Answer:
32°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the trig function relating angles to the opposite and adjacent sides of the triangle is ...
Tan = Opposite/Adjacent
The side opposite the angle x is shown as having measure 5; the side adjacent has measure 8. Putting all this in the above equation gives ...
tan(x) = 5/8
To find the angle from the value of the tangent, you use the inverse of the tangent function. The name of that is the <em>arctangent</em> function. It is often written as tan⁻¹(x) and often accessible on your calculator using a "second function" key. Some calculators, like the one shown in the attachment, recognize the arctan function name.
x = arctan(5/8) ≈ 32°
The value of x rounded to the nearest whole degree is 32°.
The perimeter of RSTU can be calculated alone without the help of MNPQ. It would be just 2(4) + 2(3) = 14 units. However, it would be much sensible if you want to find the parameter of the bigger rectangle. Since they are similar, you could use ratio and proportion.
(length/width)∨MNPQ = (length/width)∨RSTU
(x/9) = (3/4)
x = 6.75 units
Thus the perimeter of MNPQ is 2(6.75) + 2(9) = 31.5 units
9514 1404 393
Answer:
110 units
Step-by-step explanation:
Fill in the given value and solve for x.
c = x^2 -10x +35
11035 = x^2 -10x +35
11025 = x^2 -10x +25 = (x -5)^2 . . . . subtract 10 to complete the square
x = 5 +√11025 = 5 +105 . . . . find the positive solution
x = 110
The number of units manufactured at a cost of 11,035 is 110 units.
Answer:
<em>50° is the correct answer</em>
Step-by-step explanation:
<u>Right Triangles</u>
The right triangles are identified because they have an internal angle of 90°. The basic trigonometric ratios can be used to find angles and side lengths as needed.
We have a right triangle with the following characteristics:
The hypotenuse is 13 units long
The indicated angle is opposite to the leg of 10 units long.
When we know the length of the opposite side, we use the sine ratio. Let's call θ to the required angle:
Using a calculator set in mode <em>degrees</em>, the angle is:
First choice: 52° is not correct because is not a good approximation to 50.3°
Second choice:38° is not correct because is not a good approximation to 50.3°
Third choice: 50° is a good approximation to 50.3°. Correct Answer
Fourth choice: 40° is not correct because is not a good approximation to 50.3°
-2a + 3b = 9 / x 2;
-4a + 6b = 18;
Then, -4a + 6b = 18
+4a - 2b = 3
__________________(+)
We obtain 4b = 21;
b = 21/4;
-2a + 63/4 = 9;
-8a + 63 = 36;
-8a = - 27;
a = 27/8 ;