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defon
3 years ago
12

A 10-foot board is to be cut into 3 pieces. Two of the pieces will be the same length and one piece will be 2 feet longer than t

he other two.
Mathematics
1 answer:
ira [324]3 years ago
6 0

Answer:

Step-by-step explanation:

According to the given statement two pieces are of same length:

If the length of one piece is x,

Then the length of other piece is also x.

And one piece is 2 feet longer than the other two = x+2

Total length of a board = 10 foot

Now make the equation from these terms:

x+x+x+2= 10

This is the equation of the given question.

You can further solve this equation:

x+x+x+2=10

3x+2=10

Now combine the constants:

3x=10-2

3x=8

x=8/3

x=2.67

It means that the length of two pieces of same length is 2.67

And the length of one piece which is longer than the other two = x+2 = 2.67+2 = 4.67 ....

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The lengths of the sides of a triangle are in the ratio
Anton [14]
HOW TO SOLVE:

1) use x as a variable
2) the starting equation is:
          4x + 3x + 5x = 18

3) add all the like terms on the left side of the equation:
          12x = 18

4) Divide by 12 on both sides:
          x=1.5

5) Find the lengths of the sides:

        - 4x = 4(1.5) = 6

        - 3x = 3(1.5) =  4.5

       - 5x = 5(1.5) = 7.5

SO, the lengths of the sides of this triangle are: 6, 4.5, and 7.5
5 0
3 years ago
When 5 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
wariber [46]

Answer:

-1

Step-by-step explanation:

You can write it as...

x^{2} -5=4x

Carry the 4x

x^{2} -4x-5=0

Then use the quadratic formula to solve, since you want to find the negative solution, you don't need to find the positive solution, so we will have

(4-\sqrt{16+20}) /2=\frac{4-6}{2}=\frac{-2}{2} =-1

Therefore our answer is -1

8 0
3 years ago
A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What
ivann1987 [24]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the measures of other two angles of triangle.

\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

  • The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.

Angle sum property,

  • The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.

\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

  • 3x
  • 3 × 10
  • 30°

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

  • 14x
  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

5 0
2 years ago
Find the nature of the root
GREYUIT [131]

Answer:

1) Real and same.

2) Real and distinct

3) Real and distinct

4) Real and distinct

5) Real and distinct

6) Real and distinct

7) Real and distinct

8) Real and distinct

Step-by-step explanation:

If a quadratic equation is in the form of ax² + bx + c = 0, then Discriminant of the equation D = b² - 4ac, which governs the nature of roots the equation has.

If D > 0, then there will be two different real roots.

If D = 0, then two same and real roots.

If D < 0, then two distinct but imaginary roots.

Now, 1) x² + 6x + 9 = 0 has D = 6² - 4 × 9 × 1 = 0. So, there will be two same and real roots.

2) 5x² - x = 4x² + 2

⇒ x² - x - 2 = 0

It has D = (-1)² - 4 × 1 × (-2) = 9. Therefore, the roots will be two distinct and real.

3) \frac{2}{x} + \frac{3}{x} = x - 4

⇒ 5 = x² - 4x

⇒ x² - 4x - 5 = 0.

So, D = (-4)² - 4 × (1) × (- 5) = 36. So, the equation has two real and distinct rools.

4) x(x - 5) = 4(5 - x)

⇒ x² - x - 20 = 0

Hence, D = (-1)² - 4 × 1 × (-20) = 81

So, the roots will be real and distinct.

5) x² + 7x + 1 = 0 has D = 7² - 4 × 1 × 1 = 45

So, the roots will be real and distinct.

6) 2x² + 9x + 3 = 0, has D = 9² - 4 × 2 × 3 = 57.

Hence, the roots will be real and distinct.

7) 5x² - 6 = 13x

⇒ 5x² - 13x - 6 = 0

So, D = (-13)² - 4 × 5 × (-6) = 289

So, the roots will be real and distinct.

8) x² - x = 3(x + 7)

⇒ x² - 4x - 21 = 0

It has D = (-4)² - 4 × 1 × (-21) = 100

So, the roots will be real and distinct. (Answer)

6 0
3 years ago
An airplane covers 94 miles in 6 of an hour.<br> The plane can cover<br> miles in 6 hours.
Mekhanik [1.2K]

Answer:

in 6 hours it will be 3384

7 0
3 years ago
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