A playground is (4x + 4) feet wide and 6x feet long. Find the area of the playground.

Answers

Answer 1
Answer:

Area of a rectangle= length*width

So:

Area of the playground= (6x)(4x+4)

Use distributive property.

Area of the playground= (6x*4x)+(6x*4)

=24x^2+24x

Answer: 24x^2+24x


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Suppose you have $75 in your savings account and you save an additional $5 each week. Your friend has $30 in his savings account and saves an additional $10per week. In how many weeks will you have the same amount of money?

Answers

it will take 9 weeks for you and your friend to have the same amount of money in your savings accounts.

To determine the number of weeks it takes for both you and your friend to have the same amount of money in your savings accounts, we need to set up an equation.

Let's denote the number of weeks as 'x'. For you, the amount of money in your savings account after 'x' weeks can be calculated as follows:

Amount of money in your account = $75 + $5x

For your friend, the amount of money in his savings account after 'x' weeks can be calculated as:

Amount of money in your friend's account = $30 + $10x

To find the number of weeks where you both have the same amount of money, we set up the equation:

$75 + $5x = $30 + $10x

Simplifying the equation:

$5x - $10x = $30 - $75

-$5x = -$45

Dividing both sides of the equation by -5 gives us:

x = 9

Therefore, it will take 9 weeks for you and your friend to have the same amount of money in your savings accounts.

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Answer:

9 weeks

Step-by-step explanation:

5x+75=10x+30

-5x        -5x

75=5x+30

-30      -30

45=5x

÷5    ÷5

9=x

x=9

5)Trevon's school is selling tickets to the annual dance competition. On the first day of ticket salesthe school sold 5 senior citizen tickets and 8 student tickets for a total of $94. The school took in
$164 on the second day by selling 10 senior citizen tickets and 13 student tickets. Find the price
of a senior citizen ticket and the price of a student ticket

Answers

Answer:

$8 for student tickets and $4.40 for senior tickets

Step-by-step explanation:

10 (5x +8y=94)

5 (10x +13y=164)

50x+80y=940

- 50x +65y=820

80y-65y= 940-820

15y= 120/15

y=8

(y is the cost of student tickets)

5x+8y=94

5x+8(9)=94

5x+72=94-72

5x=22/5

x= 4.4

Cho số phức z thỏa mãn 2iz-5+i=i-(z-2i) tính modun của số phức w=z-1+i

Answers

Solve the given equation for z :

2iz - 5 + i = i - (z - 2i )

2iz - 5 = 2i - z

(2i + 1) z = 2i + 5

z = (2i + 5)/(2i + 1)

z = (2i + 5)/(2i + 1) × (2i - 1)/(2i - 1)

z = (4i ² + 10i - 2i - 5) / (4i ² - 1)

z = (8i - 9)/(-5)

z = 9/5 - 8/5 i

Then

w = z - 1 + i = 4/5 - 3/5 i

Crater Lake Oregon is a roughly circular lake. The lake basin formed about 7000 years ago when the top of a volcano exploded in an immense explosion. Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2). Find the coordinates of the center of the lake.

Answers

To solve the problem we must find the equation of the circumference of the form:
 (Xa) ² + (Yb) ² = r²
 They do not give us the center or the radio, but we have 3 points.
 With the points H (-4,1), G (-2, -3) and C (5, -2) we find 3 equations
 1) (-4-a) ² + (1-b) ² = r²
 2) (-2-a) ² + (-3-b) ² = r ²
 3) (5-a) ² + (-2-b) ² = r ²
 Now we have a system of 3 equations with 3 unknowns: r, a, b
 When solving the system we have to:
 r = 5
 a = 1
 b = 1
 Therefore, the center of the circumference of the lake is the point (a, b)
 That is, the point (1,1)

Answer:

The coordinates of the center of the lake are ((-1)/(3),(-4)/(3)).

Step-by-step explanation:

It is given that Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2).

If we joint these points, then we get a triangle and the center of a triangle is known as centroid.

The formula for centroid of a triangle is

Centroid=((x_1+x_2+x_3)/(3),(y_1+y_2+y_3)/(3))

The centroid of the triangle H(-4,1), G(-2,-3), and C(5,-2) is

Centroid=((-4-2+5)/(3),(1-3-2)/(3))

Centroid=((-1)/(3),(-4)/(3))

Therefore the coordinates of the center of the lake are ((-1)/(3),(-4)/(3)).

15% of what number equals 12

Answers

.15x=12

x= 12/.15

x= 80

15% of 80 equals 12


I hope that's help !


Which of the following ratios are equivalent to 6:8?9:12
12 to 16
24:36
16 to 24

Answers

12 to 16 should be the only one.
i looked over ti and 9/12 is also equivalent.
if you multiple by 1.5 that gets you 9/12