The area of a rectangle is 440 square inches. The length of the rectangle is 29 inches more than its width. What is the length of the rectangle?

Adam is 4 years old. This conclusion is reached by setting up a system of equations based on the information that Mark and Adam's ages add up to 28 years and Mark is 20 years older than Adam.

The student is asking how old Adam is, given that the total age of Mark and Adam is 28 years, and Mark is 20 years older than Adam. To solve this, we can set up a system of equations. Let Mark's age be represented by M and Adam's age be represented by A. The two equations based on the given information would be:

Now, substituting the second equation into the first one, we get:

A + 20 + A = 28

This simplifies to:

2A + 20 = 28

Subtracting 20 from both sides, we have:

2A = 8

Dividing both sides by 2, we find:

A = 4

So, Adam is 4 years old.

Answer:

The vertex of the function is (h,k)=(3,3)

The axis of symmetry is x=3.    

Step-by-step explanation:

Given : Function [tex]y=2x^2-12x+21[/tex]

To find : Determine the axis of symmetry and the vertex of the given function.

Solution :  

The quadratic function is in the form, [tex]y=ax^2+bx+c[/tex]

On comparing, a=2 , b=-12 and c=21

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

[tex]h=-\frac{b}{2a}[/tex]

[tex]h=-\frac{-12}{2(2)}[/tex]

[tex]h=\frac{12}{4}[/tex]

[tex]h=3[/tex]

For k, The y-coordinate of the vertex is given by,

[tex]k=f(h)[/tex]

[tex]k=2h^2-12h+21[/tex]

[tex]k=2(3)^2-12(3)+21[/tex]

[tex]k=18-36+21[/tex]

[tex]k=3[/tex]

The vertex of the function is (h,k)=(3,3)

The x-coordinate of the vertex i.e. [tex]x=-\frac{b}{2a}[/tex] is the axis of symmetry,

So, [tex]x=-\frac{b}{2a}=3[/tex] (solved above)

So, The axis of symmetry is x=3.    

The length of GQ is 25/3 units.

To find the length of GQ, we need to equate GQ to GH and solve for x. Since Q is the midpoint of GH, the lengths GQ and QH are equal. Therefore, we have the equation:

2x + 3 = 5x - 5

Subtract 2x from both sides:

3 = 3x - 5

Add 5 to both sides:

8 = 3x

Divide both sides by 3:

x = 8/3

To find the length of GQ, substitute the value of x back into 2x + 3:

GQ = 2(8/3) + 3

GQ = 16/3 + 3

GQ = 16/3 + 9/3

GQ = 25/3 units

Even and Odd Functions U3L2

1. f(x)=-x^2/x^4-25
2. The function is neither even nor odd.
3. The graph is symmetric about the origin.
4. 2ND graph from the question's photos (looks like mcdonalds logo)

youre welcome !

When comparing two sets of data, choose the median for skewed data and mean with standard deviation for symmetric data.

When comparing two sets of data where one is strongly skewed and the other is symmetric, for the comparison, it is advisable to choose the median as the measure of the center for the skewed data since it is resistant to outliers, and the mean and standard deviation for the symmetric data to give an overall representation of the data.

The slope intercept equation which models the data in the table given ls y = 3x + 1

General form of a slope - intercept equation :

Slope can be calculated thus:

Slope = (y2 - y1) /(x2 - x1)

Slope = (-2 + 8) / (-1 + 3)

Slope = 6/2 = 3

Taking any pair of points, we can calculate the intercept, c :

y = 3x + c

10 = 3(3) + c

10 = 9 + c

c = 10 - 9

c = 1

Therefore, the slope - intercept equation is y = 3x + 1

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Answer: 0.73 since 1 - 1.27 = 0.73 so the drivers probability of not speeding is 0.73 hope it helps

If probability that a driver is speeding on a stretch of road is 0.27 then probability that a driver is not speeding is 0.73.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that the  probability that a driver is speeding on a stretch of road is 0.27.

Probability(Speeding)=0.27

We need to find the probability that a driver is not speeding.

Probability(Not Speeding)=1-Probability(Speeding)

One minus zero point two seven

=1-0.27

We get zero point seven three

=0.73

Hence, if probability that a driver is speeding on a stretch of road is 0.27 then probability that a driver is not speeding is 0.73.

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Answer:

The correct option is D. The image and preimage are congruent.

Step-by-step explanation:

Let us understand the this concept with the help of an example.

Consider the figure 1:

From the figure 1, it is clear that the size of image doesn't change.

Thus, option A and C are invalid.

Or we can say that, the image and preimage remain the same.

Therefore, the correct option is D. The image and preimage are congruent.

see attached picture for answer:

 for the format you need it would be 1.5x +-y = 12

The correct answer is option a. 2.77 is an element of the set real numbers.

To determine which set(s) the number 2.77 is an element of, let's analyze each option:

1. Real numbers: The set of real numbers includes all rational and irrational numbers. This means any number that can be placed on the number line, including integers, fractions, and decimals. Since 2.77 is a decimal number, it is indeed a real number.

2. Real numbers and natural numbers: While 2.77 is a real number, natural numbers are a subset of real numbers that consist of all positive integers (1, 2, 3, ...). Since 2.77 is not a positive integer, it is not a natural number. Therefore, this option is incorrect because 2.77 is not a natural number.

3. Natural numbers and whole numbers: As mentioned, natural numbers are positive integers. Whole numbers include all natural numbers and the number 0 (0, 1, 2, 3, ...). Since 2.77 is neither a natural number nor a whole number, this option is incorrect.

4. Null set: The null set (or empty set) contains no elements. If 2.77 were in the null set, it would imply that the null set is not empty, which contradicts the definition of the null set. Therefore, this option is incorrect.

The complete question is

"Which shows the set(s) the number 2.77 is an element of?

a. real numbers

b. real numbers and natural numbers

c. natural numbers and whole numbers

d. null set"

Answer:

(2x + 1) - (–x² + 3x) is difference .

Step-by-step explanation:

Given : r(x) = –x² + 3x  and  s(x) = 2x + 1

To find : Find the difference of functions s and r .

Solution :  We have given that  r(x) = –x² + 3x and s(x) = 2x + 1.

Difference :

(s – r)(x) = s(x) - r(x)

              =(2x + 1) - (–x² + 3x)

              = 2x +1 + x²-3x

             = x²-x +1.

Therefore, (2x + 1) - (–x² + 3x) is difference .

The difference of the function is (2x+1)-(x^2 + 3x)

Given the following functions

r(x) = –x² + 3x

s(x) = 2x + 1

Taking the difference of the function will give:

(s – r)(x) = 2x - 1 - (-x^2 + 3x)

Expand

(s – r)(x) = 2x - 1  + x^2 - 3x

(s – r)(x) = x^2 - x - 1

Hence the difference of the function is (2x+1)-(x^2 + 3x)

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Answer:

p>[tex]\frac{8}{7}[/tex]

Step-by-step explanation:

The equation is 6(2 P-1) > 5 P +2

6(2 P-1)> 5 P+2

6×2 P-6×1> 5 P+2

12 P-6> 5 P+2

12 P - 5 P > 2+6

 7 P > 8

P > [tex]\frac{8}{7}[/tex]

P is greater than[tex]\frac{8}{7}[/tex]

Hence, the correct answer is p greater than [tex]\frac{8}{7}[/tex]

cubed root of 4896 = 16.98

round to 17

17-1 = 16

17 +1 = 18

16* 17 *18 = 4896

 bin is 16 in x 17 in x 18 in

Answer:

The dimension of the rectangle is [tex]16\times 17\times 18[/tex]

Step-by-step explanation:

Given : The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches.

To find : What are the dimensions of the bin?

Solution :

The dimensions of a rectangular bin are consecutive integers.

Let the consecutive integers are x,x+1,x+2

So let, length, l=x

Breadth b=x+1

Height h=x+2

The volume of the bin is

[tex]V=l\times b\times h[/tex]

[tex]4896=x\times (x+1)\times (x+2)[/tex]

[tex]4896=(x^2+x)(x+2)[/tex]

[tex]4896=x^3+2x^2+x^2+2x[/tex]

[tex]x^3+3x^2+2x-4896=0[/tex]

Plot the equation graphically to find the value of x.

Refer the attached figure below.

The value of x is 16.

So, Length is l=16

Breadth is b=x+1=16+1=17

Height is h=x+2=16+2=18

The dimension of the rectangle is [tex]16\times 17\times 18[/tex]

The net weekly pay is $633.4

The gross pay is given as:

Gross = $800.00

The deductions are:

The net pay is then calculated as:

Net pay = 800.00 - (53 + 6.2% * 800 + 1.45% * 800 + 1.5% * 800 + 28.40 + 12.00)

Evaluate

Net pay = 633.4

Hence, the net weekly pay is $633.4

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