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3 years ago

The square of a number is 12 less than 7 times the number. What is the number?

Mathematics

1 answer:

hjlf3 years ago

7 0

Answer:

The number is either 3 or 4

Explanation:

Assume that the number we are looking for is x

The square of the number would be x²

7 times the number would be 7x

We are given that:

square of the number (x²) is 12 less than 7 times the number (7x)

Translating this into an equation, we would have:

x² = 7x - 12

Rearranging the quadratic equation:

x² - 7x + 12 = 0

Now, we factor the equation:

(x-4)(x-3) = 0

This means that:

either x-4 = 0 ..................> x = 4

or x-3 = 0 ........................> x = 3

Let's check if any of the solutions is an extrovert:

For x = 3 .............> (3)² = 7(3) - 12 .........> 9 = 21 - 12 .......> 9 = 9 .......> not extrovert

For x = 4 .............> (4)² = 7(4) - 12 .........> 16 = 28 - 12 .....> 16 = 16 ....> not extrovert

Since we have no restrictions on the number, therefore, both solutions would be accepted

Hope this helps :)

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In the right triangle shown Ac=BC and AB=6 to the square root of 3, how long are each of the legs

Inga [223]

Answer:

6 units

Step-by-step explanation:

I will just assume that you made a typo when typing the question when saying AB is 6√3. Here is the solution if AB = 6√2.

Since it is given that ABC is a right triangle and x labels each of the legs, the triangle is a right isoceles triangle.

Now we can use the right isoceles triangle theorem to solve the problem. This theorem states that if a leg is "x" in a right isoceles triangle, then the hypotenuse is equal to x√2.

Here, the hypotenuse is equal to 6√2. To figure out the legs, you need to solve the equation 6√2 = x√2. It is solved here:

6√2 = x√2 (Divide by √2)

x = 6

The length of the legs are 6 units.

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3 years ago

The melting point of nitrogen is -210 °C. The melting point of magnesium is 650 °C.

scoray [572]

Answer:

860 degrees

Step-by-step explanation:

-210+210=0

0+650=650

650+210=860

7 0

1 year ago

Graph linear system and estimate the solution y=5x + 2 y=3x

NeTakaya

Y = 5x + 2
y = 3x

5x + 2 = 3x
- 5x - 5x
      2 = -2x
   -2 - 2
       -1 = x
y = 3x
y = 3(-1)
y = -3
(x, y) = (-1, -3)

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3 years ago

Directions: for questions 1 through 4, find the diagonal length of each solid figure.

Alex787 [66]

$\text{The length of the diagonal is }11.2\text{ mm}$

Here, we want to find the diagonal of the given solid

To do this, we need the appropriate triangle

Firstly, we need the diagonal of the base

To get this, we use Pythagoras' theorem for the base

The other measures are 6 mm and 8 mm

According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides

Let us have the diagonal as l

Mathematically;

$\begin{gathered} l^2=6^2+8^2 \\ l^2\text{ = 36 + 64} \\ l^2\text{ =100} \\ l\text{ = }\sqrt[]{100} \\ l\text{ = 10 mm} \end{gathered}$

Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above

Thus, we calculate this using the Pytthagoras' theorem as follows;

$\begin{gathered} d^2=5^2+10^2 \\ d^2\text{ = 25 + 100} \\ d^2\text{ = 125} \\ d\text{ = }\sqrt[]{125} \\ d\text{ = }11.2\text{ mm} \end{gathered}$

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1 year ago

It’s you birthday and you bought a giant sandwich to feed all of your guests. The sandwich is 10 1/2 feet long and you need to f

Hoochie [10]

Answer: $1\dfrac{3}{4}\text{ feet}$

Step-by-step explanation:

Given: Length of sandwich = $10\dfrac12\text{ feet}=\dfrac{21}{2}\text{ feet}$

Total people = 14

If everyone gets a same sized piece , then length of each piece should be

$\dfrac{\text{ Length of sandwich}}{\text{Total people}}$

$=\dfrac{\dfrac{21}{2}}{14}\text{ feet}\\\\=\dfrac{21}{2\times14}\text{ feet}\\\\=\dfrac{7}{2\times2}\text{ feet}\\\\=\dfrac{7}{4}\text{ feet}\\\\=1\dfrac{3}{4}\text{ feet}$

Hence, length of each piece = $1\dfrac{3}{4}\text{ feet}$

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3 years ago