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Hunter-Best [27]
2 years ago
13

How to calculate 1/2 × 24cm²​

Mathematics
1 answer:
Orlov [11]2 years ago
8 0

\frac{1}{2}  \times 24 = 12 {cm}^{2}

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If g(x) =x^2 + 1, find g(4)
Papessa [141]

Answer:

17

Step-by-step explanation:

Since we are evaluating <em>g(x)</em> for g(4), we would substitute <em>x</em> in the equation with 4.

<em>x</em>² + 1

(4)²+ 1

16 + 1

17

I hope this helps

4 0
2 years ago
Solve the equation to find the value of m and n.<br> 2m + 3n = -5<br> 5m + 3n = 1
Leokris [45]

Answer:

m = 2, n = - 3

Step-by-step explanation:

Given the 2 equations

2m + 3n = - 5 → (1)

5m + 3n = 1 → (2)

Subtract (2) from (1) term by term to eliminate n

2m - 5m = - 5 - 1

- 3m = - 6 ( divide both sides by - 3 )

m = 2

Substitute m = 2 into either of the 2 equations and solve for n

Substituting into (1)

2(2) + 3n = - 5

4 + 3n = - 5 ( subtract 4 from both sides )

3n = - 9 ( divide both sides by 3 )

n = - 3

3 0
3 years ago
Read 2 more answers
A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr
seraphim [82]

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

Perimeter = a\sqrt{2} + b\sqrt{10}

Required

a + b

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

(x_1,y_1) = A(0,1)

(x_2,y_2) = B(3,4)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}

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

AB = \sqrt{9+ 9}

AB = \sqrt{18}

AB = \sqrt{9*2}

AB = \sqrt{9}*\sqrt{2}

AB = 3\sqrt{2}

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

(x_1,y_1) = B (3,4)

(x_2,y_2) = C(4,3)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}

BC = \sqrt{(-1)^2 + (1)^2}

BC = \sqrt{1 + 1}

BC = \sqrt{2}

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

(x_1,y_1) = C(4,3)

(x_2,y_2) = D (3,0)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}

CD = \sqrt{(1)^2 + (3)^2}

CD = \sqrt{1 + 9}

CD = \sqrt{10}

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

(x_1,y_1) = D (3,0)

(x_2,y_2) = A (0,1)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}

DA = \sqrt{(3)^2 + (- 1)^2}

DA = \sqrt{9 +  1}

DA = \sqrt{10}

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}

Perimeter = 4\sqrt{2} + 2\sqrt{10}

Recall that

Perimeter = a\sqrt{2} + b\sqrt{10}

This implies that

a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}

By comparison

a\sqrt{2} = 4\sqrt{2}

Divide both sides by \sqrt{2}

a = 4

By comparison

b\sqrt{10} = 2\sqrt{10}

Divide both sides by \sqrt{10}

b = 2

Hence,

a + b = 2 + 10

a + b = 12

3 0
3 years ago
If B is the midpoint of AC, and AB=5/2x+12 and AC=12x-4, what is the length of BC?
Setler [38]

Answer:

22

Step-by-step explanation:

We know that AC = 2 * AB so we can write:

12x - 4 = 2(5/2 x + 12)

12x - 4 = 5x + 24

7x = 28

x = 4

Since AB = BC the answer is 5/2 * 4 + 12 = 22.

8 0
3 years ago
Determine whether a relation is a function, as well as its domain and range: State the domain and range for the function f(x)=x^
Anna35 [415]
F(x) = x^2 + 3 is a function.
domain of f(x) = x^2 + 3 is all real numbers.
range is all real numbers greater or equal to 3.
6 0
3 years ago
Read 2 more answers
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