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3 years ago

1 point

Mathematics

1 answer:

galina1969 [7]3 years ago

3 0

Answer:

(B) 20

Step-by-step explanation:

Let small puppet be represented by-----------------s

Let large puppet be represented by-----------------l

Total number of puppets expression will be: s+l =25---------a

The expression for total costs will be : 1$ s + $2l=$30-------b

Equation a can be written as; s= 25-l ------------c

Use equation c in equation b as

$1( 25-l )+$ 2l = $30

25-l + 2l = 30

25+l =30

l= 30-25 =5

l, large puppets = 5

s, small puppets = 25-5 = 20

Answer choice A is incorrect because 25 is the total number of all puppets

Answer choice C and D are incorrect because the numbers are less that that of small puppets.

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A rhombus has a side length equal to one of the diagonals. The other diagonal is 4cm longer. Find the area of the rhombus.

klasskru [66]

Answer:

The area of the rhombus is 25.83 cm².

Step-by-step explanation:

The area of a rhombus is given by:

$A = \frac{d_{1} \times d_{2}}{2}$

Where:

d₁: is one diagonal

d₂: is the other diagonal = d₁ + 4 cm

We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:

h: hypotenuse of the right triangle

a: one side of the right triangle

b: is the other side of the right triangle

From the above we know that:

h = d₁

$a = \frac{d_{2}}{2} = \frac{d_{1} + 4}{2}$

$b = \frac{d_{1}}{2}$

We can find d₁ with Pitagoras:

$h^{2} = a^{2} + b^{2}$

$d_{1}^{2} = (\frac{d_{1} + 4}{2})^{2} + (\frac{d_{1}}{2})^{2}$

$d_{1}^{2} = \frac{1}{4}(d_{1}^{2} + 8d_{1} + 16 + d_{1}^{2})$

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$d_{1} = 5.46 cm$

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Now, we can find the area:

$A = \frac{d_{1} \times d_{2}}{2} = \frac{5.46 cm \times 9.46 cm}{2} = 25.83 cm^{2}$

Therefore, the area of the rhombus is 25.83 cm².

I hope it helps you!

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