If you have 24 square pieces of wood, describe all the different ways you could make a rectangle by placing them side by side

Answer: The  average rate of change of f(t) from t = 2 to t = 6 is 1.5 thousand owners per year.

Step-by-step explanation:

Given: The function below shows the number of car owners f(t), in thousands, in a city in different years t:

[tex]f(t) = 0.25^2 - 0.5t + 3.5[/tex]

Now,

[tex]f(2) = 0.25(2)^2 - 0.5(2) + 3.5=3.5\\\\= f(6) = 0.25(6)^2-0.5(6)+ =9.5[/tex]

Now, the  average rate of change of f(t) from t = 2 to t = 6 is given by :-

[tex]k=\dfrac{f(6)-f(2)}{6-2}\\\\=\dfrac{9.5-3.5}{4}=1.5[/tex]

Hence, the  average rate of change of f(t) from t = 2 to t = 6 is 1.5 thousand owners per year.

646-54 = 592

592/2 = 296

296+54 = 350

350+296 = 646

 there were 350 hamburgers and 296 cheeseburgers sold

The equation is

4(q-10)=76

The amount of questions is

29 questions

D. All counting numbers are whole numbers.

All integers are counting numbers. This is not true. Counting numbers (also known as natural numbers) are positive whole numbers starting from 1, 2, 3, and so on. Integers include all positive and negative whole numbers, as well as zero. Thus, not all integers are counting numbers.

All rational numbers are integers. This is not true. Rational numbers include all fractions where the numerator and denominator are integers (denominator not zero). For example, 1/2 is a rational number but not an integer.

All integers are whole numbers. This is not true. Whole numbers include all non-negative integers (0, 1, 2, 3, ...), but integers also include negative numbers, which are not whole numbers.

Counting numbers (1, 2, 3, ...) are included in the set of whole numbers, which consists of all non-negative integers (0, 1, 2, 3, ...).

The equation is A ( A + 2 ) = 674 + ( A + ( A + 2 ) )

The first integer is A = 26

The second integer is B = 28

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the two numbers be A and B

where , the first integer is = A

The second integer is = B

B is the consecutive integer of A , so

The value of B = A + 2

Now , the equation will be

The product of two consecutive even positive integers is 674 more than the sum of the two integers

So , substituting the values in the equation , we get

A ( A + 2 ) = 674 + ( A + ( A + 2 ) )

On simplifying the equation , we get

A² + 2A = 674 + 2A + 2

Subtracting 2A on both sides of the equation , we get

A² = 674 + 2

A² = 676

Taking square roots on both sides of the equation , we get

A = 26

The value of B = A + 2

B = 28

Therefore , the value of A = 26

The value of B = 28

Hence ,

The first integer is A = 26

The second integer is B = 28

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Answer:

[tex]f(n) = 1.9 +0.6n[/tex]

Step-by-step explanation:

The nth term of the arithmetic sequence is given by:

[tex]a_n = a_1+(n-1)d[/tex]            ....[1]

where

[tex]a_1[/tex] is the first term

d is the common difference and n is the number of terms.

Here, f(n) represent diameter in centimeters and n the term number in the sequence.

Given the sequence represents the diameters of circles used to create an art project:

2.5 cm, 3.1 cm, 3.7 cm , 4.3 cm

This sequence is an arithmetic sequence with

[tex]a_1[/tex] = 2.5 and d = 0.6

Since,

3.1-2.5 = 0.6,

3.7-3.1 = 0.6

4.3-3.7 = 0.6

Substitute the given values in [1] we have;

[tex]f(n) =2.5+(n-1)(0.6)[/tex]

Using distributive property, [tex]a\cdot (b+c) = a \cdot b+ a\cdot c[/tex]we have;

[tex]f(n) = 2.5+0.6n-0.6[/tex]

Simplify:

[tex]f(n) = 1.9 +0.6n[/tex]

Therefore, the equation represents the sequence of diameters is, [tex]f(n) = 1.9 +0.6n[/tex]

Answer:

(0,0)

Step-by-step explanation:

We have,

U = { (x,y) : x,y belong to real numbers }

A = { (x,y) : (x,y) is a solution of y=x }

B = { (x,y) : (x,y) is a solution of y=2x }

We need to find the ordered pair (x,y) that belong to A[tex]\bigcap[/tex]B.

Let, (x,y) belong to A[tex]\bigcap[/tex]B

i.e. (x,y) belong to A and (x,y) belong to B

i.e. y = x and y = 2x

i.e. x = 2x

i.e. x = 0

Now, substitute x= 0 in any of the equation say y = x, we get y = 0.

Hence, the ordered pair satisfying A[tex]\bigcap[/tex]B is (0,0).

For a set U, The ordered pair satisfies A ∩ B is mathematically given as

x = 0,  y = 0 (0,0)

Question Parameter(s):

U = {ordered pairs on a coordinate plane}

A = {ordered pair solutions to y = x}

B = {ordered pair solutions to y = 2x}

if  (x,y) belongs to AnB

y = x and y = 2x

x = 0

In conclusion, subsituting we have

y = x and y = 2x

y = 0

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Answer:

False

The correct point slope form passing through points (x1,y1) is [tex](y-y1)=m (x-x1)[/tex] .

Step-by-step explanation:

The formula for the point slope form passing through the point (a,b) is given by.

[tex](y-b)=m (x-a)[/tex]

Where m is the slope .

As given in the question.

m is the slope and (x1, y1) is a point on the line.

Thus the point slope form becomes

[tex](y-y1)=m (x-x1)[/tex]

Therefore the correct point slope form passing through points (x1,y1) is [tex](y-y1)=m (x-x1)[/tex] .

The function for the area of the circle if x is the radius of the circle and y is the area of the circle is y = πx².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.

Given:

The area of a circle is a function equal to the product of pi (pi) and the square of the radius (r),

The area of the circle can be written as shown below,

Area of circle = π × R²

Here π is a constant, R is the radius of the circle,

When we put the value of the radius, we will get the value of the area,

Hence, the radius is an independent function and the area is dependent on the value of R (dependent function),

Replace y with area and radius with x as shown below,

y = πx²

Thus, y = πx² is the function for the area of the circle.

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0 to 1 is broken down into 9 equal spaces

the dot is on the 5th line

 so it would be 5/9