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4 years ago

8

Robyn has a 2" wide board and a 1 1/2" wide board. She would like to cut the narrower board at an angle so the is 2" long and th

e boards will fit together. At what angle does she need to cut the board

1 answer:

jek_recluse [69]4 years ago

8 0

The answer is 4 feet pi square

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There are 20 marbles in a bag. 1/5 are red and others are blue. What is the ratio of red to blue marbles

Levart [38]

Answer:

4:16 or 1:4

Step-by-step explanation:

1/5 of 20 = 4

there are 4 red marbles

there are 16 blue marbles

4:16 or 1:4

3 0

2 years ago

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Eighty-three and seventy-four hundredths minus sixty-one and ninety-seven hundredths equals _____.

beks73 [17]

21.77 you can also type that in in the google search bar and your answer will pop up

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3 years ago

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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

The formula for velocity of an object is the equals d over t where he is a velocity of the object t is the distance traveled and

butalik [34]

Answer:

$(a)\ t =\frac{d}{v}$

$(b)\ d = vt$

Step-by-step explanation:

<em>The question is mixed up with details of another question. See comment for original question</em>

<em />

<u>Given</u>

$v = \frac{d}{t}$

$v \to velocity$

$d \to distance$

$t \to time$

Solving (a): Solve for time

We have:

$v = \frac{d}{t}$

Cross multiply

$t * v = d$

Make t the subject

$t =\frac{d}{v}$

Solving (b): Solve for distance

We have:

$v = \frac{d}{t}$

Cross multiply

$d = v * t$

$d = vt$

7 0

3 years ago

a person can pay 14$ for a membership to the science museum and then go to the mesum for just 1$ per visit what is the maxium nu

Naddika [18.5K]

Answer:

I think 43 visits

Step-by-step explanation:

I hope this helps you and I hope this is right and have a wonderful day:)

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3 years ago

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