MATHEMATICS HIGH SCHOOL

What is the area of a rectangle with vertices at (4, 3), (11, 3), (11, 9), and (4, 9)?

Answers

Answer 1

Answer:

Answer:

The area of a rectangle is 42 units ².

Step-by-step explanation:

As the diagram is given below.

Distance Formula

$Distance\ formula = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}$

As the rectangle with vertices at A (4, 3), B(11, 3),C (11, 9), and D (4, 9).

Take A (4, 3) to B(11, 3)

$AB = \sqrt{(11-4)^(2)+(3-3)^(2)}$

$AB = \sqrt{(7)^(2)+(0)^(2)}$

$AB = √(49)$

$√(49) =7$

AB = 7 units

As take B(11, 3) to C (11, 9).

$BC = \sqrt{(11-11)^(2)+(9-3)^(2)}$

$BC = \sqrt{(0)^(2)+(6)^(2)}$

$BC = √(36)$

$√(36) =6$

BC = 6 units

As take C (11, 9) toD (4, 9).

$CD = \sqrt{(4-11)^(2)+(9- 9)^(2)}$

$CD = \sqrt{(7)^(2)+(0)^(2)}$

$CD = √(49)$

$√(49) =7$

CD = 7 units

As take D (4, 9) to A (4, 3)

$DA = \sqrt{(4-4)^(2)+(3-9)^(2)}$

$DA = \sqrt{(0)^(2)+(-6)^(2)}$

$DA = √(36)$

$√(36) =6$

DA = 6 units

Thus

AB = DC= 7 units

AD = BC = 6 units

Formula

Area of rectangle = Length × Breadth

Length = 7 units

Breadth = 6 units

Put value in the above

Area of rectangle = 7 × 6

= 42 units ²

Therefore the area of a rectangle is 42 units ².

Answer 2

Answer: This is rectangle ABCD, where coordinates of the vertices are: A ( ( 4, 3 ); B ( 11, 3 ); C ( 11, 9 ) and D ( 4, 9 ). The area of the rectangle is: A = L x W ( L - length and W - width ). Length = AB = 11 - 4 = 7. Width = BC = 9 - 3 = 6. Finally: A = 7 * 6 = 42. Answer: The area of a rectangle is 42. Hope this helps. Let me know if you need additional help!

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hey sales person sells $2900 and merchandise and earns a commission of 522 what is the commission rate?

Answers

Answer: 18%

Step-by-step explanation: To find the commission rate, we can divide the commission earned by the total merchandise sold.

Given:

Total merchandise sold = $2900

Commission earned = $522

To calculate the commission rate:

Commission rate = (Commission earned / Total merchandise sold) * 100%

Substituting the given values into the formula:

Commission rate = (522 / 2900) * 100%

Calculating the commission rate:

Commission rate = 0.18 * 100% = 18%

Therefore, the commission rate for this salesperson is 18%.

Which phrase describes the variable expression 11 • x ?1. The product of 11 and x 2. 11 decreased by x 3. The quotient of 11 and x 4. 11 increased by x

Answers

One product means multiply to decreased knee subtract three quotes is divide and for increased by

A jar contains jelly beans that are red, yellow, blue, and purple. Several people reach in and grab handfuls of jelly beans, then collectively tally the number of each color: 15 red, 20 yellow, 12 blue, and 8 purple. If someone pulls out 22 jelly beans, about how many would you expect to be yellow?A.4
B.20
C.13
D.8

Answers

Total jellybeans pulled out: 15 + 20 + 12 + 8 = 55

Proportion of yellow jellybeans: 20 / 55 = 4/11

(4/11) * 22 = 8.

Answer: 8

Write an equation of the line below.

Answers

Answer: y = -2x+3

Explanation

The two marked points on the blue line are (0,3) and (5,-7)

Use the slope formula.

$\text{Given Points: }(x_1,y_1) = (0,3) \text{ and } (x_2,y_2) = (5,-7)\n\nm = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\n\nm = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\n\nm = (-7 - 3)/(5 - 0)\n\nm = (-10)/(5)\n\nm = -2\n\n$

The slope is -2.

A slope of -2 or -2/1 means "down 2, right 1".

Following this motion pattern has us go from (0,3) to (1,1) to (2,-1) to (3,-3) to (4,-5) to (5,-7) and so on.

The y intercept is 3 as this is where the blue line crosses the y axis.

--------

We found the following

m = -2 = slope

b = 3 = y intercept

The template y = mx+b updates to y = -2x+3 which is the final answer.

Jane Hilman went to her bank. She had a balance of $2,539.78 in her savings account. She withdrew $150.00 and the teller credited her account with $6.19. What is her new balance?The new balance will be $ ____

Answers

Answer:

New Balance of Jane Hilman savings account = $2395.97

Step-by-step explanation:

Amount of money Jane Hilman had in her account = $2539.78

Amount of money withdrew by her when she went to the bank = $150

Amount of money left in her account after withdraw = 2539.78 - 150

= $2389.78

Also, Teller credited her account with $6.19

And we need to find the new balance of Jane Hilman account

Thus, New Balance of Jane Hilman savings account = 2389.78 + 6.19

= $2395.97

$150-$6.19=$143.81

2,539.78-143.81=2395.97

A construction worker tosses a brick from a tall building. The brick's height (in meters above the ground) t tt seconds after being thrown is modeled by h ( t ) = − 5 t 2 + 20 t + 105 h(t)=−5t 2 +20t+105h, left parenthesis, t, right parenthesis, equals, minus, 5, t, squared, plus, 20, t, plus, 105 Suppose we want to know the height of the brick above the ground at its highest point. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h ( t ) = h(t)=h, left parenthesis, t, right parenthesis, equals 2) At its highest point, how far above the ground was the brick?