02.05) simplify i22. (1 point) 1 −1 −i i

The perimeter of rectangular park is 450m.the length of the sides is in the ratio 3:2.find the area of the rectangle

matrenka [14]

Answer: 12,150 m²

<u>Step-by-step explanation:</u>

The ratio is 3:2 which means

Length (L) = 3x

Width (w) = 2x

Perimeter (P) = 2L + 2w

450 = 2(3x) + 2(2x)

450 = 6x + 4x

450 = 10x

45 = x

L = 3x w = 2x

= 3(45) = 2(45)

= 135 = 90

Area (A) = L × w

= 135 × 90

= 12,150

6 0

2 years ago

The graph of the quadratic function y = ax^2 + bx + c is given.<br> Find a + b + c.

andrey2020 [161]

Answer:

$\frac{145}{24}\approx 6$ ***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

$(0,3)$

$(2,8)$

$(6,5)$

Step-by-step explanation:

I see that the graph crosses at $(0,3)$ , $(2,8)$ , and $(6,5)$ .

The equation $y=ax^2+bx+c$ tells us the $y$ -intercept is $c$ since when $x=0$ we have $y=a(0)^2+b(0)+c=0+0+c=c$ .

The $y$ -intercept for our graph is $3$ . Therefore, $c=3$ .

So far we have the equation:

$y=ax^2+bx+3$ .

Let's enter the other points creating a system of linear equations to solve:

$8=a(2)^2+b(2)+3$

$5=a(6)^2+b(6)+3$

Let's simplify:

$8=4a+2b+3$

$5=36a+6b+3$

Let's subtract 3 on both sides:

$5=4a+2b$

$2=36a+6b$

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

$-15=-12a-6b$

$2=36a+6b$

Now adding the equations results in:

$-13=24a$

Divide both sides by 24:

$\frac{-13}{24}=a$

Now using one of the equations we can find $b$ :

$5=4a+2b$ with $a=\frac{-13}{24}$

$5=4\frac{-13}{24}+2b$

$5=\frac{-13}{6}+2b$

Add 13/6 on both sides:

$5+\frac{13}{6}=2b$

$\frac{30+13}{6}=2b$

$\frac{43}{6}=2b$

Divide both sides by 2:

$\frac{43}{2(6)}=b$

$\frac{43}{12}=b$

So we have the equation:

$y=\frac{-13}{24}x^2+\frac{43}{12}+3$

Let's evaluate $a+b+c$ now:

$\frac{-13}{24}+\frac{43}{12}+3$

$\frac{-13+86+72}{24}$

$\frac{73+72}{24}$

$\frac{145}{24}$

4 0

3 years ago

practice counting in 2's , 5's and 10's, starting on 0. whats patterns do you notice ? can you write sentences to explain these

Mice21 [21]

When you multiply 5 by 1 you get 5. When you multiply 5 by 2 you get 10. If you keep doing this, you get a list of multiples of 5.

5
10
15
20
25
30
35
40
45
50

All of these numbers end in either 5 or 0. We can do the same with 2's and 10's.

2
4
6
8
10
12
14
16
18
20

For all 2's we can see that they are all even and end with an even number (0,2,4,6,8)

10
20
30
40
50
60
70
80
90
100

For 10's we can see that they all end in 0.

7 0

2 years ago

Determine the measure of an interior angle of the named regular polygon. If a side of the polygon is extended, determine the sup

ladessa [460]

Answer:

A) Each interior angle of the Regular Hexagon = 120°

B)The measure of the supplementary angle of an interior angle is 60°

Step-by-step explanation:

Regular Hexagon : A 6 sided polygon which has all 6 interior angles as EQUAL is called a regular hexagon.

So, here are 6 interior angles of the hexagon are equal.

Also, Sum of all interior angles of an hexagon = 720°

Let us assume the each angle of the hexagon = m

⇒ m + m + m + m + m + m = 720°

or, 6 m = 720°

or, m = 720° / 6 = 120°

⇒ Each interior angle of the Regular Hexagon = 120°

Now, a side is extended to form an exterior angle.

Let us assume the measure of that exterior angle = k

⇒ k + m = 180 ° ( as k and m are SUPPLEMENTARY ANGLES)

or, k = 180 - 120 = 60 °

or, k = 60 °

Hence, the measure of the supplementary angle of an interior angle is 60°

6 0

3 years ago

If f(x)=3x-1 and g(x)=x+2,find (f+g)(x)

KiRa [710]

Answer:

(f + g)(x) = 4x + 1

Step-by-step explanation:

Given f(x) = 3x - 1 and g(x) = x + 2, find (f + g)(x):

We can rewrite (f + g)(x) as f(x) + g(x), and solve the composite functions through addition:

f(x) + g(x) = (3x - 1) + (x + 2)

Combine like terms:

f(x) + g(x) = 3x + x + 2 - 1 = 4x + 1

Therefore, (f + g)(x) = 4x + 1.

Please mark my answers as the Brainliest if you find my explanations/solution helpful :)

7 0

2 years ago