Ask question

Ask question

All categories

3 years ago

8

Elena harvested 75 kg of apples last autumn. This autumn, her harvest increased by 24%. How many kilograms of apples did she har

vest this autumn?

1 answer:

sergejj [24]3 years ago

8 0

She harvested 93 kg of apples.

First you need to set it up like this:
X/75=24/100

Then you cross multiply and get:
1800=100x

The you isolate the variable (divide both sides) and get 18

75+18=93

You might be interested in

A china shop receives a shipment of 125 dishes in 5 boxes. At this rate how many dishes will it receive in 15 boxes

Otrada [13]

375 dishes good luck!!

7 0

3 years ago

Read 2 more answers

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

Danni counted 48 apples in a basket of apples. The basket actually contained 46 apples. What is the percent error?

enot [183]

The answer would be 4.2%

5 0

3 years ago

Transpose v= u + t for t

LiRa [457]

Uv al dt or trace mcsorely

4 0

3 years ago

Points A(7, -5), B(-1, -2), and C(-4, 6) form triangle ABC on a coordinate plane. According to its sides, triangle ABC is a(n) _

prohojiy [21]

Isosceles Triangle, has 2 equal sides and angles.

7 0

3 years ago