentin is 18 years old

If Quentin is one thrid his Aunt's age that means his aunt is three times older.

18 * 3 = 54

So his Aunt is 54 years old

The age of Quentin's aunt is 54 years if the Quentin is one third the age of his aunt if we solve by making the Quentin's Aunt age as variable x.

An equation is a formula that expresses the equality of variables.

let the age of the aunt is x years.

According to the question the age of Quentin is x/3 years.

The age of Quentin's  sister is x/3*100/120

=5x/18

We have been given the age of Quentin's sister is 15 years.

So, 5x/18=15

=x=54 years

Hence the age of aunt is 54 years old.

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Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

Answer:

Part A:  8x + 24

Part B:  Expressions M and N are not equivalent for any value of x because if you do 8x + 24 = 8x + 10, the 8x will cancel out from both sides and you are left with 24 = 10, which is not true, and therefore has no solution.

Step-by-step explanation:

For Part A, to apply the Distributive Property, you multiple the 4 with both terms in the parentheses. So, you do 4(2x) + 4(6). This expression is equal to 8x + 24.

Hope this helped! :)

The measure of the angles formed between parallel lines and their transversals indicates;

9. m∠3 = 97°, m∠5 = 97°, m∠10 = 97°, m∠7 = 83°

Parallel lines are lines that  maintain the are equidistant from each other and have the same slope on the coordinate plane.

The angles formed between the parallel lines and their transversal are;

1. Alternate exterior angles; (c) ∠9 and ∠16
2. Supplementary angles (e);  ∠15 & ∠11

3. Alternate interior angles (a); ∠10 & ∠15

4. Vertical angles (d); ∠12 & ∠15

5. Corresponding angles (b); ∠9 & ∠11

6. None (f); ∠9 & ∠15

7. Supplementary angles (e); ∠13 & ∠14

8. Alternate interior angles; ∠14 & ∠11

9. The alternate interior angles theorem indicates that we get;

(a + 28) = 2·a

Therefore; 2·a - a = 28

2·a - a = a, therefore;

a = 28

∠MNP = (a + 28)° = (28 + 28)° = 56°

10. The alternate interior angles theorem indicates that we get;

5·y° = (2·y + 78)°

Therefore;

5·y - 2·y = 78

3·y = 78

y = 78/3 = 26

The measure of the angle WXZ, m∠WXZ = 5·y°

Therefore; m∠WXZ = 5 × 26 = 130

m∠WXZ = 130°

9. ∠2 ≅ ∠3 (Vertical angles theorem)

m∠2 = m∠3

Therefore; m∠3 = m∠2 = 97°

m∠5 + m∠6 = 180° (Linear pair angles theorem)

m∠5 + 83° = 180°

m∠5 = 180° - 83° = 97°

∠10 and ∠2 are corresponding angles, therefore;

m∠10 = m∠2 = 97°

∠7 and ∠6 are vertical angles, therefore;

m∠7 = m∠6 = 83°

∠9 and ∠3 are same side interior angles, therefore;

m∠9 + m∠3 = 180°

m∠9 = 180° - m∠3

m∠9 = 180° - 97° = 83°
∠8 and ∠6 are linear pair angles, therefore; m∠8 = 180° - 83° = 97°

∠16 and ∠6 are same side exterior angles, therefore;

m∠16 + m∠6 = 180°

m∠16 = 180° - 83° = 97°

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Step-by-step explanation:

I hope this answer is helpful ):

Answer:

-5

Step-by-step explanation:

Its negative 5 because it being given to the dad

Answer:

the last one

Step-by-step explanation:

there is no rhythm

Answer:

the midpoint is (9,5). hope this helps

Answer:

range=14

mode=9

median =9

mean =12

Step-by-step explanation:

range is B-S=20-6

mode is most common

median put in order find middle value 6,9,9,9,9,11,13,16,18,20

mean is add all divide by how many 9+9+9+9+6+11+13+16=120/10

If i get one wrong i am sorry

There were 18 time trials recorded during the experiment.

To determine the number of time trials recorded during the experiment, we count the total number of dots on the dot plot.

According to the given information, we have:

- Two dots over 15

- Three dots over 17

- Two dots over 19

- Two dots over 20

- One dot over 21

- Four dots over 23

- One dot over 24

- Three dots over 25

By adding up these counts, we get:

2 + 3 + 2 + 2 + 1 + 4 + 1 + 3 = 18

Therefore, there were 18 time trials recorded during the experiment.

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The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.

Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -

x + x + 1 + x + 2 = 12

Performing addition on Left Hand Side of the equation

3x + 3 = 12

Rewriting the equation

3x = 12 - 3

Performing subtraction on Right Hand Side of the equation

3x = 9

x = 9/3

Performing division on Right Hand Side of the equation

x = 3

So, next number = x+1

Second number = 3+1

Second number = 4

Third number = x+2

Third number = 3+2

Third number = 5

Hence, the three consecutive numbers are 3, 4 and 5.

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Answer:

the range is :

10 , 74 , 78 , 102

3 , 4 , 4 , 5 , 17

1.2, 1.2 , 3.2 , 3.5 , 3.6 , 6.5 , 8.2 , 9.2

Step-by-step explanation:

121

Step-by-step explanation:

9+2=11

4+10=14

11×14=154

6+5=11

3×11=33

154-33=121

Answer:

Step-by-step explanation:

9 + 2(14) - 3(11)

9 + 28 - 33

37 - 33 = 4

A number line which represents the given number (2.379) is plotted and shown in the image attached below.

A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

In conclusion, the number (2.379) should be placed close to 4 as plotted on the number line shown in the image attached below.

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All the three locations has been checked below.

Using Pythagoras theorem,

12² = 8² + x²

144 - 64 = x²

x= √80

x=8.9

Now, using Trigonometry

tan F = P/B

tan F= 8/8.9

and, sin F = P/H

      sin F= 8/12 = 2/3

and, cos F = B/H

        cos F= 12/8.9

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the Pythagorean theorem to find the value of z:

\(AC^2 = AD^2 + DC^2\)

Since BD is perpendicular to AC, we know that DC = BC. We can also use the fact that AB and BD are altitudes of triangle ABC to find the area of the triangle in two different ways:

Area of triangle ABC = 1/2 * AB * BD = 1/2 * AC * AD

Substituting the given values, we get:

1/2 * 10 * BD = 1/2 * z * 8

Simplifying this equation, we get:

BD = 4z/5

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

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Answer:

\(a = 8.5t\)

\(y = 32.55\)

Step-by-step explanation:

Solving (9): The equation of the table

We start by calculating the slope (m)

\(m = \frac{a_2 - a_1}{t_2 - t_1}\)

Where:

\((t_1,a_1) = (15,127.5)\)

\((t_2,a_2) = (16.5,140.25)\)

\(m = \frac{140.25 - 127.5}{16.5 - 15}\)

\(m = \frac{12.75}{1.5}\)

\(m = 8.5\)

The equation is then calculated using:

\(a = m(t - t_2) + a_2\)

So, we have:

\(a = 8.5(t - 16.5) + 140.25\)

Open bracket

\(a = 8.5t - 140.25 + 140.25\)

\(a = 8.5t\)

Solving (10):

\(4.8y = 156.24\)

Required

Find x

Divide both sides by 4.8

\(y = 32.55\)

Answer:

63 feet

Step-by-step explanation:

Let :

Given

Formula for Area

Solving

The width is : 63 feet

Answer: $171.31

Step-by-step explanation:

A = P(1 - r)ⁿ

Given: P = 200, r = 1.1% (.011), n = 14

A = 200(1 - .011)¹⁴

  = 200(.989)¹⁴

  = 171.308

Since we are talking about money, round to two decimal places.

Answer:

=14g−30

Step-by-step explanation:

I hope this helps you

Answer:

14g - 30

Step-by-step explanation:

combine like terms

The value of the missing length to the nearest tenth are;

a. x = 7.5

b. x = 7.8

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore ;

c² = a²+b²

a. x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = 7.5 ( nearest tenth)

b. using Pythagoras theorem also!

x² = 6²+5²

x² = 36+25

x² = 61

x = √61

x = 7.8( nearest tenth).

Therefore the value of the missing values are 7.5 and 7.8

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