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Find the value of x. (7x-5)* (x +3)*

How many degrees are in a right angle? You can set the equation to equal 7x - 5 + x + 3 = 90

(1 point)
x =

11 answers

To solve for \( x \) in the equation \( 7x - 5 + x + 3 = 90 \), we first simplify the left side of the equation:

\[ 7x - 5 + x + 3 = 90 \]

Combine like terms:

\[ (7x + x) + (-5 + 3) = 90 \]

This simplifies to:

\[ 8x - 2 = 90 \]

Next, add 2 to both sides:

\[ 8x = 90 + 2 \] \[ 8x = 92 \]

Now, divide both sides by 8:

\[ x = \frac{92}{8} \]

Simplifying \( \frac{92}{8} \):

\[ x = 11.5 \]

Thus, the value of \( x \) is

\[ \boxed{11.5} \]

Regarding the right angle, there are 90 degrees in a right angle.

c, ft6 , ft 8 what is the length of the hypotenuse if necessary, round to the nearest tenth
c =
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To find the length of the hypotenuse \( c \) in a right triangle given the lengths of the two other sides (let's assume they are \( a = 6 \) ft and \( b = 8 \) ft), we can use the Pythagorean theorem, which states:

\[ c^2 = a^2 + b^2 \]

Substituting the values:

\[ c^2 = 6^2 + 8^2 \]

Calculating the squares:

\[ c^2 = 36 + 64 \] \[ c^2 = 100 \]

Now, taking the square root of both sides:

\[ c = \sqrt{100} = 10 , \text{ft} \]

Thus, the length of the hypotenuse \( c \) is:

\[ \boxed{10.0} , \text{ft} \]

This is already to the nearest tenth.

20 cm , 12 cm, b ,what is the length of the missing leg if necessary, round to the nearest tenth , b=box centimeters

To find the length of the missing leg \( b \) in a right triangle where one leg is 12 cm and the other leg is 20 cm, we can again use the Pythagorean theorem, which states:

\[ c^2 = a^2 + b^2 \]

Here, if we consider \( c = 20 , \text{cm} \) (the hypotenuse) and \( a = 12 , \text{cm} \) (one leg), we can rearrange the formula to solve for \( b \):

\[ 20^2 = 12^2 + b^2 \]

Calculating the squares:

\[ 400 = 144 + b^2 \]

Now, subtract 144 from both sides:

\[ 400 - 144 = b^2 \] \[ 256 = b^2 \]

Next, take the square root of both sides:

\[ b = \sqrt{256} = 16 , \text{cm} \]

Thus, the length of the missing leg \( b \) is:

\[ \boxed{16} , \text{cm} \]

This result is exact; rounding to the nearest tenth is not necessary in this case.

aliyah correctly used diagram shown to explain the pythagorean theorem to a classmate which statement did aliyah use in her explanation

Without the specific diagram or statements that Aliyah used available to me, I can provide a general statement that is often used to explain the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (\( c \)) is equal to the sum of the squares of the lengths of the other two sides (\( a \) and \( b \)). This can be written as:

\[ c^2 = a^2 + b^2 \]

To illustrate this using a diagram, one might point out the relationship between the sides of a right triangle. For example, if there is a right triangle with legs measuring \( a \) and \( b \), and the hypotenuse measuring \( c \), Aliyah could explain that by squaring each of these lengths and summing the areas represented by \( a^2 \) and \( b^2 \), one can find the area of the square represented by \( c^2 \) (the hypotenuse).

If you have any specific options or statements that Aliyah made, please share, and I can help determine which one aligns with the explanation of the Pythagorean theorem.

5^2 + 5^2 = 3^2 , 3^2 + 4^2 = 5^2, 5^2 +5^2 <3^2, 3^2 + 4^2 > 5^2, chose

To determine which statement correctly represents or explains the Pythagorean theorem, let's evaluate each one:

  1. \( 5^2 + 5^2 = 3^2 \)
    This statement is incorrect because \( 5^2 + 5^2 = 25 + 25 = 50 \) and \( 3^2 = 9 \).

  2. \( 3^2 + 4^2 = 5^2 \)
    This statement is correct. \( 3^2 + 4^2 = 9 + 16 = 25 \) and \( 5^2 = 25 \). This is a classic example of the Pythagorean theorem, where \( 3 \), \( 4 \), and \( 5 \) are the sides of a right triangle.

  3. \( 5^2 + 5^2 < 3^2 \)
    This statement is incorrect because \( 5^2 + 5^2 = 50 \) is not less than \( 3^2 = 9 \).

  4. \( 3^2 + 4^2 > 5^2 \)
    This statement is incorrect based on the previous evaluation. \( 3^2 + 4^2 = 5^2 \), so it is not greater.

Given these evaluations, the correct statement that Aliyah would use to explain the Pythagorean theorem is:

\[ \boxed{3^2 + 4^2 = 5^2} \]

The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine which set of lengths will make a triangle to be able to use it in his design. (Hint: Use the Triangle Inequality Theorem)
Option 1: Side lengths: 3, 3, 6
Option 2: Side lengths: 6, 8, 10
Option 3: Side lengths: 4, 6, 13(1 point)
Responses

Option 1
Option 1

Option 2
Option 2

Option 3

To determine which set of side lengths will form a triangle, we can use the Triangle Inequality Theorem. This theorem states that for any three sides \( a \), \( b \), and \( c \) of a triangle, the following conditions must hold:

  1. \( a + b > c \)
  2. \( a + c > b \)
  3. \( b + c > a \)

Let's evaluate each option:

Option 1: Side lengths 3, 3, 6

  • Check the inequalities:
    1. \( 3 + 3 > 6 \) → \( 6 > 6 \) (not true)
    2. \( 3 + 6 > 3 \) → \( 9 > 3 \) (true)
    3. \( 3 + 6 > 3 \) → \( 9 > 3 \) (true)

Since the first condition fails, this set of lengths does not form a triangle.

Option 2: Side lengths 6, 8, 10

  • Check the inequalities:
    1. \( 6 + 8 > 10 \) → \( 14 > 10 \) (true)
    2. \( 6 + 10 > 8 \) → \( 16 > 8 \) (true)
    3. \( 8 + 10 > 6 \) → \( 18 > 6 \) (true)

All conditions are satisfied, so this set of lengths forms a triangle.

Option 3: Side lengths 4, 6, 13

  • Check the inequalities:
    1. \( 4 + 6 > 13 \) → \( 10 > 13 \) (not true)
    2. \( 4 + 13 > 6 \) → \( 17 > 6 \) (true)
    3. \( 6 + 13 > 4 \) → \( 19 > 4 \) (true)

Since the first condition fails, this set of lengths does not form a triangle.

Based on the evaluations:

  • Option 1: Does not form a triangle.
  • Option 2: Forms a triangle.
  • Option 3: Does not form a triangle.

Thus, the response indicating which set of lengths the carpenter can use for the triangular design is:

\[ \boxed{\text{Option 2}} \]