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Juli2301 [7.4K]

3 years ago

5

A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7. What are the side lengths of the scaled copy? Give th

e smaller length. Do not include units (inches) in your answer.

1 answer:

Liono4ka [1.6K]3 years ago

7 0

Answer:

Step-by-step explanation:

Nbv

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Which answer choice represents an equivalent number sentence that uses that associative property to rewrite "(4 x 5) x 8"?

gtnhenbr [62]

B
Explanation: Associative property basically means that the numbers stay in the same spot but the parentheses move

6 0

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 measures of the angles of ABC are given by the expressions in the table A( 6X - 1 ) ° B 20° C ( x + 14 ) ° what are the meas

lawyer [7]

Answer:

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees. This means that in triangle ABC,

Angle A + angle B + angle C = 180

Therefore,

6x - 1 + 20 + x + 14 = 180

6x + x + 20 + 14 - 1 = 180

7x + 33 = 180

Subtracting 33 from the left hand side and the right hand side of the equation, it becomes

7x + 33 - 33 = 180 - 33

7x = 147

Dividing the left hand side and the right hand side of the equation by 7, it becomes

7x/7 = 147/7

x = 21

Therefore

Angle A = 6x - 1 = 6 × 21 - 1

Angle A = 125 degrees

Angle C = x + 14 = 21 + 14

Angle C = 35 degrees.

7 0

3 years ago

Eight times the sum of a number and 4 equals 3

BigorU [14]

The algebraic expression is: $8(x+4)=3$

And Value of x is: $x=\frac{-21}{8}$

Step-by-step explanation:

We need to write the expression of the statement:

Eight times the sum of a number and 4 equals 3

Let the number = x

The expression will be:

$8(x+4)=3$

Solving the expression to find value of x:

$8(x+4)=3\\8x+24=3\\Adding\,\,-24\,\,on\,\,both\,\,sides:\\8x+24-24=3-24\\8x=-21\\x=\frac{-21}{8}$

So, The algebraic expression is: $8(x+4)=3$

And Value of x is: $x=\frac{-21}{8}$

Keywords: Algebraic Expression

Learn more about Algebraic Expression at:

#learnwithBrainly

3 0

3 years ago

Ltiply.<br> 5. 20 x 0.25

AlekseyPX

Answer:

1.30

Step-by-step explanation:

When you multiply 5.20x0.25 you get 1.30

4 0

3 years ago

Read 2 more answers