Find the domain of the following piecewise function.

[-4,3)
(-4,3]
[-4,6)
(-4,6]

We are actually given here a right triangle where EC is the hypotenuse. The length of one side is AE = 24, and the other side AC is simply twice BC, so AC = 7:

EC^2 = AE^2 + AC^2

EC^2 = 24^2 + 7^2

EC = 25

The dimensions of the rectangle are 6.4 and 12.8 respectively.

The formula for calculating the perimeter of a rectangle is given by :

P = 2 ( L + w )

The length of a rectangle is twice the width. And the perimeter is 32 cm more than the width.

L = 2w

Now substituting into the formula , we have

Width: x

Length: 2x

Perimeter P = 2 ( L + w ) = 2(3x) = 6x

Since 32 cm more than width means x+32

6x = x + 32

5x = 32

x = 6.4

Hence, Dimension is 6.4 × 12.8.

Learn more about rectangles here;

https://brainly.com/question/15019502

#SPJ5

Answer: Number of residents live in south region= 672 residents.

Step-by-step explanation:

Given:- Total residents in the city =4200

let A be the event of residents live in south region the,

Probability of residents live in south region P(A) = 0.16

So, Number of residents live in south region=Product of probability of residents live in south region and total residents in the city =0.16×4200=672 residents.

The equation 4(2x + 3y) = 4(3y + 2x) is representing the Commutative Property of Addition, which means the order in which you add numbers does not change the sum.

The equation in your question, 4(2x + 3y) = 4(3y +2x), is an example of the Commutative Property of Addition. This property means that the order in which you add numbers does not change the sum. In this case, (2x + 3y) and (3y + 2x) are the same because of the Commutative Property of Addition, the order of 2x and 3y doesn't impact the result. The multiplication by 4 on both sides does not change this property being applied.

https://brainly.com/question/5835209

#SPJ12

The total number of almonds can be represented by the equation:

x = 25b + 7

We can use the information given in the question to set up an equation to represent the total number of almonds.

Let b represent the number of bags, and

let x represent the total number of almonds.

According to the problem, each bag contains 25 almonds, and there are 7 almonds left over. Therefore, the total number of almonds can be represented by the equation:

x = 25b + 7

Read more about Algebra Word Problems at: https://brainly.com/question/21405634

#SPJ3

The Overall Change in score is 9.9 points.

What is overall change?

Overall Change is the difference of initial average and final average.

Given that you are playing a game and lose 4.8 points and again loose 7.6 points and finally win 2.5 points.

According to question we have

4.8 + 7.6 = 12.4

Then 12.4 - 2.5 = 9.9 points

Hence, Overall Change in the score is 9.9 points.

For more references about Overall Change, click:

https://brainly.com/question/16717275

#SPJ5

The width of the rectangle is 4.269ft and the length is  8.538 ft.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Given, The length of a rectangle is 1 ft more than double the width.

Assuming the width to be x ft, therefore length would be (2x + 1) ft.

We know area of a rectangle(A) = length×width.

∴ x×(2x + 1) = 45.

2x² + 2x = 45.

2x² + 2x - 45 = 0.

[tex]x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:2\left(-45\right)}}{2\cdot \:2}[/tex].

[tex]x_1=\frac{-2+2\sqrt{91}}{2\cdot \:2},\:x_2=\frac{-2-2\sqrt{91}}{2\cdot \:2}[/tex].

[tex]x=\frac{-1+\sqrt{91}}{2},\:x=-\frac{1+\sqrt{91}}{2}[/tex].

[tex]\left(\m\quad x=4.26969\dots ,\:x=-5.26969\dots \right)[/tex].

∴ x = 4.269ft is the admissible value as length can not be negative.

∴ length is 8.538 ft.

learn more about rectangles here :

https://brainly.com/question/14207995

#SPJ5

1st number = x

 2nd number = 3x

3rd number = 2x-10

x +3x + 2x-10 =92

6x - 10 = 92

6x =102

x = 102/6

x = 17

1st number = 17

2nd number = 17*3 = 51

 3rd number = 17 *2 = 34-10 = 24

17 + 51 + 24 = 92

 3 numbers are 17, 51 and 24

Answer:

The quotient is [tex]y^6[/tex]

Step-by-step explanation:

Given expression is,

[tex]y^9\div y^3[/tex]

[tex]=\frac{y^9}{y^3}[/tex]

By using quotient of powers property of exponent,

[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]

[tex]=y^{9-3}[/tex]

[tex]=y^6[/tex]

Hence, the quotient is [tex]y^6[/tex]

Second option is correct.

Answer:

D

Step-by-step explanation:

"the male interquartile is not accurate because the first quartile is missing"

Answer:

Option C is the answer: $3,090.64

Step-by-step explanation:

Lloyd opened a savings account 13 years ago with a deposit of $5,003.86 the account has an interest rate of 3.7% compounded daily.

Means p = 5003.86

r = 3.7% or 0.037

t = 13

n = 365 (assuming there are 365 days in a year)

[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]

[tex]A=5003.86(1+\frac{0.037}{365} )^{4745}[/tex]

=> [tex]A=5003.86(1.00010136)^{4745}[/tex]

A = $8094.09

Interest earned = [tex]8094.09-5003.86=3090.26[/tex] dollars

This is closest to option C, hence, option C is the answer.

There are a total of 6 groups.

And each group contains at least 4 students.

So the minimum number of students is:

minimum = 6 * 4 = 24 students

Let us say that x represents the number of students, hence:

x ≥ 24

To represent the number of students in the class, we can write the inequality 24 ≤ x.

To represent the number of students in the class, let's assume that the total number of students in the class is represented by the variable 'x'. Since the students are divided into 6 equal groups and each group has at least 4 students, we can write the inequality:
6 * 4 ≤ x

Simplifying the inequality:
24 ≤ x

This inequality represents that the total number of students in the class should be greater than or equal to 24.

https://brainly.com/question/30231190

#SPJ3

Final answer:

John received 10 nickels, 20 dimes, and 42 quarters.

Explanation:

Let's solve this problem step by step:

Let's assume the number of nickels = x

Number of dimes = x + 10 (10 more dimes than nickels)

Number of quarters = x + 10 + 22 (22 more quarters than dimes)

Given that the total value of change is $13, we can form the equation:

0.05x + 0.10(x + 10) + 0.25(x + 10 + 22) = 13

Simplifying the equation, we get:

0.05x + 0.10x + 1 + 0.25x + 7.75 = 13

Combining like terms, we get:

0.40x + 8.75 = 13

Subtracting 8.75 from both sides:

0.40x = 4.25

Dividing by 0.40:

x = 10.625

Since we can't have a fractional number of nickels, we round down to the nearest whole number.

Therefore, John received 10 nickels, 10 + 10 = 20 dimes, and 10 + 10 + 22 = 42 quarters.

Solution: As the line shown in the graph passes through (3,0) and (0,-1).

So, equation of line passing through (3,0) and (0,-1) is given by two point formula i.e equation of line passing through (p,q) and (a,b) is given by

→[tex]\frac{y-q}{x-p}=\frac{q-b}{p-a}[/tex]

→[tex]\frac{y-0}{x-3}=\frac{0+1}{3-0}[/tex]

So ,the equation of line is ,→3 y = x-3

  → x- 3 y -3= 0 or y=x/3 -1

take point (0,0) and putting in the above equation, we see that ,L.H.S>R.H.S

Similarly if you take other points , like (1,0).(0,1) we see that ,L.H.S>R.H.S.

it means the above equation can be written as , y≥x/3 -1.

None of the option is correct.