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3 years ago

Determine whether the two figures are similar if so give the similarity ratio of the smaller figure to the larger figure figures

are not drawn to scale

Mathematics

1 answer:

uranmaximum [27]3 years ago

7 0

$\bf \cfrac{\textit{small prism}}{\textit{large prism}}\qquad \qquad \stackrel{~\hfill \textit{yes 1:4}}{\cfrac{18}{72}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{4}{16}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{3}{12}\implies \boxed{\cfrac{1}{4}}}$

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I will give BRAINLIEST to whoever is CORRECT

8090 [49]

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3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago

A petting zoo owner is building an enclosure for his farm animals. He needs 353 feet of fencing. The supply store sells fencing

jolli1 [7]

353/12 =29.41. But will have to round up to 30 so the answer is 30

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3 years ago

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Which expression uses the associative property to make it easier to evalute?

mixas84 [53]

Answer:

The correct option is (c).

Step-by-step explanation:

The given expression is :

$14(\dfrac{3}{2}\times \dfrac{1}{4})$

We need to use the associative property to make it easier.

The associative property for multiplication is as follows :

$A\times (B\times C)=(A\times B)\times C$

We have,

$A=14, B=\dfrac{3}{2}\ and\ C=\dfrac{1}{4}$

$14(\dfrac{3}{2}\times \dfrac{1}{4})=(14\times \dfrac{3}{2})\times \dfrac{1}{4}$

Hence, the correct option is (c).

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3 years ago

When dividing fractions, the ________ term becomes the reciprocal.

Aleks04 [339]

Answer: Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

Step-by-step explanation:

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3 years ago

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