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3 years ago

What is the value of x? enter your answer as a decimal to the nearest tenth in the box

Mathematics

1 answer:

nikdorinn [45]3 years ago

7 0

For this case we have to define trigonometric relationships in rectangular triangles that:

The sine of an angle is given by the opposite leg to that angle on the hypotenuse of the triangle.

Then, according to the figure shown we have to:

$Sin (47) = \frac {x} {18}$

So, clearing the value of "x" we have:

$x = Sin (47) * 18\\x = 0.7314 * 18\\x = 13.16$

We round and we have the value of "x" is: $13.2 \ ft$

Answer:

$13.2 \ ft$

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How can I tell if a triangle with side lengths 10, 24, and 26 is a right triangle?

Alex777 [14]

10^2 +24^2 =26^2
=676

4 0

3 years ago

Carpet is sold in square yards. How much carpet would a person need to buy for a rectangular room that has dimensions of 10 yard

Dafna1 [17]

Alright, lets get started.

Here the dimensions of the room are given 10 yards by 18 feet.

We need to first convert this 18 feet into yards to make the units same.

3 feets = 1 yards

1 feet = $\frac{1}{3}$ yards

18 feet = $\frac{1}{3}* 18 = 6$ yards

It means the dimensions of the room is 10 yards by 6 yards.

So, the carpet we need should be equal to the area of the room.

Area of the room is = $10 * 6$

Area of the room = 60 square yards

Hence we need 60 square yards carpet for the room. : Answer

Hope it will help :)

7 0

3 years ago

Read 2 more answers

Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work. 20 Points!!

alexira [117]

|4x + 3| = 9 + 2x

Since the variable is on both sides of the equation, you would, at the end, check for extraneous solutions.

Extraneous solutions are solutions that do not work with the equation, therefore they are "extra" solutions and un-included in your final answer.

Start the problem by splitting the equation into two equations, a positive case and a negative case. Your two equations would look like:

4x + 3 = 9 + 2x {positive case}
4x + 3 = -(9 + 2x) {negative case}

<h2><u>---Solving the equations---</u></h2><h3>[POSITIVE CASE]</h3>

Let's solve for the positive case first. Start by subtracting 3 from both sides of the equation.

4x + 3 = 9 + 2x becomes 4x = 6 + 2x

Now subtract 2x from both sides of the equation.

4x = 6 + 2x becomes 2x = 6

Finish off the problem by dividing both sides by 2 to isolate the variable x.

2x = 6 becomes x = 3.

<h2>---</h2><h3>[NEGATIVE CASE]</h3>

Now let's solve for x in the negative case. Start by distributing the negative sign (-) inside the parentheses.

4x + 3 = -(9 + 2x) becomes 4x + 3 = -9 - 2x

Subtract 3 from both sides just like the positive case.

4x + 3 = -9 - 2x becomes 4x = -12 - 2x

Now add 2x to both sides of the equation.

4x = -12 - 2x becomes 6x = -12

Finish off the problem by dividing both sides by 6 to isolate the variable x.

6x = -12 becomes x = -2.

<h2><u>---Checking for extraneous solutions---</u></h2><h3>[CHECKING X = 3]</h3>

To check for extraneous solutions, or solutions that do not work, substitute what you got for x back into the original absolute value equation: |4x + 3| = 9 + 2x. Substitute 3 and -2 into the equation. Let's start by substituting 3 for x.

|4x + 3| = 9 + 2x becomes |4(3) + 3| = 9 + 2(3)

Start by multiplying 4 and 3 together inside the absolute value symbols.

|4(3) + 3| = 9 + 2(3) becomes |(12) + 3| = 9 + 2(3)

Now multiply 2 and 3 together.

|(12) + 3| = 9 + 2(3) becomes |(12) + 3| = 9 + (6)

Add 12 and 3 together inside the absolute value symbols; also add 9 and 6 together.

|(12) + 3| = 9 + (6) becomes |(15)| = (15), which is the same as 15 = 15.

15 = 15 is a true statement so this means that 3 is a solution to the absolute value equation, so it is not an extraneous solution.

<h2>---</h2><h3>[CHECKING X = -2]</h3>

Let's see if -2 is a solution or not - substitute -2 for x into the equation: |4x + 3| = 9 + 2x.

|4x + 3| = 9 + 2x becomes |4(-2) + 3| = 9 + 2(-2)

Multiply 4 and -2 inside the absolute value symbols.

|4(-2) + 3| = 9 + 2(-2) becomes |(-8) + 3| = 9 + 2(-2)

Multiply 2 and -2.

|(-8) + 3| = 9 + 2(-2) becomes |(-8) + 3| = 9 + (-4)

Add -8 and 3 inside the absolute value symbols; also add 9 and -4.

|(-8) + 3| = 9 + (-4) becomes |(-5)| = (5), which is the same as 5 = 5.

5 = 5 is a true statement so that means it is not an extraneous solution. After checking for extraneous solutions, we have come to the conclusion that the two answers for the equation --> I4x + 3I = 9 + 2x <-- are <u>x = 3 or x = 2</u>.

8 0

3 years ago

Tell whether the statement is always, sometimes, or never true. Explain.

Andrews [41]

Answer:

1. If x and y are supplementary angles, then y is sometimes acute because supplementary angles are angles that add up to 180 degrees. So, y can be acute while x can be obtuse, y can be obtuse while x can be acute, or both can be right angles.

2. If x and y are complementary angles, then x is never obtuse. Complementary angles are angles that add up to 90 degrees, and obtuse angles are angles over 90 degrees, so it's impossible to have an obtuse angle as a complementary angle.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Help me please this is dew by the end of the day

german

Answer:x = 4 1/2

19-2 1/2 x2 = 14-2 1/2 x2 = 9/2 = 4 1/2

3 0

3 years ago