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Dimas [21]
3 years ago
14

Please help explanation if possible

Mathematics
2 answers:
katrin [286]3 years ago
5 0

Answer:

Jordans' age = 31 ; Anna's age = 19

Step-by-step explanation:

Given the 2 equations relating their ages

J + A = 50 → (1)

J = 12 + A → (2)

Substitute J = 12 + A into (1)

12 + A + A = 50

12 + 2A = 50 ( subtract 12 from both sides )

2A = 38 ( divide both sides by 2 )

A = 19

Substitute A = 19 into (2)

J = 12 + 19 = 31

Then Jordans' age = 31 ; Anna's age = 19

ch4aika [34]3 years ago
4 0

Answer:

Step-by-step explanation:

J = 12 + A equation 1

J + A = 50 equation 2

Solving equation 2

J + A = 50

A = 50 - J equation 3

Putting value of A in equation 1

J = 12 + A

J = 12 + 50 - J

Bringing like terms on one side

J + J = 12 + 50

2J = 62

J = 62/2 = 31

Putting value of J in equation 3

A = 50 - J

A = 50 - 31 = 19

Checking answer by putting values in equation 2

J + A = 50

31 + 19 = 50

50 = 50

So the age of Jordan is 31 and Anna is 19

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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

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nika2105 [10]

Answer:

1200

Step-by-step explanation:

2 times 6 = 12

12 times 100 = 1200

Hope this helps if does not please let me know thanks!

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2 years ago
Please please help !!!!!!!!
adoni [48]

Answer:

98°

142°

83°

97°

Step-by-step explanation:

m(arc)JL = 2 × 49° = 98°

m(arc)MJ = 360° - 120° - 98° = 142°

m<KJM = (120° + 46°)/2 = 83°

m<KLM = (360° - 120° - 46°)/2 = 97°

8 0
1 year ago
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